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Existing approaches struggle to efficiently navigate complex codebases when identifying relevant code sections. The challenge lies in bridging natural language problem descriptions with the appropriate code elements, often requiring reasoning across hierarchical structures and multiple dependencies. We introduce LOCAGENT, a framework that addresses code localization through graph-based representation. By parsing codebases into directed heterogeneous graphs, LOCAGENT creates a lightweight representation that captures code structures (files, classes, functions) and their dependencies (imports, invocations, inheritance), enabling LLM agents to effectively search and locate relevant entities through powerful multi-hop reasoning. Experimental results on real-world benchmarks demonstrate that our approach significantly enhances accuracy in code localization. Notably, our method with the fine-tuned Qwen-2.5-Coder-Instruct-32B model achieves comparable results to SOTA proprietary models at greatly reduced cost (approximately $86\\%$ reduction), reaching up to $92.7\\%$ accuracy on file-level localization while improving downstream GitHub issue resolution success rates by $12\\%$ for multiple attempts (Pass@10). Our code is available at https://github.com/gersteinlab/LocAgent.", + "bbox": [ + 141, + 287, + 460, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction", + "text_level": 1, + "bbox": [ + 114, + 765, + 258, + 780 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Code localization can be viewed as an information retrieval (IR) task that aims to identify relevant code snippets given natural language descriptions (Yu et al., 2025; Yang et al., 2024; Xia et al., 2024). Developers spend up to $66\\%$ of their debugging time (Böhme et al., 2017) understanding code to", + "bbox": [ + 112, + 790, + 487, + 887 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c20269c8cebd98330e89168b5cf72fa71b25a1845eac8027149a6e7bbe018c9f.jpg", + "image_caption": [ + "Figure 1: Code localization across four common programming scenarios. Given a codebase and an issue description, the goal of code localization is to identify the relevant code snippets that require modification to resolve the issue." + ], + "image_footnote": [], + "bbox": [ + 510, + 255, + 882, + 444 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "make changes, and automated tools often struggle with the same challenge. Poor code localization leads to incomplete fixes, introduces new bugs, and significantly extends development cycles. Unlike traditional retrieval tasks that primarily focus on lexical or semantic matching between queries and documents (Guo et al., 2016, 2020), code localization requires bridging the gap between natural language and programming languages. It also necessitates reasoning capabilities to analyze the issue, while considering the structural and semantic properties of code (Lewis et al., 2020; Guu et al., 2020; Qu et al., 2020). This capability has become fundamental to powerful AI assistants (OpenAI, 2023; Anthropic, 2023), code-aware search engines (PerplexityAI, 2023), and automated programming agents (Cognition.ai, 2024; Wang et al., 2025; Gauthier, 2024). In particular, accurate code localization is crucial for software maintenance and evolution, as it enables precise code modifications for bug fixes, refactoring, and feature additions (Wang et al., 2024), thereby streamlining the development workflow.", + "bbox": [ + 507, + 533, + 884, + 903 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing approaches to code localization face", + "bbox": [ + 527, + 904, + 880, + 921 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2503.09089v2 [cs.SE] 29 Apr 2025", + "bbox": [ + 21, + 310, + 60, + 722 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution. This work was done during Zhaoling's time at Yale.", + "bbox": [ + 112, + 894, + 487, + 921 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "significant limitations. Dense retrieval methods require maintaining and continuously updating vector representations of the entire codebase (Wang et al., 2023b; Günther et al., 2023), creating engineering challenges for large, evolving repositories where code changes frequently. While LLMs demonstrate strong code understanding capabilities (Kang et al., 2023; Wu et al., 2023), models with large context windows cannot process entire codebases at once, necessitating strategic navigation through relevant parts. Moreover, issue descriptions often mention only symptoms rather than underlying causes. For instance, a report of 'XSS vulnerability in user profile' might require changes to a shared validation utility used throughout the codebase but not explicitly referenced in the issue. This disconnect between issue descriptions and affected code components presents a substantial challenge for traditional retrieval approaches, which struggle to trace implicit dependencies across the codebase structure. Recent agent-based methods attempt to address these limitations through iterative exploration (Yang et al., 2024; Qin et al., 2024) but still struggle to efficiently navigate and comprehend complex code structures and dependencies, particularly when multi-hop reasoning is required to trace from issue descriptions to affected code regions that aren't directly mentioned.", + "bbox": [ + 115, + 84, + 485, + 533 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This raises a key question: How can we design efficient indexing as intermediate representations that are structure-aware and both easy and performant for LLM agents to consume? It is intuitive to design an agentic retrieval system that carefully combines traditional IR methods and LLM agent's reasoning ability to achieve accurate, efficient, and cost-effective code localization in codebases.", + "bbox": [ + 115, + 535, + 485, + 662 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this challenge, we propose LOCAGENT, a framework that builds directed heterogeneous graph indexing to unify code structures, dependencies, and contents. Our approach leverages a structured graph representation that enables powerful multi-hop reasoning capabilities, allowing agents to navigate complex dependency relationships between code elements even when target code isn't explicitly mentioned in issue descriptions. This graph-based approach significantly outperforms previous methods on challenging localization tasks that require traversing multiple code relationships. Our lightweight representation, coupled with sparse indexing techniques, enables efficient entity search while maintaining rich structural information. The indexing process typically", + "bbox": [ + 115, + 664, + 485, + 920 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "takes only a few seconds per codebase, making it highly practical for real-time use. The framework integrates a set of unified tools that guide the agent through a systematic exploration of the codebase, allowing autonomous navigation based on contextual needs. Furthermore, by fine-tuning Qwen-2.5-Coder-Instruct (Hui et al., 2024) 7B and 32B models(abbr. as Qwen-2.5-7B and Qwen-2.5-32B respectively), our system achieves performance comparable to state-of-the-art models like Claude-3-5-sonnet-20241022 (Anthropic, 2023) (abbr. as Claude-3.5) while significantly reducing API costs by over $80\\%$ (from \\ $0.66 to \\$ 0.09 per example), making it practical for real-world deployment.", + "bbox": [ + 512, + 84, + 880, + 324 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Additionally, to facilitate a comprehensive evaluation of code localization methods, we introduce LOC-BENCH, a new benchmark specifically designed for this task. Existing benchmarks like SWE-Bench present significant limitations: (1) they risk contamination through data overlap with LLM training sets (Mündler et al., 2024), and (2) they primarily focus on bug fixing, lacking diversity in maintenance scenarios such as feature requests, performance optimizations, and security fixes. In contrast, LOC-BENCH covers diverse scenarios and mitigates potential contamination concerns by incorporating more recent examples from popular Python repositories collected after known LLM training cutoff dates. Additionally, we provide tooling to continuously update the benchmark with new examples, allowing researchers to maintain a fresh evaluation dataset as models evolve and training data cutoffs advance.", + "bbox": [ + 512, + 326, + 880, + 629 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions address critical gaps in existing approaches:", + "bbox": [ + 512, + 632, + 880, + 663 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a heterogeneous graph representation that captures both explicit and implicit code relationships, enabling efficient multi-hop reasoning. Our lightweight graph-based indexing process takes only seconds per repository and requires minimal storage.", + "- We design unified tools for agent-based code exploration that leverage our graph representation, allowing LLM agents to perform complex multi-hop navigation and reasoning across code dependencies even when target code isn't explicitly mentioned in issue descriptions.", + "- We introduce Loc-Bench, a new benchmark" + ], + "bbox": [ + 534, + 675, + 880, + 919 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "specifically designed for code localization that addresses limitations in existing datasets. Unlike previous benchmarks dominated by bug reports, Loc-Bench offers a balanced distribution across bug fixes, feature requests, security patches, and performance optimizations.", + "bbox": [ + 149, + 84, + 487, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- By fine-tuning open-source models on this task, we reduce the cost of code localization by $86\\%$ while maintaining competitive performance.", + "bbox": [ + 136, + 195, + 489, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2 Related Work", + "text_level": 1, + "bbox": [ + 112, + 288, + 268, + 304 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1 Traditional Retrieval-based Methods", + "text_level": 1, + "bbox": [ + 112, + 316, + 448, + 331 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Traditional IR methods rely on lexical or semantic matching to return ranked lists of code snippets. Sparse retrievers, such as BM25 (Robertson et al., 1994, 2009), have demonstrated robustness to domain adaptation. Dense retrievers utilize embeddings for improved semantic searching, including models with open checkpoints such as general text embedding models E5-base-v2 (Wang et al., 2022) and proprietary APIs (VoyageAI, 2024). Code embedding models such as Jina-Code-v2 (Günther et al., 2023), Codesage-large-v2 (Zhang et al., 2024), and CodeRankEmbed (Suresh et al., 2024), trained specifically for code related tasks, showing significant performance in Code2Code and NL2Code semantic search tasks. However, while the embedding models themselves are small, the engineering challenges of maintaining these indexing systems (e.g., storage requirements, update mechanisms, and infrastructure maintenance) make them difficult to adapt to fast-evolving codebases.", + "bbox": [ + 112, + 338, + 489, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2 LLM-based Generative Retrieval Methods", + "text_level": 1, + "bbox": [ + 112, + 673, + 485, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, LLMs with advanced code reasoning capabilities have demonstrated superior performance by directly processing queries and raw code for code localization (Kang et al., 2023; Wu et al., 2023; Xia et al., 2024; Kang et al., 2024). For example, Agentless (Xia et al., 2024), initially designed for automated program repair, uses a simplistic hierarchical localization process powered by LLM. It employs a straightforward three-phase approach that first localizes relevant code sections before attempting to fix the identified issues, challenging the assumption that complex agent architectures are necessary for effective code understanding and modification tasks.", + "bbox": [ + 112, + 696, + 489, + 920 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Expanding on these techniques, agent-based methods utilize multi-step reasoning to enable automated codebase traversal. Specifically, OpenHands (Wang et al., 2025) implements a generalist coding agent that supports bash commands like grep and tools for viewing files. SWE-Agent (Yang et al., 2024) integrates a custom Agent-Computer Interface to support agents to navigate entire repositories. MoatlessTools (Örwall, 2024) combines an agentic searching loop and semantic search to obtain code locations. However, existing agent-based methods face two critical limitations: (a) they primarily navigate codebases through directory traversal rather than understanding semantic relationships, (b) and they struggle to extract and reason about complex cross-file dependencies when these relationships aren't explicitly represented in the repository structure. This significantly impairs their ability to locate code that requires modification when the issue involves interactions between structurally distant components in the codebase.", + "bbox": [ + 507, + 84, + 884, + 437 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3 Graph-based Code Representation Methods", + "text_level": 1, + "bbox": [ + 507, + 449, + 828, + 480 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the inherent structure of code, several works have employed graph-based representations to improve code understanding by capturing key relationships between components. Aider (2023) constructs a RepoMap and uses a graph ranking algorithm to identify the most significant contextual elements. Similarly, as a plugin, RepoGraph (Ouyang et al., 2025) performs subgraph retrieval – extracting an ego-network of relevant lines and their neighbors – to provide structured context. CodexGraph (Liu et al., 2024) indexes the repository into a Neo4j graph database, where LLM agents query the database precisely using Cypher. The efficiency of its retrieval process depends heavily on the querying capabilities of the LLM. These methods focus primarily on providing relevant context but do not enhance the traversal process itself, as they do not explicitly model directory structure or file hierarchies.", + "bbox": [ + 507, + 486, + 884, + 790 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast, RepoUnderstander (Ma et al., 2024) builds hierarchical and function-call graphs, using Monte Carlo Tree Search (MCTS) guided by an LLM for exploration. While thorough, MCTS introduces extra computational overhead, making it less efficient than simpler traversal methods like BFS, particularly in large repositories. OrcaLoca (Yu et al., 2025) uses a simplified graph", + "bbox": [ + 507, + 793, + 884, + 921 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/68d78298f4ef4a0462b402972796e7a35e59e5ec5b78ccafd6cd08b74dd8ad0d.jpg", + "image_caption": [ + "Figure 2: Overview of LOCAGENT framework. LOCAGENT first parses the given codebase to build a graph-based code representation with various types of entities and relations. It then constructs sparse indexes for exploring structures and searching content. Using these indexes, it performs agent-guided searches that combine the graph and tools." + ], + "image_footnote": [], + "bbox": [ + 114, + 82, + 884, + 319 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/eff607d6667dc8fa01afca421fe5518165076b8c38bf5f9855a1411d560992d1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRelation TypesNode TypesSearch/Traversal Strategy
ContainImportInheritInvokeDirectoryFileClassFunction
CodexGraph(Liu et al., 2024)✓X✓✓XX✓✓Cypher queries
RepoGraph(Ouyang et al., 2025)✓X✓✓XX✓✓Ego-graph retrieval
RepoUnderstander(Ma et al., 2024)✓X✓✓✓✓✓✓MCTS
OrcaLoca(Yu et al., 2025)✓XX✓✓✓✓✓Simple search tools
LOCAGENT(Ours)✓✓✓✓✓✓✓✓Unified retrieval tools
", + "bbox": [ + 117, + 417, + 880, + 524 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1: Comparison of Graph-Based Code Representation Methods.", + "bbox": [ + 262, + 532, + 732, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "enhanced by priority scheduling and context pruning. It maintains efficient search but may miss complex invocation dependencies. Table 1 summarizes the differences between these methods and LOCAGENT. Compared to these approaches, LOCAGENT offers a more comprehensive and unified representation of the repository, along with efficient, unified retrieval tools specifically designed for LLM consumption.", + "bbox": [ + 112, + 562, + 489, + 707 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 The LOCAGENT Framework", + "text_level": 1, + "bbox": [ + 112, + 718, + 400, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We introduce LOCAGENT, a graph-oriented LLM-agent framework for code localization. Figure 2 illustrates the overall framework. When given a repository, LOCAGENT can locate all the relevant code sections at various granularities (file, class, function, or line level) for different types of GitHub issues (such as bug reports, feature requests, performance bottlenecks, and security vulnerabilities) through automated in-depth exploration and analysis of the codebase. Section 3.1 proposes a novel graph-based indexing approach as an intermediate", + "bbox": [ + 112, + 744, + 490, + 921 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "representation for codebases. Section 3.2 presents our agent-based code search on the indexes and Section 3.3 describes our model fine-tuning and distillation process.", + "bbox": [ + 507, + 562, + 882, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1 Graph-based Code Representation", + "text_level": 1, + "bbox": [ + 507, + 640, + 828, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Codebases contain rich structural information, both explicit and implicit, that is essential for agent reasoning. Building on this insight, we develop a graph-based indexing that comprehensively captures codebase relationships while maintaining a granularity suitable for LLM-agents to retrieve.", + "bbox": [ + 505, + 662, + 884, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Code Graph Construction. We construct a heterogeneous directed graph $\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathcal{A},\\mathcal{R})$ to index the codebase, where $\\nu = \\{v_{i}\\}_{i = 1}^{n}$ is the node set and $\\mathcal{E}\\subseteq \\mathcal{V}\\times \\mathcal{V}$ is the edge set. Each node $v\\in \\mathcal{V}$ and edge $e\\in \\mathcal{E}$ has an associated type mapping function. For nodes, $\\tau (v):\\mathcal{V}\\to \\mathcal{A}$ maps to types $\\mathcal{A} = \\{\\mathrm{directory},\\mathrm{file},\\mathrm{class},\\mathrm{function}\\}$ . For edges, $\\phi (e):\\mathcal{E}\\rightarrow \\mathcal{R}$ maps to relationships $\\mathcal{R} = \\{\\mathrm{contain},\\mathrm{import},\\mathrm{invoke},\\mathrm{inherit}\\}$ . In this paper, we focus our study on Python reposito", + "bbox": [ + 507, + 760, + 885, + 921 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ries and leave codebases with other programming languages as future work.", + "bbox": [ + 112, + 84, + 485, + 116 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we include all directories and Python files as nodes. Then, we parse each Python file using the abstract syntax tree (AST) to identify inner functions and classes recursively as nodes. We set the function level as the smallest node granularity and use each function's code content as the document for agent retrieval. This approach creates a good balance of information density between the index and documents, allowing LLMs to reason effectively within their context window limitations.", + "bbox": [ + 112, + 118, + 487, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Figure 2, all nodes with different types can be connected as a single tree using the contain relationship. This structure supports standard codebase-navigation operations from existing works. Our code graph further incorporates more advanced codebase relationships as edges: (1) the invoke relationship from function/class to function/class, where an invoke to a class represents class instantiation; (2) the import relationship from file to function/class; and (3) the inherit relationship between classes.", + "bbox": [ + 115, + 282, + 489, + 458 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sparse Hierarchical Entity Indexing. We treat nodes in our code graph as entities and build hierarchical indexing based on their contents. For each keyword, we lookup the indexes from top to bottom: (1) We build an entity ID index as a unique identifier for each node using its fully qualified name. For example, a function calculate_sum in the MathUtils class located in src/utils.py would be represented as: src/utils.py:MathUtilscalculate_sum. (2) We construct a global dictionary to map the entity name (e.g., calculate_sum) to all nodes that share the same name. (3) We index entity IDs through an inverted index (i.e., BM25) to handle keyword searches that don't exactly match the IDs or names of entities. (4) For cases where input keywords aren't part of the entities' IDs (e.g., when a keyword refers to a global variable), we build an inverted index that maps code chunk(s) to each entity to cover all possible matches.", + "bbox": [ + 115, + 461, + 489, + 783 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark. Rather than relying solely on directory structures or hierarchical module indexing, our approach captures module dependencies that transcend directory boundaries. Two modules in distant directories (A and B) may appear unrelated in traditional navigation, but if they invoke each other or share inheritance, they're syntactically close in our graph representation. This syntactic", + "bbox": [ + 112, + 791, + 489, + 921 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3ee9190f79ad7623fb4b180523bd53a7f66d2934c043f7c4febdadae07f9b9c0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Tool NameInput ParamsOutput
SearchEntityKeywordsRelated Entities with Code Snippets
TraverseGraphStart Entity IDs Direction Traverse Hops Entity Types Relation TypesTraversed Subgraph, including Entities and Relations
RetrieveEntityEntity IDsComplete Code of Specified Entities
", + "bbox": [ + 514, + 80, + 880, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2: List of unified APIs provided by LocAgent for code search and exploration.", + "bbox": [ + 507, + 244, + 882, + 275 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "proximity is essential for code localization because issues typically manifest through call relationships rather than directory structure. By capturing these functional dependencies, our approach efficiently identifies related components even when physically distant in the codebase.", + "bbox": [ + 505, + 286, + 882, + 381 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2 Agent-guided Code Search", + "text_level": 1, + "bbox": [ + 507, + 397, + 766, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We develop tools based on the indexes built offline. During runtime, LOCAGENT takes issue statements as input and launches agents that autonomously use tools to localize target code sections. While the agent may iteratively invoke multiple tools internally to explore the codebase, LOCAGENT presents a simplified interface to users, requiring only a single-turn interaction—users submit an issue statement and receive localization results without additional input. This autonomous, self-contained workflow makes LOCAGENT both easy to deploy and highly practical for real-world use.", + "bbox": [ + 505, + 419, + 882, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Tool Design for Codebase Exploration. Recent works (Örwall, 2024; Wang et al., 2025), inspired by GUI-based IDEs, have developed numerous specialized tools for agents to explore codebases. However, these tools are initially designed for human readability, which sacrifices the compactness and efficiency that LLM agents prefer (Yang et al., 2024). Building upon our graph-based code representation, we can develop tools that support efficient higher-order codebase exploration to address these challenges. We unify all codebase navigation, search, and view operations into three tools (Table 2), introduced as follows.", + "bbox": [ + 505, + 614, + 884, + 822 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SearchEntity: This tool searches codebases using keywords to locate relevant entities through our Hierarchical Entity Index. When an exact match isn't found in the upper index, the system performs a fuzzy search using the lower index. For each entity found, we return its code snippet in three detail", + "bbox": [ + 507, + 824, + 882, + 921 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "levels: fold, preview, and full code (Figure 6). This effectively prevents lengthy code context and reduces noise fed into agents.", + "bbox": [ + 112, + 84, + 487, + 131 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "**TraverseGraph:** This tool performs a type-aware breadth-first search (BFS) on the code graph, starting from input entities and allowing control over both traversal direction and number of hops. This supports agents to perform arbitrary multi-hop codebase navigation through only one action, significantly improving the efficiency compared with existing agent systems. Note that by allowing agents to select entity types and relation types for each traversal, this tool effectively leverages the LLM agents' coding expertise to generate proper meta paths—a crucial element for heterogeneous graph analysis (Lv et al., 2021). For example, by specifying entity types to {class, function} and relation types to {contain, inherit}, this tool returns the UML diagram. Additionally, we design an expanded tree-based format for the output subgraph that encodes both relation types and directions (Figure 7). (Fatemi et al., 2023) demonstrates that LLM performance on graph reasoning depends on the input graph format. Converting a graph into a tree structure encodes topology through the spatial distance between entity names, thereby deriving better performance. For detailed comparisons with alternative graph formats, please see Appendix A.1.2.", + "bbox": [ + 115, + 133, + 489, + 533 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RetreiveEntity: This tool retrieves complete entity attributes for each input entity ID, including essential information such as file path, line number, and code content.", + "bbox": [ + 112, + 535, + 487, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Chain-of-Thought Agent Planning. We use chain-of-thought (CoT) prompting (shown in Appendix D) to guide the agent in solving code localization problems step by step. The agent systematically follows these steps: (1) Keyword extraction. The agent begins by breaking down the issue statement into different categories and then extracts relevant keywords that are closely related to the problem. (2) Linking keywords to code entities. The agent invokes SearchEntity to complete and clarify each extracted keyword.", + "bbox": [ + 115, + 599, + 489, + 775 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(3) Generate the logical flow from fault to failure. The agent first identifies the entry points that trigger the problem. Then, it iteratively traverse the codebase with TraverseGraph, retrieves code contents with RetrieveEntity, and searches new keywords with SearchEntity. Finally, it generates the logic flow based on the issue and additional context. (4) Locate the target entities. The agent pinpoints all suspicious code entities that need modification", + "bbox": [ + 112, + 777, + 487, + 920 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "based on the logic flow. Then, it ranks these entities based on their relevance.", + "bbox": [ + 507, + 84, + 880, + 115 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Confidence Estimation Based on Consistency. After generating a complete ranked list of candidate entities, to obtain a more consistent ranking, we measure the consistency (Wang et al., 2023a) of the LLM's predictions across multiple iterations. Specifically, we use the Reciprocal Rank as the initial confidence score for each predicted location. We then aggregate the scores for each entity across iterations to compute its final confidence score. The intuition behind this approach is that if the LLM consistently ranks a location higher in multiple iterations, it is more likely to be relevant.", + "bbox": [ + 507, + 117, + 882, + 309 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3 Open-source Model Fine-tuning", + "text_level": 1, + "bbox": [ + 507, + 322, + 808, + 338 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Given the high costs of proprietary LLM APIs and data security concerns, we fine-tuned open-source models to improve their code localization capabilities and enable local deployment. We collect 433 successful trajectories generated with Claude-3.5, where the agent completed tasks from the SWEBench training set. Due to budget constraints, we sample an additional 335 trajectories generated by the initially fine-tuned Qwen2.5-32B model. Importantly, we only select successful trajectories where the model correctly localized the issues, creating a high-quality dataset of correct reasoning paths. These successful examples are then used to refine the same 32B model further, reinforcing effective reasoning patterns through this self-improvement loop. The entire dataset, combining both Claude-3.5 trajectories and successful Qwen2.5-32B samples, was then used to distill knowledge to a smaller 7B model.", + "bbox": [ + 507, + 343, + 882, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To fine-tune the smaller model, we employ Supervised Fine-Tuning (SFT) with LoRA (Hu et al., 2021). Our experiments show that this straightforward distillation method significantly enhances the performance of smaller models. See Appendix C.1.3 for more training details.", + "bbox": [ + 507, + 650, + 882, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 LOC-BENCH: A New Benchmark for Code Localization", + "text_level": 1, + "bbox": [ + 507, + 760, + 863, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1 Revisiting Existing Benchmark", + "text_level": 1, + "bbox": [ + 507, + 803, + 800, + 818 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SWE-Bench(Jimenez et al., 2023) is a widely used benchmark that collects GitHub issues and corresponding code patches that resolve them. Xia et al. (2024); Suresh et al. (2024) adapt its subset, SWE-Bench-Lite, for code localization, treating the patched files and functions as the targets.", + "bbox": [ + 507, + 824, + 882, + 921 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "However, existing datasets, including SWE-Bench, present challenges for effectively evaluating code localization methods. First, they are at risk of contamination, as they may include data overlapping with the repositories or issues used by modern models during pre-training. Second, existing datasets are not specifically designed for code localization (Tomassi et al., 2019). SWE-Bench, for instance, was created primarily to evaluate end-to-end bug-fixing capabilities, with localization being only an implicit intermediate step. This focus results in datasets dominated by bug reports (85% of SWE-Bench-Lite examples) while severely underrepresenting other common software maintenance tasks such as feature requests (14%), security vulnerabilities (1%), and performance optimizations (0%). This imbalance fails to capture the diverse localization challenges faced in real-world software development.", + "bbox": [ + 115, + 84, + 489, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2 Dataset Construction", + "text_level": 1, + "bbox": [ + 115, + 401, + 324, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To address the limitations of existing benchmarks, we introduce LOC-BENCH, a new dataset specifically designed for code localization. This dataset collects up-to-date issues from Python repositories to mitigate the influence of pre-training bias in the latest LLMs. Additionally, LOC-BENCH covers wider categories, including bug reports, feature requests, security, and performance issues, enabling a more comprehensive evaluation of code localization methods. The statistics of LOC-BENCH are shown in Table 3.", + "bbox": [ + 115, + 420, + 487, + 596 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the Bug Report category, we collect GitHub issues created after October 2024, which is later than the release dates of most modern LLMs. To enrich the dataset with more instances of security and performance issues, we use the GitHub Search API to search for relevant keywords, such as \"latency improvement\" for performance-related issues. We exclude instances that involve modifying more than five Python files or more than ten functions in the corresponding patch. For further details, see Appendix B.1.", + "bbox": [ + 115, + 598, + 487, + 774 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5 Experiments", + "text_level": 1, + "bbox": [ + 115, + 785, + 257, + 802 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our experiments aim to evaluate four key aspects of LOCAGENT: (1) the effectiveness of our graph-based representation and tooling for code localization compared to existing methods, (2) the performance of fine-tuned open-source models as cost-effective alternatives to proprietary LLMs, (3) a detailed analysis of how performance varies across", + "bbox": [ + 115, + 809, + 487, + 919 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dffede0cb6e1140d33ef35874b6f55be329c72cec08ada3fd8a7e8684a261136.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetCategory#Sample
SWE-Bench-Lite (Total = 300)Bug Report254
Feature Request43
Security Issue3
Performance Issue0
Loc-Bench (Totoal = 560)Bug Report242
Feature Request150
Security Issue29
Performance Issue139
", + "bbox": [ + 524, + 82, + 868, + 265 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Distribution of samples across different categories in the SWE-Bench-Lite and Loc-Bench datasets.", + "bbox": [ + 510, + 275, + 880, + 304 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "task categories, and (4) the contribution of each component in our framework through comprehensive ablation studies. We evaluate on both SWE-Bench-Lite and our introduced Loc-Bench dataset. Additionally, we examine the impact of improved localization on downstream software maintenance tasks.", + "bbox": [ + 510, + 317, + 880, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1 Experimental Settings", + "text_level": 1, + "bbox": [ + 510, + 432, + 727, + 449 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets. We first conduct experiments on SWEBench-Lite, treating the patched files and functions as the targets for localization. Following Suresh et al. (2024), we excluded examples where no existing functions were modified by the patch, ultimately retaining 274 out of the original 300 examples.", + "bbox": [ + 510, + 455, + 880, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics. To assess performance, we use a modified accuracy metric inspired by R-Precision from information retrieval, following Agentless(Xia et al., 2024). To assess performance, we use Acc@k (Accuracy at k) as our evaluation metric, following Agentless(Xia et al., 2024). For each example, we select the top-k predicted locations and consider a localization attempt successful only if all relevant locations are correctly identified within these top-k predictions. This approach measures the ability to fully identify all necessary code sections that require modification. We report results across multiple $k$ values: file localization at Acc@1, Acc@3, and Acc@5, and function localization at Acc@5 and Acc@10. Additionally, to provide a more relaxed evaluation criteria, we assess module localization, which only requires finding any function within the patched class.", + "bbox": [ + 510, + 568, + 880, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2 Baselines", + "text_level": 1, + "bbox": [ + 510, + 868, + 626, + 882 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate LOCAGENT against three categories of competitive baselines: (a) Retrieval-based meth", + "bbox": [ + 510, + 890, + 880, + 919 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ad9888427e4959ea8df866a9f22f434e24d97aa01a98851cc1f0d57d84fed76f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TypeMethodLoc-ModelFile (%)Module (%)Function (%)
Acc@1Acc@3Acc@5Acc@5Acc@10Acc@5Acc@10
Embedding-BasedBM25 (Robertson et al., 1994)38.6951.8261.6845.2652.9231.7536.86
E5-base-v2 (Wang et al., 2022)49.6474.4580.2967.8872.2639.4251.09
Jina-Code-v2 (Günther et al., 2023)43.4371.1780.2963.5072.6342.3452.19
Codesage-large-v2 (Zhang et al., 2024)47.8169.3478.1060.5869.7133.9444.53
CodeRankEmbed (Suresh et al., 2024)52.5577.7484.6771.9078.8351.8258.76
Procedure-BasedAgentless (Xia et al., 2024)GPT-4o67.1574.4574.4567.1567.1555.4755.47
Claude-3.572.6379.2079.5668.9868.9858.7658.76
Agent-BasedMoutlessTools (Örwall, 2024)GPT-4o73.3684.3185.0474.8276.2857.3059.49
Claude-3.572.6385.7786.1376.2876.2864.6064.96
SWE-agent (Yang et al., 2024)GPT-4o57.3064.9668.9858.0358.0345.9946.35
Claude-3.577.3787.2390.1577.7478.1064.2364.60
Openhands (Wang et al., 2025)GPT-4o60.9571.9073.7262.4163.8749.6450.36
Claude-3.576.2889.7890.1583.2183.5868.2570.07
LOCAGENT (Ours)Qwen2.5-7B(ft)70.8084.6788.3281.0282.8564.2371.53
Qwen2.5-32B(ft)75.9190.5192.7085.7787.2371.9077.01
Claude-3.577.7491.9794.1686.5087.5973.3677.37
", + "bbox": [ + 119, + 64, + 882, + 300 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4: Performance comparison with baseline methods on code localization on SWE-bench lite. Results show the accuracy at file, module, and function levels. For Agent-Based methods, we use GPT-4o-2024-0513 (abbr. as GPT-4o) and Claude-3-5-sonnet-20241022 (abbr. as Claude-3.5) as the localization model. Additionally, the performance of our fine-tuned open-source models, Qwen2.5-7B(ft) and Qwen2.5-32B(ft), are included for comparison.", + "bbox": [ + 112, + 309, + 884, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ods: We include the sparse retrieval approach BM25 (Robertson et al., 1994) and several state-of-the-art embedding models, including the general-purpose E5-base-v2 (Wang et al., 2022) and specialized code embedding models such as JinaCode-v2 (Günther et al., 2023), Codesage-large-v2 (Zhang et al., 2024), and the current SOTA code embedding model CodeRankEmbed (Suresh et al., 2024). Proprietary embedding solutions were excluded due to API costs. (b) Procedure-based methods: We compare against Agentless (Xia et al., 2024), which employs a structured hierarchical approach to code localization without complex agent architectures. (c) Agent-based methods: We include several advanced agent frameworks designed for code exploration and modification, specifically OpenHands (Wang et al., 2025) (using its default CodeActAgent implementation), SWE-Agent (Yang et al., 2024), and MoatlessTools (Örwall, 2024). For implementation details, please refer to Appendix C.1.1.", + "bbox": [ + 110, + 388, + 490, + 728 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3 Evaluation Results on SWE-Bench-Lite", + "text_level": 1, + "bbox": [ + 112, + 739, + 472, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Table 4, Agent-Based methods consistently outperform other approaches, and our method demonstrates competitive performance by achieving the best results across all levels of code localization. Unlike traditional retrieval-based methods, Agentless identifies only a limited number of locations due to its narrow repository scope, which hinders performance gains when considering a broader set of candidates. The results of the NDCG are presented in Table 11 in the Appendix.", + "bbox": [ + 112, + 760, + 490, + 921 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f929dd53f4adf74c47eab0524e9c10d9df2c8753a81e68bd756d7c86d5d4876b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 384, + 870, + 511 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dd0a043ec99e4aa7d3cdd9cab21f0f8c8ff70d258cc383c3b7961f81be3880dc.jpg", + "image_caption": [ + "Figure 3: Performance analysis at different difficulty levels for file- and function-level localization. All agent-based methods and Agentless use Claude-3.5 as the localization model. Hop $N$ refers to the distances between functions mentioned in the issue description and the ground truth patch on our code graph." + ], + "image_footnote": [], + "bbox": [ + 522, + 514, + 870, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further analyze the results, we examine performance across different task difficulty levels. We measure the task difficulty by calculating the shortest hops between the functions mentioned in the issue descriptions and the patched functions on our code graph (See Appendix C.1.2 for more details). As shown in Figure 3, performance decreases for all methods as the task becomes more challenging. However, Agent-based methods demonstrate better robustness as the difficulty increases, with", + "bbox": [ + 507, + 760, + 884, + 921 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/594e4e848668151fa0f0d585dcf3a37fcc51677d8a82c5fdceaf97947d73c7bb.jpg", + "image_caption": [ + "Figure 4: Comparison of performance between the original and fine-tuned Qwen models. The metrics used are file-level Acc@5 and module/function-level Acc@10. Dashed lines represent the performance of the Claude-3.5 model for reference." + ], + "image_footnote": [], + "bbox": [ + 126, + 74, + 475, + 209 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "our method maintaining competitive performance across various difficulty levels. Retrieval-based methods, such as E5-Base-v2 and CodeRankEmbed, perform poorly at the function level, even when the patched functions are explicitly mentioned in the query. This is because they treat the query as a whole, failing to capture fine-grained details. Agentless performs even worse than retrieval-based methods when exploration beyond the query is needed ( $hop \\geq 0$ ) due to its simplistic localization process and limited view focused only on the repository structure.", + "bbox": [ + 112, + 309, + 489, + 502 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.4 Fine-tuned Open-source Models", + "text_level": 1, + "bbox": [ + 112, + 514, + 413, + 529 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Figure 4 demonstrates that after fine-tuning, both the 7B and 32B models show significant improvements on this task. LOCAGENT with finetuned Qwen-2.5-Coder-Instruct-32B (abbreviated as Qwen2.5-32B(ft)) achieves performance comparable to Claude-3.5, and LOCAGENT with Qwen2.5-7B(ft) also delivers results on par with that obtained using GPT-4o. As shown in Table 4, our method with Qwen2.5-32B(ft) outperforms nearly all baselines, including those that use larger and more powerful LLMs. The original 7B model performs poorly due to its limited tool-use capability (Chen et al., 2024). These results validate the feasibility of deploying our fine-tuned open-source models as promising alternatives to proprietary APIs, especially in resource-constrained applications.", + "bbox": [ + 112, + 533, + 489, + 808 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.5 Efficiency Analysis", + "text_level": 1, + "bbox": [ + 112, + 819, + 310, + 835 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 5 presents an efficiency analysis comparing agent-based methods in terms of cost and the number of agent interactions required. MoatlessTools demonstrates good cost-efficiency and requires relatively fewer rounds of interaction. However, the", + "bbox": [ + 112, + 841, + 489, + 921 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/ca58188c6fe4c2ffec34aeccdb6ee5a73bdf63c458fea192f02d6865ca76db6a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLM#RoundCost($)Acc@10
Cost
MoatlessToolsGPT-4o50.461.3
Claude-3.550.461.4
SWE-agentGPT-4o80.560.8
Claude-3.590.671.0
OpenhandsGPT-4o150.830.6
Claude-3.5130.790.9
OursClaude-3.570.661.2
Qwen2.5-7B(ft)60.0513.2
Qwen2.5-32B(ft)90.098.6
", + "bbox": [ + 507, + 80, + 873, + 214 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/cbbf57fce918f5d0e7521a35c3e24e9a0612bad18584b2403a531e9d40562501.jpg", + "table_caption": [ + "Table 5: Efficiency analysis comparing the average cost and number of agent interaction rounds required by different methods. The cost-efficiency of each method is evaluated using the ratio of function-level Acc@10 to average cost." + ], + "table_footnote": [], + "table_body": "
Model SettingFile Acc@5Module Acc@10Function Acc@10
Ours88.3282.8571.53
w/o TraverseGraph86.1378.4766.06
Relation Types: contain86.5079.5666.42
Traverse Hops: 186.8680.2966.79
w/o RetrieveEntity87.5981.3969.34
w/o SearchEntity68.9861.3153.28
w/o BM25 index75.1868.9860.22
", + "bbox": [ + 510, + 300, + 878, + 441 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 6: The ablation study of our model. The metrics used here are file-level Acc@5, module-level Acc@10, and function-level Acc@10. The impact of removing or fixing components is analyzed to observe how each component contributes to the overall accuracy.", + "bbox": [ + 507, + 451, + 882, + 524 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "dense embeddings it uses make it difficult and slow to adapt to fast-evolving codebases. SWE-agent and Openhands also show moderate costs but still do not match the efficiency of LOCAGENT. For LOCAGENT with Claude-3.5, although more rounds of interaction are required, the cost remains lower than that of Openhands, illustrating the token efficiency of our tool's outputs. LOCAGENT with fine-tuned Qwen models stands out for its superior efficiency1. Qwen2.5-7B(ft) is the most cost-efficient option, requiring only $0.05 per example, while Qwen2.5-32B(ft) offers a more cost-effective alternative to Claude-3.5. These results highlight the potential of fine-tuned open-source models as efficient alternatives, providing an optimal balance of cost-effectiveness and performance that surpasses other methods.", + "bbox": [ + 505, + 546, + 884, + 820 + ], + "page_idx": 8 + }, + { + "type": "page_footnote", + "text": "1We calculate the cost based on the prices from AI inference providers (Hyperbolic, 2025; artificialanalysis.ai, 2025). Specifically, for the Qwen2.5-32B(ft) model, the cost is $0.20/1M tokens for both input and output. For the Qwen2.5-7B(ft) model, the cost is $0.14/1M tokens for input and $0.28/1M tokens for output.", + "bbox": [ + 507, + 847, + 882, + 921 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.6 Ablation Study", + "text_level": 1, + "bbox": [ + 114, + 84, + 278, + 99 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "We conduct an ablation study to evaluate the effectiveness of each component of our toolsets. Due to budget constraints, we use the fine-tuned Qwen-2.5-7B as the localization model for these experiments.", + "bbox": [ + 112, + 107, + 487, + 185 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) Each tool in our toolset plays a critical role in code localization performance. As shown in Table 6, removing any tool, especially the SearchEntity tool, leads to varying degrees of accuracy degradation, particularly in module and function level localization. This highlights the critical role each tool plays in identifying relevant modules and functions.", + "(2) The graph structure provides essential information for accurate code localization. Removing TraverseGraph tool decreases module and function level performance since the agent cannot obtain any structure information about the codebase and relies on reasoning capability to identify call relationship or directory structure. Adding contain relationship provides only marginal improvements compared to fully removing TraverseGraph, emphasizing the importance of the other three relationship types and explaining why our method surpasses others relying only on the repository structure.", + "(3) Multi-hop exploration is crucial for deep code understanding. When compared to the full setting, fixing $Hops = 1$ leads to a moderate decline in file and module-level accuracy, but it causes a more significant decrease in function-level accuracy, underscoring the importance of multi-hop exploration for identifying relevant entities.", + "(4) Sparse indexing significantly enhances localization performance. Removing SearchEntity tool, or even partial removal of its index, causes a substantial drop in performance across all metrics. This demonstrates the effectiveness of building a sparse index on our code graph for improving localization performance." + ], + "bbox": [ + 112, + 187, + 489, + 753 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "5.7 Evaluation Results on Loc-Bench", + "text_level": 1, + "bbox": [ + 112, + 769, + 420, + 784 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "To ensure the robustness and generalization of our methods and fine-tuned Qwen models, and to eliminate potential data leakage, we evaluate our new dataset. Since Loc-Bench includes examples that edit 1 to 5 files, we assess file localization at top-5 and top-10 ranks, and function/module localization at top-10 and top-15 ranks. Table 7 shows that our fine-tuned Qwen2.5-7B model exhibits strong gen", + "bbox": [ + 112, + 791, + 487, + 921 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/40113cdec1e1feca7000cb77d3a5294a6135d63a0d343288699aecc05a7b7a58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 79, + 870, + 195 + ], + "page_idx": 9 + }, + { + "type": "image", + "img_path": "images/f3ff500f60d006d9ab2100b2e34cdaaed024cc944a6d5f1861937bb334d1a3cf.jpg", + "image_caption": [ + "Figure 5: Performance analysis at different difficulty category for file- and function-level localization. All agent-based baselines and Agentless use Claude-3.5 as the localization model." + ], + "image_footnote": [], + "bbox": [ + 522, + 199, + 870, + 315 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "eralization capabilities, maintaining competitive performance compared to SWE-agent using more expensive and strong model. These results highlight the practicality of the fine-tuned Qwen2.5-7B model for real-world applications. Despite being an open-source alternative, it achieves a performance comparable to Claude-3.5, supporting its feasibility as a cost-effective substitute for commercial models in practical scenarios.", + "bbox": [ + 505, + 399, + 882, + 543 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Additionally, we evaluate the performance across four different difficulty categories. Figure 5 clearly shows that our method outperforms other methods in almost all categories of code localization. However, it also highlights a noticeable decrease in performance across the other three categories compared to the Bug Report category. This performance gap likely reflects our training data distribution, which contained more bug report examples, potentially leading to scaffolds better optimized for bug localization tasks. This trend suggests that while our method is highly effective for bug report localization, there is still room for improvement in handling the other categories through more balanced training data and category-specific optimization strategies.", + "bbox": [ + 507, + 545, + 882, + 802 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "5.8 Application: Better Localization Leads to More Solved GitHub Issues", + "text_level": 1, + "bbox": [ + 507, + 816, + 880, + 848 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "To assess the impact of localization methods on downstream tasks, we evaluated their effectiveness in solving GitHub issues. We choose Agentless as the baseline, ranking among the top-performing", + "bbox": [ + 507, + 856, + 880, + 921 + ], + "page_idx": 9 + }, + { + "type": "table", + "img_path": "images/6c9737e3fa48ebc0fa6a563806676ce4a098be8490a88f39f510258c9a12539f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLoc ModelFile (%)Module (%)Function (%)
Acc@5Acc@10Acc@10Acc@15Acc@10Acc@15
IR-BasedCodeRankEmbed74.2980.8963.2167.5043.3946.61
AgentlessClaude-3.567.5067.5053.3953.3942.6842.68
OpenHandsClaude-3.579.8280.0068.9369.1159.1159.29
SWE-agentClaude-3.577.6877.6863.5763.7551.9651.96
LocAgent (Ours)Qwen2.5-7B(ft)78.5779.6463.0463.0451.4351.79
Claude-3.583.3986.0770.8971.0759.2960.71
", + "bbox": [ + 147, + 80, + 845, + 225 + ], + "page_idx": 10 + }, + { + "type": "table", + "img_path": "images/cd90b427caeb94e68300cb0963a3939e90034375ecc1b70e22bb7ba12b53914b.jpg", + "table_caption": [ + "Table 7: Performance evaluation on the real-world LocBench dataset." + ], + "table_footnote": [], + "table_body": "
MethodLocalization LMAcc@5Pass@1Pass@10
AgentlessClaude-3.558.3926.3133.58
OursQwen2.5-32B(ft)69.3426.7936.13
Claude-3.573.3627.9237.59
", + "bbox": [ + 114, + 273, + 482, + 344 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Table 8: Impact of localization accuracy on downstream bug repair tasks.", + "bbox": [ + 112, + 353, + 485, + 384 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "open-source submissions on SWE-Bench-Lite. For consistency, we utilized Claude-3.5 as the editing model in conjunction with the Agentless editing method. Table 8 shows that the success rate for solving GitHub issues improves significantly with better code localization accuracy.", + "bbox": [ + 112, + 397, + 487, + 494 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "6 Conclusion", + "text_level": 1, + "bbox": [ + 112, + 505, + 247, + 519 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "In conclusion, LOCAGENT enhances code localization by structuring codebases as graphs, enabling efficient repository-level exploration for LLM agents. With fine-tuned open-source models, our method achieves high localization accuracy while significantly reducing costs compared to larger proprietary models. Experimental results demonstrate the effectiveness of LOCAGENT in identifying relevant code components and improving downstream tasks.", + "bbox": [ + 112, + 530, + 489, + 690 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Limitations", + "text_level": 1, + "bbox": [ + 112, + 703, + 218, + 717 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "First, our study primarily focused on fine-tuning Qwen-2.5-Coder models. Exploring a broader range of base models, including other open-source LLMs like CodeLlama, Mistral, or Yi, could provide valuable insights into model selection trade-offs. Additionally, investigating different finetuning approaches beyond LoRA, such as full finetuning or other parameter-efficient methods, could potentially yield better performance.", + "bbox": [ + 112, + 728, + 487, + 872 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Second, though we demonstrated improved bug repair performance with better localization, we only scratched the surface of potential downstream", + "bbox": [ + 112, + 873, + 487, + 922 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "applications. Future work should evaluate LocAgent's impact on other software engineering tasks like refactoring, feature addition, security vulnerability patching, and performance optimization. This would provide a more comprehensive understanding of the framework's practical utility.", + "bbox": [ + 507, + 275, + 884, + 370 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Moreover, our fine-tuning process relied heavily on trajectories generated by Claude-3.5 and the fine-tuned Qwen2.5-32B model. A more diverse training dataset incorporating examples from different models, tasks, and repositories could improve the robustness and generalization of fine-tuned models. Additionally, analyzing the impact of different dataset compositions and filtering strategies on model performance could yield valuable insights.", + "bbox": [ + 507, + 372, + 884, + 533 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Finally, the current evaluation focuses primarily on Python codebases. Extending LOCAGENT to support other programming languages and evaluating its performance across different language paradigms would better demonstrate its generalizability. Further, our evaluation metrics could be expanded to include more nuanced measures of localization quality beyond accuracy and NDCG.", + "bbox": [ + 507, + 533, + 885, + 663 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 510, + 690, + 608, + 705 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "Aider. 2023. Building a better repository map with tree sitter. Accessed: April 15, 2025.", + "Anthropic. 2023. Claude: Conversational ai by anthropic. Accessed: January 21, 2025.", + "artificialanalysis.ai. 2025. Artificial analysis. https://artificialanalysis.ai/models/. Accessed: 2025-04-28.", + "Marcel Böhme, Ezekiel O Soremekun, Sudipta Chattopadhyay, Emamurho Ugherughe, and Andreas Zeller. 2017. Where is the bug and how is it fixed? an experiment with practitioners. 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Moatless tools." + ], + "bbox": [ + 510, + 85, + 882, + 438 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "A LOCAGENT Design Details", + "text_level": 1, + "bbox": [ + 112, + 83, + 386, + 99 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A.1 Tool Output Design", + "text_level": 1, + "bbox": [ + 112, + 109, + 319, + 124 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A.1.1 Three-level format for SearchEntity output", + "text_level": 1, + "bbox": [ + 112, + 130, + 467, + 162 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Once invoked by the LLM agent, the retrieval APIs search for files, classes, methods, and code snippets in the codebase, and return the results back to the agent. To avoid forming very lengthy code context that may containing noisy information to LLM, we return only necessary information as API outputs. To achieve this, we desgined four granular standard output formats (Figure 6): fold, preview, full code.", + "bbox": [ + 112, + 166, + 487, + 309 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A.1.2 Tree-based Subgraph Formatting for TraverseGraph Output", + "text_level": 1, + "bbox": [ + 112, + 319, + 468, + 351 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "The TraverseGraph tool traverses the code graph and returns a local subgraph for each input entity. The agent reasons about these subgraphs to understand each entity's complex dependencies. However, reasoning about graphs remains challenging for LLMs. Research by (Fatemi et al., 2023) demonstrates that LLM performance varies significantly based on graph formatting (how graphs are encoded as text). This makes the format design for output subgraphs crucial.", + "bbox": [ + 112, + 356, + 487, + 516 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We have developed a new tree-based format, shown in Figure 7, with several features that enhance LLM reasoning: (1) We represent subgraphs as trees, allowing LLMs to use indentation to determine a node's distance from the root, (2) We display complete entity IDs for each node (e.g., django/core-validators.py:RegexValidator) to help LLMs locate nodes easily, and (3) We explicitly specify relation types for each edge, including reversed relations", + "bbox": [ + 112, + 517, + 490, + 676 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "To evaluate how different graph formats impact code localization performance, we conducted an experiment using 37 challenging samples from SWEBench-Lite. These samples were considered \"challenging\" because they could not be solved by any baseline agent methods. Using Claude-3.5 as the Localization Model across all settings, we compared various output formats. Table 9 presents our findings. The baseline output formats we tested are described below:", + "bbox": [ + 112, + 678, + 489, + 837 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "- row: For each line, list one row of the adjacency matrix. For example,", + "bbox": [ + 134, + 851, + 487, + 883 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "function \"fileA.py:funcA\" invokes function \"fileA.py:funcB\", \"fileA.py:funcC\"", + "bbox": [ + 147, + 889, + 487, + 921 + ], + "page_idx": 13 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- row (w/ entity attributes): Additionally include entity attributes for format row.", + "- incident: The incident format mentioned in (Fatemi et al., 2023). An integer instead of entity ID is used to represent each node. For example," + ], + "bbox": [ + 529, + 84, + 882, + 190 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Map function \"fileA.py:funcA\" to index 0. Map function \"fileA.py:funcB\" to index 1. Map function \"fileA.py:funcC\" to index 2.", + "bbox": [ + 541, + 196, + 880, + 243 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "function $O$ invokes function 1,2.", + "bbox": [ + 542, + 249, + 779, + 265 + ], + "page_idx": 13 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Graphviz DOT: Represent graph in Graphviz DOT language (Ellson et al., 2002).", + "- JSON: Expand the subgraph as a tree, and convert it to JSON format." + ], + "bbox": [ + 531, + 274, + 880, + 348 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "As shown in Table 9, expanding subgraphs as trees (i.e., JSON, tree-based) can significantly improve the performance. Our tree-based format achieves the best overall performance across different levels of localization tasks. We also test returning entity attributes along with subgraphs. We notice that row (w/ entity attributes) consistently underperforms row, indicating the attributes for all the nodes may be very noisy. Besides, although using incident format can simplify the output and show improvements in file-level localization, it degradation the module- and file-level localization.", + "bbox": [ + 507, + 359, + 884, + 551 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A.2 Implementation", + "text_level": 1, + "bbox": [ + 507, + 563, + 685, + 577 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "To enable the LLM agent to invoke the Code Localization APIs, we handle the interaction differently based on the LLM's capabilities. For LLMs that support tool-calling features, we define the tools as a list of JSON objects, which are then used as parameters for the API calls. For LLMs that do not support tool-calling (such as Qwen), we provide the description of the API and the expected output as part of the LLM's prompt. When the agent decides to invoke a set of retrieval APIs, it responds with a list of API call names and their corresponding arguments. These retrieval API requests are processed locally by searching over the built code graph. The results from executing these APIs locally are returned to the agent.", + "bbox": [ + 505, + 583, + 882, + 824 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "By default, we query the LLM with a temperature setting of 1.0. We conduct two interactions, after which we rerank the results based on mean reciprocal rank (MRR) scores. We also leverage multiprocessing execution to speed up the process. Since all our tools are read-only, LOCAGENT does", + "bbox": [ + 507, + 825, + 882, + 921 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/e3da4d4339e99b1a14d6f8d73ea975c643cc44ad95a8dc1803fff42294d4f99a.jpg", + "image_caption": [ + "Figure 6: Different output formats designed for efficient agent-code interaction. Left: Full code output when matched entities $\\leq 3$ . Middle: Preview output showing module skeleton for large files. Right: Fold output showing only entity IDs when matches $>3$ ." + ], + "image_footnote": [], + "bbox": [ + 127, + 85, + 366, + 343 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/003dcde246a439f5b9b36cc33df7c37daaa5e4eaf0478ed30be80b30cbe72965.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 374, + 86, + 621, + 343 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/86b464c56ef20eb2e4a58b1077f46f88aa113910e37ea427df9e03b94670489d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 86, + 872, + 343 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/503072355158697ea6cb6ac7e2712ec0ffc412f1cd70207465e4cb36e21f3c9b.jpg", + "image_caption": [ + "Figure 7: A truncated example of the expanded tree-based format for the output subgraph of tool TraverseGraph." + ], + "image_footnote": [], + "bbox": [ + 268, + 410, + 727, + 636 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "not require a specialized Docker environment to operate.", + "bbox": [ + 112, + 686, + 485, + 717 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "B Dataset construction and statistics", + "text_level": 1, + "bbox": [ + 114, + 730, + 445, + 744 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "B.1 Dataset construction details", + "text_level": 1, + "bbox": [ + 114, + 755, + 381, + 769 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Example collection. We collected examples on popular Python repositories on Github follow (Jimenez et al., 2023). To gather issues related to performance and security, we searched for the keywords listed in Table 10 using the GitHub Search APIs. We then used GPT-4o-2024-0513 as the classifier based on the issue descriptions.", + "bbox": [ + 112, + 776, + 487, + 888 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Ground Truth Locations. The affected files or functions in the original codebase, as identified in", + "bbox": [ + 112, + 889, + 487, + 921 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "the patches, are considered the target locations for the given issue. While it is possible to fix a bug in a location different from the ground truth, the extracted ground-truth locations still serve as approximate targets for localization. Additionally, edited code such as documents, import statements, and comments are excluded from the localization target. These elements are not considered relevant for bug localization, as they do not directly impact the functionality of the code or its execution. By filtering out these elements, the focus is maintained on the core code changes that are relevant for localization.", + "bbox": [ + 507, + 686, + 884, + 892 + ], + "page_idx": 14 + }, + { + "type": "table", + "img_path": "images/65aa2b242676fd4ce7ba9e60ceadb537140f50dff384a8c6651710edad591512.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Output FormatFile(%)Module(%)Function(%)
Acc@1Acc@3Acc@5Acc@5Acc@10Acc@5Acc@10
row41.1867.6570.5961.7661.7635.2938.24
row (w/ entity attributes)41.1864.7164.7150.0050.0032.3532.35
incident41.1870.5973.5355.8855.8829.4132.35
Graphviz DOT41.1873.5382.3564.7164.7135.2935.29
JSON41.1867.6576.4767.6570.5938.2441.18
tree-based (Ours)47.0679.4179.4164.7164.7138.2441.18
", + "bbox": [ + 157, + 80, + 840, + 225 + ], + "page_idx": 15 + }, + { + "type": "table", + "img_path": "images/2976dea7e0ff07dfee13b430fc8f8efa94af68a9c7230eb416ed229809e5c751.jpg", + "table_caption": [ + "Table 9: Localization performance under different TraverseGraph output formats." + ], + "table_footnote": [], + "table_body": "
CategoryKeywords
Performancebottleneck, performance improvement, memory usage optimization, time complexity reduction, latency improvement, scalability improvement, CPU usage reduction, caching improvement, concurrency optimization
SecurityOut-of-bounds Write, Out-of-bounds Read, NULL Pointer Dereference, Missing Authorization, memory leak fix, security vulnerability, security issue, authentication bypass, authentication issue, better maintained, buffer overflow, denial of service, security hardening, security patch, unsafe deserialization, Use After Free, Integer Overflow or Wraparound, Uncontrolled Resource Consumption, Missing Authentication for Critical Function
", + "bbox": [ + 157, + 260, + 840, + 439 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Table 10: We use these Keywords to search for Performance and Security related issues with Github Search APIs.", + "bbox": [ + 112, + 448, + 880, + 464 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "C Additional Experiments", + "text_level": 1, + "bbox": [ + 112, + 488, + 359, + 505 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "C.1 Implementation Details", + "text_level": 1, + "bbox": [ + 112, + 514, + 349, + 530 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "C.1.1 Baselines Implementation", + "text_level": 1, + "bbox": [ + 112, + 535, + 381, + 551 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Regarding the embedding-based methods in our evaluation, these approaches operate primarily at the function level, where each function is embedded as a separate unit. The function's context (its containing file and class) is appended to the function representation before embedding, rather than being embedded separately. While theoretically these methods could employ hierarchical indexing, the standard implementations we evaluated use flat indexing structures where each function is embedded as a single unit.", + "bbox": [ + 112, + 554, + 489, + 731 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "We use OpenHands's remote runtime feature to parallelize evaluation on OpenHands and SWEagent. We use Openhands version 0.12.0 released on Oct 31, 2024.", + "bbox": [ + 112, + 732, + 489, + 796 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "C.1.2 Quantifying Task Difficulty Based on Code Graph Distance", + "text_level": 1, + "bbox": [ + 112, + 804, + 470, + 837 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "We measure task difficulty by computing the average shortest hop distance between the functions mentioned in the issue descriptions and the patched functions within our code graph. Specifically, we first extract potential function names from each", + "bbox": [ + 112, + 841, + 489, + 921 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "issue description using GPT-4o-2024-0513, and identify their corresponding nodes in the code graph using the global dictionary. These identified nodes form the set of predicted nodes, denoted as $\\mathcal{C}$ . Similarly, we link the ground truth functions from the patch to their corresponding nodes in the code graph, forming the set of target nodes, denoted as $\\mathcal{T}$ . To quantify the difficulty $\\delta$ , we calculate the average shortest hop distance between the predicted nodes $\\mathcal{C}$ and the target nodes $\\mathcal{T}$ , defined as:", + "bbox": [ + 507, + 489, + 884, + 650 + ], + "page_idx": 15 + }, + { + "type": "equation", + "text": "\n$$\n\\delta = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\frac {1}{m i n _ {t \\in \\mathcal {T}} d (c , t) + 1}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 656, + 815, + 693 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "where $d(c, t)$ represents the shortest hop distance between nodes $c$ and $t$ in the graph. For performance analysis stratified by difficulty, we round $\\delta$ down to $\\lfloor \\delta \\rfloor$ to group samples by difficulty levels, and we exclude samples where the LLM fails to extract any valid function names.", + "bbox": [ + 507, + 701, + 884, + 797 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "C.1.3 Training details.", + "text_level": 1, + "bbox": [ + 507, + 804, + 702, + 821 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Fine-tuning Settings. We use Qwen-2.5-Coder-Instruct (Hui et al., 2024) 7B and 32B variants as our base models. We fine-tuned Qwen-2.5-Coder-Instruct 7B and 32B models on 768 training samples from the SWE-Bench training dataset, leveraging LoRA", + "bbox": [ + 507, + 825, + 882, + 921 + ], + "page_idx": 15 + }, + { + "type": "table", + "img_path": "images/d58f8658622664aa6fdd9f0ba4233e824e52755bf040929bc8346fe186a5d5e3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TypeMethodLoc-ModelFile (%)Module (%)Function (%)
NDCG@1NDCG@3NDCG@5NDCG@5NDCG@10NDCG@5NDCG@10
Embedding-BasedBM25 (Robertson et al., 2009)38.6946.550.6137.3139.8626.1527.92
E5-base-v2 (Wang et al., 2022)49.6464.1966.653.1554.4531.3935.3
Jina-Code-v2 (Günther et al., 2023)43.4359.9363.751.0254.1333.2836.44
Codesage-large-v2 (Zhang et al., 2024)47.8160.8264.3949.3852.2227.0330.74
CodeRankEmbed (Suresh et al., 2024)52.5567.5470.3957.5159.7640.2842.55
Procedure-BasedAgentless (Xia et al., 2024)GPT-4o67.1571.7671.7664.3164.3153.8153.81
Claude-3.572.6376.7276.8767.3667.3657.5557.55
Agent-BasedMoatlessTools (Örwall, 2024)GPT-4o73.3680.0380.3368.5769.0949.7750.62
Claude-3.572.6380.7380.8869.1169.1153.0353.16
SWE-agent (Yang et al., 2024)GPT-4o57.363.9664.1253.9553.9542.3242.44
Claude-3.577.3784.3284.9372.7772.959.6759.79
Openshands (Wang et al., 2025)GPT-4o60.9567.6268.3958.1858.644.3444.66
Claude-3.576.2884.2784.4375.7975.9263.1363.8
LocAgent (Ours)Qwen2.5-7B(ft)70.8079.3680.970.9971.6855.6258.09
Qwen2.5-32B(ft)75.9184.7485.6476.2876.7764.2765.93
Claude-3.577.7486.1987.1477.7378.164.3465.57
", + "bbox": [ + 119, + 82, + 878, + 284 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Table 11: NDCG scores comparison showing ranking quality of different methods.", + "bbox": [ + 218, + 294, + 776, + 309 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "for efficient adaptation. The training set included 447 samples generated by Claude-3.5, while the remaining samples were iteratively generated using the fine-tuned Qwen2.5-32B model. The fine-tuning process was conducted over 5 epochs with max_token set to $128k$ and a learning rate of $2 \\times 10^{-4}$ .", + "bbox": [ + 112, + 335, + 487, + 447 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "D Prompt", + "text_level": 1, + "bbox": [ + 114, + 458, + 220, + 475 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "In this section, we go through the prompt template that make up the agent's history.", + "bbox": [ + 112, + 485, + 485, + 517 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Prompt", + "text_level": 1, + "bbox": [ + 127, + 254, + 171, + 265 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Given the following GitHub problem description, your objective is to localize the specific files, classes or functions, and lines of code that need modification or contain key information to resolve the issue.", + "bbox": [ + 127, + 268, + 870, + 287 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Follow these steps to localize the issue:", + "bbox": [ + 127, + 292, + 366, + 302 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Step 1: Categorize and Extract Key Problem Information", + "bbox": [ + 127, + 302, + 458, + 310 + ], + "page_idx": 17 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Classify the problem statement into the following categories:", + "Problem description, error trace, code to reproduce the bug, and additional context.", + "- Identify modules in the '{package_name}' package mentioned in each category.", + "- Use extracted keywords and line numbers to search for relevant code references for additional context." + ], + "bbox": [ + 127, + 311, + 724, + 342 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Step 2: Locate Referenced Modules", + "bbox": [ + 127, + 349, + 337, + 357 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Accurately determine specific modules", + "bbox": [ + 139, + 359, + 354, + 365 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Explore the repo to familiarize yourself with its structure.", + "bbox": [ + 139, + 366, + 495, + 373 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Analyze the described execution flow to identify specific modules or components being referenced.", + "bbox": [ + 139, + 374, + 707, + 381 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Pay special attention to distinguishing between modules with similar names using context and described execution flow.", + "bbox": [ + 127, + 382, + 816, + 388 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Output Format for collected relevant modules:", + "bbox": [ + 127, + 390, + 400, + 397 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Use the format: 'file path:QualifiedName'", + "bbox": [ + 139, + 398, + 383, + 405 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- E.q., for a function `calculate_sum` in the `MathUtilities` class located in `src/helpers/mathHelpers.py`, represent it as:", + "bbox": [ + 139, + 406, + 840, + 413 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "'src/helpers/mathHelpers.py:MathUtil calculator_sum'.", + "bbox": [ + 156, + 414, + 462, + 422 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "## Step 3: Analyze and Reproducing the Problem", + "bbox": [ + 127, + 428, + 394, + 437 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Clarify the Purpose of the Issue", + "bbox": [ + 139, + 438, + 324, + 445 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- If expanding capabilities: Identify where and how to incorporate new behavior, fields, or modules.", + "bbox": [ + 139, + 445, + 714, + 454 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- If addressing unexpected behavior: Focus on localizing modules containing potential bugs.", + "bbox": [ + 139, + 455, + 663, + 462 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Reconstruct the execution flow", + "bbox": [ + 127, + 463, + 315, + 470 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Identify main entry points triggering the issue.", + "bbox": [ + 139, + 470, + 426, + 479 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Trace function calls, class interactions, and sequences of events.", + "bbox": [ + 139, + 479, + 531, + 486 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Identify potential breakpoints causing the issue.", + "bbox": [ + 139, + 487, + 433, + 494 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Important: Keep the reconstructed flow focused on the problem, avoiding irrelevant details.", + "bbox": [ + 139, + 495, + 662, + 502 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "## Step 4: Locate Areas for Modification", + "bbox": [ + 127, + 508, + 361, + 517 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Locate specific files, functions, or lines of code requiring changes or containing critical information for resolving the issue.", + "bbox": [ + 127, + 518, + 873, + 526 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Consider upstream and downstream dependencies that may affect or be affected by the issue.", + "bbox": [ + 127, + 527, + 657, + 533 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- If applicable, identify where to introduce new fields, functions, or variables.", + "bbox": [ + 127, + 535, + 594, + 542 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "- Think Thoroughly: List multiple potential solutions and consider edge cases that could impact the resolution.", + "bbox": [ + 127, + 543, + 766, + 550 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Output Format for Final Results:", + "bbox": [ + 127, + 557, + 329, + 565 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Your final output should list the locations requiring modification, wrapped with triple back ticks", + "bbox": [ + 127, + 567, + 685, + 574 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Each location should include the file path, class name (if applicable), function name, or line numbers, ordered by importance.", + "bbox": [ + 127, + 575, + 850, + 582 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Your answer would better include about 5 files.", + "bbox": [ + 127, + 583, + 400, + 590 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Examples:", + "bbox": [ + 127, + 596, + 205, + 607 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "full_path1/file1.py", + "bbox": [ + 127, + 613, + 240, + 621 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "line: 10", + "bbox": [ + 129, + 623, + 176, + 629 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "class: MyClass1", + "bbox": [ + 129, + 630, + 216, + 638 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "function: my_function1", + "bbox": [ + 129, + 638, + 257, + 646 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "full path2/file2.py", + "bbox": [ + 129, + 653, + 240, + 662 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "line:76", + "bbox": [ + 129, + 663, + 176, + 670 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "function: MyClass2.my_function2", + "bbox": [ + 129, + 670, + 307, + 678 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "full_path3/file3.py", + "bbox": [ + 129, + 684, + 240, + 694 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "line: 24", + "bbox": [ + 129, + 695, + 176, + 702 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "line: 156", + "bbox": [ + 129, + 702, + 183, + 709 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "function: my_function3", + "bbox": [ + 129, + 709, + 257, + 718 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "#", + "bbox": [ + 129, + 718, + 144, + 724 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Return just the location(s)", + "bbox": [ + 127, + 733, + 284, + 741 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Note: Your thinking should be thorough and so it's fine if it's very long.", + "bbox": [ + 127, + 743, + 554, + 751 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Figure 8: The task instruction prompt for LOCAGENT.", + "bbox": [ + 310, + 766, + 682, + 781 + ], + "page_idx": 17 + } +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09089/c2c2c95f-facf-4f82-977c-1820c00d4eb0_model.json b/data/2025/2503_09xxx/2503.09089/c2c2c95f-facf-4f82-977c-1820c00d4eb0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a3e0f59e4c80cc9831ca325b8147e7751be984be --- /dev/null +++ b/data/2025/2503_09xxx/2503.09089/c2c2c95f-facf-4f82-977c-1820c00d4eb0_model.json @@ -0,0 +1,3261 @@ +[ + [ + { + "type": "title", + "bbox": [ + 0.178, + 0.091, + 0.82, + 0.113 + ], + "angle": 0, + "content": "LocAgent: Graph-Guided LLM Agents for Code Localization" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.136, + 0.898, + 0.176 + ], + "angle": 0, + "content": "Zhaoling Chen\\*, Xiangru Tang\\*, Gangda Deng\\*, Fang Wu\\*, Jialong Wu\\*, Zhiwei Jiang, Viktor Prasanna\\*, Arman Cohan\\*, Xingyao Wang" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.177, + 0.894, + 0.213 + ], + "angle": 0, + "content": "\\(^{\\spadesuit}\\)Yale University \\(^{\\spadesuit}\\)University of Southern California \\(^{\\spadesuit}\\)Stanford University \\(^{\\spadesuit}\\)All Hands AI xiangru.tang@yale.edu, gangdade@usc.edu, xingyao@all-hands.dev" + }, + { + "type": "title", + "bbox": [ + 0.261, + 0.261, + 0.341, + 0.276 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.288, + 0.461, + 0.743 + ], + "angle": 0, + "content": "Code localization—identifying precisely where in a codebase changes need to be made—is a fundamental yet challenging task in software maintenance. Existing approaches struggle to efficiently navigate complex codebases when identifying relevant code sections. The challenge lies in bridging natural language problem descriptions with the appropriate code elements, often requiring reasoning across hierarchical structures and multiple dependencies. We introduce LOCAGENT, a framework that addresses code localization through graph-based representation. By parsing codebases into directed heterogeneous graphs, LOCAGENT creates a lightweight representation that captures code structures (files, classes, functions) and their dependencies (imports, invocations, inheritance), enabling LLM agents to effectively search and locate relevant entities through powerful multi-hop reasoning. Experimental results on real-world benchmarks demonstrate that our approach significantly enhances accuracy in code localization. Notably, our method with the fine-tuned Qwen-2.5-Coder-Instruct-32B model achieves comparable results to SOTA proprietary models at greatly reduced cost (approximately \\(86\\%\\) reduction), reaching up to \\(92.7\\%\\) accuracy on file-level localization while improving downstream GitHub issue resolution success rates by \\(12\\%\\) for multiple attempts (Pass@10). Our code is available at https://github.com/gersteinlab/LocAgent." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.766, + 0.26, + 0.781 + ], + "angle": 0, + "content": "1 Introduction" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.791, + 0.489, + 0.888 + ], + "angle": 0, + "content": "Code localization can be viewed as an information retrieval (IR) task that aims to identify relevant code snippets given natural language descriptions (Yu et al., 2025; Yang et al., 2024; Xia et al., 2024). Developers spend up to \\(66\\%\\) of their debugging time (Böhme et al., 2017) understanding code to" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.256, + 0.883, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.455, + 0.884, + 0.526 + ], + "angle": 0, + "content": "Figure 1: Code localization across four common programming scenarios. Given a codebase and an issue description, the goal of code localization is to identify the relevant code snippets that require modification to resolve the issue." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.535, + 0.885, + 0.904 + ], + "angle": 0, + "content": "make changes, and automated tools often struggle with the same challenge. Poor code localization leads to incomplete fixes, introduces new bugs, and significantly extends development cycles. Unlike traditional retrieval tasks that primarily focus on lexical or semantic matching between queries and documents (Guo et al., 2016, 2020), code localization requires bridging the gap between natural language and programming languages. It also necessitates reasoning capabilities to analyze the issue, while considering the structural and semantic properties of code (Lewis et al., 2020; Guu et al., 2020; Qu et al., 2020). This capability has become fundamental to powerful AI assistants (OpenAI, 2023; Anthropic, 2023), code-aware search engines (PerplexityAI, 2023), and automated programming agents (Cognition.ai, 2024; Wang et al., 2025; Gauthier, 2024). In particular, accurate code localization is crucial for software maintenance and evolution, as it enables precise code modifications for bug fixes, refactoring, and feature additions (Wang et al., 2024), thereby streamlining the development workflow." + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.906, + 0.882, + 0.922 + ], + "angle": 0, + "content": "Existing approaches to code localization face" + }, + { + "type": "aside_text", + "bbox": [ + 0.023, + 0.311, + 0.061, + 0.724 + ], + "angle": 270, + "content": "arXiv:2503.09089v2 [cs.SE] 29 Apr 2025" + }, + { + "type": "page_footnote", + "bbox": [ + 0.114, + 0.895, + 0.489, + 0.922 + ], + "angle": 0, + "content": "* Equal contribution. This work was done during Zhaoling's time at Yale." + } + ], + [ + { + "type": "text", + "bbox": [ + 0.117, + 0.085, + 0.486, + 0.535 + ], + "angle": 0, + "content": "significant limitations. Dense retrieval methods require maintaining and continuously updating vector representations of the entire codebase (Wang et al., 2023b; Günther et al., 2023), creating engineering challenges for large, evolving repositories where code changes frequently. While LLMs demonstrate strong code understanding capabilities (Kang et al., 2023; Wu et al., 2023), models with large context windows cannot process entire codebases at once, necessitating strategic navigation through relevant parts. Moreover, issue descriptions often mention only symptoms rather than underlying causes. For instance, a report of 'XSS vulnerability in user profile' might require changes to a shared validation utility used throughout the codebase but not explicitly referenced in the issue. This disconnect between issue descriptions and affected code components presents a substantial challenge for traditional retrieval approaches, which struggle to trace implicit dependencies across the codebase structure. Recent agent-based methods attempt to address these limitations through iterative exploration (Yang et al., 2024; Qin et al., 2024) but still struggle to efficiently navigate and comprehend complex code structures and dependencies, particularly when multi-hop reasoning is required to trace from issue descriptions to affected code regions that aren't directly mentioned." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.536, + 0.486, + 0.663 + ], + "angle": 0, + "content": "This raises a key question: How can we design efficient indexing as intermediate representations that are structure-aware and both easy and performant for LLM agents to consume? It is intuitive to design an agentic retrieval system that carefully combines traditional IR methods and LLM agent's reasoning ability to achieve accurate, efficient, and cost-effective code localization in codebases." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.665, + 0.486, + 0.921 + ], + "angle": 0, + "content": "To address this challenge, we propose LOCAGENT, a framework that builds directed heterogeneous graph indexing to unify code structures, dependencies, and contents. Our approach leverages a structured graph representation that enables powerful multi-hop reasoning capabilities, allowing agents to navigate complex dependency relationships between code elements even when target code isn't explicitly mentioned in issue descriptions. This graph-based approach significantly outperforms previous methods on challenging localization tasks that require traversing multiple code relationships. Our lightweight representation, coupled with sparse indexing techniques, enables efficient entity search while maintaining rich structural information. The indexing process typically" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.085, + 0.882, + 0.325 + ], + "angle": 0, + "content": "takes only a few seconds per codebase, making it highly practical for real-time use. The framework integrates a set of unified tools that guide the agent through a systematic exploration of the codebase, allowing autonomous navigation based on contextual needs. Furthermore, by fine-tuning Qwen-2.5-Coder-Instruct (Hui et al., 2024) 7B and 32B models(abbr. as Qwen-2.5-7B and Qwen-2.5-32B respectively), our system achieves performance comparable to state-of-the-art models like Claude-3-5-sonnet-20241022 (Anthropic, 2023) (abbr. as Claude-3.5) while significantly reducing API costs by over \\(80\\%\\) (from \\\\(0.66 to \\\\)0.09 per example), making it practical for real-world deployment." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.327, + 0.882, + 0.63 + ], + "angle": 0, + "content": "Additionally, to facilitate a comprehensive evaluation of code localization methods, we introduce LOC-BENCH, a new benchmark specifically designed for this task. Existing benchmarks like SWE-Bench present significant limitations: (1) they risk contamination through data overlap with LLM training sets (Mündler et al., 2024), and (2) they primarily focus on bug fixing, lacking diversity in maintenance scenarios such as feature requests, performance optimizations, and security fixes. In contrast, LOC-BENCH covers diverse scenarios and mitigates potential contamination concerns by incorporating more recent examples from popular Python repositories collected after known LLM training cutoff dates. Additionally, we provide tooling to continuously update the benchmark with new examples, allowing researchers to maintain a fresh evaluation dataset as models evolve and training data cutoffs advance." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.633, + 0.882, + 0.664 + ], + "angle": 0, + "content": "Our contributions address critical gaps in existing approaches:" + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.676, + 0.882, + 0.771 + ], + "angle": 0, + "content": "- We introduce a heterogeneous graph representation that captures both explicit and implicit code relationships, enabling efficient multi-hop reasoning. Our lightweight graph-based indexing process takes only seconds per repository and requires minimal storage." + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.783, + 0.882, + 0.894 + ], + "angle": 0, + "content": "- We design unified tools for agent-based code exploration that leverage our graph representation, allowing LLM agents to perform complex multi-hop navigation and reasoning across code dependencies even when target code isn't explicitly mentioned in issue descriptions." + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.906, + 0.881, + 0.92 + ], + "angle": 0, + "content": "- We introduce Loc-Bench, a new benchmark" + }, + { + "type": "list", + "bbox": [ + 0.536, + 0.676, + 0.882, + 0.92 + ], + "angle": 0, + "content": null + } + ], + [ + { + "type": "text", + "bbox": [ + 0.15, + 0.085, + 0.488, + 0.182 + ], + "angle": 0, + "content": "specifically designed for code localization that addresses limitations in existing datasets. Unlike previous benchmarks dominated by bug reports, Loc-Bench offers a balanced distribution across bug fixes, feature requests, security patches, and performance optimizations." + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.196, + 0.49, + 0.259 + ], + "angle": 0, + "content": "- By fine-tuning open-source models on this task, we reduce the cost of code localization by \\(86\\%\\) while maintaining competitive performance." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.289, + 0.27, + 0.305 + ], + "angle": 0, + "content": "2 Related Work" + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.317, + 0.45, + 0.332 + ], + "angle": 0, + "content": "2.1 Traditional Retrieval-based Methods" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.339, + 0.49, + 0.66 + ], + "angle": 0, + "content": "Traditional IR methods rely on lexical or semantic matching to return ranked lists of code snippets. Sparse retrievers, such as BM25 (Robertson et al., 1994, 2009), have demonstrated robustness to domain adaptation. Dense retrievers utilize embeddings for improved semantic searching, including models with open checkpoints such as general text embedding models E5-base-v2 (Wang et al., 2022) and proprietary APIs (VoyageAI, 2024). Code embedding models such as Jina-Code-v2 (Günther et al., 2023), Codesage-large-v2 (Zhang et al., 2024), and CodeRankEmbed (Suresh et al., 2024), trained specifically for code related tasks, showing significant performance in Code2Code and NL2Code semantic search tasks. However, while the embedding models themselves are small, the engineering challenges of maintaining these indexing systems (e.g., storage requirements, update mechanisms, and infrastructure maintenance) make them difficult to adapt to fast-evolving codebases." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.674, + 0.486, + 0.689 + ], + "angle": 0, + "content": "2.2 LLM-based Generative Retrieval Methods" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.697, + 0.49, + 0.921 + ], + "angle": 0, + "content": "Recently, LLMs with advanced code reasoning capabilities have demonstrated superior performance by directly processing queries and raw code for code localization (Kang et al., 2023; Wu et al., 2023; Xia et al., 2024; Kang et al., 2024). For example, Agentless (Xia et al., 2024), initially designed for automated program repair, uses a simplistic hierarchical localization process powered by LLM. It employs a straightforward three-phase approach that first localizes relevant code sections before attempting to fix the identified issues, challenging the assumption that complex agent architectures are necessary for effective code understanding and modification tasks." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.085, + 0.885, + 0.438 + ], + "angle": 0, + "content": "Expanding on these techniques, agent-based methods utilize multi-step reasoning to enable automated codebase traversal. Specifically, OpenHands (Wang et al., 2025) implements a generalist coding agent that supports bash commands like grep and tools for viewing files. SWE-Agent (Yang et al., 2024) integrates a custom Agent-Computer Interface to support agents to navigate entire repositories. MoatlessTools (Örwall, 2024) combines an agentic searching loop and semantic search to obtain code locations. However, existing agent-based methods face two critical limitations: (a) they primarily navigate codebases through directory traversal rather than understanding semantic relationships, (b) and they struggle to extract and reason about complex cross-file dependencies when these relationships aren't explicitly represented in the repository structure. This significantly impairs their ability to locate code that requires modification when the issue involves interactions between structurally distant components in the codebase." + }, + { + "type": "title", + "bbox": [ + 0.509, + 0.45, + 0.829, + 0.481 + ], + "angle": 0, + "content": "2.3 Graph-based Code Representation Methods" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.487, + 0.885, + 0.791 + ], + "angle": 0, + "content": "Due to the inherent structure of code, several works have employed graph-based representations to improve code understanding by capturing key relationships between components. Aider (2023) constructs a RepoMap and uses a graph ranking algorithm to identify the most significant contextual elements. Similarly, as a plugin, RepoGraph (Ouyang et al., 2025) performs subgraph retrieval – extracting an ego-network of relevant lines and their neighbors – to provide structured context. CodexGraph (Liu et al., 2024) indexes the repository into a Neo4j graph database, where LLM agents query the database precisely using Cypher. The efficiency of its retrieval process depends heavily on the querying capabilities of the LLM. These methods focus primarily on providing relevant context but do not enhance the traversal process itself, as they do not explicitly model directory structure or file hierarchies." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.794, + 0.885, + 0.922 + ], + "angle": 0, + "content": "In contrast, RepoUnderstander (Ma et al., 2024) builds hierarchical and function-call graphs, using Monte Carlo Tree Search (MCTS) guided by an LLM for exploration. While thorough, MCTS introduces extra computational overhead, making it less efficient than simpler traversal methods like BFS, particularly in large repositories. OrcaLoca (Yu et al., 2025) uses a simplified graph" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.083, + 0.885, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.347, + 0.884, + 0.404 + ], + "angle": 0, + "content": "Figure 2: Overview of LOCAGENT framework. LOCAGENT first parses the given codebase to build a graph-based code representation with various types of entities and relations. It then constructs sparse indexes for exploring structures and searching content. Using these indexes, it performs agent-guided searches that combine the graph and tools." + }, + { + "type": "table", + "bbox": [ + 0.119, + 0.418, + 0.882, + 0.525 + ], + "angle": 0, + "content": "
MethodRelation TypesNode TypesSearch/Traversal Strategy
ContainImportInheritInvokeDirectoryFileClassFunction
CodexGraph(Liu et al., 2024)✓X✓✓XX✓✓Cypher queries
RepoGraph(Ouyang et al., 2025)✓X✓✓XX✓✓Ego-graph retrieval
RepoUnderstander(Ma et al., 2024)✓X✓✓✓✓✓✓MCTS
OrcaLoca(Yu et al., 2025)✓XX✓✓✓✓✓Simple search tools
LOCAGENT(Ours)✓✓✓✓✓✓✓✓Unified retrieval tools
" + }, + { + "type": "table_caption", + "bbox": [ + 0.263, + 0.533, + 0.733, + 0.548 + ], + "angle": 0, + "content": "Table 1: Comparison of Graph-Based Code Representation Methods." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.563, + 0.49, + 0.708 + ], + "angle": 0, + "content": "enhanced by priority scheduling and context pruning. It maintains efficient search but may miss complex invocation dependencies. Table 1 summarizes the differences between these methods and LOCAGENT. Compared to these approaches, LOCAGENT offers a more comprehensive and unified representation of the repository, along with efficient, unified retrieval tools specifically designed for LLM consumption." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.719, + 0.401, + 0.735 + ], + "angle": 0, + "content": "3 The LOCAGENT Framework" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.745, + 0.491, + 0.922 + ], + "angle": 0, + "content": "We introduce LOCAGENT, a graph-oriented LLM-agent framework for code localization. Figure 2 illustrates the overall framework. When given a repository, LOCAGENT can locate all the relevant code sections at various granularities (file, class, function, or line level) for different types of GitHub issues (such as bug reports, feature requests, performance bottlenecks, and security vulnerabilities) through automated in-depth exploration and analysis of the codebase. Section 3.1 proposes a novel graph-based indexing approach as an intermediate" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.563, + 0.883, + 0.627 + ], + "angle": 0, + "content": "representation for codebases. Section 3.2 presents our agent-based code search on the indexes and Section 3.3 describes our model fine-tuning and distillation process." + }, + { + "type": "title", + "bbox": [ + 0.509, + 0.641, + 0.83, + 0.658 + ], + "angle": 0, + "content": "3.1 Graph-based Code Representation" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.663, + 0.885, + 0.759 + ], + "angle": 0, + "content": "Codebases contain rich structural information, both explicit and implicit, that is essential for agent reasoning. Building on this insight, we develop a graph-based indexing that comprehensively captures codebase relationships while maintaining a granularity suitable for LLM-agents to retrieve." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.761, + 0.886, + 0.922 + ], + "angle": 0, + "content": "Code Graph Construction. We construct a heterogeneous directed graph \\(\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathcal{A},\\mathcal{R})\\) to index the codebase, where \\(\\nu = \\{v_{i}\\}_{i = 1}^{n}\\) is the node set and \\(\\mathcal{E}\\subseteq \\mathcal{V}\\times \\mathcal{V}\\) is the edge set. Each node \\(v\\in \\mathcal{V}\\) and edge \\(e\\in \\mathcal{E}\\) has an associated type mapping function. For nodes, \\(\\tau (v):\\mathcal{V}\\to \\mathcal{A}\\) maps to types \\(\\mathcal{A} = \\{\\mathrm{directory},\\mathrm{file},\\mathrm{class},\\mathrm{function}\\}\\). For edges, \\(\\phi (e):\\mathcal{E}\\rightarrow \\mathcal{R}\\) maps to relationships \\(\\mathcal{R} = \\{\\mathrm{contain},\\mathrm{import},\\mathrm{invoke},\\mathrm{inherit}\\}\\). In this paper, we focus our study on Python reposito" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.113, + 0.085, + 0.486, + 0.117 + ], + "angle": 0, + "content": "ries and leave codebases with other programming languages as future work." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.119, + 0.489, + 0.28 + ], + "angle": 0, + "content": "First, we include all directories and Python files as nodes. Then, we parse each Python file using the abstract syntax tree (AST) to identify inner functions and classes recursively as nodes. We set the function level as the smallest node granularity and use each function's code content as the document for agent retrieval. This approach creates a good balance of information density between the index and documents, allowing LLMs to reason effectively within their context window limitations." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.283, + 0.49, + 0.459 + ], + "angle": 0, + "content": "As shown in Figure 2, all nodes with different types can be connected as a single tree using the contain relationship. This structure supports standard codebase-navigation operations from existing works. Our code graph further incorporates more advanced codebase relationships as edges: (1) the invoke relationship from function/class to function/class, where an invoke to a class represents class instantiation; (2) the import relationship from file to function/class; and (3) the inherit relationship between classes." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.462, + 0.49, + 0.784 + ], + "angle": 0, + "content": "Sparse Hierarchical Entity Indexing. We treat nodes in our code graph as entities and build hierarchical indexing based on their contents. For each keyword, we lookup the indexes from top to bottom: (1) We build an entity ID index as a unique identifier for each node using its fully qualified name. For example, a function calculate_sum in the MathUtils class located in src/utils.py would be represented as: src/utils.py:MathUtilscalculate_sum. (2) We construct a global dictionary to map the entity name (e.g., calculate_sum) to all nodes that share the same name. (3) We index entity IDs through an inverted index (i.e., BM25) to handle keyword searches that don't exactly match the IDs or names of entities. (4) For cases where input keywords aren't part of the entities' IDs (e.g., when a keyword refers to a global variable), we build an inverted index that maps code chunk(s) to each entity to cover all possible matches." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.793, + 0.49, + 0.922 + ], + "angle": 0, + "content": "Remark. Rather than relying solely on directory structures or hierarchical module indexing, our approach captures module dependencies that transcend directory boundaries. Two modules in distant directories (A and B) may appear unrelated in traditional navigation, but if they invoke each other or share inheritance, they're syntactically close in our graph representation. This syntactic" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.082, + 0.881, + 0.238 + ], + "angle": 0, + "content": "
Tool NameInput ParamsOutput
SearchEntityKeywordsRelated Entities with Code Snippets
TraverseGraphStart Entity IDs Direction Traverse Hops Entity Types Relation TypesTraversed Subgraph, including Entities and Relations
RetrieveEntityEntity IDsComplete Code of Specified Entities
" + }, + { + "type": "table_caption", + "bbox": [ + 0.508, + 0.246, + 0.883, + 0.276 + ], + "angle": 0, + "content": "Table 2: List of unified APIs provided by LocAgent for code search and exploration." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.287, + 0.884, + 0.382 + ], + "angle": 0, + "content": "proximity is essential for code localization because issues typically manifest through call relationships rather than directory structure. By capturing these functional dependencies, our approach efficiently identifies related components even when physically distant in the codebase." + }, + { + "type": "title", + "bbox": [ + 0.509, + 0.398, + 0.767, + 0.413 + ], + "angle": 0, + "content": "3.2 Agent-guided Code Search" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.42, + 0.884, + 0.612 + ], + "angle": 0, + "content": "We develop tools based on the indexes built offline. During runtime, LOCAGENT takes issue statements as input and launches agents that autonomously use tools to localize target code sections. While the agent may iteratively invoke multiple tools internally to explore the codebase, LOCAGENT presents a simplified interface to users, requiring only a single-turn interaction—users submit an issue statement and receive localization results without additional input. This autonomous, self-contained workflow makes LOCAGENT both easy to deploy and highly practical for real-world use." + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.615, + 0.885, + 0.823 + ], + "angle": 0, + "content": "Tool Design for Codebase Exploration. Recent works (Örwall, 2024; Wang et al., 2025), inspired by GUI-based IDEs, have developed numerous specialized tools for agents to explore codebases. However, these tools are initially designed for human readability, which sacrifices the compactness and efficiency that LLM agents prefer (Yang et al., 2024). Building upon our graph-based code representation, we can develop tools that support efficient higher-order codebase exploration to address these challenges. We unify all codebase navigation, search, and view operations into three tools (Table 2), introduced as follows." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.825, + 0.884, + 0.922 + ], + "angle": 0, + "content": "SearchEntity: This tool searches codebases using keywords to locate relevant entities through our Hierarchical Entity Index. When an exact match isn't found in the upper index, the system performs a fuzzy search using the lower index. For each entity found, we return its code snippet in three detail" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.113, + 0.085, + 0.488, + 0.132 + ], + "angle": 0, + "content": "levels: fold, preview, and full code (Figure 6). This effectively prevents lengthy code context and reduces noise fed into agents." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.134, + 0.49, + 0.535 + ], + "angle": 0, + "content": "**TraverseGraph:** This tool performs a type-aware breadth-first search (BFS) on the code graph, starting from input entities and allowing control over both traversal direction and number of hops. This supports agents to perform arbitrary multi-hop codebase navigation through only one action, significantly improving the efficiency compared with existing agent systems. Note that by allowing agents to select entity types and relation types for each traversal, this tool effectively leverages the LLM agents' coding expertise to generate proper meta paths—a crucial element for heterogeneous graph analysis (Lv et al., 2021). For example, by specifying entity types to {class, function} and relation types to {contain, inherit}, this tool returns the UML diagram. Additionally, we design an expanded tree-based format for the output subgraph that encodes both relation types and directions (Figure 7). (Fatemi et al., 2023) demonstrates that LLM performance on graph reasoning depends on the input graph format. Converting a graph into a tree structure encodes topology through the spatial distance between entity names, thereby deriving better performance. For detailed comparisons with alternative graph formats, please see Appendix A.1.2." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.536, + 0.489, + 0.599 + ], + "angle": 0, + "content": "RetreiveEntity: This tool retrieves complete entity attributes for each input entity ID, including essential information such as file path, line number, and code content." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.6, + 0.49, + 0.776 + ], + "angle": 0, + "content": "Chain-of-Thought Agent Planning. We use chain-of-thought (CoT) prompting (shown in Appendix D) to guide the agent in solving code localization problems step by step. The agent systematically follows these steps: (1) Keyword extraction. The agent begins by breaking down the issue statement into different categories and then extracts relevant keywords that are closely related to the problem. (2) Linking keywords to code entities. The agent invokes SearchEntity to complete and clarify each extracted keyword." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.778, + 0.489, + 0.921 + ], + "angle": 0, + "content": "(3) Generate the logical flow from fault to failure. The agent first identifies the entry points that trigger the problem. Then, it iteratively traverse the codebase with TraverseGraph, retrieves code contents with RetrieveEntity, and searches new keywords with SearchEntity. Finally, it generates the logic flow based on the issue and additional context. (4) Locate the target entities. The agent pinpoints all suspicious code entities that need modification" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.085, + 0.882, + 0.116 + ], + "angle": 0, + "content": "based on the logic flow. Then, it ranks these entities based on their relevance." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.118, + 0.884, + 0.31 + ], + "angle": 0, + "content": "Confidence Estimation Based on Consistency. After generating a complete ranked list of candidate entities, to obtain a more consistent ranking, we measure the consistency (Wang et al., 2023a) of the LLM's predictions across multiple iterations. Specifically, we use the Reciprocal Rank as the initial confidence score for each predicted location. We then aggregate the scores for each entity across iterations to compute its final confidence score. The intuition behind this approach is that if the LLM consistently ranks a location higher in multiple iterations, it is more likely to be relevant." + }, + { + "type": "title", + "bbox": [ + 0.509, + 0.323, + 0.809, + 0.339 + ], + "angle": 0, + "content": "3.3 Open-source Model Fine-tuning" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.344, + 0.884, + 0.649 + ], + "angle": 0, + "content": "Given the high costs of proprietary LLM APIs and data security concerns, we fine-tuned open-source models to improve their code localization capabilities and enable local deployment. We collect 433 successful trajectories generated with Claude-3.5, where the agent completed tasks from the SWEBench training set. Due to budget constraints, we sample an additional 335 trajectories generated by the initially fine-tuned Qwen2.5-32B model. Importantly, we only select successful trajectories where the model correctly localized the issues, creating a high-quality dataset of correct reasoning paths. These successful examples are then used to refine the same 32B model further, reinforcing effective reasoning patterns through this self-improvement loop. The entire dataset, combining both Claude-3.5 trajectories and successful Qwen2.5-32B samples, was then used to distill knowledge to a smaller 7B model." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.651, + 0.884, + 0.747 + ], + "angle": 0, + "content": "To fine-tune the smaller model, we employ Supervised Fine-Tuning (SFT) with LoRA (Hu et al., 2021). Our experiments show that this straightforward distillation method significantly enhances the performance of smaller models. See Appendix C.1.3 for more training details." + }, + { + "type": "title", + "bbox": [ + 0.508, + 0.761, + 0.865, + 0.792 + ], + "angle": 0, + "content": "4 LOC-BENCH: A New Benchmark for Code Localization" + }, + { + "type": "title", + "bbox": [ + 0.508, + 0.804, + 0.8, + 0.819 + ], + "angle": 0, + "content": "4.1 Revisiting Existing Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.825, + 0.884, + 0.922 + ], + "angle": 0, + "content": "SWE-Bench(Jimenez et al., 2023) is a widely used benchmark that collects GitHub issues and corresponding code patches that resolve them. Xia et al. (2024); Suresh et al. (2024) adapt its subset, SWE-Bench-Lite, for code localization, treating the patched files and functions as the targets." + } + ], + [ + { + "type": "text", + "bbox": [ + 0.117, + 0.085, + 0.49, + 0.39 + ], + "angle": 0, + "content": "However, existing datasets, including SWE-Bench, present challenges for effectively evaluating code localization methods. First, they are at risk of contamination, as they may include data overlapping with the repositories or issues used by modern models during pre-training. Second, existing datasets are not specifically designed for code localization (Tomassi et al., 2019). SWE-Bench, for instance, was created primarily to evaluate end-to-end bug-fixing capabilities, with localization being only an implicit intermediate step. This focus results in datasets dominated by bug reports (85% of SWE-Bench-Lite examples) while severely underrepresenting other common software maintenance tasks such as feature requests (14%), security vulnerabilities (1%), and performance optimizations (0%). This imbalance fails to capture the diverse localization challenges faced in real-world software development." + }, + { + "type": "title", + "bbox": [ + 0.117, + 0.402, + 0.326, + 0.416 + ], + "angle": 0, + "content": "4.2 Dataset Construction" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.422, + 0.488, + 0.597 + ], + "angle": 0, + "content": "To address the limitations of existing benchmarks, we introduce LOC-BENCH, a new dataset specifically designed for code localization. This dataset collects up-to-date issues from Python repositories to mitigate the influence of pre-training bias in the latest LLMs. Additionally, LOC-BENCH covers wider categories, including bug reports, feature requests, security, and performance issues, enabling a more comprehensive evaluation of code localization methods. The statistics of LOC-BENCH are shown in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.599, + 0.488, + 0.775 + ], + "angle": 0, + "content": "For the Bug Report category, we collect GitHub issues created after October 2024, which is later than the release dates of most modern LLMs. To enrich the dataset with more instances of security and performance issues, we use the GitHub Search API to search for relevant keywords, such as \"latency improvement\" for performance-related issues. We exclude instances that involve modifying more than five Python files or more than ten functions in the corresponding patch. For further details, see Appendix B.1." + }, + { + "type": "title", + "bbox": [ + 0.117, + 0.787, + 0.258, + 0.803 + ], + "angle": 0, + "content": "5 Experiments" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.81, + 0.488, + 0.92 + ], + "angle": 0, + "content": "Our experiments aim to evaluate four key aspects of LOCAGENT: (1) the effectiveness of our graph-based representation and tooling for code localization compared to existing methods, (2) the performance of fine-tuned open-source models as cost-effective alternatives to proprietary LLMs, (3) a detailed analysis of how performance varies across" + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.083, + 0.869, + 0.266 + ], + "angle": 0, + "content": "
DatasetCategory#Sample
SWE-Bench-Lite (Total = 300)Bug Report254
Feature Request43
Security Issue3
Performance Issue0
Loc-Bench (Totoal = 560)Bug Report242
Feature Request150
Security Issue29
Performance Issue139
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.277, + 0.882, + 0.305 + ], + "angle": 0, + "content": "Table 3: Distribution of samples across different categories in the SWE-Bench-Lite and Loc-Bench datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.318, + 0.882, + 0.428 + ], + "angle": 0, + "content": "task categories, and (4) the contribution of each component in our framework through comprehensive ablation studies. We evaluate on both SWE-Bench-Lite and our introduced Loc-Bench dataset. Additionally, we examine the impact of improved localization on downstream software maintenance tasks." + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.434, + 0.729, + 0.45 + ], + "angle": 0, + "content": "5.1 Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.456, + 0.882, + 0.567 + ], + "angle": 0, + "content": "Datasets. We first conduct experiments on SWEBench-Lite, treating the patched files and functions as the targets for localization. Following Suresh et al. (2024), we excluded examples where no existing functions were modified by the patch, ultimately retaining 274 out of the original 300 examples." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.569, + 0.882, + 0.856 + ], + "angle": 0, + "content": "Metrics. To assess performance, we use a modified accuracy metric inspired by R-Precision from information retrieval, following Agentless(Xia et al., 2024). To assess performance, we use Acc@k (Accuracy at k) as our evaluation metric, following Agentless(Xia et al., 2024). For each example, we select the top-k predicted locations and consider a localization attempt successful only if all relevant locations are correctly identified within these top-k predictions. This approach measures the ability to fully identify all necessary code sections that require modification. We report results across multiple \\( k \\) values: file localization at Acc@1, Acc@3, and Acc@5, and function localization at Acc@5 and Acc@10. Additionally, to provide a more relaxed evaluation criteria, we assess module localization, which only requires finding any function within the patched class." + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.869, + 0.627, + 0.883 + ], + "angle": 0, + "content": "5.2 Baselines" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.891, + 0.882, + 0.92 + ], + "angle": 0, + "content": "We evaluate LOCAGENT against three categories of competitive baselines: (a) Retrieval-based meth" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.065, + 0.883, + 0.301 + ], + "angle": 0, + "content": "
TypeMethodLoc-ModelFile (%)Module (%)Function (%)
Acc@1Acc@3Acc@5Acc@5Acc@10Acc@5Acc@10
Embedding-BasedBM25 (Robertson et al., 1994)38.6951.8261.6845.2652.9231.7536.86
E5-base-v2 (Wang et al., 2022)49.6474.4580.2967.8872.2639.4251.09
Jina-Code-v2 (Günther et al., 2023)43.4371.1780.2963.5072.6342.3452.19
Codesage-large-v2 (Zhang et al., 2024)47.8169.3478.1060.5869.7133.9444.53
CodeRankEmbed (Suresh et al., 2024)52.5577.7484.6771.9078.8351.8258.76
Procedure-BasedAgentless (Xia et al., 2024)GPT-4o67.1574.4574.4567.1567.1555.4755.47
Claude-3.572.6379.2079.5668.9868.9858.7658.76
Agent-BasedMoutlessTools (Örwall, 2024)GPT-4o73.3684.3185.0474.8276.2857.3059.49
Claude-3.572.6385.7786.1376.2876.2864.6064.96
SWE-agent (Yang et al., 2024)GPT-4o57.3064.9668.9858.0358.0345.9946.35
Claude-3.577.3787.2390.1577.7478.1064.2364.60
Openhands (Wang et al., 2025)GPT-4o60.9571.9073.7262.4163.8749.6450.36
Claude-3.576.2889.7890.1583.2183.5868.2570.07
LOCAGENT (Ours)Qwen2.5-7B(ft)70.8084.6788.3281.0282.8564.2371.53
Qwen2.5-32B(ft)75.9190.5192.7085.7787.2371.9077.01
Claude-3.577.7491.9794.1686.5087.5973.3677.37
" + }, + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.31, + 0.885, + 0.382 + ], + "angle": 0, + "content": "Table 4: Performance comparison with baseline methods on code localization on SWE-bench lite. Results show the accuracy at file, module, and function levels. For Agent-Based methods, we use GPT-4o-2024-0513 (abbr. as GPT-4o) and Claude-3-5-sonnet-20241022 (abbr. as Claude-3.5) as the localization model. Additionally, the performance of our fine-tuned open-source models, Qwen2.5-7B(ft) and Qwen2.5-32B(ft), are included for comparison." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.39, + 0.492, + 0.729 + ], + "angle": 0, + "content": "ods: We include the sparse retrieval approach BM25 (Robertson et al., 1994) and several state-of-the-art embedding models, including the general-purpose E5-base-v2 (Wang et al., 2022) and specialized code embedding models such as JinaCode-v2 (Günther et al., 2023), Codesage-large-v2 (Zhang et al., 2024), and the current SOTA code embedding model CodeRankEmbed (Suresh et al., 2024). Proprietary embedding solutions were excluded due to API costs. (b) Procedure-based methods: We compare against Agentless (Xia et al., 2024), which employs a structured hierarchical approach to code localization without complex agent architectures. (c) Agent-based methods: We include several advanced agent frameworks designed for code exploration and modification, specifically OpenHands (Wang et al., 2025) (using its default CodeActAgent implementation), SWE-Agent (Yang et al., 2024), and MoatlessTools (Örwall, 2024). For implementation details, please refer to Appendix C.1.1." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.74, + 0.473, + 0.755 + ], + "angle": 0, + "content": "5.3 Evaluation Results on SWE-Bench-Lite" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.761, + 0.491, + 0.922 + ], + "angle": 0, + "content": "As shown in Table 4, Agent-Based methods consistently outperform other approaches, and our method demonstrates competitive performance by achieving the best results across all levels of code localization. Unlike traditional retrieval-based methods, Agentless identifies only a limited number of locations due to its narrow repository scope, which hinders performance gains when considering a broader set of candidates. The results of the NDCG are presented in Table 11 in the Appendix." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.385, + 0.872, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.516, + 0.872, + 0.643 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.653, + 0.885, + 0.741 + ], + "angle": 0, + "content": "Figure 3: Performance analysis at different difficulty levels for file- and function-level localization. All agent-based methods and Agentless use Claude-3.5 as the localization model. Hop \\(N\\) refers to the distances between functions mentioned in the issue description and the ground truth patch on our code graph." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.761, + 0.885, + 0.922 + ], + "angle": 0, + "content": "To further analyze the results, we examine performance across different task difficulty levels. We measure the task difficulty by calculating the shortest hops between the functions mentioned in the issue descriptions and the patched functions on our code graph (See Appendix C.1.2 for more details). As shown in Figure 3, performance decreases for all methods as the task becomes more challenging. However, Agent-based methods demonstrate better robustness as the difficulty increases, with" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.076, + 0.476, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.226, + 0.49, + 0.298 + ], + "angle": 0, + "content": "Figure 4: Comparison of performance between the original and fine-tuned Qwen models. The metrics used are file-level Acc@5 and module/function-level Acc@10. Dashed lines represent the performance of the Claude-3.5 model for reference." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.31, + 0.49, + 0.504 + ], + "angle": 0, + "content": "our method maintaining competitive performance across various difficulty levels. Retrieval-based methods, such as E5-Base-v2 and CodeRankEmbed, perform poorly at the function level, even when the patched functions are explicitly mentioned in the query. This is because they treat the query as a whole, failing to capture fine-grained details. Agentless performs even worse than retrieval-based methods when exploration beyond the query is needed (\\(hop \\geq 0\\)) due to its simplistic localization process and limited view focused only on the repository structure." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.515, + 0.414, + 0.53 + ], + "angle": 0, + "content": "5.4 Fine-tuned Open-source Models" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.535, + 0.49, + 0.809 + ], + "angle": 0, + "content": "Figure 4 demonstrates that after fine-tuning, both the 7B and 32B models show significant improvements on this task. LOCAGENT with finetuned Qwen-2.5-Coder-Instruct-32B (abbreviated as Qwen2.5-32B(ft)) achieves performance comparable to Claude-3.5, and LOCAGENT with Qwen2.5-7B(ft) also delivers results on par with that obtained using GPT-4o. As shown in Table 4, our method with Qwen2.5-32B(ft) outperforms nearly all baselines, including those that use larger and more powerful LLMs. The original 7B model performs poorly due to its limited tool-use capability (Chen et al., 2024). These results validate the feasibility of deploying our fine-tuned open-source models as promising alternatives to proprietary APIs, especially in resource-constrained applications." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.82, + 0.312, + 0.837 + ], + "angle": 0, + "content": "5.5 Efficiency Analysis" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.842, + 0.49, + 0.922 + ], + "angle": 0, + "content": "Table 5 presents an efficiency analysis comparing agent-based methods in terms of cost and the number of agent interactions required. MoatlessTools demonstrates good cost-efficiency and requires relatively fewer rounds of interaction. However, the" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.082, + 0.875, + 0.215 + ], + "angle": 0, + "content": "
MethodLM#RoundCost($)Acc@10
Cost
MoatlessToolsGPT-4o50.461.3
Claude-3.550.461.4
SWE-agentGPT-4o80.560.8
Claude-3.590.671.0
OpenhandsGPT-4o150.830.6
Claude-3.5130.790.9
OursClaude-3.570.661.2
Qwen2.5-7B(ft)60.0513.2
Qwen2.5-32B(ft)90.098.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.508, + 0.219, + 0.883, + 0.291 + ], + "angle": 0, + "content": "Table 5: Efficiency analysis comparing the average cost and number of agent interaction rounds required by different methods. The cost-efficiency of each method is evaluated using the ratio of function-level Acc@10 to average cost." + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.302, + 0.879, + 0.442 + ], + "angle": 0, + "content": "
Model SettingFile Acc@5Module Acc@10Function Acc@10
Ours88.3282.8571.53
w/o TraverseGraph86.1378.4766.06
Relation Types: contain86.5079.5666.42
Traverse Hops: 186.8680.2966.79
w/o RetrieveEntity87.5981.3969.34
w/o SearchEntity68.9861.3153.28
w/o BM25 index75.1868.9860.22
" + }, + { + "type": "table_caption", + "bbox": [ + 0.508, + 0.452, + 0.884, + 0.525 + ], + "angle": 0, + "content": "Table 6: The ablation study of our model. The metrics used here are file-level Acc@5, module-level Acc@10, and function-level Acc@10. The impact of removing or fixing components is analyzed to observe how each component contributes to the overall accuracy." + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.548, + 0.885, + 0.821 + ], + "angle": 0, + "content": "dense embeddings it uses make it difficult and slow to adapt to fast-evolving codebases. SWE-agent and Openhands also show moderate costs but still do not match the efficiency of LOCAGENT. For LOCAGENT with Claude-3.5, although more rounds of interaction are required, the cost remains lower than that of Openhands, illustrating the token efficiency of our tool's outputs. LOCAGENT with fine-tuned Qwen models stands out for its superior efficiency1. Qwen2.5-7B(ft) is the most cost-efficient option, requiring only $0.05 per example, while Qwen2.5-32B(ft) offers a more cost-effective alternative to Claude-3.5. These results highlight the potential of fine-tuned open-source models as efficient alternatives, providing an optimal balance of cost-effectiveness and performance that surpasses other methods." + }, + { + "type": "page_footnote", + "bbox": [ + 0.508, + 0.848, + 0.883, + 0.922 + ], + "angle": 0, + "content": "1We calculate the cost based on the prices from AI inference providers (Hyperbolic, 2025; artificialanalysis.ai, 2025). Specifically, for the Qwen2.5-32B(ft) model, the cost is $0.20/1M tokens for both input and output. For the Qwen2.5-7B(ft) model, the cost is $0.14/1M tokens for input and $0.28/1M tokens for output." + } + ], + [ + { + "type": "title", + "bbox": [ + 0.115, + 0.085, + 0.279, + 0.1 + ], + "angle": 0, + "content": "5.6 Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.108, + 0.489, + 0.186 + ], + "angle": 0, + "content": "We conduct an ablation study to evaluate the effectiveness of each component of our toolsets. Due to budget constraints, we use the fine-tuned Qwen-2.5-7B as the localization model for these experiments." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.189, + 0.489, + 0.317 + ], + "angle": 0, + "content": "(1) Each tool in our toolset plays a critical role in code localization performance. As shown in Table 6, removing any tool, especially the SearchEntity tool, leads to varying degrees of accuracy degradation, particularly in module and function level localization. This highlights the critical role each tool plays in identifying relevant modules and functions." + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.32, + 0.49, + 0.526 + ], + "angle": 0, + "content": "(2) The graph structure provides essential information for accurate code localization. Removing TraverseGraph tool decreases module and function level performance since the agent cannot obtain any structure information about the codebase and relies on reasoning capability to identify call relationship or directory structure. Adding contain relationship provides only marginal improvements compared to fully removing TraverseGraph, emphasizing the importance of the other three relationship types and explaining why our method surpasses others relying only on the repository structure." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.529, + 0.489, + 0.641 + ], + "angle": 0, + "content": "(3) Multi-hop exploration is crucial for deep code understanding. When compared to the full setting, fixing \\( Hops = 1 \\) leads to a moderate decline in file and module-level accuracy, but it causes a more significant decrease in function-level accuracy, underscoring the importance of multi-hop exploration for identifying relevant entities." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.643, + 0.489, + 0.755 + ], + "angle": 0, + "content": "(4) Sparse indexing significantly enhances localization performance. Removing SearchEntity tool, or even partial removal of its index, causes a substantial drop in performance across all metrics. This demonstrates the effectiveness of building a sparse index on our code graph for improving localization performance." + }, + { + "type": "list", + "bbox": [ + 0.113, + 0.189, + 0.49, + 0.755 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.77, + 0.421, + 0.785 + ], + "angle": 0, + "content": "5.7 Evaluation Results on Loc-Bench" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.793, + 0.489, + 0.922 + ], + "angle": 0, + "content": "To ensure the robustness and generalization of our methods and fine-tuned Qwen models, and to eliminate potential data leakage, we evaluate our new dataset. Since Loc-Bench includes examples that edit 1 to 5 files, we assess file localization at top-5 and top-10 ranks, and function/module localization at top-10 and top-15 ranks. Table 7 shows that our fine-tuned Qwen2.5-7B model exhibits strong gen" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.08, + 0.872, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.2, + 0.872, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.325, + 0.883, + 0.382 + ], + "angle": 0, + "content": "Figure 5: Performance analysis at different difficulty category for file- and function-level localization. All agent-based baselines and Agentless use Claude-3.5 as the localization model." + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.4, + 0.884, + 0.544 + ], + "angle": 0, + "content": "eralization capabilities, maintaining competitive performance compared to SWE-agent using more expensive and strong model. These results highlight the practicality of the fine-tuned Qwen2.5-7B model for real-world applications. Despite being an open-source alternative, it achieves a performance comparable to Claude-3.5, supporting its feasibility as a cost-effective substitute for commercial models in practical scenarios." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.546, + 0.884, + 0.803 + ], + "angle": 0, + "content": "Additionally, we evaluate the performance across four different difficulty categories. Figure 5 clearly shows that our method outperforms other methods in almost all categories of code localization. However, it also highlights a noticeable decrease in performance across the other three categories compared to the Bug Report category. This performance gap likely reflects our training data distribution, which contained more bug report examples, potentially leading to scaffolds better optimized for bug localization tasks. This trend suggests that while our method is highly effective for bug report localization, there is still room for improvement in handling the other categories through more balanced training data and category-specific optimization strategies." + }, + { + "type": "title", + "bbox": [ + 0.509, + 0.818, + 0.881, + 0.849 + ], + "angle": 0, + "content": "5.8 Application: Better Localization Leads to More Solved GitHub Issues" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.857, + 0.882, + 0.922 + ], + "angle": 0, + "content": "To assess the impact of localization methods on downstream tasks, we evaluated their effectiveness in solving GitHub issues. We choose Agentless as the baseline, ranking among the top-performing" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.149, + 0.082, + 0.847, + 0.226 + ], + "angle": 0, + "content": "
MethodLoc ModelFile (%)Module (%)Function (%)
Acc@5Acc@10Acc@10Acc@15Acc@10Acc@15
IR-BasedCodeRankEmbed74.2980.8963.2167.5043.3946.61
AgentlessClaude-3.567.5067.5053.3953.3942.6842.68
OpenHandsClaude-3.579.8280.0068.9369.1159.1159.29
SWE-agentClaude-3.577.6877.6863.5763.7551.9651.96
LocAgent (Ours)Qwen2.5-7B(ft)78.5779.6463.0463.0451.4351.79
Claude-3.583.3986.0770.8971.0759.2960.71
" + }, + { + "type": "table_caption", + "bbox": [ + 0.263, + 0.236, + 0.733, + 0.25 + ], + "angle": 0, + "content": "Table 7: Performance evaluation on the real-world LocBench dataset." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.274, + 0.484, + 0.345 + ], + "angle": 0, + "content": "
MethodLocalization LMAcc@5Pass@1Pass@10
AgentlessClaude-3.558.3926.3133.58
OursQwen2.5-32B(ft)69.3426.7936.13
Claude-3.573.3627.9237.59
" + }, + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.354, + 0.486, + 0.385 + ], + "angle": 0, + "content": "Table 8: Impact of localization accuracy on downstream bug repair tasks." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.398, + 0.489, + 0.495 + ], + "angle": 0, + "content": "open-source submissions on SWE-Bench-Lite. For consistency, we utilized Claude-3.5 as the editing model in conjunction with the Agentless editing method. Table 8 shows that the success rate for solving GitHub issues improves significantly with better code localization accuracy." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.506, + 0.248, + 0.52 + ], + "angle": 0, + "content": "6 Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.531, + 0.49, + 0.692 + ], + "angle": 0, + "content": "In conclusion, LOCAGENT enhances code localization by structuring codebases as graphs, enabling efficient repository-level exploration for LLM agents. With fine-tuned open-source models, our method achieves high localization accuracy while significantly reducing costs compared to larger proprietary models. Experimental results demonstrate the effectiveness of LOCAGENT in identifying relevant code components and improving downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.704, + 0.22, + 0.718 + ], + "angle": 0, + "content": "Limitations" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.729, + 0.489, + 0.873 + ], + "angle": 0, + "content": "First, our study primarily focused on fine-tuning Qwen-2.5-Coder models. Exploring a broader range of base models, including other open-source LLMs like CodeLlama, Mistral, or Yi, could provide valuable insights into model selection trade-offs. Additionally, investigating different finetuning approaches beyond LoRA, such as full finetuning or other parameter-efficient methods, could potentially yield better performance." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.874, + 0.489, + 0.923 + ], + "angle": 0, + "content": "Second, though we demonstrated improved bug repair performance with better localization, we only scratched the surface of potential downstream" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.276, + 0.885, + 0.372 + ], + "angle": 0, + "content": "applications. Future work should evaluate LocAgent's impact on other software engineering tasks like refactoring, feature addition, security vulnerability patching, and performance optimization. This would provide a more comprehensive understanding of the framework's practical utility." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.373, + 0.885, + 0.534 + ], + "angle": 0, + "content": "Moreover, our fine-tuning process relied heavily on trajectories generated by Claude-3.5 and the fine-tuned Qwen2.5-32B model. A more diverse training dataset incorporating examples from different models, tasks, and repositories could improve the robustness and generalization of fine-tuned models. Additionally, analyzing the impact of different dataset compositions and filtering strategies on model performance could yield valuable insights." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.535, + 0.886, + 0.664 + ], + "angle": 0, + "content": "Finally, the current evaluation focuses primarily on Python codebases. Extending LOCAGENT to support other programming languages and evaluating its performance across different language paradigms would better demonstrate its generalizability. 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Moatless tools." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.086, + 0.883, + 0.439 + ], + "angle": 0, + "content": null + } + ], + [ + { + "type": "title", + "bbox": [ + 0.114, + 0.084, + 0.388, + 0.101 + ], + "angle": 0, + "content": "A LOCAGENT Design Details" + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.11, + 0.32, + 0.126 + ], + "angle": 0, + "content": "A.1 Tool Output Design" + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.131, + 0.468, + 0.163 + ], + "angle": 0, + "content": "A.1.1 Three-level format for SearchEntity output" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.167, + 0.489, + 0.31 + ], + "angle": 0, + "content": "Once invoked by the LLM agent, the retrieval APIs search for files, classes, methods, and code snippets in the codebase, and return the results back to the agent. To avoid forming very lengthy code context that may containing noisy information to LLM, we return only necessary information as API outputs. To achieve this, we desgined four granular standard output formats (Figure 6): fold, preview, full code." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.321, + 0.469, + 0.353 + ], + "angle": 0, + "content": "A.1.2 Tree-based Subgraph Formatting for TraverseGraph Output" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.357, + 0.489, + 0.517 + ], + "angle": 0, + "content": "The TraverseGraph tool traverses the code graph and returns a local subgraph for each input entity. The agent reasons about these subgraphs to understand each entity's complex dependencies. However, reasoning about graphs remains challenging for LLMs. Research by (Fatemi et al., 2023) demonstrates that LLM performance varies significantly based on graph formatting (how graphs are encoded as text). This makes the format design for output subgraphs crucial." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.518, + 0.491, + 0.677 + ], + "angle": 0, + "content": "We have developed a new tree-based format, shown in Figure 7, with several features that enhance LLM reasoning: (1) We represent subgraphs as trees, allowing LLMs to use indentation to determine a node's distance from the root, (2) We display complete entity IDs for each node (e.g., django/core-validators.py:RegexValidator) to help LLMs locate nodes easily, and (3) We explicitly specify relation types for each edge, including reversed relations" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.679, + 0.49, + 0.838 + ], + "angle": 0, + "content": "To evaluate how different graph formats impact code localization performance, we conducted an experiment using 37 challenging samples from SWEBench-Lite. These samples were considered \"challenging\" because they could not be solved by any baseline agent methods. Using Claude-3.5 as the Localization Model across all settings, we compared various output formats. Table 9 presents our findings. The baseline output formats we tested are described below:" + }, + { + "type": "text", + "bbox": [ + 0.136, + 0.852, + 0.489, + 0.884 + ], + "angle": 0, + "content": "- row: For each line, list one row of the adjacency matrix. For example," + }, + { + "type": "text", + "bbox": [ + 0.148, + 0.89, + 0.488, + 0.922 + ], + "angle": 0, + "content": "function \"fileA.py:funcA\" invokes function \"fileA.py:funcB\", \"fileA.py:funcC\"" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.085, + 0.883, + 0.116 + ], + "angle": 0, + "content": "- row (w/ entity attributes): Additionally include entity attributes for format row." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.127, + 0.883, + 0.191 + ], + "angle": 0, + "content": "- incident: The incident format mentioned in (Fatemi et al., 2023). An integer instead of entity ID is used to represent each node. For example," + }, + { + "type": "list", + "bbox": [ + 0.531, + 0.085, + 0.883, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.542, + 0.197, + 0.882, + 0.244 + ], + "angle": 0, + "content": "Map function \"fileA.py:funcA\" to index 0. Map function \"fileA.py:funcB\" to index 1. Map function \"fileA.py:funcC\" to index 2." + }, + { + "type": "text", + "bbox": [ + 0.543, + 0.25, + 0.78, + 0.266 + ], + "angle": 0, + "content": "function \\(O\\) invokes function 1,2." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.275, + 0.882, + 0.307 + ], + "angle": 0, + "content": "Graphviz DOT: Represent graph in Graphviz DOT language (Ellson et al., 2002)." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.318, + 0.882, + 0.349 + ], + "angle": 0, + "content": "- JSON: Expand the subgraph as a tree, and convert it to JSON format." + }, + { + "type": "list", + "bbox": [ + 0.532, + 0.275, + 0.882, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.36, + 0.885, + 0.552 + ], + "angle": 0, + "content": "As shown in Table 9, expanding subgraphs as trees (i.e., JSON, tree-based) can significantly improve the performance. Our tree-based format achieves the best overall performance across different levels of localization tasks. We also test returning entity attributes along with subgraphs. We notice that row (w/ entity attributes) consistently underperforms row, indicating the attributes for all the nodes may be very noisy. Besides, although using incident format can simplify the output and show improvements in file-level localization, it degradation the module- and file-level localization." + }, + { + "type": "title", + "bbox": [ + 0.509, + 0.564, + 0.687, + 0.579 + ], + "angle": 0, + "content": "A.2 Implementation" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.584, + 0.884, + 0.825 + ], + "angle": 0, + "content": "To enable the LLM agent to invoke the Code Localization APIs, we handle the interaction differently based on the LLM's capabilities. For LLMs that support tool-calling features, we define the tools as a list of JSON objects, which are then used as parameters for the API calls. For LLMs that do not support tool-calling (such as Qwen), we provide the description of the API and the expected output as part of the LLM's prompt. When the agent decides to invoke a set of retrieval APIs, it responds with a list of API call names and their corresponding arguments. These retrieval API requests are processed locally by searching over the built code graph. The results from executing these APIs locally are returned to the agent." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.826, + 0.884, + 0.922 + ], + "angle": 0, + "content": "By default, we query the LLM with a temperature setting of 1.0. We conduct two interactions, after which we rerank the results based on mean reciprocal rank (MRR) scores. We also leverage multiprocessing execution to speed up the process. Since all our tools are read-only, LOCAGENT does" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.086, + 0.368, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.087, + 0.622, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.087, + 0.873, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.354, + 0.883, + 0.397 + ], + "angle": 0, + "content": "Figure 6: Different output formats designed for efficient agent-code interaction. Left: Full code output when matched entities \\(\\leq 3\\). Middle: Preview output showing module skeleton for large files. Right: Fold output showing only entity IDs when matches \\(>3\\)." + }, + { + "type": "image", + "bbox": [ + 0.27, + 0.411, + 0.729, + 0.637 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.646, + 0.881, + 0.662 + ], + "angle": 0, + "content": "Figure 7: A truncated example of the expanded tree-based format for the output subgraph of tool TraverseGraph." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.687, + 0.486, + 0.718 + ], + "angle": 0, + "content": "not require a specialized Docker environment to operate." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.731, + 0.447, + 0.745 + ], + "angle": 0, + "content": "B Dataset construction and statistics" + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.756, + 0.382, + 0.77 + ], + "angle": 0, + "content": "B.1 Dataset construction details" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.777, + 0.489, + 0.889 + ], + "angle": 0, + "content": "Example collection. We collected examples on popular Python repositories on Github follow (Jimenez et al., 2023). To gather issues related to performance and security, we searched for the keywords listed in Table 10 using the GitHub Search APIs. We then used GPT-4o-2024-0513 as the classifier based on the issue descriptions." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.89, + 0.489, + 0.922 + ], + "angle": 0, + "content": "Ground Truth Locations. The affected files or functions in the original codebase, as identified in" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.687, + 0.885, + 0.894 + ], + "angle": 0, + "content": "the patches, are considered the target locations for the given issue. While it is possible to fix a bug in a location different from the ground truth, the extracted ground-truth locations still serve as approximate targets for localization. Additionally, edited code such as documents, import statements, and comments are excluded from the localization target. These elements are not considered relevant for bug localization, as they do not directly impact the functionality of the code or its execution. By filtering out these elements, the focus is maintained on the core code changes that are relevant for localization." + } + ], + [ + { + "type": "table", + "bbox": [ + 0.159, + 0.082, + 0.842, + 0.226 + ], + "angle": 0, + "content": "
Output FormatFile(%)Module(%)Function(%)
Acc@1Acc@3Acc@5Acc@5Acc@10Acc@5Acc@10
row41.1867.6570.5961.7661.7635.2938.24
row (w/ entity attributes)41.1864.7164.7150.0050.0032.3532.35
incident41.1870.5973.5355.8855.8829.4132.35
Graphviz DOT41.1873.5382.3564.7164.7135.2935.29
JSON41.1867.6576.4767.6570.5938.2441.18
tree-based (Ours)47.0679.4179.4164.7164.7138.2441.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.218, + 0.233, + 0.778, + 0.248 + ], + "angle": 0, + "content": "Table 9: Localization performance under different TraverseGraph output formats." + }, + { + "type": "table", + "bbox": [ + 0.159, + 0.261, + 0.842, + 0.441 + ], + "angle": 0, + "content": "
CategoryKeywords
Performancebottleneck, performance improvement, memory usage optimization, time complexity reduction, latency improvement, scalability improvement, CPU usage reduction, caching improvement, concurrency optimization
SecurityOut-of-bounds Write, Out-of-bounds Read, NULL Pointer Dereference, Missing Authorization, memory leak fix, security vulnerability, security issue, authentication bypass, authentication issue, better maintained, buffer overflow, denial of service, security hardening, security patch, unsafe deserialization, Use After Free, Integer Overflow or Wraparound, Uncontrolled Resource Consumption, Missing Authentication for Critical Function
" + }, + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.449, + 0.882, + 0.465 + ], + "angle": 0, + "content": "Table 10: We use these Keywords to search for Performance and Security related issues with Github Search APIs." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.489, + 0.361, + 0.506 + ], + "angle": 0, + "content": "C Additional Experiments" + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.515, + 0.35, + 0.531 + ], + "angle": 0, + "content": "C.1 Implementation Details" + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.536, + 0.382, + 0.552 + ], + "angle": 0, + "content": "C.1.1 Baselines Implementation" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.555, + 0.49, + 0.732 + ], + "angle": 0, + "content": "Regarding the embedding-based methods in our evaluation, these approaches operate primarily at the function level, where each function is embedded as a separate unit. The function's context (its containing file and class) is appended to the function representation before embedding, rather than being embedded separately. While theoretically these methods could employ hierarchical indexing, the standard implementations we evaluated use flat indexing structures where each function is embedded as a single unit." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.733, + 0.49, + 0.797 + ], + "angle": 0, + "content": "We use OpenHands's remote runtime feature to parallelize evaluation on OpenHands and SWEagent. We use Openhands version 0.12.0 released on Oct 31, 2024." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.806, + 0.471, + 0.838 + ], + "angle": 0, + "content": "C.1.2 Quantifying Task Difficulty Based on Code Graph Distance" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.842, + 0.49, + 0.922 + ], + "angle": 0, + "content": "We measure task difficulty by computing the average shortest hop distance between the functions mentioned in the issue descriptions and the patched functions within our code graph. Specifically, we first extract potential function names from each" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.49, + 0.885, + 0.651 + ], + "angle": 0, + "content": "issue description using GPT-4o-2024-0513, and identify their corresponding nodes in the code graph using the global dictionary. These identified nodes form the set of predicted nodes, denoted as \\(\\mathcal{C}\\). Similarly, we link the ground truth functions from the patch to their corresponding nodes in the code graph, forming the set of target nodes, denoted as \\(\\mathcal{T}\\). To quantify the difficulty \\(\\delta\\), we calculate the average shortest hop distance between the predicted nodes \\(\\mathcal{C}\\) and the target nodes \\(\\mathcal{T}\\), defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.657, + 0.816, + 0.694 + ], + "angle": 0, + "content": "\\[\n\\delta = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\frac {1}{m i n _ {t \\in \\mathcal {T}} d (c , t) + 1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.702, + 0.885, + 0.798 + ], + "angle": 0, + "content": "where \\( d(c, t) \\) represents the shortest hop distance between nodes \\( c \\) and \\( t \\) in the graph. For performance analysis stratified by difficulty, we round \\( \\delta \\) down to \\( \\lfloor \\delta \\rfloor \\) to group samples by difficulty levels, and we exclude samples where the LLM fails to extract any valid function names." + }, + { + "type": "title", + "bbox": [ + 0.509, + 0.806, + 0.704, + 0.822 + ], + "angle": 0, + "content": "C.1.3 Training details." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.826, + 0.884, + 0.922 + ], + "angle": 0, + "content": "Fine-tuning Settings. We use Qwen-2.5-Coder-Instruct (Hui et al., 2024) 7B and 32B variants as our base models. We fine-tuned Qwen-2.5-Coder-Instruct 7B and 32B models on 768 training samples from the SWE-Bench training dataset, leveraging LoRA" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.083, + 0.88, + 0.285 + ], + "angle": 0, + "content": "
TypeMethodLoc-ModelFile (%)Module (%)Function (%)
NDCG@1NDCG@3NDCG@5NDCG@5NDCG@10NDCG@5NDCG@10
Embedding-BasedBM25 (Robertson et al., 2009)38.6946.550.6137.3139.8626.1527.92
E5-base-v2 (Wang et al., 2022)49.6464.1966.653.1554.4531.3935.3
Jina-Code-v2 (Günther et al., 2023)43.4359.9363.751.0254.1333.2836.44
Codesage-large-v2 (Zhang et al., 2024)47.8160.8264.3949.3852.2227.0330.74
CodeRankEmbed (Suresh et al., 2024)52.5567.5470.3957.5159.7640.2842.55
Procedure-BasedAgentless (Xia et al., 2024)GPT-4o67.1571.7671.7664.3164.3153.8153.81
Claude-3.572.6376.7276.8767.3667.3657.5557.55
Agent-BasedMoatlessTools (Örwall, 2024)GPT-4o73.3680.0380.3368.5769.0949.7750.62
Claude-3.572.6380.7380.8869.1169.1153.0353.16
SWE-agent (Yang et al., 2024)GPT-4o57.363.9664.1253.9553.9542.3242.44
Claude-3.577.3784.3284.9372.7772.959.6759.79
Openshands (Wang et al., 2025)GPT-4o60.9567.6268.3958.1858.644.3444.66
Claude-3.576.2884.2784.4375.7975.9263.1363.8
LocAgent (Ours)Qwen2.5-7B(ft)70.8079.3680.970.9971.6855.6258.09
Qwen2.5-32B(ft)75.9184.7485.6476.2876.7764.2765.93
Claude-3.577.7486.1987.1477.7378.164.3465.57
" + }, + { + "type": "table_caption", + "bbox": [ + 0.219, + 0.296, + 0.778, + 0.31 + ], + "angle": 0, + "content": "Table 11: NDCG scores comparison showing ranking quality of different methods." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.336, + 0.489, + 0.448 + ], + "angle": 0, + "content": "for efficient adaptation. The training set included 447 samples generated by Claude-3.5, while the remaining samples were iteratively generated using the fine-tuned Qwen2.5-32B model. The fine-tuning process was conducted over 5 epochs with max_token set to \\(128k\\) and a learning rate of \\(2 \\times 10^{-4}\\)." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.46, + 0.221, + 0.476 + ], + "angle": 0, + "content": "D Prompt" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.486, + 0.486, + 0.518 + ], + "angle": 0, + "content": "In this section, we go through the prompt template that make up the agent's history." + } + ], + [ + { + "type": "title", + "bbox": [ + 0.129, + 0.255, + 0.173, + 0.266 + ], + "angle": 0, + "content": "Prompt" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.269, + 0.872, + 0.288 + ], + "angle": 0, + "content": "Given the following GitHub problem description, your objective is to localize the specific files, classes or functions, and lines of code that need modification or contain key information to resolve the issue." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.293, + 0.367, + 0.303 + ], + "angle": 0, + "content": "Follow these steps to localize the issue:" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.303, + 0.46, + 0.311 + ], + "angle": 0, + "content": "Step 1: Categorize and Extract Key Problem Information" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.312, + 0.491, + 0.32 + ], + "angle": 0, + "content": "- Classify the problem statement into the following categories:" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.32, + 0.624, + 0.327 + ], + "angle": 0, + "content": "Problem description, error trace, code to reproduce the bug, and additional context." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.328, + 0.589, + 0.335 + ], + "angle": 0, + "content": "- Identify modules in the '{package_name}' package mentioned in each category." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.335, + 0.726, + 0.343 + ], + "angle": 0, + "content": "- Use extracted keywords and line numbers to search for relevant code references for additional context." + }, + { + "type": "list", + "bbox": [ + 0.129, + 0.312, + 0.726, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.35, + 0.339, + 0.359 + ], + "angle": 0, + "content": "Step 2: Locate Referenced Modules" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.36, + 0.356, + 0.366 + ], + "angle": 0, + "content": "Accurately determine specific modules" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.367, + 0.497, + 0.374 + ], + "angle": 0, + "content": "- Explore the repo to familiarize yourself with its structure." + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.375, + 0.709, + 0.382 + ], + "angle": 0, + "content": "- Analyze the described execution flow to identify specific modules or components being referenced." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.383, + 0.817, + 0.39 + ], + "angle": 0, + "content": "- Pay special attention to distinguishing between modules with similar names using context and described execution flow." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.391, + 0.4, + 0.398 + ], + "angle": 0, + "content": "- Output Format for collected relevant modules:" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.399, + 0.384, + 0.406 + ], + "angle": 0, + "content": "- Use the format: 'file path:QualifiedName'" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.407, + 0.841, + 0.414 + ], + "angle": 0, + "content": "- E.q., for a function `calculate_sum` in the `MathUtilities` class located in `src/helpers/mathHelpers.py`, represent it as:" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.415, + 0.463, + 0.423 + ], + "angle": 0, + "content": "'src/helpers/mathHelpers.py:MathUtil calculator_sum'." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.429, + 0.396, + 0.438 + ], + "angle": 0, + "content": "## Step 3: Analyze and Reproducing the Problem" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.439, + 0.326, + 0.446 + ], + "angle": 0, + "content": "Clarify the Purpose of the Issue" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.447, + 0.715, + 0.455 + ], + "angle": 0, + "content": "- If expanding capabilities: Identify where and how to incorporate new behavior, fields, or modules." + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.456, + 0.664, + 0.463 + ], + "angle": 0, + "content": "- If addressing unexpected behavior: Focus on localizing modules containing potential bugs." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.464, + 0.317, + 0.471 + ], + "angle": 0, + "content": "- Reconstruct the execution flow" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.472, + 0.428, + 0.48 + ], + "angle": 0, + "content": "- Identify main entry points triggering the issue." + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.48, + 0.532, + 0.487 + ], + "angle": 0, + "content": "- Trace function calls, class interactions, and sequences of events." + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.488, + 0.434, + 0.495 + ], + "angle": 0, + "content": "- Identify potential breakpoints causing the issue." + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.496, + 0.663, + 0.504 + ], + "angle": 0, + "content": "Important: Keep the reconstructed flow focused on the problem, avoiding irrelevant details." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.509, + 0.362, + 0.518 + ], + "angle": 0, + "content": "## Step 4: Locate Areas for Modification" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.519, + 0.875, + 0.527 + ], + "angle": 0, + "content": "- Locate specific files, functions, or lines of code requiring changes or containing critical information for resolving the issue." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.528, + 0.658, + 0.535 + ], + "angle": 0, + "content": "- Consider upstream and downstream dependencies that may affect or be affected by the issue." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.536, + 0.595, + 0.543 + ], + "angle": 0, + "content": "- If applicable, identify where to introduce new fields, functions, or variables." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.544, + 0.767, + 0.551 + ], + "angle": 0, + "content": "- Think Thoroughly: List multiple potential solutions and consider edge cases that could impact the resolution." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.558, + 0.331, + 0.567 + ], + "angle": 0, + "content": "Output Format for Final Results:" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.568, + 0.687, + 0.575 + ], + "angle": 0, + "content": "Your final output should list the locations requiring modification, wrapped with triple back ticks" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.576, + 0.852, + 0.583 + ], + "angle": 0, + "content": "Each location should include the file path, class name (if applicable), function name, or line numbers, ordered by importance." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.584, + 0.4, + 0.591 + ], + "angle": 0, + "content": "Your answer would better include about 5 files." + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.598, + 0.206, + 0.608 + ], + "angle": 0, + "content": "Examples:" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.614, + 0.241, + 0.623 + ], + "angle": 0, + "content": "full_path1/file1.py" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.624, + 0.178, + 0.63 + ], + "angle": 0, + "content": "line: 10" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.631, + 0.218, + 0.639 + ], + "angle": 0, + "content": "class: MyClass1" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.639, + 0.258, + 0.647 + ], + "angle": 0, + "content": "function: my_function1" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.655, + 0.241, + 0.663 + ], + "angle": 0, + "content": "full path2/file2.py" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.664, + 0.178, + 0.671 + ], + "angle": 0, + "content": "line:76" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.671, + 0.309, + 0.68 + ], + "angle": 0, + "content": "function: MyClass2.my_function2" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.686, + 0.241, + 0.695 + ], + "angle": 0, + "content": "full_path3/file3.py" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.696, + 0.178, + 0.703 + ], + "angle": 0, + "content": "line: 24" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.703, + 0.184, + 0.71 + ], + "angle": 0, + "content": "line: 156" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.711, + 0.258, + 0.719 + ], + "angle": 0, + "content": "function: my_function3" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.719, + 0.146, + 0.725 + ], + "angle": 0, + "content": "#" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.734, + 0.285, + 0.743 + ], + "angle": 0, + "content": "Return just the location(s)" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.744, + 0.555, + 0.752 + ], + "angle": 0, + "content": "Note: Your thinking should be thorough and so it's fine if it's very long." + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.768, + 0.684, + 0.782 + ], + "angle": 0, + "content": "Figure 8: The task instruction prompt for LOCAGENT." + } + ] +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09089/c2c2c95f-facf-4f82-977c-1820c00d4eb0_origin.pdf b/data/2025/2503_09xxx/2503.09089/c2c2c95f-facf-4f82-977c-1820c00d4eb0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4eaed77dbafd09cd07de04f914d2425241f50f1c --- /dev/null +++ b/data/2025/2503_09xxx/2503.09089/c2c2c95f-facf-4f82-977c-1820c00d4eb0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1fcd0ff4b8f624de14b00fe1f8de43f88471336de8b18bb06c84278e17c1d2e4 +size 777937 diff --git a/data/2025/2503_09xxx/2503.09089/full.md b/data/2025/2503_09xxx/2503.09089/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ca210656d90190b6b90bc732771a0494b937c4f7 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09089/full.md @@ -0,0 +1,504 @@ +# LocAgent: Graph-Guided LLM Agents for Code Localization + +Zhaoling Chen\*, Xiangru Tang\*, Gangda Deng\*, Fang Wu\*, Jialong Wu\*, Zhiwei Jiang, Viktor Prasanna\*, Arman Cohan\*, Xingyao Wang + +$^{\spadesuit}$ Yale University $^{\spadesuit}$ University of Southern California $^{\spadesuit}$ Stanford University $^{\spadesuit}$ All Hands AI xiangru.tang@yale.edu, gangdade@usc.edu, xingyao@all-hands.dev + +# Abstract + +Code localization—identifying precisely where in a codebase changes need to be made—is a fundamental yet challenging task in software maintenance. Existing approaches struggle to efficiently navigate complex codebases when identifying relevant code sections. The challenge lies in bridging natural language problem descriptions with the appropriate code elements, often requiring reasoning across hierarchical structures and multiple dependencies. We introduce LOCAGENT, a framework that addresses code localization through graph-based representation. By parsing codebases into directed heterogeneous graphs, LOCAGENT creates a lightweight representation that captures code structures (files, classes, functions) and their dependencies (imports, invocations, inheritance), enabling LLM agents to effectively search and locate relevant entities through powerful multi-hop reasoning. Experimental results on real-world benchmarks demonstrate that our approach significantly enhances accuracy in code localization. Notably, our method with the fine-tuned Qwen-2.5-Coder-Instruct-32B model achieves comparable results to SOTA proprietary models at greatly reduced cost (approximately $86\%$ reduction), reaching up to $92.7\%$ accuracy on file-level localization while improving downstream GitHub issue resolution success rates by $12\%$ for multiple attempts (Pass@10). Our code is available at https://github.com/gersteinlab/LocAgent. + +# 1 Introduction + +Code localization can be viewed as an information retrieval (IR) task that aims to identify relevant code snippets given natural language descriptions (Yu et al., 2025; Yang et al., 2024; Xia et al., 2024). Developers spend up to $66\%$ of their debugging time (Böhme et al., 2017) understanding code to + +![](images/c20269c8cebd98330e89168b5cf72fa71b25a1845eac8027149a6e7bbe018c9f.jpg) +Figure 1: Code localization across four common programming scenarios. Given a codebase and an issue description, the goal of code localization is to identify the relevant code snippets that require modification to resolve the issue. + +make changes, and automated tools often struggle with the same challenge. Poor code localization leads to incomplete fixes, introduces new bugs, and significantly extends development cycles. Unlike traditional retrieval tasks that primarily focus on lexical or semantic matching between queries and documents (Guo et al., 2016, 2020), code localization requires bridging the gap between natural language and programming languages. It also necessitates reasoning capabilities to analyze the issue, while considering the structural and semantic properties of code (Lewis et al., 2020; Guu et al., 2020; Qu et al., 2020). This capability has become fundamental to powerful AI assistants (OpenAI, 2023; Anthropic, 2023), code-aware search engines (PerplexityAI, 2023), and automated programming agents (Cognition.ai, 2024; Wang et al., 2025; Gauthier, 2024). In particular, accurate code localization is crucial for software maintenance and evolution, as it enables precise code modifications for bug fixes, refactoring, and feature additions (Wang et al., 2024), thereby streamlining the development workflow. + +Existing approaches to code localization face + +significant limitations. Dense retrieval methods require maintaining and continuously updating vector representations of the entire codebase (Wang et al., 2023b; Günther et al., 2023), creating engineering challenges for large, evolving repositories where code changes frequently. While LLMs demonstrate strong code understanding capabilities (Kang et al., 2023; Wu et al., 2023), models with large context windows cannot process entire codebases at once, necessitating strategic navigation through relevant parts. Moreover, issue descriptions often mention only symptoms rather than underlying causes. For instance, a report of 'XSS vulnerability in user profile' might require changes to a shared validation utility used throughout the codebase but not explicitly referenced in the issue. This disconnect between issue descriptions and affected code components presents a substantial challenge for traditional retrieval approaches, which struggle to trace implicit dependencies across the codebase structure. Recent agent-based methods attempt to address these limitations through iterative exploration (Yang et al., 2024; Qin et al., 2024) but still struggle to efficiently navigate and comprehend complex code structures and dependencies, particularly when multi-hop reasoning is required to trace from issue descriptions to affected code regions that aren't directly mentioned. + +This raises a key question: How can we design efficient indexing as intermediate representations that are structure-aware and both easy and performant for LLM agents to consume? It is intuitive to design an agentic retrieval system that carefully combines traditional IR methods and LLM agent's reasoning ability to achieve accurate, efficient, and cost-effective code localization in codebases. + +To address this challenge, we propose LOCAGENT, a framework that builds directed heterogeneous graph indexing to unify code structures, dependencies, and contents. Our approach leverages a structured graph representation that enables powerful multi-hop reasoning capabilities, allowing agents to navigate complex dependency relationships between code elements even when target code isn't explicitly mentioned in issue descriptions. This graph-based approach significantly outperforms previous methods on challenging localization tasks that require traversing multiple code relationships. Our lightweight representation, coupled with sparse indexing techniques, enables efficient entity search while maintaining rich structural information. The indexing process typically + +takes only a few seconds per codebase, making it highly practical for real-time use. The framework integrates a set of unified tools that guide the agent through a systematic exploration of the codebase, allowing autonomous navigation based on contextual needs. Furthermore, by fine-tuning Qwen-2.5-Coder-Instruct (Hui et al., 2024) 7B and 32B models(abbr. as Qwen-2.5-7B and Qwen-2.5-32B respectively), our system achieves performance comparable to state-of-the-art models like Claude-3-5-sonnet-20241022 (Anthropic, 2023) (abbr. as Claude-3.5) while significantly reducing API costs by over $80\%$ (from \ $0.66 to \$ 0.09 per example), making it practical for real-world deployment. + +Additionally, to facilitate a comprehensive evaluation of code localization methods, we introduce LOC-BENCH, a new benchmark specifically designed for this task. Existing benchmarks like SWE-Bench present significant limitations: (1) they risk contamination through data overlap with LLM training sets (Mündler et al., 2024), and (2) they primarily focus on bug fixing, lacking diversity in maintenance scenarios such as feature requests, performance optimizations, and security fixes. In contrast, LOC-BENCH covers diverse scenarios and mitigates potential contamination concerns by incorporating more recent examples from popular Python repositories collected after known LLM training cutoff dates. Additionally, we provide tooling to continuously update the benchmark with new examples, allowing researchers to maintain a fresh evaluation dataset as models evolve and training data cutoffs advance. + +Our contributions address critical gaps in existing approaches: + +- We introduce a heterogeneous graph representation that captures both explicit and implicit code relationships, enabling efficient multi-hop reasoning. Our lightweight graph-based indexing process takes only seconds per repository and requires minimal storage. +- We design unified tools for agent-based code exploration that leverage our graph representation, allowing LLM agents to perform complex multi-hop navigation and reasoning across code dependencies even when target code isn't explicitly mentioned in issue descriptions. +- We introduce Loc-Bench, a new benchmark + +specifically designed for code localization that addresses limitations in existing datasets. Unlike previous benchmarks dominated by bug reports, Loc-Bench offers a balanced distribution across bug fixes, feature requests, security patches, and performance optimizations. + +- By fine-tuning open-source models on this task, we reduce the cost of code localization by $86\%$ while maintaining competitive performance. + +# 2 Related Work + +# 2.1 Traditional Retrieval-based Methods + +Traditional IR methods rely on lexical or semantic matching to return ranked lists of code snippets. Sparse retrievers, such as BM25 (Robertson et al., 1994, 2009), have demonstrated robustness to domain adaptation. Dense retrievers utilize embeddings for improved semantic searching, including models with open checkpoints such as general text embedding models E5-base-v2 (Wang et al., 2022) and proprietary APIs (VoyageAI, 2024). Code embedding models such as Jina-Code-v2 (Günther et al., 2023), Codesage-large-v2 (Zhang et al., 2024), and CodeRankEmbed (Suresh et al., 2024), trained specifically for code related tasks, showing significant performance in Code2Code and NL2Code semantic search tasks. However, while the embedding models themselves are small, the engineering challenges of maintaining these indexing systems (e.g., storage requirements, update mechanisms, and infrastructure maintenance) make them difficult to adapt to fast-evolving codebases. + +# 2.2 LLM-based Generative Retrieval Methods + +Recently, LLMs with advanced code reasoning capabilities have demonstrated superior performance by directly processing queries and raw code for code localization (Kang et al., 2023; Wu et al., 2023; Xia et al., 2024; Kang et al., 2024). For example, Agentless (Xia et al., 2024), initially designed for automated program repair, uses a simplistic hierarchical localization process powered by LLM. It employs a straightforward three-phase approach that first localizes relevant code sections before attempting to fix the identified issues, challenging the assumption that complex agent architectures are necessary for effective code understanding and modification tasks. + +Expanding on these techniques, agent-based methods utilize multi-step reasoning to enable automated codebase traversal. Specifically, OpenHands (Wang et al., 2025) implements a generalist coding agent that supports bash commands like grep and tools for viewing files. SWE-Agent (Yang et al., 2024) integrates a custom Agent-Computer Interface to support agents to navigate entire repositories. MoatlessTools (Örwall, 2024) combines an agentic searching loop and semantic search to obtain code locations. However, existing agent-based methods face two critical limitations: (a) they primarily navigate codebases through directory traversal rather than understanding semantic relationships, (b) and they struggle to extract and reason about complex cross-file dependencies when these relationships aren't explicitly represented in the repository structure. This significantly impairs their ability to locate code that requires modification when the issue involves interactions between structurally distant components in the codebase. + +# 2.3 Graph-based Code Representation Methods + +Due to the inherent structure of code, several works have employed graph-based representations to improve code understanding by capturing key relationships between components. Aider (2023) constructs a RepoMap and uses a graph ranking algorithm to identify the most significant contextual elements. Similarly, as a plugin, RepoGraph (Ouyang et al., 2025) performs subgraph retrieval – extracting an ego-network of relevant lines and their neighbors – to provide structured context. CodexGraph (Liu et al., 2024) indexes the repository into a Neo4j graph database, where LLM agents query the database precisely using Cypher. The efficiency of its retrieval process depends heavily on the querying capabilities of the LLM. These methods focus primarily on providing relevant context but do not enhance the traversal process itself, as they do not explicitly model directory structure or file hierarchies. + +In contrast, RepoUnderstander (Ma et al., 2024) builds hierarchical and function-call graphs, using Monte Carlo Tree Search (MCTS) guided by an LLM for exploration. While thorough, MCTS introduces extra computational overhead, making it less efficient than simpler traversal methods like BFS, particularly in large repositories. OrcaLoca (Yu et al., 2025) uses a simplified graph + +![](images/68d78298f4ef4a0462b402972796e7a35e59e5ec5b78ccafd6cd08b74dd8ad0d.jpg) +Figure 2: Overview of LOCAGENT framework. LOCAGENT first parses the given codebase to build a graph-based code representation with various types of entities and relations. It then constructs sparse indexes for exploring structures and searching content. Using these indexes, it performs agent-guided searches that combine the graph and tools. + +
MethodRelation TypesNode TypesSearch/Traversal Strategy
ContainImportInheritInvokeDirectoryFileClassFunction
CodexGraph(Liu et al., 2024)✓X✓✓XX✓✓Cypher queries
RepoGraph(Ouyang et al., 2025)✓X✓✓XX✓✓Ego-graph retrieval
RepoUnderstander(Ma et al., 2024)✓X✓✓✓✓✓✓MCTS
OrcaLoca(Yu et al., 2025)✓XX✓✓✓✓✓Simple search tools
LOCAGENT(Ours)✓✓✓✓✓✓✓✓Unified retrieval tools
+ +Table 1: Comparison of Graph-Based Code Representation Methods. + +enhanced by priority scheduling and context pruning. It maintains efficient search but may miss complex invocation dependencies. Table 1 summarizes the differences between these methods and LOCAGENT. Compared to these approaches, LOCAGENT offers a more comprehensive and unified representation of the repository, along with efficient, unified retrieval tools specifically designed for LLM consumption. + +# 3 The LOCAGENT Framework + +We introduce LOCAGENT, a graph-oriented LLM-agent framework for code localization. Figure 2 illustrates the overall framework. When given a repository, LOCAGENT can locate all the relevant code sections at various granularities (file, class, function, or line level) for different types of GitHub issues (such as bug reports, feature requests, performance bottlenecks, and security vulnerabilities) through automated in-depth exploration and analysis of the codebase. Section 3.1 proposes a novel graph-based indexing approach as an intermediate + +representation for codebases. Section 3.2 presents our agent-based code search on the indexes and Section 3.3 describes our model fine-tuning and distillation process. + +# 3.1 Graph-based Code Representation + +Codebases contain rich structural information, both explicit and implicit, that is essential for agent reasoning. Building on this insight, we develop a graph-based indexing that comprehensively captures codebase relationships while maintaining a granularity suitable for LLM-agents to retrieve. + +Code Graph Construction. We construct a heterogeneous directed graph $\mathcal{G}(\mathcal{V},\mathcal{E},\mathcal{A},\mathcal{R})$ to index the codebase, where $\nu = \{v_{i}\}_{i = 1}^{n}$ is the node set and $\mathcal{E}\subseteq \mathcal{V}\times \mathcal{V}$ is the edge set. Each node $v\in \mathcal{V}$ and edge $e\in \mathcal{E}$ has an associated type mapping function. For nodes, $\tau (v):\mathcal{V}\to \mathcal{A}$ maps to types $\mathcal{A} = \{\mathrm{directory},\mathrm{file},\mathrm{class},\mathrm{function}\}$ . For edges, $\phi (e):\mathcal{E}\rightarrow \mathcal{R}$ maps to relationships $\mathcal{R} = \{\mathrm{contain},\mathrm{import},\mathrm{invoke},\mathrm{inherit}\}$ . In this paper, we focus our study on Python reposito + +ries and leave codebases with other programming languages as future work. + +First, we include all directories and Python files as nodes. Then, we parse each Python file using the abstract syntax tree (AST) to identify inner functions and classes recursively as nodes. We set the function level as the smallest node granularity and use each function's code content as the document for agent retrieval. This approach creates a good balance of information density between the index and documents, allowing LLMs to reason effectively within their context window limitations. + +As shown in Figure 2, all nodes with different types can be connected as a single tree using the contain relationship. This structure supports standard codebase-navigation operations from existing works. Our code graph further incorporates more advanced codebase relationships as edges: (1) the invoke relationship from function/class to function/class, where an invoke to a class represents class instantiation; (2) the import relationship from file to function/class; and (3) the inherit relationship between classes. + +Sparse Hierarchical Entity Indexing. We treat nodes in our code graph as entities and build hierarchical indexing based on their contents. For each keyword, we lookup the indexes from top to bottom: (1) We build an entity ID index as a unique identifier for each node using its fully qualified name. For example, a function calculate_sum in the MathUtils class located in src/utils.py would be represented as: src/utils.py:MathUtilscalculate_sum. (2) We construct a global dictionary to map the entity name (e.g., calculate_sum) to all nodes that share the same name. (3) We index entity IDs through an inverted index (i.e., BM25) to handle keyword searches that don't exactly match the IDs or names of entities. (4) For cases where input keywords aren't part of the entities' IDs (e.g., when a keyword refers to a global variable), we build an inverted index that maps code chunk(s) to each entity to cover all possible matches. + +Remark. Rather than relying solely on directory structures or hierarchical module indexing, our approach captures module dependencies that transcend directory boundaries. Two modules in distant directories (A and B) may appear unrelated in traditional navigation, but if they invoke each other or share inheritance, they're syntactically close in our graph representation. This syntactic + +
Tool NameInput ParamsOutput
SearchEntityKeywordsRelated Entities with Code Snippets
TraverseGraphStart Entity IDs Direction Traverse Hops Entity Types Relation TypesTraversed Subgraph, including Entities and Relations
RetrieveEntityEntity IDsComplete Code of Specified Entities
+ +Table 2: List of unified APIs provided by LocAgent for code search and exploration. + +proximity is essential for code localization because issues typically manifest through call relationships rather than directory structure. By capturing these functional dependencies, our approach efficiently identifies related components even when physically distant in the codebase. + +# 3.2 Agent-guided Code Search + +We develop tools based on the indexes built offline. During runtime, LOCAGENT takes issue statements as input and launches agents that autonomously use tools to localize target code sections. While the agent may iteratively invoke multiple tools internally to explore the codebase, LOCAGENT presents a simplified interface to users, requiring only a single-turn interaction—users submit an issue statement and receive localization results without additional input. This autonomous, self-contained workflow makes LOCAGENT both easy to deploy and highly practical for real-world use. + +Tool Design for Codebase Exploration. Recent works (Örwall, 2024; Wang et al., 2025), inspired by GUI-based IDEs, have developed numerous specialized tools for agents to explore codebases. However, these tools are initially designed for human readability, which sacrifices the compactness and efficiency that LLM agents prefer (Yang et al., 2024). Building upon our graph-based code representation, we can develop tools that support efficient higher-order codebase exploration to address these challenges. We unify all codebase navigation, search, and view operations into three tools (Table 2), introduced as follows. + +SearchEntity: This tool searches codebases using keywords to locate relevant entities through our Hierarchical Entity Index. When an exact match isn't found in the upper index, the system performs a fuzzy search using the lower index. For each entity found, we return its code snippet in three detail + +levels: fold, preview, and full code (Figure 6). This effectively prevents lengthy code context and reduces noise fed into agents. + +**TraverseGraph:** This tool performs a type-aware breadth-first search (BFS) on the code graph, starting from input entities and allowing control over both traversal direction and number of hops. This supports agents to perform arbitrary multi-hop codebase navigation through only one action, significantly improving the efficiency compared with existing agent systems. Note that by allowing agents to select entity types and relation types for each traversal, this tool effectively leverages the LLM agents' coding expertise to generate proper meta paths—a crucial element for heterogeneous graph analysis (Lv et al., 2021). For example, by specifying entity types to {class, function} and relation types to {contain, inherit}, this tool returns the UML diagram. Additionally, we design an expanded tree-based format for the output subgraph that encodes both relation types and directions (Figure 7). (Fatemi et al., 2023) demonstrates that LLM performance on graph reasoning depends on the input graph format. Converting a graph into a tree structure encodes topology through the spatial distance between entity names, thereby deriving better performance. For detailed comparisons with alternative graph formats, please see Appendix A.1.2. + +RetreiveEntity: This tool retrieves complete entity attributes for each input entity ID, including essential information such as file path, line number, and code content. + +Chain-of-Thought Agent Planning. We use chain-of-thought (CoT) prompting (shown in Appendix D) to guide the agent in solving code localization problems step by step. The agent systematically follows these steps: (1) Keyword extraction. The agent begins by breaking down the issue statement into different categories and then extracts relevant keywords that are closely related to the problem. (2) Linking keywords to code entities. The agent invokes SearchEntity to complete and clarify each extracted keyword. + +(3) Generate the logical flow from fault to failure. The agent first identifies the entry points that trigger the problem. Then, it iteratively traverse the codebase with TraverseGraph, retrieves code contents with RetrieveEntity, and searches new keywords with SearchEntity. Finally, it generates the logic flow based on the issue and additional context. (4) Locate the target entities. The agent pinpoints all suspicious code entities that need modification + +based on the logic flow. Then, it ranks these entities based on their relevance. + +Confidence Estimation Based on Consistency. After generating a complete ranked list of candidate entities, to obtain a more consistent ranking, we measure the consistency (Wang et al., 2023a) of the LLM's predictions across multiple iterations. Specifically, we use the Reciprocal Rank as the initial confidence score for each predicted location. We then aggregate the scores for each entity across iterations to compute its final confidence score. The intuition behind this approach is that if the LLM consistently ranks a location higher in multiple iterations, it is more likely to be relevant. + +# 3.3 Open-source Model Fine-tuning + +Given the high costs of proprietary LLM APIs and data security concerns, we fine-tuned open-source models to improve their code localization capabilities and enable local deployment. We collect 433 successful trajectories generated with Claude-3.5, where the agent completed tasks from the SWEBench training set. Due to budget constraints, we sample an additional 335 trajectories generated by the initially fine-tuned Qwen2.5-32B model. Importantly, we only select successful trajectories where the model correctly localized the issues, creating a high-quality dataset of correct reasoning paths. These successful examples are then used to refine the same 32B model further, reinforcing effective reasoning patterns through this self-improvement loop. The entire dataset, combining both Claude-3.5 trajectories and successful Qwen2.5-32B samples, was then used to distill knowledge to a smaller 7B model. + +To fine-tune the smaller model, we employ Supervised Fine-Tuning (SFT) with LoRA (Hu et al., 2021). Our experiments show that this straightforward distillation method significantly enhances the performance of smaller models. See Appendix C.1.3 for more training details. + +# 4 LOC-BENCH: A New Benchmark for Code Localization + +# 4.1 Revisiting Existing Benchmark + +SWE-Bench(Jimenez et al., 2023) is a widely used benchmark that collects GitHub issues and corresponding code patches that resolve them. Xia et al. (2024); Suresh et al. (2024) adapt its subset, SWE-Bench-Lite, for code localization, treating the patched files and functions as the targets. + +However, existing datasets, including SWE-Bench, present challenges for effectively evaluating code localization methods. First, they are at risk of contamination, as they may include data overlapping with the repositories or issues used by modern models during pre-training. Second, existing datasets are not specifically designed for code localization (Tomassi et al., 2019). SWE-Bench, for instance, was created primarily to evaluate end-to-end bug-fixing capabilities, with localization being only an implicit intermediate step. This focus results in datasets dominated by bug reports (85% of SWE-Bench-Lite examples) while severely underrepresenting other common software maintenance tasks such as feature requests (14%), security vulnerabilities (1%), and performance optimizations (0%). This imbalance fails to capture the diverse localization challenges faced in real-world software development. + +# 4.2 Dataset Construction + +To address the limitations of existing benchmarks, we introduce LOC-BENCH, a new dataset specifically designed for code localization. This dataset collects up-to-date issues from Python repositories to mitigate the influence of pre-training bias in the latest LLMs. Additionally, LOC-BENCH covers wider categories, including bug reports, feature requests, security, and performance issues, enabling a more comprehensive evaluation of code localization methods. The statistics of LOC-BENCH are shown in Table 3. + +For the Bug Report category, we collect GitHub issues created after October 2024, which is later than the release dates of most modern LLMs. To enrich the dataset with more instances of security and performance issues, we use the GitHub Search API to search for relevant keywords, such as "latency improvement" for performance-related issues. We exclude instances that involve modifying more than five Python files or more than ten functions in the corresponding patch. For further details, see Appendix B.1. + +# 5 Experiments + +Our experiments aim to evaluate four key aspects of LOCAGENT: (1) the effectiveness of our graph-based representation and tooling for code localization compared to existing methods, (2) the performance of fine-tuned open-source models as cost-effective alternatives to proprietary LLMs, (3) a detailed analysis of how performance varies across + +
DatasetCategory#Sample
SWE-Bench-Lite (Total = 300)Bug Report254
Feature Request43
Security Issue3
Performance Issue0
Loc-Bench (Totoal = 560)Bug Report242
Feature Request150
Security Issue29
Performance Issue139
+ +Table 3: Distribution of samples across different categories in the SWE-Bench-Lite and Loc-Bench datasets. + +task categories, and (4) the contribution of each component in our framework through comprehensive ablation studies. We evaluate on both SWE-Bench-Lite and our introduced Loc-Bench dataset. Additionally, we examine the impact of improved localization on downstream software maintenance tasks. + +# 5.1 Experimental Settings + +Datasets. We first conduct experiments on SWEBench-Lite, treating the patched files and functions as the targets for localization. Following Suresh et al. (2024), we excluded examples where no existing functions were modified by the patch, ultimately retaining 274 out of the original 300 examples. + +Metrics. To assess performance, we use a modified accuracy metric inspired by R-Precision from information retrieval, following Agentless(Xia et al., 2024). To assess performance, we use Acc@k (Accuracy at k) as our evaluation metric, following Agentless(Xia et al., 2024). For each example, we select the top-k predicted locations and consider a localization attempt successful only if all relevant locations are correctly identified within these top-k predictions. This approach measures the ability to fully identify all necessary code sections that require modification. We report results across multiple $k$ values: file localization at Acc@1, Acc@3, and Acc@5, and function localization at Acc@5 and Acc@10. Additionally, to provide a more relaxed evaluation criteria, we assess module localization, which only requires finding any function within the patched class. + +# 5.2 Baselines + +We evaluate LOCAGENT against three categories of competitive baselines: (a) Retrieval-based meth + +
TypeMethodLoc-ModelFile (%)Module (%)Function (%)
Acc@1Acc@3Acc@5Acc@5Acc@10Acc@5Acc@10
Embedding-BasedBM25 (Robertson et al., 1994)38.6951.8261.6845.2652.9231.7536.86
E5-base-v2 (Wang et al., 2022)49.6474.4580.2967.8872.2639.4251.09
Jina-Code-v2 (Günther et al., 2023)43.4371.1780.2963.5072.6342.3452.19
Codesage-large-v2 (Zhang et al., 2024)47.8169.3478.1060.5869.7133.9444.53
CodeRankEmbed (Suresh et al., 2024)52.5577.7484.6771.9078.8351.8258.76
Procedure-BasedAgentless (Xia et al., 2024)GPT-4o67.1574.4574.4567.1567.1555.4755.47
Claude-3.572.6379.2079.5668.9868.9858.7658.76
Agent-BasedMoutlessTools (Örwall, 2024)GPT-4o73.3684.3185.0474.8276.2857.3059.49
Claude-3.572.6385.7786.1376.2876.2864.6064.96
SWE-agent (Yang et al., 2024)GPT-4o57.3064.9668.9858.0358.0345.9946.35
Claude-3.577.3787.2390.1577.7478.1064.2364.60
Openhands (Wang et al., 2025)GPT-4o60.9571.9073.7262.4163.8749.6450.36
Claude-3.576.2889.7890.1583.2183.5868.2570.07
LOCAGENT (Ours)Qwen2.5-7B(ft)70.8084.6788.3281.0282.8564.2371.53
Qwen2.5-32B(ft)75.9190.5192.7085.7787.2371.9077.01
Claude-3.577.7491.9794.1686.5087.5973.3677.37
+ +Table 4: Performance comparison with baseline methods on code localization on SWE-bench lite. Results show the accuracy at file, module, and function levels. For Agent-Based methods, we use GPT-4o-2024-0513 (abbr. as GPT-4o) and Claude-3-5-sonnet-20241022 (abbr. as Claude-3.5) as the localization model. Additionally, the performance of our fine-tuned open-source models, Qwen2.5-7B(ft) and Qwen2.5-32B(ft), are included for comparison. + +ods: We include the sparse retrieval approach BM25 (Robertson et al., 1994) and several state-of-the-art embedding models, including the general-purpose E5-base-v2 (Wang et al., 2022) and specialized code embedding models such as JinaCode-v2 (Günther et al., 2023), Codesage-large-v2 (Zhang et al., 2024), and the current SOTA code embedding model CodeRankEmbed (Suresh et al., 2024). Proprietary embedding solutions were excluded due to API costs. (b) Procedure-based methods: We compare against Agentless (Xia et al., 2024), which employs a structured hierarchical approach to code localization without complex agent architectures. (c) Agent-based methods: We include several advanced agent frameworks designed for code exploration and modification, specifically OpenHands (Wang et al., 2025) (using its default CodeActAgent implementation), SWE-Agent (Yang et al., 2024), and MoatlessTools (Örwall, 2024). For implementation details, please refer to Appendix C.1.1. + +# 5.3 Evaluation Results on SWE-Bench-Lite + +As shown in Table 4, Agent-Based methods consistently outperform other approaches, and our method demonstrates competitive performance by achieving the best results across all levels of code localization. Unlike traditional retrieval-based methods, Agentless identifies only a limited number of locations due to its narrow repository scope, which hinders performance gains when considering a broader set of candidates. The results of the NDCG are presented in Table 11 in the Appendix. + +![](images/f929dd53f4adf74c47eab0524e9c10d9df2c8753a81e68bd756d7c86d5d4876b.jpg) + +![](images/dd0a043ec99e4aa7d3cdd9cab21f0f8c8ff70d258cc383c3b7961f81be3880dc.jpg) +Figure 3: Performance analysis at different difficulty levels for file- and function-level localization. All agent-based methods and Agentless use Claude-3.5 as the localization model. Hop $N$ refers to the distances between functions mentioned in the issue description and the ground truth patch on our code graph. + +To further analyze the results, we examine performance across different task difficulty levels. We measure the task difficulty by calculating the shortest hops between the functions mentioned in the issue descriptions and the patched functions on our code graph (See Appendix C.1.2 for more details). As shown in Figure 3, performance decreases for all methods as the task becomes more challenging. However, Agent-based methods demonstrate better robustness as the difficulty increases, with + +![](images/594e4e848668151fa0f0d585dcf3a37fcc51677d8a82c5fdceaf97947d73c7bb.jpg) +Figure 4: Comparison of performance between the original and fine-tuned Qwen models. The metrics used are file-level Acc@5 and module/function-level Acc@10. Dashed lines represent the performance of the Claude-3.5 model for reference. + +our method maintaining competitive performance across various difficulty levels. Retrieval-based methods, such as E5-Base-v2 and CodeRankEmbed, perform poorly at the function level, even when the patched functions are explicitly mentioned in the query. This is because they treat the query as a whole, failing to capture fine-grained details. Agentless performs even worse than retrieval-based methods when exploration beyond the query is needed ( $hop \geq 0$ ) due to its simplistic localization process and limited view focused only on the repository structure. + +# 5.4 Fine-tuned Open-source Models + +Figure 4 demonstrates that after fine-tuning, both the 7B and 32B models show significant improvements on this task. LOCAGENT with finetuned Qwen-2.5-Coder-Instruct-32B (abbreviated as Qwen2.5-32B(ft)) achieves performance comparable to Claude-3.5, and LOCAGENT with Qwen2.5-7B(ft) also delivers results on par with that obtained using GPT-4o. As shown in Table 4, our method with Qwen2.5-32B(ft) outperforms nearly all baselines, including those that use larger and more powerful LLMs. The original 7B model performs poorly due to its limited tool-use capability (Chen et al., 2024). These results validate the feasibility of deploying our fine-tuned open-source models as promising alternatives to proprietary APIs, especially in resource-constrained applications. + +# 5.5 Efficiency Analysis + +Table 5 presents an efficiency analysis comparing agent-based methods in terms of cost and the number of agent interactions required. MoatlessTools demonstrates good cost-efficiency and requires relatively fewer rounds of interaction. However, the + +
MethodLM#RoundCost($)Acc@10
Cost
MoatlessToolsGPT-4o50.461.3
Claude-3.550.461.4
SWE-agentGPT-4o80.560.8
Claude-3.590.671.0
OpenhandsGPT-4o150.830.6
Claude-3.5130.790.9
OursClaude-3.570.661.2
Qwen2.5-7B(ft)60.0513.2
Qwen2.5-32B(ft)90.098.6
+ +Table 5: Efficiency analysis comparing the average cost and number of agent interaction rounds required by different methods. The cost-efficiency of each method is evaluated using the ratio of function-level Acc@10 to average cost. + +
Model SettingFile Acc@5Module Acc@10Function Acc@10
Ours88.3282.8571.53
w/o TraverseGraph86.1378.4766.06
Relation Types: contain86.5079.5666.42
Traverse Hops: 186.8680.2966.79
w/o RetrieveEntity87.5981.3969.34
w/o SearchEntity68.9861.3153.28
w/o BM25 index75.1868.9860.22
+ +Table 6: The ablation study of our model. The metrics used here are file-level Acc@5, module-level Acc@10, and function-level Acc@10. The impact of removing or fixing components is analyzed to observe how each component contributes to the overall accuracy. + +dense embeddings it uses make it difficult and slow to adapt to fast-evolving codebases. SWE-agent and Openhands also show moderate costs but still do not match the efficiency of LOCAGENT. For LOCAGENT with Claude-3.5, although more rounds of interaction are required, the cost remains lower than that of Openhands, illustrating the token efficiency of our tool's outputs. LOCAGENT with fine-tuned Qwen models stands out for its superior efficiency1. Qwen2.5-7B(ft) is the most cost-efficient option, requiring only $0.05 per example, while Qwen2.5-32B(ft) offers a more cost-effective alternative to Claude-3.5. These results highlight the potential of fine-tuned open-source models as efficient alternatives, providing an optimal balance of cost-effectiveness and performance that surpasses other methods. + +# 5.6 Ablation Study + +We conduct an ablation study to evaluate the effectiveness of each component of our toolsets. Due to budget constraints, we use the fine-tuned Qwen-2.5-7B as the localization model for these experiments. + +(1) Each tool in our toolset plays a critical role in code localization performance. As shown in Table 6, removing any tool, especially the SearchEntity tool, leads to varying degrees of accuracy degradation, particularly in module and function level localization. This highlights the critical role each tool plays in identifying relevant modules and functions. +(2) The graph structure provides essential information for accurate code localization. Removing TraverseGraph tool decreases module and function level performance since the agent cannot obtain any structure information about the codebase and relies on reasoning capability to identify call relationship or directory structure. Adding contain relationship provides only marginal improvements compared to fully removing TraverseGraph, emphasizing the importance of the other three relationship types and explaining why our method surpasses others relying only on the repository structure. +(3) Multi-hop exploration is crucial for deep code understanding. When compared to the full setting, fixing $Hops = 1$ leads to a moderate decline in file and module-level accuracy, but it causes a more significant decrease in function-level accuracy, underscoring the importance of multi-hop exploration for identifying relevant entities. +(4) Sparse indexing significantly enhances localization performance. Removing SearchEntity tool, or even partial removal of its index, causes a substantial drop in performance across all metrics. This demonstrates the effectiveness of building a sparse index on our code graph for improving localization performance. + +# 5.7 Evaluation Results on Loc-Bench + +To ensure the robustness and generalization of our methods and fine-tuned Qwen models, and to eliminate potential data leakage, we evaluate our new dataset. Since Loc-Bench includes examples that edit 1 to 5 files, we assess file localization at top-5 and top-10 ranks, and function/module localization at top-10 and top-15 ranks. Table 7 shows that our fine-tuned Qwen2.5-7B model exhibits strong gen + +![](images/40113cdec1e1feca7000cb77d3a5294a6135d63a0d343288699aecc05a7b7a58.jpg) + +![](images/f3ff500f60d006d9ab2100b2e34cdaaed024cc944a6d5f1861937bb334d1a3cf.jpg) +Figure 5: Performance analysis at different difficulty category for file- and function-level localization. All agent-based baselines and Agentless use Claude-3.5 as the localization model. + +eralization capabilities, maintaining competitive performance compared to SWE-agent using more expensive and strong model. These results highlight the practicality of the fine-tuned Qwen2.5-7B model for real-world applications. Despite being an open-source alternative, it achieves a performance comparable to Claude-3.5, supporting its feasibility as a cost-effective substitute for commercial models in practical scenarios. + +Additionally, we evaluate the performance across four different difficulty categories. Figure 5 clearly shows that our method outperforms other methods in almost all categories of code localization. However, it also highlights a noticeable decrease in performance across the other three categories compared to the Bug Report category. This performance gap likely reflects our training data distribution, which contained more bug report examples, potentially leading to scaffolds better optimized for bug localization tasks. This trend suggests that while our method is highly effective for bug report localization, there is still room for improvement in handling the other categories through more balanced training data and category-specific optimization strategies. + +# 5.8 Application: Better Localization Leads to More Solved GitHub Issues + +To assess the impact of localization methods on downstream tasks, we evaluated their effectiveness in solving GitHub issues. We choose Agentless as the baseline, ranking among the top-performing + +
MethodLoc ModelFile (%)Module (%)Function (%)
Acc@5Acc@10Acc@10Acc@15Acc@10Acc@15
IR-BasedCodeRankEmbed74.2980.8963.2167.5043.3946.61
AgentlessClaude-3.567.5067.5053.3953.3942.6842.68
OpenHandsClaude-3.579.8280.0068.9369.1159.1159.29
SWE-agentClaude-3.577.6877.6863.5763.7551.9651.96
LocAgent (Ours)Qwen2.5-7B(ft)78.5779.6463.0463.0451.4351.79
Claude-3.583.3986.0770.8971.0759.2960.71
+ +Table 7: Performance evaluation on the real-world LocBench dataset. + +
MethodLocalization LMAcc@5Pass@1Pass@10
AgentlessClaude-3.558.3926.3133.58
OursQwen2.5-32B(ft)69.3426.7936.13
Claude-3.573.3627.9237.59
+ +Table 8: Impact of localization accuracy on downstream bug repair tasks. + +open-source submissions on SWE-Bench-Lite. For consistency, we utilized Claude-3.5 as the editing model in conjunction with the Agentless editing method. Table 8 shows that the success rate for solving GitHub issues improves significantly with better code localization accuracy. + +# 6 Conclusion + +In conclusion, LOCAGENT enhances code localization by structuring codebases as graphs, enabling efficient repository-level exploration for LLM agents. With fine-tuned open-source models, our method achieves high localization accuracy while significantly reducing costs compared to larger proprietary models. Experimental results demonstrate the effectiveness of LOCAGENT in identifying relevant code components and improving downstream tasks. + +# Limitations + +First, our study primarily focused on fine-tuning Qwen-2.5-Coder models. Exploring a broader range of base models, including other open-source LLMs like CodeLlama, Mistral, or Yi, could provide valuable insights into model selection trade-offs. Additionally, investigating different finetuning approaches beyond LoRA, such as full finetuning or other parameter-efficient methods, could potentially yield better performance. + +Second, though we demonstrated improved bug repair performance with better localization, we only scratched the surface of potential downstream + +applications. Future work should evaluate LocAgent's impact on other software engineering tasks like refactoring, feature addition, security vulnerability patching, and performance optimization. This would provide a more comprehensive understanding of the framework's practical utility. + +Moreover, our fine-tuning process relied heavily on trajectories generated by Claude-3.5 and the fine-tuned Qwen2.5-32B model. A more diverse training dataset incorporating examples from different models, tasks, and repositories could improve the robustness and generalization of fine-tuned models. Additionally, analyzing the impact of different dataset compositions and filtering strategies on model performance could yield valuable insights. + +Finally, the current evaluation focuses primarily on Python codebases. Extending LOCAGENT to support other programming languages and evaluating its performance across different language paradigms would better demonstrate its generalizability. Further, our evaluation metrics could be expanded to include more nuanced measures of localization quality beyond accuracy and NDCG. + +# References + +Aider. 2023. Building a better repository map with tree sitter. Accessed: April 15, 2025. +Anthropic. 2023. Claude: Conversational ai by anthropic. Accessed: January 21, 2025. +artificialanalysis.ai. 2025. Artificial analysis. https://artificialanalysis.ai/models/. 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Ocaloca: An llm agent framework for software issue localization. arXiv preprint arXiv:2502.00350. +Dejiao Zhang, Wasi Uddin Ahmad, Ming Tan, Hantian Ding, Ramesh Nallapati, Dan Roth, Xiaofei Ma, and Bing Xiang. 2024. CODE REPRESENTATION LEARNING AT SCALE. In The Twelfth International Conference on Learning Representations. +Albert Örwall. 2024. Moatless tools. + +# A LOCAGENT Design Details + +# A.1 Tool Output Design + +# A.1.1 Three-level format for SearchEntity output + +Once invoked by the LLM agent, the retrieval APIs search for files, classes, methods, and code snippets in the codebase, and return the results back to the agent. To avoid forming very lengthy code context that may containing noisy information to LLM, we return only necessary information as API outputs. To achieve this, we desgined four granular standard output formats (Figure 6): fold, preview, full code. + +# A.1.2 Tree-based Subgraph Formatting for TraverseGraph Output + +The TraverseGraph tool traverses the code graph and returns a local subgraph for each input entity. The agent reasons about these subgraphs to understand each entity's complex dependencies. However, reasoning about graphs remains challenging for LLMs. Research by (Fatemi et al., 2023) demonstrates that LLM performance varies significantly based on graph formatting (how graphs are encoded as text). This makes the format design for output subgraphs crucial. + +We have developed a new tree-based format, shown in Figure 7, with several features that enhance LLM reasoning: (1) We represent subgraphs as trees, allowing LLMs to use indentation to determine a node's distance from the root, (2) We display complete entity IDs for each node (e.g., django/core-validators.py:RegexValidator) to help LLMs locate nodes easily, and (3) We explicitly specify relation types for each edge, including reversed relations + +To evaluate how different graph formats impact code localization performance, we conducted an experiment using 37 challenging samples from SWEBench-Lite. These samples were considered "challenging" because they could not be solved by any baseline agent methods. Using Claude-3.5 as the Localization Model across all settings, we compared various output formats. Table 9 presents our findings. The baseline output formats we tested are described below: + +- row: For each line, list one row of the adjacency matrix. For example, + +function "fileA.py:funcA" invokes function "fileA.py:funcB", "fileA.py:funcC" + +- row (w/ entity attributes): Additionally include entity attributes for format row. +- incident: The incident format mentioned in (Fatemi et al., 2023). An integer instead of entity ID is used to represent each node. For example, + +Map function "fileA.py:funcA" to index 0. Map function "fileA.py:funcB" to index 1. Map function "fileA.py:funcC" to index 2. + +function $O$ invokes function 1,2. + +Graphviz DOT: Represent graph in Graphviz DOT language (Ellson et al., 2002). +- JSON: Expand the subgraph as a tree, and convert it to JSON format. + +As shown in Table 9, expanding subgraphs as trees (i.e., JSON, tree-based) can significantly improve the performance. Our tree-based format achieves the best overall performance across different levels of localization tasks. We also test returning entity attributes along with subgraphs. We notice that row (w/ entity attributes) consistently underperforms row, indicating the attributes for all the nodes may be very noisy. Besides, although using incident format can simplify the output and show improvements in file-level localization, it degradation the module- and file-level localization. + +# A.2 Implementation + +To enable the LLM agent to invoke the Code Localization APIs, we handle the interaction differently based on the LLM's capabilities. For LLMs that support tool-calling features, we define the tools as a list of JSON objects, which are then used as parameters for the API calls. For LLMs that do not support tool-calling (such as Qwen), we provide the description of the API and the expected output as part of the LLM's prompt. When the agent decides to invoke a set of retrieval APIs, it responds with a list of API call names and their corresponding arguments. These retrieval API requests are processed locally by searching over the built code graph. The results from executing these APIs locally are returned to the agent. + +By default, we query the LLM with a temperature setting of 1.0. We conduct two interactions, after which we rerank the results based on mean reciprocal rank (MRR) scores. We also leverage multiprocessing execution to speed up the process. Since all our tools are read-only, LOCAGENT does + +![](images/e3da4d4339e99b1a14d6f8d73ea975c643cc44ad95a8dc1803fff42294d4f99a.jpg) +Figure 6: Different output formats designed for efficient agent-code interaction. Left: Full code output when matched entities $\leq 3$ . Middle: Preview output showing module skeleton for large files. Right: Fold output showing only entity IDs when matches $>3$ . + +![](images/003dcde246a439f5b9b36cc33df7c37daaa5e4eaf0478ed30be80b30cbe72965.jpg) + +![](images/86b464c56ef20eb2e4a58b1077f46f88aa113910e37ea427df9e03b94670489d.jpg) + +![](images/503072355158697ea6cb6ac7e2712ec0ffc412f1cd70207465e4cb36e21f3c9b.jpg) +Figure 7: A truncated example of the expanded tree-based format for the output subgraph of tool TraverseGraph. + +not require a specialized Docker environment to operate. + +# B Dataset construction and statistics + +# B.1 Dataset construction details + +Example collection. We collected examples on popular Python repositories on Github follow (Jimenez et al., 2023). To gather issues related to performance and security, we searched for the keywords listed in Table 10 using the GitHub Search APIs. We then used GPT-4o-2024-0513 as the classifier based on the issue descriptions. + +Ground Truth Locations. The affected files or functions in the original codebase, as identified in + +the patches, are considered the target locations for the given issue. While it is possible to fix a bug in a location different from the ground truth, the extracted ground-truth locations still serve as approximate targets for localization. Additionally, edited code such as documents, import statements, and comments are excluded from the localization target. These elements are not considered relevant for bug localization, as they do not directly impact the functionality of the code or its execution. By filtering out these elements, the focus is maintained on the core code changes that are relevant for localization. + +
Output FormatFile(%)Module(%)Function(%)
Acc@1Acc@3Acc@5Acc@5Acc@10Acc@5Acc@10
row41.1867.6570.5961.7661.7635.2938.24
row (w/ entity attributes)41.1864.7164.7150.0050.0032.3532.35
incident41.1870.5973.5355.8855.8829.4132.35
Graphviz DOT41.1873.5382.3564.7164.7135.2935.29
JSON41.1867.6576.4767.6570.5938.2441.18
tree-based (Ours)47.0679.4179.4164.7164.7138.2441.18
+ +Table 9: Localization performance under different TraverseGraph output formats. + +
CategoryKeywords
Performancebottleneck, performance improvement, memory usage optimization, time complexity reduction, latency improvement, scalability improvement, CPU usage reduction, caching improvement, concurrency optimization
SecurityOut-of-bounds Write, Out-of-bounds Read, NULL Pointer Dereference, Missing Authorization, memory leak fix, security vulnerability, security issue, authentication bypass, authentication issue, better maintained, buffer overflow, denial of service, security hardening, security patch, unsafe deserialization, Use After Free, Integer Overflow or Wraparound, Uncontrolled Resource Consumption, Missing Authentication for Critical Function
+ +Table 10: We use these Keywords to search for Performance and Security related issues with Github Search APIs. + +# C Additional Experiments + +# C.1 Implementation Details + +# C.1.1 Baselines Implementation + +Regarding the embedding-based methods in our evaluation, these approaches operate primarily at the function level, where each function is embedded as a separate unit. The function's context (its containing file and class) is appended to the function representation before embedding, rather than being embedded separately. While theoretically these methods could employ hierarchical indexing, the standard implementations we evaluated use flat indexing structures where each function is embedded as a single unit. + +We use OpenHands's remote runtime feature to parallelize evaluation on OpenHands and SWEagent. We use Openhands version 0.12.0 released on Oct 31, 2024. + +# C.1.2 Quantifying Task Difficulty Based on Code Graph Distance + +We measure task difficulty by computing the average shortest hop distance between the functions mentioned in the issue descriptions and the patched functions within our code graph. Specifically, we first extract potential function names from each + +issue description using GPT-4o-2024-0513, and identify their corresponding nodes in the code graph using the global dictionary. These identified nodes form the set of predicted nodes, denoted as $\mathcal{C}$ . Similarly, we link the ground truth functions from the patch to their corresponding nodes in the code graph, forming the set of target nodes, denoted as $\mathcal{T}$ . To quantify the difficulty $\delta$ , we calculate the average shortest hop distance between the predicted nodes $\mathcal{C}$ and the target nodes $\mathcal{T}$ , defined as: + +$$ +\delta = \frac {1}{| \mathcal {C} |} \sum_ {c \in \mathcal {C}} \frac {1}{m i n _ {t \in \mathcal {T}} d (c , t) + 1} +$$ + +where $d(c, t)$ represents the shortest hop distance between nodes $c$ and $t$ in the graph. For performance analysis stratified by difficulty, we round $\delta$ down to $\lfloor \delta \rfloor$ to group samples by difficulty levels, and we exclude samples where the LLM fails to extract any valid function names. + +# C.1.3 Training details. + +Fine-tuning Settings. We use Qwen-2.5-Coder-Instruct (Hui et al., 2024) 7B and 32B variants as our base models. We fine-tuned Qwen-2.5-Coder-Instruct 7B and 32B models on 768 training samples from the SWE-Bench training dataset, leveraging LoRA + +
TypeMethodLoc-ModelFile (%)Module (%)Function (%)
NDCG@1NDCG@3NDCG@5NDCG@5NDCG@10NDCG@5NDCG@10
Embedding-BasedBM25 (Robertson et al., 2009)38.6946.550.6137.3139.8626.1527.92
E5-base-v2 (Wang et al., 2022)49.6464.1966.653.1554.4531.3935.3
Jina-Code-v2 (Günther et al., 2023)43.4359.9363.751.0254.1333.2836.44
Codesage-large-v2 (Zhang et al., 2024)47.8160.8264.3949.3852.2227.0330.74
CodeRankEmbed (Suresh et al., 2024)52.5567.5470.3957.5159.7640.2842.55
Procedure-BasedAgentless (Xia et al., 2024)GPT-4o67.1571.7671.7664.3164.3153.8153.81
Claude-3.572.6376.7276.8767.3667.3657.5557.55
Agent-BasedMoatlessTools (Örwall, 2024)GPT-4o73.3680.0380.3368.5769.0949.7750.62
Claude-3.572.6380.7380.8869.1169.1153.0353.16
SWE-agent (Yang et al., 2024)GPT-4o57.363.9664.1253.9553.9542.3242.44
Claude-3.577.3784.3284.9372.7772.959.6759.79
Openshands (Wang et al., 2025)GPT-4o60.9567.6268.3958.1858.644.3444.66
Claude-3.576.2884.2784.4375.7975.9263.1363.8
LocAgent (Ours)Qwen2.5-7B(ft)70.8079.3680.970.9971.6855.6258.09
Qwen2.5-32B(ft)75.9184.7485.6476.2876.7764.2765.93
Claude-3.577.7486.1987.1477.7378.164.3465.57
+ +Table 11: NDCG scores comparison showing ranking quality of different methods. + +for efficient adaptation. The training set included 447 samples generated by Claude-3.5, while the remaining samples were iteratively generated using the fine-tuned Qwen2.5-32B model. The fine-tuning process was conducted over 5 epochs with max_token set to $128k$ and a learning rate of $2 \times 10^{-4}$ . + +# D Prompt + +In this section, we go through the prompt template that make up the agent's history. + +# Prompt + +Given the following GitHub problem description, your objective is to localize the specific files, classes or functions, and lines of code that need modification or contain key information to resolve the issue. + +Follow these steps to localize the issue: + +Step 1: Categorize and Extract Key Problem Information + +- Classify the problem statement into the following categories: +Problem description, error trace, code to reproduce the bug, and additional context. +- Identify modules in the '{package_name}' package mentioned in each category. +- Use extracted keywords and line numbers to search for relevant code references for additional context. + +Step 2: Locate Referenced Modules + +Accurately determine specific modules + +- Explore the repo to familiarize yourself with its structure. + +- Analyze the described execution flow to identify specific modules or components being referenced. + +- Pay special attention to distinguishing between modules with similar names using context and described execution flow. + +- Output Format for collected relevant modules: + +- Use the format: 'file path:QualifiedName' + +- E.q., for a function `calculate_sum` in the `MathUtilities` class located in `src/helpers/mathHelpers.py`, represent it as: + +'src/helpers/mathHelpers.py:MathUtil calculator_sum'. + +## Step 3: Analyze and Reproducing the Problem + +Clarify the Purpose of the Issue + +- If expanding capabilities: Identify where and how to incorporate new behavior, fields, or modules. + +- If addressing unexpected behavior: Focus on localizing modules containing potential bugs. + +- Reconstruct the execution flow + +- Identify main entry points triggering the issue. + +- Trace function calls, class interactions, and sequences of events. + 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b/data/2025/2503_09xxx/2503.09089/layout.json @@ -0,0 +1,10733 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 105, + 76, + 487, + 95 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 76, + 487, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 76, + 487, + 95 + ], + "type": "text", + "content": "LocAgent: Graph-Guided LLM Agents for Code Localization" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 114, + 534, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 114, + 534, + 148 + ], + "spans": [ + { + "bbox": [ + 61, + 114, + 534, + 148 + ], + "type": "text", + "content": "Zhaoling Chen\\*, Xiangru Tang\\*, Gangda Deng\\*, Fang Wu\\*, Jialong Wu\\*, Zhiwei Jiang, Viktor Prasanna\\*, Arman Cohan\\*, Xingyao Wang" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 148, + 531, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 148, + 531, + 179 + ], + "spans": [ + { + 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+ ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 155, + 219, + 202, + 232 + ], + "spans": [ + { + "bbox": [ + 155, + 219, + 202, + 232 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "spans": [ + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "type": "text", + "content": "Code localization—identifying precisely where in a codebase changes need to be made—is a fundamental yet challenging task in software maintenance. Existing approaches struggle to efficiently navigate complex codebases when identifying relevant code sections. The challenge lies in bridging natural language problem descriptions with the appropriate code elements, often requiring reasoning across hierarchical structures and multiple dependencies. We introduce LOCAGENT, a framework that addresses code localization through graph-based representation. By parsing codebases into directed heterogeneous graphs, LOCAGENT creates a lightweight representation that captures code structures (files, classes, functions) and their dependencies (imports, invocations, inheritance), enabling LLM agents to effectively search and locate relevant entities through powerful multi-hop reasoning. Experimental results on real-world benchmarks demonstrate that our approach significantly enhances accuracy in code localization. Notably, our method with the fine-tuned Qwen-2.5-Coder-Instruct-32B model achieves comparable results to SOTA proprietary models at greatly reduced cost (approximately " + }, + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "type": "inline_equation", + "content": "86\\%" + }, + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "type": "text", + "content": " reduction), reaching up to " + }, + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "type": "inline_equation", + "content": "92.7\\%" + }, + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "type": "text", + "content": " accuracy on file-level localization while improving downstream GitHub issue resolution success rates by " + }, + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "type": "inline_equation", + "content": "12\\%" + }, + { + "bbox": [ + 84, + 242, + 274, + 624 + ], + "type": "text", + "content": " for multiple attempts (Pass@10). Our code is available at https://github.com/gersteinlab/LocAgent." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 644, + 154, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 644, + 154, + 656 + ], + "spans": [ + { + "bbox": [ + 68, + 644, + 154, + 656 + ], + "type": "text", + "content": "1 Introduction" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 665, + 290, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 665, + 290, + 746 + ], + "spans": [ + { + "bbox": [ + 67, + 665, + 290, + 746 + ], + "type": "text", + "content": "Code localization can be viewed as an information retrieval (IR) task that aims to identify relevant code snippets given natural language descriptions (Yu et al., 2025; Yang et al., 2024; Xia et al., 2024). Developers spend up to " + }, + { + "bbox": [ + 67, + 665, + 290, + 746 + ], + "type": "inline_equation", + "content": "66\\%" + }, + { + "bbox": [ + 67, + 665, + 290, + 746 + ], + "type": "text", + "content": " of their debugging time (Böhme et al., 2017) understanding code to" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 304, + 215, + 525, + 374 + ], + "blocks": [ + { + "bbox": [ + 304, + 215, + 525, + 374 + ], + "lines": [ + { + "bbox": [ + 304, + 215, + 525, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 525, + 374 + ], + "type": "image", + "image_path": "c20269c8cebd98330e89168b5cf72fa71b25a1845eac8027149a6e7bbe018c9f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 302, + 382, + 525, + 442 + ], + "lines": [ + { + "bbox": [ + 302, + 382, + 525, + 442 + ], + "spans": [ + { + "bbox": [ + 302, + 382, + 525, + 442 + ], + "type": "text", + "content": "Figure 1: Code localization across four common programming scenarios. Given a codebase and an issue description, the goal of code localization is to identify the relevant code snippets that require modification to resolve the issue." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 302, + 449, + 526, + 760 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 449, + 526, + 760 + ], + "spans": [ + { + "bbox": [ + 302, + 449, + 526, + 760 + ], + "type": "text", + "content": "make changes, and automated tools often struggle with the same challenge. Poor code localization leads to incomplete fixes, introduces new bugs, and significantly extends development cycles. Unlike traditional retrieval tasks that primarily focus on lexical or semantic matching between queries and documents (Guo et al., 2016, 2020), code localization requires bridging the gap between natural language and programming languages. It also necessitates reasoning capabilities to analyze the issue, while considering the structural and semantic properties of code (Lewis et al., 2020; Guu et al., 2020; Qu et al., 2020). This capability has become fundamental to powerful AI assistants (OpenAI, 2023; Anthropic, 2023), code-aware search engines (PerplexityAI, 2023), and automated programming agents (Cognition.ai, 2024; Wang et al., 2025; Gauthier, 2024). In particular, accurate code localization is crucial for software maintenance and evolution, as it enables precise code modifications for bug fixes, refactoring, and feature additions (Wang et al., 2024), thereby streamlining the development workflow." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 761, + 524, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 761, + 524, + 775 + ], + "spans": [ + { + "bbox": [ + 314, + 761, + 524, + 775 + ], + "type": "text", + "content": "Existing approaches to code localization face" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 13, + 261, + 36, + 608 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 13, + 261, + 36, + 608 + ], + "spans": [ + { + "bbox": [ + 13, + 261, + 36, + 608 + ], + "type": "text", + "content": "arXiv:2503.09089v2 [cs.SE] 29 Apr 2025" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 67, + 752, + 290, + 775 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 752, + 290, + 775 + ], + "spans": [ + { + "bbox": [ + 67, + 752, + 290, + 775 + ], + "type": "text", + "content": "* Equal contribution. This work was done during Zhaoling's time at Yale." + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 71, + 289, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 71, + 289, + 449 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 289, + 449 + ], + "type": "text", + "content": "significant limitations. Dense retrieval methods require maintaining and continuously updating vector representations of the entire codebase (Wang et al., 2023b; Günther et al., 2023), creating engineering challenges for large, evolving repositories where code changes frequently. While LLMs demonstrate strong code understanding capabilities (Kang et al., 2023; Wu et al., 2023), models with large context windows cannot process entire codebases at once, necessitating strategic navigation through relevant parts. Moreover, issue descriptions often mention only symptoms rather than underlying causes. For instance, a report of 'XSS vulnerability in user profile' might require changes to a shared validation utility used throughout the codebase but not explicitly referenced in the issue. This disconnect between issue descriptions and affected code components presents a substantial challenge for traditional retrieval approaches, which struggle to trace implicit dependencies across the codebase structure. Recent agent-based methods attempt to address these limitations through iterative exploration (Yang et al., 2024; Qin et al., 2024) but still struggle to efficiently navigate and comprehend complex code structures and dependencies, particularly when multi-hop reasoning is required to trace from issue descriptions to affected code regions that aren't directly mentioned." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 450, + 289, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 450, + 289, + 557 + ], + "spans": [ + { + "bbox": [ + 69, + 450, + 289, + 557 + ], + "type": "text", + "content": "This raises a key question: How can we design efficient indexing as intermediate representations that are structure-aware and both easy and performant for LLM agents to consume? It is intuitive to design an agentic retrieval system that carefully combines traditional IR methods and LLM agent's reasoning ability to achieve accurate, efficient, and cost-effective code localization in codebases." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 559, + 289, + 774 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 559, + 289, + 774 + ], + "spans": [ + { + "bbox": [ + 69, + 559, + 289, + 774 + ], + "type": "text", + "content": "To address this challenge, we propose LOCAGENT, a framework that builds directed heterogeneous graph indexing to unify code structures, dependencies, and contents. Our approach leverages a structured graph representation that enables powerful multi-hop reasoning capabilities, allowing agents to navigate complex dependency relationships between code elements even when target code isn't explicitly mentioned in issue descriptions. This graph-based approach significantly outperforms previous methods on challenging localization tasks that require traversing multiple code relationships. Our lightweight representation, coupled with sparse indexing techniques, enables efficient entity search while maintaining rich structural information. The indexing process typically" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 71, + 524, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 524, + 273 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 524, + 273 + ], + "type": "text", + "content": "takes only a few seconds per codebase, making it highly practical for real-time use. The framework integrates a set of unified tools that guide the agent through a systematic exploration of the codebase, allowing autonomous navigation based on contextual needs. Furthermore, by fine-tuning Qwen-2.5-Coder-Instruct (Hui et al., 2024) 7B and 32B models(abbr. as Qwen-2.5-7B and Qwen-2.5-32B respectively), our system achieves performance comparable to state-of-the-art models like Claude-3-5-sonnet-20241022 (Anthropic, 2023) (abbr. as Claude-3.5) while significantly reducing API costs by over " + }, + { + "bbox": [ + 305, + 71, + 524, + 273 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 305, + 71, + 524, + 273 + ], + "type": "text", + "content": " (from \\" + }, + { + "bbox": [ + 305, + 71, + 524, + 273 + ], + "type": "inline_equation", + "content": "0.66 to \\" + }, + { + "bbox": [ + 305, + 71, + 524, + 273 + ], + "type": "text", + "content": "0.09 per example), making it practical for real-world deployment." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 275, + 524, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 275, + 524, + 529 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 524, + 529 + ], + "type": "text", + "content": "Additionally, to facilitate a comprehensive evaluation of code localization methods, we introduce LOC-BENCH, a new benchmark specifically designed for this task. Existing benchmarks like SWE-Bench present significant limitations: (1) they risk contamination through data overlap with LLM training sets (Mündler et al., 2024), and (2) they primarily focus on bug fixing, lacking diversity in maintenance scenarios such as feature requests, performance optimizations, and security fixes. In contrast, LOC-BENCH covers diverse scenarios and mitigates potential contamination concerns by incorporating more recent examples from popular Python repositories collected after known LLM training cutoff dates. Additionally, we provide tooling to continuously update the benchmark with new examples, allowing researchers to maintain a fresh evaluation dataset as models evolve and training data cutoffs advance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 532, + 524, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 532, + 524, + 558 + ], + "spans": [ + { + "bbox": [ + 305, + 532, + 524, + 558 + ], + "type": "text", + "content": "Our contributions address critical gaps in existing approaches:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 568, + 524, + 773 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 318, + 568, + 524, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 568, + 524, + 648 + ], + "spans": [ + { + "bbox": [ + 318, + 568, + 524, + 648 + ], + "type": "text", + "content": "- We introduce a heterogeneous graph representation that captures both explicit and implicit code relationships, enabling efficient multi-hop reasoning. Our lightweight graph-based indexing process takes only seconds per repository and requires minimal storage." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 318, + 658, + 524, + 751 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 658, + 524, + 751 + ], + "spans": [ + { + "bbox": [ + 318, + 658, + 524, + 751 + ], + "type": "text", + "content": "- We design unified tools for agent-based code exploration that leverage our graph representation, allowing LLM agents to perform complex multi-hop navigation and reasoning across code dependencies even when target code isn't explicitly mentioned in issue descriptions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 318, + 761, + 524, + 773 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 761, + 524, + 773 + ], + "spans": [ + { + "bbox": [ + 318, + 761, + 524, + 773 + ], + "type": "text", + "content": "- We introduce Loc-Bench, a new benchmark" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 89, + 71, + 290, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 71, + 290, + 153 + ], + "spans": [ + { + "bbox": [ + 89, + 71, + 290, + 153 + ], + "type": "text", + "content": "specifically designed for code localization that addresses limitations in existing datasets. Unlike previous benchmarks dominated by bug reports, Loc-Bench offers a balanced distribution across bug fixes, feature requests, security patches, and performance optimizations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 81, + 164, + 291, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 164, + 291, + 217 + ], + "spans": [ + { + "bbox": [ + 81, + 164, + 291, + 217 + ], + "type": "text", + "content": "- By fine-tuning open-source models on this task, we reduce the cost of code localization by " + }, + { + "bbox": [ + 81, + 164, + 291, + 217 + ], + "type": "inline_equation", + "content": "86\\%" + }, + { + "bbox": [ + 81, + 164, + 291, + 217 + ], + "type": "text", + "content": " while maintaining competitive performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 243, + 160, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 243, + 160, + 256 + ], + "spans": [ + { + "bbox": [ + 67, + 243, + 160, + 256 + ], + "type": "text", + "content": "2 Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 266, + 267, + 279 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 266, + 267, + 279 + ], + "spans": [ + { + "bbox": [ + 67, + 266, + 267, + 279 + ], + "type": "text", + "content": "2.1 Traditional Retrieval-based Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 285, + 291, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 285, + 291, + 555 + ], + "spans": [ + { + "bbox": [ + 67, + 285, + 291, + 555 + ], + "type": "text", + "content": "Traditional IR methods rely on lexical or semantic matching to return ranked lists of code snippets. Sparse retrievers, such as BM25 (Robertson et al., 1994, 2009), have demonstrated robustness to domain adaptation. Dense retrievers utilize embeddings for improved semantic searching, including models with open checkpoints such as general text embedding models E5-base-v2 (Wang et al., 2022) and proprietary APIs (VoyageAI, 2024). Code embedding models such as Jina-Code-v2 (Günther et al., 2023), Codesage-large-v2 (Zhang et al., 2024), and CodeRankEmbed (Suresh et al., 2024), trained specifically for code related tasks, showing significant performance in Code2Code and NL2Code semantic search tasks. However, while the embedding models themselves are small, the engineering challenges of maintaining these indexing systems (e.g., storage requirements, update mechanisms, and infrastructure maintenance) make them difficult to adapt to fast-evolving codebases." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 566, + 289, + 579 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 566, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 67, + 566, + 289, + 579 + ], + "type": "text", + "content": "2.2 LLM-based Generative Retrieval Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 586, + 291, + 774 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 586, + 291, + 774 + ], + "spans": [ + { + "bbox": [ + 67, + 586, + 291, + 774 + ], + "type": "text", + "content": "Recently, LLMs with advanced code reasoning capabilities have demonstrated superior performance by directly processing queries and raw code for code localization (Kang et al., 2023; Wu et al., 2023; Xia et al., 2024; Kang et al., 2024). For example, Agentless (Xia et al., 2024), initially designed for automated program repair, uses a simplistic hierarchical localization process powered by LLM. It employs a straightforward three-phase approach that first localizes relevant code sections before attempting to fix the identified issues, challenging the assumption that complex agent architectures are necessary for effective code understanding and modification tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 302, + 71, + 526, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 71, + 526, + 368 + ], + "spans": [ + { + "bbox": [ + 302, + 71, + 526, + 368 + ], + "type": "text", + "content": "Expanding on these techniques, agent-based methods utilize multi-step reasoning to enable automated codebase traversal. Specifically, OpenHands (Wang et al., 2025) implements a generalist coding agent that supports bash commands like grep and tools for viewing files. SWE-Agent (Yang et al., 2024) integrates a custom Agent-Computer Interface to support agents to navigate entire repositories. MoatlessTools (Örwall, 2024) combines an agentic searching loop and semantic search to obtain code locations. However, existing agent-based methods face two critical limitations: (a) they primarily navigate codebases through directory traversal rather than understanding semantic relationships, (b) and they struggle to extract and reason about complex cross-file dependencies when these relationships aren't explicitly represented in the repository structure. This significantly impairs their ability to locate code that requires modification when the issue involves interactions between structurally distant components in the codebase." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 302, + 378, + 493, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 378, + 493, + 404 + ], + "spans": [ + { + "bbox": [ + 302, + 378, + 493, + 404 + ], + "type": "text", + "content": "2.3 Graph-based Code Representation Methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 302, + 409, + 526, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 409, + 526, + 665 + ], + "spans": [ + { + "bbox": [ + 302, + 409, + 526, + 665 + ], + "type": "text", + "content": "Due to the inherent structure of code, several works have employed graph-based representations to improve code understanding by capturing key relationships between components. Aider (2023) constructs a RepoMap and uses a graph ranking algorithm to identify the most significant contextual elements. Similarly, as a plugin, RepoGraph (Ouyang et al., 2025) performs subgraph retrieval – extracting an ego-network of relevant lines and their neighbors – to provide structured context. CodexGraph (Liu et al., 2024) indexes the repository into a Neo4j graph database, where LLM agents query the database precisely using Cypher. The efficiency of its retrieval process depends heavily on the querying capabilities of the LLM. These methods focus primarily on providing relevant context but do not enhance the traversal process itself, as they do not explicitly model directory structure or file hierarchies." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 302, + 667, + 526, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 667, + 526, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 667, + 526, + 775 + ], + "type": "text", + "content": "In contrast, RepoUnderstander (Ma et al., 2024) builds hierarchical and function-call graphs, using Monte Carlo Tree Search (MCTS) guided by an LLM for exploration. While thorough, MCTS introduces extra computational overhead, making it less efficient than simpler traversal methods like BFS, particularly in large repositories. OrcaLoca (Yu et al., 2025) uses a simplified graph" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 68, + 69, + 526, + 269 + ], + "blocks": [ + { + "bbox": [ + 68, + 69, + 526, + 269 + ], + "lines": [ + { + "bbox": [ + 68, + 69, + 526, + 269 + ], + "spans": [ + { + "bbox": [ + 68, + 69, + 526, + 269 + ], + "type": "image", + "image_path": "68d78298f4ef4a0462b402972796e7a35e59e5ec5b78ccafd6cd08b74dd8ad0d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 291, + 525, + 339 + ], + "lines": [ + { + "bbox": [ + 66, + 291, + 525, + 339 + ], + "spans": [ + { + "bbox": [ + 66, + 291, + 525, + 339 + ], + "type": "text", + "content": "Figure 2: Overview of LOCAGENT framework. LOCAGENT first parses the given codebase to build a graph-based code representation with various types of entities and relations. It then constructs sparse indexes for exploring structures and searching content. Using these indexes, it performs agent-guided searches that combine the graph and tools." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 70, + 351, + 524, + 441 + ], + "blocks": [ + { + "bbox": [ + 70, + 351, + 524, + 441 + ], + "lines": [ + { + "bbox": [ + 70, + 351, + 524, + 441 + ], + "spans": [ + { + "bbox": [ + 70, + 351, + 524, + 441 + ], + "type": "table", + "html": "
MethodRelation TypesNode TypesSearch/Traversal Strategy
ContainImportInheritInvokeDirectoryFileClassFunction
CodexGraph(Liu et al., 2024)✓X✓✓XX✓✓Cypher queries
RepoGraph(Ouyang et al., 2025)✓X✓✓XX✓✓Ego-graph retrieval
RepoUnderstander(Ma et al., 2024)✓X✓✓✓✓✓✓MCTS
OrcaLoca(Yu et al., 2025)✓XX✓✓✓✓✓Simple search tools
LOCAGENT(Ours)✓✓✓✓✓✓✓✓Unified retrieval tools
", + "image_path": "eff607d6667dc8fa01afca421fe5518165076b8c38bf5f9855a1411d560992d1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 156, + 448, + 436, + 460 + ], + "lines": [ + { + "bbox": [ + 156, + 448, + 436, + 460 + ], + "spans": [ + { + "bbox": [ + 156, + 448, + 436, + 460 + ], + "type": "text", + "content": "Table 1: Comparison of Graph-Based Code Representation Methods." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 67, + 473, + 291, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 473, + 291, + 595 + ], + "spans": [ + { + "bbox": [ + 67, + 473, + 291, + 595 + ], + "type": "text", + "content": "enhanced by priority scheduling and context pruning. It maintains efficient search but may miss complex invocation dependencies. Table 1 summarizes the differences between these methods and LOCAGENT. Compared to these approaches, LOCAGENT offers a more comprehensive and unified representation of the repository, along with efficient, unified retrieval tools specifically designed for LLM consumption." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 604, + 238, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 604, + 238, + 618 + ], + "spans": [ + { + "bbox": [ + 67, + 604, + 238, + 618 + ], + "type": "text", + "content": "3 The LOCAGENT Framework" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 626, + 292, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 626, + 292, + 775 + ], + "spans": [ + { + "bbox": [ + 67, + 626, + 292, + 775 + ], + "type": "text", + "content": "We introduce LOCAGENT, a graph-oriented LLM-agent framework for code localization. Figure 2 illustrates the overall framework. When given a repository, LOCAGENT can locate all the relevant code sections at various granularities (file, class, function, or line level) for different types of GitHub issues (such as bug reports, feature requests, performance bottlenecks, and security vulnerabilities) through automated in-depth exploration and analysis of the codebase. Section 3.1 proposes a novel graph-based indexing approach as an intermediate" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 302, + 473, + 525, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 473, + 525, + 527 + ], + "spans": [ + { + "bbox": [ + 302, + 473, + 525, + 527 + ], + "type": "text", + "content": "representation for codebases. Section 3.2 presents our agent-based code search on the indexes and Section 3.3 describes our model fine-tuning and distillation process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 302, + 539, + 493, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 539, + 493, + 553 + ], + "spans": [ + { + "bbox": [ + 302, + 539, + 493, + 553 + ], + "type": "text", + "content": "3.1 Graph-based Code Representation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 301, + 557, + 526, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 557, + 526, + 638 + ], + "spans": [ + { + "bbox": [ + 301, + 557, + 526, + 638 + ], + "type": "text", + "content": "Codebases contain rich structural information, both explicit and implicit, that is essential for agent reasoning. Building on this insight, we develop a graph-based indexing that comprehensively captures codebase relationships while maintaining a granularity suitable for LLM-agents to retrieve." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": "Code Graph Construction. We construct a heterogeneous directed graph " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\mathcal{V},\\mathcal{E},\\mathcal{A},\\mathcal{R})" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": " to index the codebase, where " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "\\nu = \\{v_{i}\\}_{i = 1}^{n}" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": " is the node set and " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "\\mathcal{E}\\subseteq \\mathcal{V}\\times \\mathcal{V}" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": " is the edge set. Each node " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "v\\in \\mathcal{V}" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": " and edge " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "e\\in \\mathcal{E}" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": " has an associated type mapping function. For nodes, " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "\\tau (v):\\mathcal{V}\\to \\mathcal{A}" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": " maps to types " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "\\mathcal{A} = \\{\\mathrm{directory},\\mathrm{file},\\mathrm{class},\\mathrm{function}\\}" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": ". For edges, " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "\\phi (e):\\mathcal{E}\\rightarrow \\mathcal{R}" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": " maps to relationships " + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "inline_equation", + "content": "\\mathcal{R} = \\{\\mathrm{contain},\\mathrm{import},\\mathrm{invoke},\\mathrm{inherit}\\}" + }, + { + "bbox": [ + 302, + 640, + 527, + 775 + ], + "type": "text", + "content": ". In this paper, we focus our study on Python reposito" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 71, + 289, + 98 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 71, + 289, + 98 + ], + "spans": [ + { + "bbox": [ + 67, + 71, + 289, + 98 + ], + "type": "text", + "content": "ries and leave codebases with other programming languages as future work." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 100, + 290, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 100, + 290, + 235 + ], + "spans": [ + { + "bbox": [ + 67, + 100, + 290, + 235 + ], + "type": "text", + "content": "First, we include all directories and Python files as nodes. Then, we parse each Python file using the abstract syntax tree (AST) to identify inner functions and classes recursively as nodes. We set the function level as the smallest node granularity and use each function's code content as the document for agent retrieval. This approach creates a good balance of information density between the index and documents, allowing LLMs to reason effectively within their context window limitations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 238, + 291, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 238, + 291, + 386 + ], + "spans": [ + { + "bbox": [ + 69, + 238, + 291, + 386 + ], + "type": "text", + "content": "As shown in Figure 2, all nodes with different types can be connected as a single tree using the contain relationship. This structure supports standard codebase-navigation operations from existing works. Our code graph further incorporates more advanced codebase relationships as edges: (1) the invoke relationship from function/class to function/class, where an invoke to a class represents class instantiation; (2) the import relationship from file to function/class; and (3) the inherit relationship between classes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 388, + 291, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 388, + 291, + 659 + ], + "spans": [ + { + "bbox": [ + 69, + 388, + 291, + 659 + ], + "type": "text", + "content": "Sparse Hierarchical Entity Indexing. We treat nodes in our code graph as entities and build hierarchical indexing based on their contents. For each keyword, we lookup the indexes from top to bottom: (1) We build an entity ID index as a unique identifier for each node using its fully qualified name. For example, a function calculate_sum in the MathUtils class located in src/utils.py would be represented as: src/utils.py:MathUtilscalculate_sum. (2) We construct a global dictionary to map the entity name (e.g., calculate_sum) to all nodes that share the same name. (3) We index entity IDs through an inverted index (i.e., BM25) to handle keyword searches that don't exactly match the IDs or names of entities. (4) For cases where input keywords aren't part of the entities' IDs (e.g., when a keyword refers to a global variable), we build an inverted index that maps code chunk(s) to each entity to cover all possible matches." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 666, + 291, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 666, + 291, + 775 + ], + "spans": [ + { + "bbox": [ + 67, + 666, + 291, + 775 + ], + "type": "text", + "content": "Remark. Rather than relying solely on directory structures or hierarchical module indexing, our approach captures module dependencies that transcend directory boundaries. Two modules in distant directories (A and B) may appear unrelated in traditional navigation, but if they invoke each other or share inheritance, they're syntactically close in our graph representation. This syntactic" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 306, + 68, + 524, + 200 + ], + "blocks": [ + { + "bbox": [ + 306, + 68, + 524, + 200 + ], + "lines": [ + { + "bbox": [ + 306, + 68, + 524, + 200 + ], + "spans": [ + { + "bbox": [ + 306, + 68, + 524, + 200 + ], + "type": "table", + "html": "
Tool NameInput ParamsOutput
SearchEntityKeywordsRelated Entities with Code Snippets
TraverseGraphStart Entity IDs Direction Traverse Hops Entity Types Relation TypesTraversed Subgraph, including Entities and Relations
RetrieveEntityEntity IDsComplete Code of Specified Entities
", + "image_path": "3ee9190f79ad7623fb4b180523bd53a7f66d2934c043f7c4febdadae07f9b9c0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 302, + 206, + 525, + 232 + ], + "lines": [ + { + "bbox": [ + 302, + 206, + 525, + 232 + ], + "spans": [ + { + "bbox": [ + 302, + 206, + 525, + 232 + ], + "type": "text", + "content": "Table 2: List of unified APIs provided by LocAgent for code search and exploration." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 301, + 241, + 525, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 241, + 525, + 321 + ], + "spans": [ + { + "bbox": [ + 301, + 241, + 525, + 321 + ], + "type": "text", + "content": "proximity is essential for code localization because issues typically manifest through call relationships rather than directory structure. By capturing these functional dependencies, our approach efficiently identifies related components even when physically distant in the codebase." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 302, + 334, + 456, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 334, + 456, + 347 + ], + "spans": [ + { + "bbox": [ + 302, + 334, + 456, + 347 + ], + "type": "text", + "content": "3.2 Agent-guided Code Search" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 301, + 353, + 525, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 353, + 525, + 514 + ], + "spans": [ + { + "bbox": [ + 301, + 353, + 525, + 514 + ], + "type": "text", + "content": "We develop tools based on the indexes built offline. During runtime, LOCAGENT takes issue statements as input and launches agents that autonomously use tools to localize target code sections. While the agent may iteratively invoke multiple tools internally to explore the codebase, LOCAGENT presents a simplified interface to users, requiring only a single-turn interaction—users submit an issue statement and receive localization results without additional input. This autonomous, self-contained workflow makes LOCAGENT both easy to deploy and highly practical for real-world use." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 301, + 517, + 526, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 517, + 526, + 692 + ], + "spans": [ + { + "bbox": [ + 301, + 517, + 526, + 692 + ], + "type": "text", + "content": "Tool Design for Codebase Exploration. Recent works (Örwall, 2024; Wang et al., 2025), inspired by GUI-based IDEs, have developed numerous specialized tools for agents to explore codebases. However, these tools are initially designed for human readability, which sacrifices the compactness and efficiency that LLM agents prefer (Yang et al., 2024). Building upon our graph-based code representation, we can develop tools that support efficient higher-order codebase exploration to address these challenges. We unify all codebase navigation, search, and view operations into three tools (Table 2), introduced as follows." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 302, + 693, + 525, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 693, + 525, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 693, + 525, + 775 + ], + "type": "text", + "content": "SearchEntity: This tool searches codebases using keywords to locate relevant entities through our Hierarchical Entity Index. When an exact match isn't found in the upper index, the system performs a fuzzy search using the lower index. For each entity found, we return its code snippet in three detail" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 71, + 290, + 111 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 71, + 290, + 111 + ], + "spans": [ + { + "bbox": [ + 67, + 71, + 290, + 111 + ], + "type": "text", + "content": "levels: fold, preview, and full code (Figure 6). This effectively prevents lengthy code context and reduces noise fed into agents." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 112, + 291, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 112, + 291, + 449 + ], + "spans": [ + { + "bbox": [ + 69, + 112, + 291, + 449 + ], + "type": "text", + "content": "**TraverseGraph:** This tool performs a type-aware breadth-first search (BFS) on the code graph, starting from input entities and allowing control over both traversal direction and number of hops. This supports agents to perform arbitrary multi-hop codebase navigation through only one action, significantly improving the efficiency compared with existing agent systems. Note that by allowing agents to select entity types and relation types for each traversal, this tool effectively leverages the LLM agents' coding expertise to generate proper meta paths—a crucial element for heterogeneous graph analysis (Lv et al., 2021). For example, by specifying entity types to {class, function} and relation types to {contain, inherit}, this tool returns the UML diagram. Additionally, we design an expanded tree-based format for the output subgraph that encodes both relation types and directions (Figure 7). (Fatemi et al., 2023) demonstrates that LLM performance on graph reasoning depends on the input graph format. Converting a graph into a tree structure encodes topology through the spatial distance between entity names, thereby deriving better performance. For detailed comparisons with alternative graph formats, please see Appendix A.1.2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 450, + 290, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 450, + 290, + 503 + ], + "spans": [ + { + "bbox": [ + 67, + 450, + 290, + 503 + ], + "type": "text", + "content": "RetreiveEntity: This tool retrieves complete entity attributes for each input entity ID, including essential information such as file path, line number, and code content." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 504, + 291, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 504, + 291, + 652 + ], + "spans": [ + { + "bbox": [ + 69, + 504, + 291, + 652 + ], + "type": "text", + "content": "Chain-of-Thought Agent Planning. We use chain-of-thought (CoT) prompting (shown in Appendix D) to guide the agent in solving code localization problems step by step. The agent systematically follows these steps: (1) Keyword extraction. The agent begins by breaking down the issue statement into different categories and then extracts relevant keywords that are closely related to the problem. (2) Linking keywords to code entities. The agent invokes SearchEntity to complete and clarify each extracted keyword." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 654, + 290, + 774 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 654, + 290, + 774 + ], + "spans": [ + { + "bbox": [ + 67, + 654, + 290, + 774 + ], + "type": "text", + "content": "(3) Generate the logical flow from fault to failure. The agent first identifies the entry points that trigger the problem. Then, it iteratively traverse the codebase with TraverseGraph, retrieves code contents with RetrieveEntity, and searches new keywords with SearchEntity. Finally, it generates the logic flow based on the issue and additional context. (4) Locate the target entities. The agent pinpoints all suspicious code entities that need modification" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 302, + 71, + 524, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 71, + 524, + 97 + ], + "spans": [ + { + "bbox": [ + 302, + 71, + 524, + 97 + ], + "type": "text", + "content": "based on the logic flow. Then, it ranks these entities based on their relevance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 302, + 99, + 525, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 99, + 525, + 260 + ], + "spans": [ + { + "bbox": [ + 302, + 99, + 525, + 260 + ], + "type": "text", + "content": "Confidence Estimation Based on Consistency. After generating a complete ranked list of candidate entities, to obtain a more consistent ranking, we measure the consistency (Wang et al., 2023a) of the LLM's predictions across multiple iterations. Specifically, we use the Reciprocal Rank as the initial confidence score for each predicted location. We then aggregate the scores for each entity across iterations to compute its final confidence score. The intuition behind this approach is that if the LLM consistently ranks a location higher in multiple iterations, it is more likely to be relevant." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 302, + 271, + 481, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 271, + 481, + 285 + ], + "spans": [ + { + "bbox": [ + 302, + 271, + 481, + 285 + ], + "type": "text", + "content": "3.3 Open-source Model Fine-tuning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 302, + 289, + 525, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 289, + 525, + 545 + ], + "spans": [ + { + "bbox": [ + 302, + 289, + 525, + 545 + ], + "type": "text", + "content": "Given the high costs of proprietary LLM APIs and data security concerns, we fine-tuned open-source models to improve their code localization capabilities and enable local deployment. We collect 433 successful trajectories generated with Claude-3.5, where the agent completed tasks from the SWEBench training set. Due to budget constraints, we sample an additional 335 trajectories generated by the initially fine-tuned Qwen2.5-32B model. Importantly, we only select successful trajectories where the model correctly localized the issues, creating a high-quality dataset of correct reasoning paths. These successful examples are then used to refine the same 32B model further, reinforcing effective reasoning patterns through this self-improvement loop. The entire dataset, combining both Claude-3.5 trajectories and successful Qwen2.5-32B samples, was then used to distill knowledge to a smaller 7B model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 302, + 547, + 525, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 547, + 525, + 628 + ], + "spans": [ + { + "bbox": [ + 302, + 547, + 525, + 628 + ], + "type": "text", + "content": "To fine-tune the smaller model, we employ Supervised Fine-Tuning (SFT) with LoRA (Hu et al., 2021). Our experiments show that this straightforward distillation method significantly enhances the performance of smaller models. See Appendix C.1.3 for more training details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 302, + 640, + 514, + 666 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 640, + 514, + 666 + ], + "spans": [ + { + "bbox": [ + 302, + 640, + 514, + 666 + ], + "type": "text", + "content": "4 LOC-BENCH: A New Benchmark for Code Localization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 302, + 676, + 476, + 688 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 676, + 476, + 688 + ], + "spans": [ + { + "bbox": [ + 302, + 676, + 476, + 688 + ], + "type": "text", + "content": "4.1 Revisiting Existing Benchmark" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 302, + 693, + 525, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 693, + 525, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 693, + 525, + 775 + ], + "type": "text", + "content": "SWE-Bench(Jimenez et al., 2023) is a widely used benchmark that collects GitHub issues and corresponding code patches that resolve them. Xia et al. (2024); Suresh et al. (2024) adapt its subset, SWE-Bench-Lite, for code localization, treating the patched files and functions as the targets." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 71, + 291, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 71, + 291, + 327 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 291, + 327 + ], + "type": "text", + "content": "However, existing datasets, including SWE-Bench, present challenges for effectively evaluating code localization methods. First, they are at risk of contamination, as they may include data overlapping with the repositories or issues used by modern models during pre-training. Second, existing datasets are not specifically designed for code localization (Tomassi et al., 2019). SWE-Bench, for instance, was created primarily to evaluate end-to-end bug-fixing capabilities, with localization being only an implicit intermediate step. This focus results in datasets dominated by bug reports (85% of SWE-Bench-Lite examples) while severely underrepresenting other common software maintenance tasks such as feature requests (14%), security vulnerabilities (1%), and performance optimizations (0%). This imbalance fails to capture the diverse localization challenges faced in real-world software development." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 338, + 193, + 349 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 338, + 193, + 349 + ], + "spans": [ + { + "bbox": [ + 69, + 338, + 193, + 349 + ], + "type": "text", + "content": "4.2 Dataset Construction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 354, + 290, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 354, + 290, + 502 + ], + "spans": [ + { + "bbox": [ + 69, + 354, + 290, + 502 + ], + "type": "text", + "content": "To address the limitations of existing benchmarks, we introduce LOC-BENCH, a new dataset specifically designed for code localization. This dataset collects up-to-date issues from Python repositories to mitigate the influence of pre-training bias in the latest LLMs. Additionally, LOC-BENCH covers wider categories, including bug reports, feature requests, security, and performance issues, enabling a more comprehensive evaluation of code localization methods. The statistics of LOC-BENCH are shown in Table 3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 503, + 290, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 503, + 290, + 651 + ], + "spans": [ + { + "bbox": [ + 69, + 503, + 290, + 651 + ], + "type": "text", + "content": "For the Bug Report category, we collect GitHub issues created after October 2024, which is later than the release dates of most modern LLMs. To enrich the dataset with more instances of security and performance issues, we use the GitHub Search API to search for relevant keywords, such as \"latency improvement\" for performance-related issues. We exclude instances that involve modifying more than five Python files or more than ten functions in the corresponding patch. For further details, see Appendix B.1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 661, + 153, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 661, + 153, + 675 + ], + "spans": [ + { + "bbox": [ + 69, + 661, + 153, + 675 + ], + "type": "text", + "content": "5 Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 681, + 290, + 773 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 681, + 290, + 773 + ], + "spans": [ + { + "bbox": [ + 69, + 681, + 290, + 773 + ], + "type": "text", + "content": "Our experiments aim to evaluate four key aspects of LOCAGENT: (1) the effectiveness of our graph-based representation and tooling for code localization compared to existing methods, (2) the performance of fine-tuned open-source models as cost-effective alternatives to proprietary LLMs, (3) a detailed analysis of how performance varies across" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 312, + 69, + 517, + 223 + ], + "blocks": [ + { + "bbox": [ + 312, + 69, + 517, + 223 + ], + "lines": [ + { + "bbox": [ + 312, + 69, + 517, + 223 + ], + "spans": [ + { + "bbox": [ + 312, + 69, + 517, + 223 + ], + "type": "table", + "html": "
DatasetCategory#Sample
SWE-Bench-Lite (Total = 300)Bug Report254
Feature Request43
Security Issue3
Performance Issue0
Loc-Bench (Totoal = 560)Bug Report242
Feature Request150
Security Issue29
Performance Issue139
", + "image_path": "dffede0cb6e1140d33ef35874b6f55be329c72cec08ada3fd8a7e8684a261136.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 232, + 524, + 256 + ], + "lines": [ + { + "bbox": [ + 304, + 232, + 524, + 256 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 524, + 256 + ], + "type": "text", + "content": "Table 3: Distribution of samples across different categories in the SWE-Bench-Lite and Loc-Bench datasets." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 267, + 524, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 524, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 524, + 359 + ], + "type": "text", + "content": "task categories, and (4) the contribution of each component in our framework through comprehensive ablation studies. We evaluate on both SWE-Bench-Lite and our introduced Loc-Bench dataset. Additionally, we examine the impact of improved localization on downstream software maintenance tasks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 364, + 433, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 433, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 433, + 378 + ], + "type": "text", + "content": "5.1 Experimental Settings" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 383, + 524, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 524, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 524, + 476 + ], + "type": "text", + "content": "Datasets. We first conduct experiments on SWEBench-Lite, treating the patched files and functions as the targets for localization. Following Suresh et al. (2024), we excluded examples where no existing functions were modified by the patch, ultimately retaining 274 out of the original 300 examples." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 478, + 524, + 719 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 478, + 524, + 719 + ], + "spans": [ + { + "bbox": [ + 304, + 478, + 524, + 719 + ], + "type": "text", + "content": "Metrics. To assess performance, we use a modified accuracy metric inspired by R-Precision from information retrieval, following Agentless(Xia et al., 2024). To assess performance, we use Acc@k (Accuracy at k) as our evaluation metric, following Agentless(Xia et al., 2024). For each example, we select the top-k predicted locations and consider a localization attempt successful only if all relevant locations are correctly identified within these top-k predictions. This approach measures the ability to fully identify all necessary code sections that require modification. We report results across multiple " + }, + { + "bbox": [ + 304, + 478, + 524, + 719 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 478, + 524, + 719 + ], + "type": "text", + "content": " values: file localization at Acc@1, Acc@3, and Acc@5, and function localization at Acc@5 and Acc@10. Additionally, to provide a more relaxed evaluation criteria, we assess module localization, which only requires finding any function within the patched class." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 730, + 373, + 742 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 730, + 373, + 742 + ], + "spans": [ + { + "bbox": [ + 304, + 730, + 373, + 742 + ], + "type": "text", + "content": "5.2 Baselines" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 749, + 524, + 773 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 749, + 524, + 773 + ], + "spans": [ + { + "bbox": [ + 304, + 749, + 524, + 773 + ], + "type": "text", + "content": "We evaluate LOCAGENT against three categories of competitive baselines: (a) Retrieval-based meth" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 54, + 525, + 253 + ], + "blocks": [ + { + "bbox": [ + 71, + 54, + 525, + 253 + ], + "lines": [ + { + "bbox": [ + 71, + 54, + 525, + 253 + ], + "spans": [ + { + "bbox": [ + 71, + 54, + 525, + 253 + ], + "type": "table", + "html": "
TypeMethodLoc-ModelFile (%)Module (%)Function (%)
Acc@1Acc@3Acc@5Acc@5Acc@10Acc@5Acc@10
Embedding-BasedBM25 (Robertson et al., 1994)38.6951.8261.6845.2652.9231.7536.86
E5-base-v2 (Wang et al., 2022)49.6474.4580.2967.8872.2639.4251.09
Jina-Code-v2 (Günther et al., 2023)43.4371.1780.2963.5072.6342.3452.19
Codesage-large-v2 (Zhang et al., 2024)47.8169.3478.1060.5869.7133.9444.53
CodeRankEmbed (Suresh et al., 2024)52.5577.7484.6771.9078.8351.8258.76
Procedure-BasedAgentless (Xia et al., 2024)GPT-4o67.1574.4574.4567.1567.1555.4755.47
Claude-3.572.6379.2079.5668.9868.9858.7658.76
Agent-BasedMoutlessTools (Örwall, 2024)GPT-4o73.3684.3185.0474.8276.2857.3059.49
Claude-3.572.6385.7786.1376.2876.2864.6064.96
SWE-agent (Yang et al., 2024)GPT-4o57.3064.9668.9858.0358.0345.9946.35
Claude-3.577.3787.2390.1577.7478.1064.2364.60
Openhands (Wang et al., 2025)GPT-4o60.9571.9073.7262.4163.8749.6450.36
Claude-3.576.2889.7890.1583.2183.5868.2570.07
LOCAGENT (Ours)Qwen2.5-7B(ft)70.8084.6788.3281.0282.8564.2371.53
Qwen2.5-32B(ft)75.9190.5192.7085.7787.2371.9077.01
Claude-3.577.7491.9794.1686.5087.5973.3677.37
", + "image_path": "ad9888427e4959ea8df866a9f22f434e24d97aa01a98851cc1f0d57d84fed76f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 260, + 526, + 321 + ], + "lines": [ + { + "bbox": [ + 67, + 260, + 526, + 321 + ], + "spans": [ + { + "bbox": [ + 67, + 260, + 526, + 321 + ], + "type": "text", + "content": "Table 4: Performance comparison with baseline methods on code localization on SWE-bench lite. Results show the accuracy at file, module, and function levels. For Agent-Based methods, we use GPT-4o-2024-0513 (abbr. as GPT-4o) and Claude-3-5-sonnet-20241022 (abbr. as Claude-3.5) as the localization model. Additionally, the performance of our fine-tuned open-source models, Qwen2.5-7B(ft) and Qwen2.5-32B(ft), are included for comparison." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 66, + 327, + 292, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 327, + 292, + 613 + ], + "spans": [ + { + "bbox": [ + 66, + 327, + 292, + 613 + ], + "type": "text", + "content": "ods: We include the sparse retrieval approach BM25 (Robertson et al., 1994) and several state-of-the-art embedding models, including the general-purpose E5-base-v2 (Wang et al., 2022) and specialized code embedding models such as JinaCode-v2 (Günther et al., 2023), Codesage-large-v2 (Zhang et al., 2024), and the current SOTA code embedding model CodeRankEmbed (Suresh et al., 2024). Proprietary embedding solutions were excluded due to API costs. (b) Procedure-based methods: We compare against Agentless (Xia et al., 2024), which employs a structured hierarchical approach to code localization without complex agent architectures. (c) Agent-based methods: We include several advanced agent frameworks designed for code exploration and modification, specifically OpenHands (Wang et al., 2025) (using its default CodeActAgent implementation), SWE-Agent (Yang et al., 2024), and MoatlessTools (Örwall, 2024). For implementation details, please refer to Appendix C.1.1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 622, + 281, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 622, + 281, + 634 + ], + "spans": [ + { + "bbox": [ + 67, + 622, + 281, + 634 + ], + "type": "text", + "content": "5.3 Evaluation Results on SWE-Bench-Lite" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 640, + 292, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 640, + 292, + 775 + ], + "spans": [ + { + "bbox": [ + 67, + 640, + 292, + 775 + ], + "type": "text", + "content": "As shown in Table 4, Agent-Based methods consistently outperform other approaches, and our method demonstrates competitive performance by achieving the best results across all levels of code localization. Unlike traditional retrieval-based methods, Agentless identifies only a limited number of locations due to its narrow repository scope, which hinders performance gains when considering a broader set of candidates. The results of the NDCG are presented in Table 11 in the Appendix." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 310, + 323, + 518, + 430 + ], + "blocks": [ + { + "bbox": [ + 310, + 323, + 518, + 430 + ], + "lines": [ + { + "bbox": [ + 310, + 323, + 518, + 430 + ], + "spans": [ + { + "bbox": [ + 310, + 323, + 518, + 430 + ], + "type": "image", + "image_path": "f929dd53f4adf74c47eab0524e9c10d9df2c8753a81e68bd756d7c86d5d4876b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 311, + 433, + 518, + 540 + ], + "blocks": [ + { + "bbox": [ + 311, + 433, + 518, + 540 + ], + "lines": [ + { + "bbox": [ + 311, + 433, + 518, + 540 + ], + "spans": [ + { + "bbox": [ + 311, + 433, + 518, + 540 + ], + "type": "image", + "image_path": "dd0a043ec99e4aa7d3cdd9cab21f0f8c8ff70d258cc383c3b7961f81be3880dc.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 302, + 549, + 526, + 623 + ], + "lines": [ + { + "bbox": [ + 302, + 549, + 526, + 623 + ], + "spans": [ + { + "bbox": [ + 302, + 549, + 526, + 623 + ], + "type": "text", + "content": "Figure 3: Performance analysis at different difficulty levels for file- and function-level localization. All agent-based methods and Agentless use Claude-3.5 as the localization model. Hop " + }, + { + "bbox": [ + 302, + 549, + 526, + 623 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 302, + 549, + 526, + 623 + ], + "type": "text", + "content": " refers to the distances between functions mentioned in the issue description and the ground truth patch on our code graph." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 302, + 640, + 526, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 640, + 526, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 640, + 526, + 775 + ], + "type": "text", + "content": "To further analyze the results, we examine performance across different task difficulty levels. We measure the task difficulty by calculating the shortest hops between the functions mentioned in the issue descriptions and the patched functions on our code graph (See Appendix C.1.2 for more details). As shown in Figure 3, performance decreases for all methods as the task becomes more challenging. However, Agent-based methods demonstrate better robustness as the difficulty increases, with" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 63, + 283, + 176 + ], + "blocks": [ + { + "bbox": [ + 75, + 63, + 283, + 176 + ], + "lines": [ + { + "bbox": [ + 75, + 63, + 283, + 176 + ], + "spans": [ + { + "bbox": [ + 75, + 63, + 283, + 176 + ], + "type": "image", + "image_path": "594e4e848668151fa0f0d585dcf3a37fcc51677d8a82c5fdceaf97947d73c7bb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 190, + 291, + 250 + ], + "lines": [ + { + "bbox": [ + 67, + 190, + 291, + 250 + ], + "spans": [ + { + "bbox": [ + 67, + 190, + 291, + 250 + ], + "type": "text", + "content": "Figure 4: Comparison of performance between the original and fine-tuned Qwen models. The metrics used are file-level Acc@5 and module/function-level Acc@10. Dashed lines represent the performance of the Claude-3.5 model for reference." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 260, + 291, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 260, + 291, + 423 + ], + "spans": [ + { + "bbox": [ + 67, + 260, + 291, + 423 + ], + "type": "text", + "content": "our method maintaining competitive performance across various difficulty levels. Retrieval-based methods, such as E5-Base-v2 and CodeRankEmbed, perform poorly at the function level, even when the patched functions are explicitly mentioned in the query. This is because they treat the query as a whole, failing to capture fine-grained details. Agentless performs even worse than retrieval-based methods when exploration beyond the query is needed (" + }, + { + "bbox": [ + 67, + 260, + 291, + 423 + ], + "type": "inline_equation", + "content": "hop \\geq 0" + }, + { + "bbox": [ + 67, + 260, + 291, + 423 + ], + "type": "text", + "content": ") due to its simplistic localization process and limited view focused only on the repository structure." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 433, + 246, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 433, + 246, + 445 + ], + "spans": [ + { + "bbox": [ + 67, + 433, + 246, + 445 + ], + "type": "text", + "content": "5.4 Fine-tuned Open-source Models" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 449, + 291, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 449, + 291, + 680 + ], + "spans": [ + { + "bbox": [ + 67, + 449, + 291, + 680 + ], + "type": "text", + "content": "Figure 4 demonstrates that after fine-tuning, both the 7B and 32B models show significant improvements on this task. LOCAGENT with finetuned Qwen-2.5-Coder-Instruct-32B (abbreviated as Qwen2.5-32B(ft)) achieves performance comparable to Claude-3.5, and LOCAGENT with Qwen2.5-7B(ft) also delivers results on par with that obtained using GPT-4o. As shown in Table 4, our method with Qwen2.5-32B(ft) outperforms nearly all baselines, including those that use larger and more powerful LLMs. The original 7B model performs poorly due to its limited tool-use capability (Chen et al., 2024). These results validate the feasibility of deploying our fine-tuned open-source models as promising alternatives to proprietary APIs, especially in resource-constrained applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 689, + 185, + 703 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 689, + 185, + 703 + ], + "spans": [ + { + "bbox": [ + 67, + 689, + 185, + 703 + ], + "type": "text", + "content": "5.5 Efficiency Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 708, + 291, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 708, + 291, + 775 + ], + "spans": [ + { + "bbox": [ + 67, + 708, + 291, + 775 + ], + "type": "text", + "content": "Table 5 presents an efficiency analysis comparing agent-based methods in terms of cost and the number of agent interactions required. MoatlessTools demonstrates good cost-efficiency and requires relatively fewer rounds of interaction. However, the" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 302, + 68, + 520, + 180 + ], + "blocks": [ + { + "bbox": [ + 302, + 68, + 520, + 180 + ], + "lines": [ + { + "bbox": [ + 302, + 68, + 520, + 180 + ], + "spans": [ + { + "bbox": [ + 302, + 68, + 520, + 180 + ], + "type": "table", + "html": "
MethodLM#RoundCost($)Acc@10
Cost
MoatlessToolsGPT-4o50.461.3
Claude-3.550.461.4
SWE-agentGPT-4o80.560.8
Claude-3.590.671.0
OpenhandsGPT-4o150.830.6
Claude-3.5130.790.9
OursClaude-3.570.661.2
Qwen2.5-7B(ft)60.0513.2
Qwen2.5-32B(ft)90.098.6
", + "image_path": "ca58188c6fe4c2ffec34aeccdb6ee5a73bdf63c458fea192f02d6865ca76db6a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 304, + 253, + 523, + 371 + ], + "blocks": [ + { + "bbox": [ + 302, + 184, + 525, + 244 + ], + "lines": [ + { + "bbox": [ + 302, + 184, + 525, + 244 + ], + "spans": [ + { + "bbox": [ + 302, + 184, + 525, + 244 + ], + "type": "text", + "content": "Table 5: Efficiency analysis comparing the average cost and number of agent interaction rounds required by different methods. The cost-efficiency of each method is evaluated using the ratio of function-level Acc@10 to average cost." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 304, + 253, + 523, + 371 + ], + "lines": [ + { + "bbox": [ + 304, + 253, + 523, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 523, + 371 + ], + "type": "table", + "html": "
Model SettingFile Acc@5Module Acc@10Function Acc@10
Ours88.3282.8571.53
w/o TraverseGraph86.1378.4766.06
Relation Types: contain86.5079.5666.42
Traverse Hops: 186.8680.2966.79
w/o RetrieveEntity87.5981.3969.34
w/o SearchEntity68.9861.3153.28
w/o BM25 index75.1868.9860.22
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The impact of removing or fixing components is analyzed to observe how each component contributes to the overall accuracy." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 301, + 460, + 526, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 460, + 526, + 690 + ], + "spans": [ + { + "bbox": [ + 301, + 460, + 526, + 690 + ], + "type": "text", + "content": "dense embeddings it uses make it difficult and slow to adapt to fast-evolving codebases. SWE-agent and Openhands also show moderate costs but still do not match the efficiency of LOCAGENT. For LOCAGENT with Claude-3.5, although more rounds of interaction are required, the cost remains lower than that of Openhands, illustrating the token efficiency of our tool's outputs. LOCAGENT with fine-tuned Qwen models stands out for its superior efficiency1. Qwen2.5-7B(ft) is the most cost-efficient option, requiring only $0.05 per example, while Qwen2.5-32B(ft) offers a more cost-effective alternative to Claude-3.5. These results highlight the potential of fine-tuned open-source models as efficient alternatives, providing an optimal balance of cost-effectiveness and performance that surpasses other methods." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 713, + 525, + 775 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 713, + 525, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 713, + 525, + 775 + ], + "type": "text", + "content": "1We calculate the cost based on the prices from AI inference providers (Hyperbolic, 2025; artificialanalysis.ai, 2025). Specifically, for the Qwen2.5-32B(ft) model, the cost is $0.20/1M tokens for both input and output. For the Qwen2.5-7B(ft) model, the cost is $0.14/1M tokens for input and $0.28/1M tokens for output." + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 68, + 71, + 166, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 71, + 166, + 84 + ], + "spans": [ + { + "bbox": [ + 68, + 71, + 166, + 84 + ], + "type": "text", + "content": "5.6 Ablation Study" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 90, + 290, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 90, + 290, + 156 + ], + "spans": [ + { + "bbox": [ + 67, + 90, + 290, + 156 + ], + "type": "text", + "content": "We conduct an ablation study to evaluate the effectiveness of each component of our toolsets. Due to budget constraints, we use the fine-tuned Qwen-2.5-7B as the localization model for these experiments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 158, + 291, + 634 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 67, + 158, + 290, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 158, + 290, + 266 + ], + "spans": [ + { + "bbox": [ + 67, + 158, + 290, + 266 + ], + "type": "text", + "content": "(1) Each tool in our toolset plays a critical role in code localization performance. As shown in Table 6, removing any tool, especially the SearchEntity tool, leads to varying degrees of accuracy degradation, particularly in module and function level localization. This highlights the critical role each tool plays in identifying relevant modules and functions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 269, + 291, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 269, + 291, + 442 + ], + "spans": [ + { + "bbox": [ + 69, + 269, + 291, + 442 + ], + "type": "text", + "content": "(2) The graph structure provides essential information for accurate code localization. Removing TraverseGraph tool decreases module and function level performance since the agent cannot obtain any structure information about the codebase and relies on reasoning capability to identify call relationship or directory structure. Adding contain relationship provides only marginal improvements compared to fully removing TraverseGraph, emphasizing the importance of the other three relationship types and explaining why our method surpasses others relying only on the repository structure." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 444, + 290, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 444, + 290, + 539 + ], + "spans": [ + { + "bbox": [ + 67, + 444, + 290, + 539 + ], + "type": "text", + "content": "(3) Multi-hop exploration is crucial for deep code understanding. When compared to the full setting, fixing " + }, + { + "bbox": [ + 67, + 444, + 290, + 539 + ], + "type": "inline_equation", + "content": "Hops = 1" + }, + { + "bbox": [ + 67, + 444, + 290, + 539 + ], + "type": "text", + "content": " leads to a moderate decline in file and module-level accuracy, but it causes a more significant decrease in function-level accuracy, underscoring the importance of multi-hop exploration for identifying relevant entities." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 540, + 290, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 540, + 290, + 634 + ], + "spans": [ + { + "bbox": [ + 67, + 540, + 290, + 634 + ], + "type": "text", + "content": "(4) Sparse indexing significantly enhances localization performance. Removing SearchEntity tool, or even partial removal of its index, causes a substantial drop in performance across all metrics. This demonstrates the effectiveness of building a sparse index on our code graph for improving localization performance." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 67, + 647, + 250, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 647, + 250, + 660 + ], + "spans": [ + { + "bbox": [ + 67, + 647, + 250, + 660 + ], + "type": "text", + "content": "5.7 Evaluation Results on Loc-Bench" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 666, + 290, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 666, + 290, + 775 + ], + "spans": [ + { + "bbox": [ + 67, + 666, + 290, + 775 + ], + "type": "text", + "content": "To ensure the robustness and generalization of our methods and fine-tuned Qwen models, and to eliminate potential data leakage, we evaluate our new dataset. Since Loc-Bench includes examples that edit 1 to 5 files, we assess file localization at top-5 and top-10 ranks, and function/module localization at top-10 and top-15 ranks. Table 7 shows that our fine-tuned Qwen2.5-7B model exhibits strong gen" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 67, + 518, + 164 + ], + "blocks": [ + { + "bbox": [ + 310, + 67, + 518, + 164 + ], + "lines": [ + { + "bbox": [ + 310, + 67, + 518, + 164 + ], + "spans": [ + { + "bbox": [ + 310, + 67, + 518, + 164 + ], + "type": "image", + "image_path": "40113cdec1e1feca7000cb77d3a5294a6135d63a0d343288699aecc05a7b7a58.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 311, + 168, + 518, + 265 + ], + "blocks": [ + { + "bbox": [ + 311, + 168, + 518, + 265 + ], + "lines": [ + { + "bbox": [ + 311, + 168, + 518, + 265 + ], + "spans": [ + { + "bbox": [ + 311, + 168, + 518, + 265 + ], + "type": "image", + "image_path": "f3ff500f60d006d9ab2100b2e34cdaaed024cc944a6d5f1861937bb334d1a3cf.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 302, + 273, + 525, + 321 + ], + "lines": [ + { + "bbox": [ + 302, + 273, + 525, + 321 + ], + "spans": [ + { + "bbox": [ + 302, + 273, + 525, + 321 + ], + "type": "text", + "content": "Figure 5: Performance analysis at different difficulty category for file- and function-level localization. All agent-based baselines and Agentless use Claude-3.5 as the localization model." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 301, + 336, + 525, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 336, + 525, + 457 + ], + "spans": [ + { + "bbox": [ + 301, + 336, + 525, + 457 + ], + "type": "text", + "content": "eralization capabilities, maintaining competitive performance compared to SWE-agent using more expensive and strong model. These results highlight the practicality of the fine-tuned Qwen2.5-7B model for real-world applications. Despite being an open-source alternative, it achieves a performance comparable to Claude-3.5, supporting its feasibility as a cost-effective substitute for commercial models in practical scenarios." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 302, + 459, + 525, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 459, + 525, + 675 + ], + "spans": [ + { + "bbox": [ + 302, + 459, + 525, + 675 + ], + "type": "text", + "content": "Additionally, we evaluate the performance across four different difficulty categories. Figure 5 clearly shows that our method outperforms other methods in almost all categories of code localization. However, it also highlights a noticeable decrease in performance across the other three categories compared to the Bug Report category. This performance gap likely reflects our training data distribution, which contained more bug report examples, potentially leading to scaffolds better optimized for bug localization tasks. This trend suggests that while our method is highly effective for bug report localization, there is still room for improvement in handling the other categories through more balanced training data and category-specific optimization strategies." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 302, + 687, + 524, + 714 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 687, + 524, + 714 + ], + "spans": [ + { + "bbox": [ + 302, + 687, + 524, + 714 + ], + "type": "text", + "content": "5.8 Application: Better Localization Leads to More Solved GitHub Issues" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 302, + 720, + 524, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 720, + 524, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 720, + 524, + 775 + ], + "type": "text", + "content": "To assess the impact of localization methods on downstream tasks, we evaluated their effectiveness in solving GitHub issues. We choose Agentless as the baseline, ranking among the top-performing" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 9 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 88, + 68, + 503, + 190 + ], + "blocks": [ + { + "bbox": [ + 88, + 68, + 503, + 190 + ], + "lines": [ + { + "bbox": [ + 88, + 68, + 503, + 190 + ], + "spans": [ + { + "bbox": [ + 88, + 68, + 503, + 190 + ], + "type": "table", + "html": "
MethodLoc ModelFile (%)Module (%)Function (%)
Acc@5Acc@10Acc@10Acc@15Acc@10Acc@15
IR-BasedCodeRankEmbed74.2980.8963.2167.5043.3946.61
AgentlessClaude-3.567.5067.5053.3953.3942.6842.68
OpenHandsClaude-3.579.8280.0068.9369.1159.1159.29
SWE-agentClaude-3.577.6877.6863.5763.7551.9651.96
LocAgent (Ours)Qwen2.5-7B(ft)78.5779.6463.0463.0451.4351.79
Claude-3.583.3986.0770.8971.0759.2960.71
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MethodLocalization LMAcc@5Pass@1Pass@10
AgentlessClaude-3.558.3926.3133.58
OursQwen2.5-32B(ft)69.3426.7936.13
Claude-3.573.3627.9237.59
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Table 8 shows that the success rate for solving GitHub issues improves significantly with better code localization accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 425, + 147, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 425, + 147, + 437 + ], + "spans": [ + { + "bbox": [ + 67, + 425, + 147, + 437 + ], + "type": "text", + "content": "6 Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 446, + 291, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 446, + 291, + 581 + ], + "spans": [ + { + "bbox": [ + 67, + 446, + 291, + 581 + ], + "type": "text", + "content": "In conclusion, LOCAGENT enhances code localization by structuring codebases as graphs, enabling efficient repository-level exploration for LLM agents. With fine-tuned open-source models, our method achieves high localization accuracy while significantly reducing costs compared to larger proprietary models. Experimental results demonstrate the effectiveness of LOCAGENT in identifying relevant code components and improving downstream tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 592, + 130, + 603 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 592, + 130, + 603 + ], + "spans": [ + { + "bbox": [ + 67, + 592, + 130, + 603 + ], + "type": "text", + "content": "Limitations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 613, + 290, + 734 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 613, + 290, + 734 + ], + "spans": [ + { + "bbox": [ + 67, + 613, + 290, + 734 + ], + "type": "text", + "content": "First, our study primarily focused on fine-tuning Qwen-2.5-Coder models. Exploring a broader range of base models, including other open-source LLMs like CodeLlama, Mistral, or Yi, could provide valuable insights into model selection trade-offs. Additionally, investigating different finetuning approaches beyond LoRA, such as full finetuning or other parameter-efficient methods, could potentially yield better performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 735, + 290, + 776 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 735, + 290, + 776 + ], + "spans": [ + { + "bbox": [ + 67, + 735, + 290, + 776 + ], + "type": "text", + "content": "Second, though we demonstrated improved bug repair performance with better localization, we only scratched the surface of potential downstream" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 302, + 232, + 526, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 232, + 526, + 312 + ], + "spans": [ + { + "bbox": [ + 302, + 232, + 526, + 312 + ], + "type": "text", + "content": "applications. Future work should evaluate LocAgent's impact on other software engineering tasks like refactoring, feature addition, security vulnerability patching, and performance optimization. This would provide a more comprehensive understanding of the framework's practical utility." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 302, + 313, + 526, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 313, + 526, + 449 + ], + "spans": [ + { + "bbox": [ + 302, + 313, + 526, + 449 + ], + "type": "text", + "content": "Moreover, our fine-tuning process relied heavily on trajectories generated by Claude-3.5 and the fine-tuned Qwen2.5-32B model. A more diverse training dataset incorporating examples from different models, tasks, and repositories could improve the robustness and generalization of fine-tuned models. Additionally, analyzing the impact of different dataset compositions and filtering strategies on model performance could yield valuable insights." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 302, + 449, + 527, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 449, + 527, + 558 + ], + "spans": [ + { + "bbox": [ + 302, + 449, + 527, + 558 + ], + "type": "text", + "content": "Finally, the current evaluation focuses primarily on Python codebases. Extending LOCAGENT to support other programming languages and evaluating its performance across different language paradigms would better demonstrate its generalizability. Further, our evaluation metrics could be expanded to include more nuanced measures of localization quality beyond accuracy and NDCG." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 581, + 362, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 362, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 362, + 593 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 303, + 600, + 526, + 775 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 303, + 600, + 524, + 624 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 600, + 524, + 624 + ], + "spans": [ + { + "bbox": [ + 303, + 600, + 524, + 624 + ], + "type": "text", + "content": "Aider. 2023. Building a better repository map with tree sitter. Accessed: April 15, 2025." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 303, + 632, + 525, + 655 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 632, + 525, + 655 + ], + "spans": [ + { + "bbox": [ + 303, + 632, + 525, + 655 + ], + "type": "text", + "content": "Anthropic. 2023. Claude: Conversational ai by anthropic. Accessed: January 21, 2025." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 303, + 664, + 526, + 698 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 664, + 526, + 698 + ], + "spans": [ + { + "bbox": [ + 303, + 664, + 526, + 698 + ], + "type": "text", + "content": "artificialanalysis.ai. 2025. Artificial analysis. https://artificialanalysis.ai/models/. 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Moatless tools." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 12 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 70, + 230, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 70, + 230, + 84 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 230, + 84 + ], + "type": "text", + "content": "A LOCAGENT Design Details" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 92, + 190, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 92, + 190, + 105 + ], + "spans": [ + { + "bbox": [ + 67, + 92, + 190, + 105 + ], + "type": "text", + "content": "A.1 Tool Output Design" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 67, + 110, + 278, + 137 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 110, + 278, + 137 + ], + "spans": [ + { + "bbox": [ + 67, + 110, + 278, + 137 + ], + "type": "text", + "content": "A.1.1 Three-level format for SearchEntity output" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 140, + 290, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 140, + 290, + 260 + ], + "spans": [ + { + "bbox": [ + 67, + 140, + 290, + 260 + ], + "type": "text", + "content": "Once invoked by the LLM agent, the retrieval APIs search for files, classes, methods, and code snippets in the codebase, and return the results back to the agent. To avoid forming very lengthy code context that may containing noisy information to LLM, we return only necessary information as API outputs. To achieve this, we desgined four granular standard output formats (Figure 6): fold, preview, full code." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 269, + 279, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 269, + 279, + 296 + ], + "spans": [ + { + "bbox": [ + 67, + 269, + 279, + 296 + ], + "type": "text", + "content": "A.1.2 Tree-based Subgraph Formatting for TraverseGraph Output" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 300, + 290, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 300, + 290, + 434 + ], + "spans": [ + { + "bbox": [ + 67, + 300, + 290, + 434 + ], + "type": "text", + "content": "The TraverseGraph tool traverses the code graph and returns a local subgraph for each input entity. The agent reasons about these subgraphs to understand each entity's complex dependencies. However, reasoning about graphs remains challenging for LLMs. Research by (Fatemi et al., 2023) demonstrates that LLM performance varies significantly based on graph formatting (how graphs are encoded as text). This makes the format design for output subgraphs crucial." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 435, + 292, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 435, + 292, + 569 + ], + "spans": [ + { + "bbox": [ + 67, + 435, + 292, + 569 + ], + "type": "text", + "content": "We have developed a new tree-based format, shown in Figure 7, with several features that enhance LLM reasoning: (1) We represent subgraphs as trees, allowing LLMs to use indentation to determine a node's distance from the root, (2) We display complete entity IDs for each node (e.g., django/core-validators.py:RegexValidator) to help LLMs locate nodes easily, and (3) We explicitly specify relation types for each edge, including reversed relations" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 571, + 291, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 571, + 291, + 704 + ], + "spans": [ + { + "bbox": [ + 67, + 571, + 291, + 704 + ], + "type": "text", + "content": "To evaluate how different graph formats impact code localization performance, we conducted an experiment using 37 challenging samples from SWEBench-Lite. These samples were considered \"challenging\" because they could not be solved by any baseline agent methods. Using Claude-3.5 as the Localization Model across all settings, we compared various output formats. Table 9 presents our findings. The baseline output formats we tested are described below:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 80, + 716, + 290, + 743 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 716, + 290, + 743 + ], + "spans": [ + { + "bbox": [ + 80, + 716, + 290, + 743 + ], + "type": "text", + "content": "- row: For each line, list one row of the adjacency matrix. For example," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 88, + 748, + 290, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 748, + 290, + 775 + ], + "spans": [ + { + "bbox": [ + 88, + 748, + 290, + 775 + ], + "type": "text", + "content": "function \"fileA.py:funcA\" invokes function \"fileA.py:funcB\", \"fileA.py:funcC\"" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 71, + 525, + 160 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 315, + 71, + 525, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 71, + 525, + 97 + ], + "spans": [ + { + "bbox": [ + 315, + 71, + 525, + 97 + ], + "type": "text", + "content": "- row (w/ entity attributes): Additionally include entity attributes for format row." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 316, + 106, + 525, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 106, + 525, + 160 + ], + "spans": [ + { + "bbox": [ + 316, + 106, + 525, + 160 + ], + "type": "text", + "content": "- incident: The incident format mentioned in (Fatemi et al., 2023). An integer instead of entity ID is used to represent each node. For example," + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 322, + 165, + 524, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 165, + 524, + 205 + ], + "spans": [ + { + "bbox": [ + 322, + 165, + 524, + 205 + ], + "type": "text", + "content": "Map function \"fileA.py:funcA\" to index 0. Map function \"fileA.py:funcB\" to index 1. Map function \"fileA.py:funcC\" to index 2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 323, + 210, + 464, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 210, + 464, + 223 + ], + "spans": [ + { + "bbox": [ + 323, + 210, + 464, + 223 + ], + "type": "text", + "content": "function " + }, + { + "bbox": [ + 323, + 210, + 464, + 223 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 323, + 210, + 464, + 223 + ], + "type": "text", + "content": " invokes function 1,2." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 316, + 231, + 524, + 293 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 316, + 231, + 524, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 231, + 524, + 258 + ], + "spans": [ + { + "bbox": [ + 316, + 231, + 524, + 258 + ], + "type": "text", + "content": "Graphviz DOT: Represent graph in Graphviz DOT language (Ellson et al., 2002)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 316, + 267, + 524, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 267, + 524, + 293 + ], + "spans": [ + { + "bbox": [ + 316, + 267, + 524, + 293 + ], + "type": "text", + "content": "- JSON: Expand the subgraph as a tree, and convert it to JSON format." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 302, + 302, + 526, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 302, + 526, + 464 + ], + "spans": [ + { + "bbox": [ + 302, + 302, + 526, + 464 + ], + "type": "text", + "content": "As shown in Table 9, expanding subgraphs as trees (i.e., JSON, tree-based) can significantly improve the performance. Our tree-based format achieves the best overall performance across different levels of localization tasks. We also test returning entity attributes along with subgraphs. We notice that row (w/ entity attributes) consistently underperforms row, indicating the attributes for all the nodes may be very noisy. Besides, although using incident format can simplify the output and show improvements in file-level localization, it degradation the module- and file-level localization." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 302, + 474, + 408, + 486 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 474, + 408, + 486 + ], + "spans": [ + { + "bbox": [ + 302, + 474, + 408, + 486 + ], + "type": "text", + "content": "A.2 Implementation" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 301, + 491, + 525, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 491, + 525, + 693 + ], + "spans": [ + { + "bbox": [ + 301, + 491, + 525, + 693 + ], + "type": "text", + "content": "To enable the LLM agent to invoke the Code Localization APIs, we handle the interaction differently based on the LLM's capabilities. For LLMs that support tool-calling features, we define the tools as a list of JSON objects, which are then used as parameters for the API calls. For LLMs that do not support tool-calling (such as Qwen), we provide the description of the API and the expected output as part of the LLM's prompt. When the agent decides to invoke a set of retrieval APIs, it responds with a list of API call names and their corresponding arguments. These retrieval API requests are processed locally by searching over the built code graph. The results from executing these APIs locally are returned to the agent." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 302, + 694, + 525, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 694, + 525, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 694, + 525, + 775 + ], + "type": "text", + "content": "By default, we query the LLM with a temperature setting of 1.0. We conduct two interactions, after which we rerank the results based on mean reciprocal rank (MRR) scores. We also leverage multiprocessing execution to speed up the process. Since all our tools are read-only, LOCAGENT does" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 13 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 72, + 218, + 289 + ], + "blocks": [ + { + "bbox": [ + 76, + 72, + 218, + 289 + ], + "lines": [ + { + "bbox": [ + 76, + 72, + 218, + 289 + ], + "spans": [ + { + "bbox": [ + 76, + 72, + 218, + 289 + ], + "type": "image", + "image_path": "e3da4d4339e99b1a14d6f8d73ea975c643cc44ad95a8dc1803fff42294d4f99a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 297, + 525, + 333 + ], + "lines": [ + { + "bbox": [ + 67, + 297, + 525, + 333 + ], + "spans": [ + { + "bbox": [ + 67, + 297, + 525, + 333 + ], + "type": "text", + "content": "Figure 6: Different output formats designed for efficient agent-code interaction. Left: Full code output when matched entities " + }, + { + "bbox": [ + 67, + 297, + 525, + 333 + ], + "type": "inline_equation", + "content": "\\leq 3" + }, + { + "bbox": [ + 67, + 297, + 525, + 333 + ], + "type": "text", + "content": ". Middle: Preview output showing module skeleton for large files. Right: Fold output showing only entity IDs when matches " + }, + { + "bbox": [ + 67, + 297, + 525, + 333 + ], + "type": "inline_equation", + "content": ">3" + }, + { + "bbox": [ + 67, + 297, + 525, + 333 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 223, + 73, + 370, + 289 + ], + "blocks": [ + { + "bbox": [ + 223, + 73, + 370, + 289 + ], + "lines": [ + { + "bbox": [ + 223, + 73, + 370, + 289 + ], + "spans": [ + { + "bbox": [ + 223, + 73, + 370, + 289 + ], + "type": "image", + "image_path": "003dcde246a439f5b9b36cc33df7c37daaa5e4eaf0478ed30be80b30cbe72965.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 372, + 73, + 519, + 289 + ], + "blocks": [ + { + "bbox": [ + 372, + 73, + 519, + 289 + ], + "lines": [ + { + "bbox": [ + 372, + 73, + 519, + 289 + ], + "spans": [ + { + "bbox": [ + 372, + 73, + 519, + 289 + ], + "type": "image", + "image_path": "86b464c56ef20eb2e4a58b1077f46f88aa113910e37ea427df9e03b94670489d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 160, + 345, + 433, + 535 + ], + "blocks": [ + { + "bbox": [ + 160, + 345, + 433, + 535 + ], + "lines": [ + { + "bbox": [ + 160, + 345, + 433, + 535 + ], + "spans": [ + { + "bbox": [ + 160, + 345, + 433, + 535 + ], + "type": "image", + "image_path": "503072355158697ea6cb6ac7e2712ec0ffc412f1cd70207465e4cb36e21f3c9b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 543, + 524, + 556 + ], + "lines": [ + { + "bbox": [ + 67, + 543, + 524, + 556 + ], + "spans": [ + { + "bbox": [ + 67, + 543, + 524, + 556 + ], + "type": "text", + "content": "Figure 7: A truncated example of the expanded tree-based format for the output subgraph of tool TraverseGraph." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 577, + 289, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 577, + 289, + 603 + ], + "spans": [ + { + "bbox": [ + 67, + 577, + 289, + 603 + ], + "type": "text", + "content": "not require a specialized Docker environment to operate." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 614, + 265, + 626 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 614, + 265, + 626 + ], + "spans": [ + { + "bbox": [ + 68, + 614, + 265, + 626 + ], + "type": "text", + "content": "B Dataset construction and statistics" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 68, + 635, + 227, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 635, + 227, + 647 + ], + "spans": [ + { + "bbox": [ + 68, + 635, + 227, + 647 + ], + "type": "text", + "content": "B.1 Dataset construction details" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 653, + 290, + 747 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 653, + 290, + 747 + ], + "spans": [ + { + "bbox": [ + 67, + 653, + 290, + 747 + ], + "type": "text", + "content": "Example collection. We collected examples on popular Python repositories on Github follow (Jimenez et al., 2023). To gather issues related to performance and security, we searched for the keywords listed in Table 10 using the GitHub Search APIs. We then used GPT-4o-2024-0513 as the classifier based on the issue descriptions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 67, + 748, + 290, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 748, + 290, + 775 + ], + "spans": [ + { + "bbox": [ + 67, + 748, + 290, + 775 + ], + "type": "text", + "content": "Ground Truth Locations. The affected files or functions in the original codebase, as identified in" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 302, + 577, + 526, + 751 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 577, + 526, + 751 + ], + "spans": [ + { + "bbox": [ + 302, + 577, + 526, + 751 + ], + "type": "text", + "content": "the patches, are considered the target locations for the given issue. While it is possible to fix a bug in a location different from the ground truth, the extracted ground-truth locations still serve as approximate targets for localization. Additionally, edited code such as documents, import statements, and comments are excluded from the localization target. These elements are not considered relevant for bug localization, as they do not directly impact the functionality of the code or its execution. By filtering out these elements, the focus is maintained on the core code changes that are relevant for localization." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 14 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 94, + 68, + 500, + 190 + ], + "blocks": [ + { + "bbox": [ + 94, + 68, + 500, + 190 + ], + "lines": [ + { + "bbox": [ + 94, + 68, + 500, + 190 + ], + "spans": [ + { + "bbox": [ + 94, + 68, + 500, + 190 + ], + "type": "table", + "html": "
Output FormatFile(%)Module(%)Function(%)
Acc@1Acc@3Acc@5Acc@5Acc@10Acc@5Acc@10
row41.1867.6570.5961.7661.7635.2938.24
row (w/ entity attributes)41.1864.7164.7150.0050.0032.3532.35
incident41.1870.5973.5355.8855.8829.4132.35
Graphviz DOT41.1873.5382.3564.7164.7135.2935.29
JSON41.1867.6576.4767.6570.5938.2441.18
tree-based (Ours)47.0679.4179.4164.7164.7138.2441.18
", + "image_path": "65aa2b242676fd4ce7ba9e60ceadb537140f50dff384a8c6651710edad591512.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 94, + 219, + 500, + 370 + ], + "blocks": [ + { + "bbox": [ + 129, + 195, + 462, + 208 + ], + "lines": [ + { + "bbox": [ + 129, + 195, + 462, + 208 + ], + "spans": [ + { + "bbox": [ + 129, + 195, + 462, + 208 + ], + "type": "text", + "content": "Table 9: Localization performance under different TraverseGraph output formats." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 94, + 219, + 500, + 370 + ], + "lines": [ + { + "bbox": [ + 94, + 219, + 500, + 370 + ], + "spans": [ + { + "bbox": [ + 94, + 219, + 500, + 370 + ], + "type": "table", + "html": "
CategoryKeywords
Performancebottleneck, performance improvement, memory usage optimization, time complexity reduction, latency improvement, scalability improvement, CPU usage reduction, caching improvement, concurrency optimization
SecurityOut-of-bounds Write, Out-of-bounds Read, NULL Pointer Dereference, Missing Authorization, memory leak fix, security vulnerability, security issue, authentication bypass, authentication issue, better maintained, buffer overflow, denial of service, security hardening, security patch, unsafe deserialization, Use After Free, Integer Overflow or Wraparound, Uncontrolled Resource Consumption, Missing Authentication for Critical Function
", + "image_path": "2976dea7e0ff07dfee13b430fc8f8efa94af68a9c7230eb416ed229809e5c751.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 377, + 524, + 391 + ], + "lines": [ + { + "bbox": [ + 67, + 377, + 524, + 391 + ], + "spans": [ + { + "bbox": [ + 67, + 377, + 524, + 391 + ], + "type": "text", + "content": "Table 10: We use these Keywords to search for Performance and Security related issues with Github Search APIs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 67, + 411, + 214, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 411, + 214, + 425 + ], + "spans": [ + { + "bbox": [ + 67, + 411, + 214, + 425 + ], + "type": "text", + "content": "C Additional Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 433, + 208, + 446 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 433, + 208, + 446 + ], + "spans": [ + { + "bbox": [ + 67, + 433, + 208, + 446 + ], + "type": "text", + "content": "C.1 Implementation Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 450, + 227, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 450, + 227, + 464 + ], + "spans": [ + { + "bbox": [ + 67, + 450, + 227, + 464 + ], + "type": "text", + "content": "C.1.1 Baselines Implementation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 67, + 466, + 291, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 466, + 291, + 615 + ], + "spans": [ + { + "bbox": [ + 67, + 466, + 291, + 615 + ], + "type": "text", + "content": "Regarding the embedding-based methods in our evaluation, these approaches operate primarily at the function level, where each function is embedded as a separate unit. The function's context (its containing file and class) is appended to the function representation before embedding, rather than being embedded separately. While theoretically these methods could employ hierarchical indexing, the standard implementations we evaluated use flat indexing structures where each function is embedded as a single unit." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 616, + 291, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 616, + 291, + 670 + ], + "spans": [ + { + "bbox": [ + 67, + 616, + 291, + 670 + ], + "type": "text", + "content": "We use OpenHands's remote runtime feature to parallelize evaluation on OpenHands and SWEagent. We use Openhands version 0.12.0 released on Oct 31, 2024." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 677, + 280, + 704 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 677, + 280, + 704 + ], + "spans": [ + { + "bbox": [ + 67, + 677, + 280, + 704 + ], + "type": "text", + "content": "C.1.2 Quantifying Task Difficulty Based on Code Graph Distance" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 67, + 708, + 291, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 708, + 291, + 775 + ], + "spans": [ + { + "bbox": [ + 67, + 708, + 291, + 775 + ], + "type": "text", + "content": "We measure task difficulty by computing the average shortest hop distance between the functions mentioned in the issue descriptions and the patched functions within our code graph. Specifically, we first extract potential function names from each" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "spans": [ + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "text", + "content": "issue description using GPT-4o-2024-0513, and identify their corresponding nodes in the code graph using the global dictionary. These identified nodes form the set of predicted nodes, denoted as " + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "text", + "content": ". Similarly, we link the ground truth functions from the patch to their corresponding nodes in the code graph, forming the set of target nodes, denoted as " + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "text", + "content": ". To quantify the difficulty " + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "text", + "content": ", we calculate the average shortest hop distance between the predicted nodes " + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "text", + "content": " and the target nodes " + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 302, + 412, + 526, + 547 + ], + "type": "text", + "content": ", defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 343, + 552, + 485, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 552, + 485, + 583 + ], + "spans": [ + { + "bbox": [ + 343, + 552, + 485, + 583 + ], + "type": "interline_equation", + "content": "\\delta = \\frac {1}{| \\mathcal {C} |} \\sum_ {c \\in \\mathcal {C}} \\frac {1}{m i n _ {t \\in \\mathcal {T}} d (c , t) + 1}", + "image_path": "3501fac23dcf5fe773840a66ad8f7737fdc4bb7268e280936b833deb06905a3d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "spans": [ + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "inline_equation", + "content": "d(c, t)" + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "text", + "content": " represents the shortest hop distance between nodes " + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "text", + "content": " in the graph. For performance analysis stratified by difficulty, we round " + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "text", + "content": " down to " + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "inline_equation", + "content": "\\lfloor \\delta \\rfloor" + }, + { + "bbox": [ + 302, + 590, + 526, + 671 + ], + "type": "text", + "content": " to group samples by difficulty levels, and we exclude samples where the LLM fails to extract any valid function names." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 302, + 677, + 418, + 691 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 677, + 418, + 691 + ], + "spans": [ + { + "bbox": [ + 302, + 677, + 418, + 691 + ], + "type": "text", + "content": "C.1.3 Training details." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 302, + 694, + 525, + 775 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 694, + 525, + 775 + ], + "spans": [ + { + "bbox": [ + 302, + 694, + 525, + 775 + ], + "type": "text", + "content": "Fine-tuning Settings. We use Qwen-2.5-Coder-Instruct (Hui et al., 2024) 7B and 32B variants as our base models. We fine-tuned Qwen-2.5-Coder-Instruct 7B and 32B models on 768 training samples from the SWE-Bench training dataset, leveraging LoRA" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 15 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 69, + 523, + 239 + ], + "blocks": [ + { + "bbox": [ + 71, + 69, + 523, + 239 + ], + "lines": [ + { + "bbox": [ + 71, + 69, + 523, + 239 + ], + "spans": [ + { + "bbox": [ + 71, + 69, + 523, + 239 + ], + "type": "table", + "html": "
TypeMethodLoc-ModelFile (%)Module (%)Function (%)
NDCG@1NDCG@3NDCG@5NDCG@5NDCG@10NDCG@5NDCG@10
Embedding-BasedBM25 (Robertson et al., 2009)38.6946.550.6137.3139.8626.1527.92
E5-base-v2 (Wang et al., 2022)49.6464.1966.653.1554.4531.3935.3
Jina-Code-v2 (Günther et al., 2023)43.4359.9363.751.0254.1333.2836.44
Codesage-large-v2 (Zhang et al., 2024)47.8160.8264.3949.3852.2227.0330.74
CodeRankEmbed (Suresh et al., 2024)52.5567.5470.3957.5159.7640.2842.55
Procedure-BasedAgentless (Xia et al., 2024)GPT-4o67.1571.7671.7664.3164.3153.8153.81
Claude-3.572.6376.7276.8767.3667.3657.5557.55
Agent-BasedMoatlessTools (Örwall, 2024)GPT-4o73.3680.0380.3368.5769.0949.7750.62
Claude-3.572.6380.7380.8869.1169.1153.0353.16
SWE-agent (Yang et al., 2024)GPT-4o57.363.9664.1253.9553.9542.3242.44
Claude-3.577.3784.3284.9372.7772.959.6759.79
Openshands (Wang et al., 2025)GPT-4o60.9567.6268.3958.1858.644.3444.66
Claude-3.576.2884.2784.4375.7975.9263.1363.8
LocAgent (Ours)Qwen2.5-7B(ft)70.8079.3680.970.9971.6855.6258.09
Qwen2.5-32B(ft)75.9184.7485.6476.2876.7764.2765.93
Claude-3.577.7486.1987.1477.7378.164.3465.57
", + "image_path": "d58f8658622664aa6fdd9f0ba4233e824e52755bf040929bc8346fe186a5d5e3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 130, + 248, + 462, + 260 + ], + "lines": [ + { + "bbox": [ + 130, + 248, + 462, + 260 + ], + "spans": [ + { + "bbox": [ + 130, + 248, + 462, + 260 + ], + "type": "text", + "content": "Table 11: NDCG scores comparison showing ranking quality of different methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 67, + 282, + 290, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 282, + 290, + 376 + ], + "spans": [ + { + "bbox": [ + 67, + 282, + 290, + 376 + ], + "type": "text", + "content": "for efficient adaptation. The training set included 447 samples generated by Claude-3.5, while the remaining samples were iteratively generated using the fine-tuned Qwen2.5-32B model. The fine-tuning process was conducted over 5 epochs with max_token set to " + }, + { + "bbox": [ + 67, + 282, + 290, + 376 + ], + "type": "inline_equation", + "content": "128k" + }, + { + "bbox": [ + 67, + 282, + 290, + 376 + ], + "type": "text", + "content": " and a learning rate of " + }, + { + "bbox": [ + 67, + 282, + 290, + 376 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-4}" + }, + { + "bbox": [ + 67, + 282, + 290, + 376 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 386, + 131, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 386, + 131, + 400 + ], + "spans": [ + { + "bbox": [ + 68, + 386, + 131, + 400 + ], + "type": "text", + "content": "D Prompt" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 408, + 289, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 408, + 289, + 435 + ], + "spans": [ + { + "bbox": [ + 67, + 408, + 289, + 435 + ], + "type": "text", + "content": "In this section, we go through the prompt template that make up the agent's history." + } + ] + } + ], + "index": 4 + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 16 + }, + { + "para_blocks": [ + { + "bbox": [ + 76, + 214, + 102, + 223 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 214, + 102, + 223 + ], + "spans": [ + { + "bbox": [ + 76, + 214, + 102, + 223 + ], + "type": "text", + "content": "Prompt" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 76, + 226, + 518, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 226, + 518, + 242 + ], + "spans": [ + { + "bbox": [ + 76, + 226, + 518, + 242 + ], + "type": "text", + "content": "Given the following GitHub problem description, your objective is to localize the specific files, classes or functions, and lines of code that need modification or contain key information to resolve the issue." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 76, + 246, + 218, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 246, + 218, + 254 + ], + "spans": [ + { + "bbox": [ + 76, + 246, + 218, + 254 + ], + "type": "text", + "content": "Follow these steps to localize the issue:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 76, + 254, + 273, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 254, + 273, + 261 + ], + "spans": [ + { + "bbox": [ + 76, + 254, + 273, + 261 + ], + "type": "text", + "content": "Step 1: Categorize and Extract Key Problem Information" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 76, + 262, + 431, + 288 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 76, + 262, + 292, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 262, + 292, + 269 + ], + "spans": [ + { + "bbox": [ + 76, + 262, + 292, + 269 + ], + "type": "text", + "content": "- Classify the problem statement into the following categories:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 76, + 269, + 371, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 269, + 371, + 275 + ], + "spans": [ + { + "bbox": [ + 76, + 269, + 371, + 275 + ], + "type": "text", + "content": "Problem description, error trace, code to reproduce the bug, and additional context." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 76, + 275, + 350, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 275, + 350, + 281 + ], + "spans": [ + { + "bbox": [ + 76, + 275, + 350, + 281 + ], + "type": "text", + "content": "- Identify modules in the '{package_name}' package mentioned in each category." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 76, + 281, + 431, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 281, + 431, + 288 + ], + "spans": [ + { + "bbox": [ + 76, + 281, + 431, + 288 + ], + "type": "text", + "content": "- Use extracted keywords and line numbers to search for relevant code references for additional context." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 76, + 294, + 201, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 294, + 201, + 301 + ], + "spans": [ + { + "bbox": [ + 76, + 294, + 201, + 301 + ], + "type": "text", + "content": "Step 2: Locate Referenced Modules" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 83, + 302, + 211, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 302, + 211, + 307 + ], + "spans": [ + { + "bbox": [ + 83, + 302, + 211, + 307 + ], + "type": "text", + "content": "Accurately determine specific modules" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 83, + 308, + 295, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 308, + 295, + 314 + ], + "spans": [ + { + "bbox": [ + 83, + 308, + 295, + 314 + ], + "type": "text", + "content": "- Explore the repo to familiarize yourself with its structure." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 83, + 315, + 421, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 315, + 421, + 321 + ], + "spans": [ + { + "bbox": [ + 83, + 315, + 421, + 321 + ], + "type": "text", + "content": "- Analyze the described execution flow to identify specific modules or components being referenced." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 76, + 322, + 486, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 322, + 486, + 327 + ], + "spans": [ + { + "bbox": [ + 76, + 322, + 486, + 327 + ], + "type": "text", + "content": "- Pay special attention to distinguishing between modules with similar names using context and described execution flow." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 76, + 328, + 238, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 328, + 238, + 334 + ], + "spans": [ + { + "bbox": [ + 76, + 328, + 238, + 334 + ], + "type": "text", + "content": "- Output Format for collected relevant modules:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 83, + 335, + 228, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 335, + 228, + 341 + ], + "spans": [ + { + "bbox": [ + 83, + 335, + 228, + 341 + ], + "type": "text", + "content": "- Use the format: 'file path:QualifiedName'" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 83, + 342, + 500, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 342, + 500, + 348 + ], + "spans": [ + { + "bbox": [ + 83, + 342, + 500, + 348 + ], + "type": "text", + "content": "- E.q., for a function `calculate_sum` in the `MathUtilities` class located in `src/helpers/mathHelpers.py`, represent it as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 93, + 349, + 275, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 349, + 275, + 355 + ], + "spans": [ + { + "bbox": [ + 93, + 349, + 275, + 355 + ], + "type": "text", + "content": "'src/helpers/mathHelpers.py:MathUtil calculator_sum'." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 76, + 360, + 235, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 360, + 235, + 368 + ], + "spans": [ + { + "bbox": [ + 76, + 360, + 235, + 368 + ], + "type": "text", + "content": "## Step 3: Analyze and Reproducing the Problem" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 83, + 369, + 193, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 369, + 193, + 375 + ], + "spans": [ + { + "bbox": [ + 83, + 369, + 193, + 375 + ], + "type": "text", + "content": "Clarify the Purpose of the Issue" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 83, + 375, + 425, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 375, + 425, + 382 + ], + "spans": [ + { + "bbox": [ + 83, + 375, + 425, + 382 + ], + "type": "text", + "content": "- If expanding capabilities: Identify where and how to incorporate new behavior, fields, or modules." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 83, + 383, + 395, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 383, + 395, + 389 + ], + "spans": [ + { + "bbox": [ + 83, + 383, + 395, + 389 + ], + "type": "text", + "content": "- If addressing unexpected behavior: Focus on localizing modules containing potential bugs." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 76, + 390, + 188, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 390, + 188, + 396 + ], + "spans": [ + { + "bbox": [ + 76, + 390, + 188, + 396 + ], + "type": "text", + "content": "- Reconstruct the execution flow" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 83, + 396, + 254, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 396, + 254, + 403 + ], + "spans": [ + { + "bbox": [ + 83, + 396, + 254, + 403 + ], + "type": "text", + "content": "- Identify main entry points triggering the issue." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 83, + 403, + 316, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 403, + 316, + 409 + ], + "spans": [ + { + "bbox": [ + 83, + 403, + 316, + 409 + ], + "type": "text", + "content": "- Trace function calls, class interactions, and sequences of events." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 83, + 410, + 258, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 410, + 258, + 416 + ], + "spans": [ + { + "bbox": [ + 83, + 410, + 258, + 416 + ], + "type": "text", + "content": "- Identify potential breakpoints causing the issue." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 83, + 417, + 394, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 417, + 394, + 423 + ], + "spans": [ + { + "bbox": [ + 83, + 417, + 394, + 423 + ], + "type": "text", + "content": "Important: Keep the reconstructed flow focused on the problem, avoiding irrelevant details." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 76, + 428, + 215, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 428, + 215, + 435 + ], + "spans": [ + { + "bbox": [ + 76, + 428, + 215, + 435 + ], + "type": "text", + "content": "## Step 4: Locate Areas for Modification" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 76, + 436, + 520, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 436, + 520, + 443 + ], + "spans": [ + { + "bbox": [ + 76, + 436, + 520, + 443 + ], + "type": "text", + "content": "- Locate specific files, functions, or lines of code requiring changes or containing critical information for resolving the issue." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 76, + 444, + 391, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 444, + 391, + 449 + ], + "spans": [ + { + "bbox": [ + 76, + 444, + 391, + 449 + ], + "type": "text", + "content": "- Consider upstream and downstream dependencies that may affect or be affected by the issue." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 76, + 450, + 354, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 450, + 354, + 456 + ], + "spans": [ + { + "bbox": [ + 76, + 450, + 354, + 456 + ], + "type": "text", + "content": "- If applicable, identify where to introduce new fields, functions, or variables." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 76, + 457, + 456, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 457, + 456, + 463 + ], + "spans": [ + { + "bbox": [ + 76, + 457, + 456, + 463 + ], + "type": "text", + "content": "- Think Thoroughly: List multiple potential solutions and consider edge cases that could impact the resolution." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 76, + 469, + 196, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 469, + 196, + 476 + ], + "spans": [ + { + "bbox": [ + 76, + 469, + 196, + 476 + ], + "type": "text", + "content": "Output Format for Final Results:" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 76, + 477, + 408, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 477, + 408, + 483 + ], + "spans": [ + { + "bbox": [ + 76, + 477, + 408, + 483 + ], + "type": "text", + "content": "Your final output should list the locations requiring modification, wrapped with triple back ticks" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 76, + 484, + 506, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 484, + 506, + 490 + ], + "spans": [ + { + "bbox": [ + 76, + 484, + 506, + 490 + ], + "type": "text", + "content": "Each location should include the file path, class name (if applicable), function name, or line numbers, ordered by importance." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 76, + 491, + 238, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 491, + 238, + 497 + ], + "spans": [ + { + "bbox": [ + 76, + 491, + 238, + 497 + ], + "type": "text", + "content": "Your answer would better include about 5 files." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 76, + 502, + 122, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 502, + 122, + 511 + ], + "spans": [ + { + "bbox": [ + 76, + 502, + 122, + 511 + ], + "type": "text", + "content": "Examples:" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 76, + 516, + 143, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 516, + 143, + 523 + ], + "spans": [ + { + "bbox": [ + 76, + 516, + 143, + 523 + ], + "type": "text", + "content": "full_path1/file1.py" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 77, + 524, + 105, 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143, + 557 + ], + "type": "text", + "content": "full path2/file2.py" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 77, + 558, + 105, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 558, + 105, + 564 + ], + "spans": [ + { + "bbox": [ + 77, + 558, + 105, + 564 + ], + "type": "text", + "content": "line:76" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 77, + 564, + 183, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 564, + 183, + 571 + ], + "spans": [ + { + "bbox": [ + 77, + 564, + 183, + 571 + ], + "type": "text", + "content": "function: MyClass2.my_function2" + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 77, + 576, + 143, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 576, + 143, + 584 + ], + "spans": [ + { + "bbox": [ + 77, + 576, + 143, + 584 + ], + "type": "text", + "content": "full_path3/file3.py" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 77, + 585, + 105, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 585, + 105, + 591 + ], + "spans": [ + { + "bbox": [ + 77, + 585, + 105, + 591 + ], + "type": "text", + "content": "line: 24" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 77, + 591, + 109, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 591, + 109, + 597 + ], + "spans": [ + { + "bbox": [ + 77, + 591, + 109, + 597 + ], + "type": "text", + "content": "line: 156" + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 77, + 597, + 153, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 597, + 153, + 604 + ], + "spans": [ + { + "bbox": [ + 77, + 597, + 153, + 604 + ], + "type": "text", + "content": "function: my_function3" + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 77, + 604, + 86, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 604, + 86, + 609 + ], + "spans": [ + { + "bbox": [ + 77, + 604, + 86, + 609 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 76, + 617, + 169, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 617, + 169, + 624 + ], + "spans": [ + { + "bbox": [ + 76, + 617, + 169, + 624 + ], + "type": "text", + "content": "Return just the location(s)" + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 76, + 625, + 330, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 625, + 330, + 632 + ], + "spans": [ + { + "bbox": [ + 76, + 625, + 330, + 632 + ], + "type": "text", + "content": "Note: Your thinking should be thorough and so it's fine if it's very long." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 185, + 645, + 406, + 657 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 185, + 645, + 406, + 657 + ], + "spans": [ + { + "bbox": [ + 185, + 645, + 406, + 657 + ], + "type": "text", + "content": "Figure 8: The task instruction prompt for LOCAGENT." + } + ] + } + ], + "index": 51, + "type": "text" + } + ], + "discarded_blocks": [], + "page_size": [ + 595, + 841 + ], + "page_idx": 17 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_content_list.json b/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7eb3b1a494a80ebd96c987af309453b45024734f --- /dev/null +++ b/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_content_list.json @@ -0,0 +1,1213 @@ +[ + { + "type": "text", + "text": "A 3D particle visualization system for temperature management", + "text_level": 1, + "bbox": [ + 194, + 112, + 803, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lange B. $^{a}$ , Rodriguez N. $^{a}$ , Puech W. $^{a}$ , Rey H. $^{b}$ and Vasques X. $^{b}$", + "bbox": [ + 333, + 200, + 661, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{a}$ LIRMM, 141 rue ADA, Montpellier, France;", + "bbox": [ + 330, + 234, + 666, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "b IBM, Rue de la vieille poste, Montpellier,", + "bbox": [ + 338, + 252, + 658, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "France", + "bbox": [ + 470, + 270, + 527, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 465, + 314, + 531, + 328 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper deals with a 3D visualization technique proposed to analyze and manage energy efficiency from a data center. Data are extracted from sensors located in the IBM Green Data Center in Montpellier France. These sensors measure different information such as hygrometry, pressure and temperature. We want to visualize in real-time the large among of data produced by these sensors. A visualization engine has been designed, based on particles system and a client server paradigm. In order to solve performance problems, a Level Of Detail solution has been developed. These methods are based on the earlier work introduced by J. Clark in $1976^{1}$ . In this paper we introduce a particle method used for this work and subsequently we explain different simplification methods applied to improve our solution.", + "bbox": [ + 214, + 337, + 785, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Keywords: 3D Visualization, Sensors, Particles, Client/Server, Level Of Details", + "bbox": [ + 143, + 526, + 733, + 541 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. INTRODUCTION", + "text_level": 1, + "bbox": [ + 145, + 575, + 370, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present a method to produce a 3D visualization for analyzing and managing temperature. Data are extracted from sensors located in the IBM Green Data Center in Montpellier, which provides many different types of information like temperature, pressure or hygrometry. In our system, sensors are placed in a virtual room and the internal space is modeled using particles. The main constraint here is to produce a real-time rendering. However, latency appears du to the number of vertices. In this paper, we use a solution called LOD (Level Of Detail) to produce multi resolution 3D objects. This solution has been introduced in 1976 by J. Clark1. In this paper, J. Clark introduces the use of several mesh resolutions to simplify the 3D scene complexity. In our work, we use various simplification methods to provide interactive rendering and allows rendering the most important part of data extracted from sensors. In this paper, we describe how we create a room, and the methods used to produce different resolution visualization. In Section 2, we introduce related work on particles systems and LOD. In Section 3, we expose our solution to simplify particles system. In Section 4 we give some results and finally, in Section 5 we present our conclusions and future work.", + "bbox": [ + 142, + 609, + 841, + 864 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1/10", + "bbox": [ + 483, + 970, + 514, + 979 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2. RELATED WORK", + "text_level": 1, + "bbox": [ + 145, + 69, + 375, + 88 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section we present several previous works concerning data visualization, particle systems and level of detail methods.", + "bbox": [ + 143, + 104, + 828, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Some previous work present solutions to visualize large data flow extracted from mantle convection. M. Damon et al. $^{2}$ and K. E. Jordan et al. $^{3}$ present interactive viewers for this kind of data. These data are computed by using Hight Performance Computing (HPC) and visualized on a large display. The rendering is calculated by using another HPC. The data flow is very important and a real-time 3D simulation is hard to obtain. W. Kapfer and", + "bbox": [ + 143, + 138, + 836, + 222 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "T. Riser6 introduce how to use particle system to visualize astronomic simulation, particles representing space objects. The number of particles is extremely important for computing motion in real-time. GPU computing is preferred to render instead of a common HPC solution. To display their data, they have developed their own 3D graphical engine. The space objects are represented by point sprite instead of sphere. Lights are used to give a spherical aspect to the point sprite. This solution allows to render more stars than spherical object method. The 3D engine provides different rendering methods to group space objects: cell simplification or extraction of isosurface. The use of GPU seems quite well for a particle solution, parallel processing allows to render large data; the astrological data seems to be well suited.", + "bbox": [ + 143, + 234, + 851, + 404 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In 1976, J. Clark introduces Level Of Detail (LOD) concept1. LOD consists of several resolution meshes for using them at different distances from the camera. Firstly, designer produces these meshes. First algorithms, in 1992 Schroeder et al. developed a method by decimation for simplify the mesh7. It analyses mesh geometry and evaluates the complexity of triangles. Vertices are removed if only constraints set by the user are respected. Vertices are removed and gaps are filled using triangulation. These algorithms of simplification are not enough to simplify mesh efficiently because shape is not always totally respected. D. Luebke, in 1997, has proposed a taxonomy of mesh simplification8. He presented the most used algorithms. He extracted different ways to use each algorithm. But in this paper, only one solution works with volumetric mesh9. T. He et al. propose a method based on voxel simplification by using a grid for clustering voxels. A marching cube10 algorithm was applied to produce a surface mesh. But this simplification algorithm did not preserve the shape of the mesh. In our work, we look for point cloud simplification. Indeed, previous methods which deal with simplification for surface point cloud like11-13 are not adapted to our case. All of these methods produce LOD for surface mesh and point cloud is extracted from scanner.", + "bbox": [ + 143, + 406, + 851, + 676 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. PROPOSED APPROACH", + "text_level": 1, + "bbox": [ + 145, + 710, + 452, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This section presents the different methods that are used to visualize a kind of data from Green Data Center (GDC). The main goal is to be able to visualize in real-time the evolution of temperature in the data center. For this, we use a special particle method. Particles are located using a segmentation algorithm based on Voronoi cell extraction and Delaunay triangulation. The latency due to the large flow of particles is avoided by using a client server paradigm. We improve our solution by using LOD methods to simplify rendering.", + "bbox": [ + 143, + 744, + 844, + 847 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2/10", + "bbox": [ + 483, + 970, + 514, + 979 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1 Particle systems", + "text_level": 1, + "bbox": [ + 142, + 68, + 333, + 85 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rooms are the bases of our study. For modeling a room, we extract the shape of the space representation which is composed by a box with three measures: length $(l \\in \\mathbb{R})$ , width $(w \\in \\mathbb{R})$ , height $(h \\in \\mathbb{R})$ . Sensors are represented by $S = \\{\\mathrm{S}_1, \\dots, \\mathrm{S}_M\\}$ , where $M$ is the number of sensors. Sensors $\\mathrm{S}_i (\\mathrm{i} \\in \\{1, \\dots, M\\})$ are placed on the space on a layer $\\mathbf{L} \\in \\mathbb{N}$ and have a location represented by: $\\{\\mathbf{X}_i, \\mathbf{Y}_i, \\mathbf{L}_j\\}$ with $\\mathbf{X}_i \\in \\mathbb{R}$ , $\\mathbf{Y}_i \\in \\mathbb{R}$ and $j$ is the layer used. For modeling the space inside a room, we use a particle system instead of 2D map representations which have some lacks. $^{14}$ Actually 2D map does not allow having a real visualization of space. A particle visualization gives a better efficiency for modeling space. We use a large number of particles to represent the entire space. $\\mathbf{N} \\in \\mathbb{N}$ represents the number of particles in the room. It can be calculated using:", + "bbox": [ + 138, + 97, + 844, + 270 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nN = \\frac {\\left(\\left(l + 1\\right) \\times (h + 1) \\times (w + 1)\\right)}{\\delta^ {3}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 277, + 524, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\delta \\in \\mathbb{R}$ is the space between particles. The particle grid is regular. In this model, three layers of temperature sensors compose rooms. They are defined according to their real locations in the data center. Figure ?? presents the different layers of sensors in the data center.", + "bbox": [ + 138, + 329, + 841, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Particles carry information, and flow motion can be simulated if needed by changing the value of particles and the computational cost is inferior.", + "bbox": [ + 138, + 398, + 836, + 433 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2 Segmentation algorithms", + "text_level": 1, + "bbox": [ + 140, + 448, + 418, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our solution, each sensors has an influence on surrounding particules. To calculate the set of particles in the sensor range, we use two methods: Voronoi cells extraction and Delaunay triangulation.", + "bbox": [ + 138, + 477, + 834, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Voronoi cells is a method to extract a partition of space $^{15}$ . This method is available for $\\phi$ dimensions where $\\phi \\in [1, +\\infty]$ , but most of implementations are done in 2D. Tools for extracting 3D Voronoi diagrams exist: Voro++ and QHull but particles are discrete and these solutions are not suitable because they extract Voronoi diagram in a continuous way. Then we designed our own method based on sphere expansion. We search nearest sensors for each particle. This part allows to weight particles outside the sensors mesh. A second method to weight the interior of the sensors mesh is used. We extract the mesh tetrahedron of sensors using the Delaunay triangulation implemented in QHull. This method was used to analyze the location of particle. We compute the exact location using ray tracing on the soup of tetrahedron. First, we search the nearest particles inside the hull of each tetrahedron. We extract the normal of each face of tetrahedron and we apply these normals on each particle. If the ray cuts three faces or more, the particle is inside the tetrahedron. This method is cost expensive and done in preprocessing. Moreover, particles are static and position didn't need to be update.", + "bbox": [ + 138, + 527, + 854, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3 Client server paradigm", + "text_level": 1, + "bbox": [ + 140, + 782, + 398, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To improve computation, a client server paradigm is used. We define a low cost communication protocol to transfer data from a server to a client. Server computes the modification of particles and the client displays the results. This protocol works in five steps. These steps are: sending header, sending sensor data, sending particle data, sending footer and receiving acknowledgment/language command from client. At each step, the server waits the acknowledgment from the client. We develop two ways to send data. The first sends the entire point cloud (sensors and particles). The biggest problem of this method is the", + "bbox": [ + 138, + 811, + 849, + 931 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3/10", + "bbox": [ + 480, + 969, + 517, + 979 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "transmission of data. Sensors are sent with their coordinates and their value. We encode these data in bit words. For the particles data, the same method was used. The footer was sent for closing the communication. The second method is used to reduce efficiently the communication cost. We only send modified sensors and particles. The id and the new value is sent instead of coordinates. The last step is the command sent by the client. It allows the user to interact with the server. We use it to modify the camera viewpoint.", + "bbox": [ + 138, + 65, + 830, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4 Level of detail for particles", + "text_level": 1, + "bbox": [ + 142, + 183, + 434, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Level of detail (LOD) is one of the most important methods in computer graphics. It allows to solve rendering problems or performance problems. This method consists by producing several resolution of a 3D object. In our works, we use some features to define the object resolution: hardware and viewpoint. Hardware and viewpoint do not need the same data structure and we need to recompute it for each modification of the viewpoint or when hardware changes. LOD was defined by two problems statement. The first one uses a sample of original points, the second one uses a new point data set. In this part, we define six methods to produce LOD. The four first methods are for the client, the other are for the server.", + "bbox": [ + 138, + 210, + 848, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Problems statement:", + "text_level": 1, + "bbox": [ + 140, + 378, + 307, + 392 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For this two approaches, we have a set $\\omega$ of Vertices $V$ , $V = \\{V_1, \\ldots, V_\\omega\\}$ . Each vertex is defined in $\\mathbb{R}^3$ . Simplify a mesh using a sample vertex means $\\omega > \\omega 2$ , where $\\omega 2$ is the size of the second data set. For approach 1, we obtain a new object $\\mathrm{V}2 = \\{\\mathrm{V}2_1, \\ldots, \\mathrm{V}2_\\omega\\}$ with fewer points than V but V 2 is a subset of V. For approach 2, we obtain a new object $\\mathrm{V}3 = \\{\\mathrm{V}3_1, \\ldots, \\mathrm{V}3_\\omega\\}$ with fewer points than V but each point in V 3 is a new vertex.", + "bbox": [ + 138, + 393, + 854, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Section 2 we have presented methods to produce simplification. A few were designed for volumetric simplification. In this section, we propose several methods to produce different volumetric simplifications on our client. We develop four approaches to simplify 3D objects: clustering, neighbor simplification and two approaches based on server. Clustering method was based on He et al. $^{9}$ works, it consists of clustering particles using a 3D grid. Cells sizes of grid are set depending to the viewpoint of the camera. Clusters were being weight with the average of the different values of particles. The position is the barycenter of these particles. Figures 1(a)-1(e) give some examples of simplification using clustering solution. Figure 1(a) present the original point of cloud mesh. Figure", + "bbox": [ + 138, + 493, + 848, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1(b) and 1(d) give two different methods for clustering. And finally, Figure 1(c) and 1(e) give the results of clustering methods.", + "bbox": [ + 138, + 657, + 849, + 691 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ae6cbd294176dc493b50c73240c504ea8c9fc09c9e3151fba6f0be709b525025.jpg", + "image_caption": [ + "Figure 1. Clustering method for simplification point cloud." + ], + "image_footnote": [ + "The second solution used is based on neighborhood extraction. Before runtime, we extract all neighbors of a particle. We measure the distance between each particle. Some optimization can help to decrease complexity: we can estimate easily in our structure which particle is closer to another one (using the fact that particle grid is regular). After this," + ], + "bbox": [ + 148, + 696, + 849, + 821 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4/10", + "bbox": [ + 480, + 969, + 517, + 979 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we extract the main value of particles. We explore each neighbor of particles and we keep the most important. In some cases, the most important can be the high values, in other the low values and in other both of them. This solution is able to produce a low resolution model with the most important information structure. Several low resolution models are created by exploring deeper in neighborhood. Figures 2(a)-2(c) illustrate a neighbor, and two simplifications of this mesh.", + "bbox": [ + 140, + 65, + 844, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/23944f9963b290146f2ac445e8970545bcf00b2949e999067a13468653d749cc.jpg", + "image_caption": [ + "(a) Neighborhood cloud." + ], + "image_footnote": [], + "bbox": [ + 148, + 172, + 379, + 339 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0e41ba0aeddc8af5f2b6664c64abea63f9b32bfd4692c38f916d07f501d537e5.jpg", + "image_caption": [ + "(b) Simplification neighborhood of 1." + ], + "image_footnote": [], + "bbox": [ + 383, + 172, + 612, + 337 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c01c12cfcf72e187db35ff49ad4d5edb57331b8d93efa4c1f20941ebf580a3d7.jpg", + "image_caption": [ + "(c) Simplification neighborhood of 2.", + "Figure 2. Neighbor method for simplification." + ], + "image_footnote": [], + "bbox": [ + 617, + 172, + 846, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Other methods were based on server instead of client. Client sent via TCP connection his viewpoint. The server recomputes the particles structure and recreates the entire structure. With this solution, it is possible to produce a point cloud resolution depending on hardware. Figure 3(a) presents particles rendering with a distance of 2 from the camera. Figure 3(b) is the decimation produced with a distance of 3 and Figure 3(c) is a distance of 1.", + "bbox": [ + 138, + 409, + 852, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Another method was based on Voronoi diffusion of temperature. The bandwidth for transmitting data is limited. We developed Voronoi temperature diffusion to solve this communication. In this approach, we update data using sphere expansion. Each time, we update particles depending on their distance from sensors. The more particles are distant from sensors the later they will be refreshed. This method sends only modified particles. The bandwidth is saved and the visualization gives a flow effect. Figure 4(a) represents values at time 0. At time 1, values of sensors change, 4(b). After time 2, we update a first range of particles 4(c) and finally the second range 4(d).", + "bbox": [ + 138, + 506, + 856, + 642 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7eac2440a2fedd66d943c82b390c3a9df5d95d019d523a29c7a3e2f9c7218928.jpg", + "image_caption": [ + "(a) Particles server $(\\mathrm{D} = 2)$", + "Figure 3. Particle simplification using server and distance." + ], + "image_footnote": [], + "bbox": [ + 156, + 650, + 380, + 815 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c4777a0507eee1c1beaa13c04e351827098bc588e6ced9d8de6cff01430e3df5.jpg", + "image_caption": [ + "(b) Particles produce server $(\\mathrm{D} = 3)$" + ], + "image_footnote": [], + "bbox": [ + 388, + 650, + 612, + 815 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5dabdfa6b0129921b2abb27785be9608573a25f26e4646d20c6b92250fad1414.jpg", + "image_caption": [ + "(c) Particles produce by server $(\\mathrm{D} = 1)$" + ], + "image_footnote": [], + "bbox": [ + 620, + 650, + 844, + 815 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5/10", + "bbox": [ + 482, + 969, + 514, + 979 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e340d9807d4ed601eee3bd74351618a9adfda026a8dbd720f9d2aa40857dad26.jpg", + "image_caption": [ + "(a) Particles and sensors (T = 0)." + ], + "image_footnote": [], + "bbox": [ + 150, + 66, + 321, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/92c09c0b767ea453098777786fb815e8c2f833a8abc790807397f42e9a6f6887.jpg", + "image_caption": [ + "(b) Sensors update $(\\mathrm{T} = 1)$ ." + ], + "image_footnote": [], + "bbox": [ + 328, + 66, + 496, + 194 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/416dbc943d118d6834e80c8c5ad759b34f940700b96fd0b87bb23c082f10cf10.jpg", + "image_caption": [ + "(c) First range $(\\mathrm{T} = 2)$ .", + "Figure 4. Simplification using bandwidth size." + ], + "image_footnote": [], + "bbox": [ + 503, + 68, + 669, + 194 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a79e8f2104ab8c32df4137808fc6b4ce9b7465bfa15c2080bd3aabb2c58986d0.jpg", + "image_caption": [ + "(d) Second range $(\\mathrm{T} = 3)$ ." + ], + "image_footnote": [], + "bbox": [ + 674, + 68, + 848, + 194 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. EXPERIMENTAL RESULTS", + "text_level": 1, + "bbox": [ + 140, + 287, + 490, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The data are extracted from two rooms of the IBM data center. Firstly, we present our method for rendering the room, and later we present our results using Level Of Detail methods.", + "bbox": [ + 138, + 321, + 805, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1 Data visualization", + "text_level": 1, + "bbox": [ + 140, + 388, + 346, + 406 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We want to visualize and manage the consumption of a data center. For the visualization, we want to use an IFC viewer. But the IFC model for GDC is not available yet. Data center extraction of the room space is for the moment done by hand. The room is empty and was represent by a simple shape a box with 4 meters length, 3 meters width and 2.5 meters height. We use point cloud visualization based on particle paradigm. We use the two rooms of the data center and we put the same number of particles (30000) and 35 sensors distributed on three layers at 1 meter; 2 meter and on the ground. We define high and low temperature regarding the real sensors value. Figure 5(a) presents temperature color scale, Figure 5(b) and Figure 5(c) present data center sensors.", + "bbox": [ + 138, + 417, + 848, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The next step is to interpolate data from sensors. For this, we extract the sensor mesh. We use QHULL to produce a soup of tetrahedrons. Particles need to be located. We can determine which tetrahedron is the nearest, we extract the box hull of tetrahedron and we apply for each particle the norms of each tetrahedron face. If these rays cut three or more faces, then particle is inside the tetrahedron. With this method, we can determine exactly the location of each particles regarding to the tetrahedrons, a weight is given to them easily. It was used to apply a coefficient to the value of each vertex of tetrahedron. For the outside particles, another solution was used: Voronoi cells. This method is based on a discrete extraction of Voronoi cells. We use our own method because other method like Voro ++ or QHull extract Voronoi diagram in a continuous way.", + "bbox": [ + 138, + 584, + 852, + 755 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7c729f1706460b0bf0adde7a8dbd071f9ae77f611ef3f85b3d951fb62795016c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 151, + 878, + 367, + 922 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8c16ad7a59f34e5974a4322466cec0149f8905a1a1b1cfadff910a3fec50d004.jpg", + "image_caption": [ + "(b) Room one." + ], + "image_footnote": [], + "bbox": [ + 398, + 763, + 606, + 898 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2eb0e7b79700cbbd72a8a244992163f567dbbd68f9d3db6bad3e5808cda4dabb.jpg", + "image_caption": [ + "(c) Room two." + ], + "image_footnote": [], + "bbox": [ + 643, + 765, + 849, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6/10", + "bbox": [ + 482, + 969, + 514, + 979 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2 Level of details", + "text_level": 1, + "bbox": [ + 142, + 98, + 325, + 116 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the earlier days of this project, first solution proposed gives a low frame rates, about 15 FPS (Frame Per Second): visualization was not in real-time (real-time is about 24 FPS). For solving this problem, we define a client server paradigm. This solution allows to produce a real-time rendering on the client. Figure ?? gives an example of LOD for particles. We use Openscenegraph $^{20}$ as a 3D engine. It owns several features useful in LOD. A special object is defined to manage multi-resolution model. It calculates the distance of the object from the camera. For our experimentation we use five resolutions of mesh. The first mesh was the original mesh, it is set at 0 to 500. The next mesh was set at 500 to 1000, the next at 1000 to 1500 and the other at 1500 to 2000. These three meshes were constructed by specific LOD methods: clustering and significant vertices. Clustering defines a 3D grid inside the room. The size of each cell depends on the viewpoint location. The size of the cluster depends on the visibility of the clustered particles. First results are given Figure 6(a) and 6(b). Value of cluster is an average of clustered value. The number of points of the final mesh depends on the grid size. Table 1 shows the results at several distances.", + "bbox": [ + 138, + 126, + 857, + 367 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/389ef0f63a90171c14db5cd9a925792e376222c8c56a5801cacb3dcc99360c96.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X30000390024036
", + "bbox": [ + 143, + 375, + 854, + 450 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9fbe1142edda7eab13f0abb9592b84e63d1611257e7426d7d569a68b9df82b38.jpg", + "image_caption": [ + "Figure 5. Data use to model the system.", + "(a) $\\mathrm{D} = 500$ to 1000.", + "Figure 6. Clustering visualization algorithms." + ], + "image_footnote": [], + "bbox": [ + 158, + 508, + 500, + 705 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/69ae709df8988787ff641b5b6eb5a608ca0636bba7110a3a4735064168d117da.jpg", + "image_caption": [ + "Table 1. Results of clustering simplification.", + "(b) $D = 1000$ to 1500." + ], + "image_footnote": [], + "bbox": [ + 504, + 508, + 846, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Significant points method extracts the neighbors for each particle. We extract the highest and lowest temperatures, by exploring the neighborhood of a particle, in order to have significant vertices of the model. For the first step of simplified model we explore neighbor. For the second model, we explore neighbor and neighbor of neighbor, etc. This solution simplifies drastically the model. First results are given Figure ??-??. Table 2 shows the number of vertices at several distance.", + "bbox": [ + 138, + 756, + 843, + 859 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7/10", + "bbox": [ + 482, + 969, + 516, + 979 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3cd8a951d8771e165427c2faca0d2508e4c8cef94fb244dc3a04f2ca031996a3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X300002295045543524
", + "bbox": [ + 143, + 61, + 854, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4050e8f862ac40be7bc6d5c239997192325936e244911b8d69fe60a4ab8810b8.jpg", + "image_caption": [ + "(a) Neighborhood 1.", + "Figure 7. Clustering visualization algorithms using neighbor." + ], + "image_footnote": [], + "bbox": [ + 153, + 195, + 496, + 402 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dafb2130c8265a91a7faed53db3de1181cd524770896acda68d5a953df004f87.jpg", + "image_caption": [ + "(b) Neighborhood 2." + ], + "image_footnote": [], + "bbox": [ + 500, + 195, + 843, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The first server solution receives orders from client as presented Section 3.4. We calculate the viewpoint distance and we send data according to it. A new structure is recalculated if the camera is too far from the object. After the recomputing, we send the new data. This solution allows the user to receive more or less data according to its distance to the object. Table 3 shows some different resolutions produced with this method.", + "bbox": [ + 138, + 470, + 844, + 555 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9434d9911bf9b1660b16b84b9672b9a68ac66eec53e61ed383a2c752f12025a2.jpg", + "table_caption": [ + "Table 2. Results of neighbor simplification." + ], + "table_footnote": [], + "table_body": "
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X1200003000075001875
", + "bbox": [ + 143, + 566, + 854, + 640 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Several resolution of model.", + "bbox": [ + 138, + 674, + 424, + 688 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Another solution is to use bandwidth latency. We send data at several times, we do not send the entire set of data but only modified particles. We send at first time the sensors data, and subsequently we send a range of data (the nearest). After few minutes, all data are sent. This solution gives good results, and simulates a thermal diffusion in the whole structure of particles. Figure 8(a)-8(c) illustrate this method.", + "bbox": [ + 138, + 691, + 852, + 775 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2fcee6efa3b1d3c44144e2639f3857a15c4079f838c4f9132953fd427a8b1be9.jpg", + "image_caption": [ + "(a) $\\mathrm{T} = 0$" + ], + "image_footnote": [], + "bbox": [ + 148, + 779, + 380, + 912 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b2be70bd4cc7d261ac38e8bc653a0c09c537d49d2a5612ed5c067058a98ef463.jpg", + "image_caption": [ + "(b) $\\mathrm{T} = 1$" + ], + "image_footnote": [], + "bbox": [ + 383, + 779, + 616, + 912 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d4e22f04d3ea25761125c93fc6d70fe856bf840ef353c043f32d21c9633724e.jpg", + "image_caption": [ + "(c) $\\mathrm{T} = 4$" + ], + "image_footnote": [], + "bbox": [ + 617, + 779, + 849, + 912 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8/10", + "bbox": [ + 482, + 969, + 514, + 979 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. CONCLUSION", + "text_level": 1, + "bbox": [ + 142, + 114, + 339, + 135 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we have presented a method to visualize sensors data extracted from a Green Data Center. This approach produces interpolation visualization for managing and visualizing data. This interpolation used a Delaunay triangulation and a cell extraction based on Voronoi. An unusual way of use particles helps to process data. First results present the solution proposed to visualize the inside of a GDC space. The second results proposed in this paper aim to improve the rendering.", + "bbox": [ + 140, + 148, + 849, + 251 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "For this, first step introduces a client/server protocol a second step illustrates methods to simplify the model. With these different approaches we improve the rendering time, preserving most important data are kept. In future works, we will work on data \"dressing\". We want to find a way to improve rendering of the scene using meatballs or marching cube algorithms. A main constraint of this work is real-time computation. Future work also concern to add rooms to the visualization. At present, we only visualize a single room. We want to visualize building, and complex form, by using an IFC loader.", + "bbox": [ + 140, + 252, + 852, + 371 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ACKNOWLEDGMENTS", + "text_level": 1, + "bbox": [ + 142, + 402, + 419, + 422 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We want to thanks the PSSC (Products and Solutions Support Center) team of IBM Montpellier for having provided the necessary equipment and data need for this experimentation. And we thank the FUI (Fonds Unique Interministriel) for their financial support.", + "bbox": [ + 138, + 438, + 836, + 506 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "REFERENCES", + "text_level": 1, + "bbox": [ + 142, + 539, + 310, + 558 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Clark, J. H., \"Hierarchical geometric models for visible surface algorithms,\" Communications of the ACM 19(10), 547-554 (1976).", + "[2] Damon, M., Kameyama, M., Knox, M., Porter, D., Yuen, D., and Sevre, E., \"Interactive visualization of 3d mantle convection,\" Visual Geosciences (2008).", + "[3] Jordan, K. E., Yuen, D. A., Reuteler, D. M., Zhang, S., and Haimes, R., \"Parallel interactive visualization of 3d mantle convection,\" IEEE Comput. Sci. Eng. 3(4), 29-37 (1996).", + "[4] Reeves, W. 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P., and Kröller, A., \"Spyglass: a wireless sensor network visualizer,\" SIGBED Rev. 2(1), 1-6 (2005).", + "[15] Avis, D. and Bhattacharya, B., \"Algorithms for computing d-dimensional voronoi diagrams and their duals,\" 1, 159-180 (1983).", + "[16] Rycroft, C. H., \"Voro++: a three-dimensional voronoi cell library in $c++$ ,\" Chaos 19 (2009). Lawrence Berkeley National Laboratory.", + "[17] Barber, C. B., Dobkin, D. P., and Huhdanpaa, H., \"The quickhull algorithm for convex hulls,\" ACM Trans. Math. Softw. 22(4), 469-483 (1996).", + "[18] Snyder, J. M. and Barr, A. H., \"Ray tracing complex models containing surface tessellations,\" SIGGRAPH Comput. Graph. 21(4), 119-128 (1987).", + "[19] Hoppe, H., \"Progressive meshes. computer graphics,\" SIGGRAPH96 Proceedings, 99108 (1996).", + "[20] Burns, D. and Osfield, R., \"Open scene graph a: Introduction, b: Examples and applications,\" 265 (2004)." + ], + "bbox": [ + 142, + 65, + 849, + 371 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Further author information:", + "bbox": [ + 166, + 393, + 388, + 407 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Lange B.: E-mail: benoit.lange@lirmm.fr", + "bbox": [ + 166, + 411, + 480, + 426 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Rodriguez N.: E-mail: nancy.rodriguez@lirmm.fr", + "bbox": [ + 166, + 428, + 542, + 443 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Puech W.: E-mail: william.puech@lirmm.fr", + "bbox": [ + 166, + 445, + 496, + 459 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Rey H.: E-mail:REYHERVE@fr.ibm.com", + "bbox": [ + 166, + 462, + 467, + 477 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Vasques X.: E-mail: xaviervasques@fr.ibm.com", + "bbox": [ + 166, + 479, + 527, + 494 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10/10", + "bbox": [ + 480, + 969, + 517, + 979 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_model.json b/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_model.json new file mode 100644 index 0000000000000000000000000000000000000000..93a691e63f03b9354a3bce03d5bf39f7ee03e8db --- /dev/null +++ b/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_model.json @@ -0,0 +1,1639 @@ +[ + [ + { + "type": "title", + "bbox": [ + 0.195, + 0.113, + 0.804, + 0.176 + ], + "angle": 0, + "content": "A 3D particle visualization system for temperature management" + }, + { + "type": "text", + "bbox": [ + 0.334, + 0.201, + 0.663, + 0.234 + ], + "angle": 0, + "content": "Lange B. \\(^{a}\\), Rodriguez N. \\(^{a}\\), Puech W. \\(^{a}\\), Rey H. \\(^{b}\\) and Vasques X. \\(^{b}\\)" + }, + { + "type": "text", + "bbox": [ + 0.331, + 0.236, + 0.667, + 0.252 + ], + "angle": 0, + "content": "\\(^{a}\\) LIRMM, 141 rue ADA, Montpellier, France;" + }, + { + "type": "text", + "bbox": [ + 0.339, + 0.253, + 0.659, + 0.269 + ], + "angle": 0, + "content": "b IBM, Rue de la vieille poste, Montpellier," + }, + { + "type": "text", + "bbox": [ + 0.471, + 0.271, + 0.528, + 0.285 + ], + "angle": 0, + "content": "France" + }, + { + "type": "title", + "bbox": [ + 0.467, + 0.315, + 0.532, + 0.329 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.215, + 0.338, + 0.786, + 0.514 + ], + "angle": 0, + "content": "This paper deals with a 3D visualization technique proposed to analyze and manage energy efficiency from a data center. Data are extracted from sensors located in the IBM Green Data Center in Montpellier France. These sensors measure different information such as hygrometry, pressure and temperature. We want to visualize in real-time the large among of data produced by these sensors. A visualization engine has been designed, based on particles system and a client server paradigm. In order to solve performance problems, a Level Of Detail solution has been developed. These methods are based on the earlier work introduced by J. Clark in \\(1976^{1}\\). In this paper we introduce a particle method used for this work and subsequently we explain different simplification methods applied to improve our solution." + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.527, + 0.735, + 0.542 + ], + "angle": 0, + "content": "Keywords: 3D Visualization, Sensors, Particles, Client/Server, Level Of Details" + }, + { + "type": "title", + "bbox": [ + 0.147, + 0.576, + 0.371, + 0.596 + ], + "angle": 0, + "content": "1. INTRODUCTION" + }, + { + "type": "text", + "bbox": [ + 0.143, + 0.611, + 0.842, + 0.866 + ], + "angle": 0, + "content": "In this paper, we present a method to produce a 3D visualization for analyzing and managing temperature. Data are extracted from sensors located in the IBM Green Data Center in Montpellier, which provides many different types of information like temperature, pressure or hygrometry. In our system, sensors are placed in a virtual room and the internal space is modeled using particles. The main constraint here is to produce a real-time rendering. However, latency appears du to the number of vertices. In this paper, we use a solution called LOD (Level Of Detail) to produce multi resolution 3D objects. This solution has been introduced in 1976 by J. Clark1. In this paper, J. Clark introduces the use of several mesh resolutions to simplify the 3D scene complexity. In our work, we use various simplification methods to provide interactive rendering and allows rendering the most important part of data extracted from sensors. In this paper, we describe how we create a room, and the methods used to produce different resolution visualization. In Section 2, we introduce related work on particles systems and LOD. In Section 3, we expose our solution to simplify particles system. In Section 4 we give some results and finally, in Section 5 we present our conclusions and future work." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.971, + 0.516, + 0.98 + ], + "angle": 0, + "content": "1/10" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.147, + 0.07, + 0.376, + 0.089 + ], + "angle": 0, + "content": "2. RELATED WORK" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.105, + 0.83, + 0.137 + ], + "angle": 0, + "content": "In this section we present several previous works concerning data visualization, particle systems and level of detail methods." + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.139, + 0.837, + 0.223 + ], + "angle": 0, + "content": "Some previous work present solutions to visualize large data flow extracted from mantle convection. M. Damon et al. \\(^{2}\\) and K. E. Jordan et al. \\(^{3}\\) present interactive viewers for this kind of data. These data are computed by using Hight Performance Computing (HPC) and visualized on a large display. The rendering is calculated by using another HPC. The data flow is very important and a real-time 3D simulation is hard to obtain. W. Kapfer and" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.235, + 0.852, + 0.405 + ], + "angle": 0, + "content": "T. Riser6 introduce how to use particle system to visualize astronomic simulation, particles representing space objects. The number of particles is extremely important for computing motion in real-time. GPU computing is preferred to render instead of a common HPC solution. To display their data, they have developed their own 3D graphical engine. The space objects are represented by point sprite instead of sphere. Lights are used to give a spherical aspect to the point sprite. This solution allows to render more stars than spherical object method. The 3D engine provides different rendering methods to group space objects: cell simplification or extraction of isosurface. The use of GPU seems quite well for a particle solution, parallel processing allows to render large data; the astrological data seems to be well suited." + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.407, + 0.852, + 0.678 + ], + "angle": 0, + "content": "In 1976, J. Clark introduces Level Of Detail (LOD) concept1. LOD consists of several resolution meshes for using them at different distances from the camera. Firstly, designer produces these meshes. First algorithms, in 1992 Schroeder et al. developed a method by decimation for simplify the mesh7. It analyses mesh geometry and evaluates the complexity of triangles. Vertices are removed if only constraints set by the user are respected. Vertices are removed and gaps are filled using triangulation. These algorithms of simplification are not enough to simplify mesh efficiently because shape is not always totally respected. D. Luebke, in 1997, has proposed a taxonomy of mesh simplification8. He presented the most used algorithms. He extracted different ways to use each algorithm. But in this paper, only one solution works with volumetric mesh9. T. He et al. propose a method based on voxel simplification by using a grid for clustering voxels. A marching cube10 algorithm was applied to produce a surface mesh. But this simplification algorithm did not preserve the shape of the mesh. In our work, we look for point cloud simplification. Indeed, previous methods which deal with simplification for surface point cloud like11-13 are not adapted to our case. All of these methods produce LOD for surface mesh and point cloud is extracted from scanner." + }, + { + "type": "title", + "bbox": [ + 0.147, + 0.711, + 0.453, + 0.731 + ], + "angle": 0, + "content": "3. PROPOSED APPROACH" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.746, + 0.845, + 0.848 + ], + "angle": 0, + "content": "This section presents the different methods that are used to visualize a kind of data from Green Data Center (GDC). The main goal is to be able to visualize in real-time the evolution of temperature in the data center. For this, we use a special particle method. Particles are located using a segmentation algorithm based on Voronoi cell extraction and Delaunay triangulation. The latency due to the large flow of particles is avoided by using a client server paradigm. We improve our solution by using LOD methods to simplify rendering." + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.971, + 0.515, + 0.98 + ], + "angle": 0, + "content": "2/10" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.143, + 0.069, + 0.334, + 0.087 + ], + "angle": 0, + "content": "3.1 Particle systems" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.098, + 0.845, + 0.271 + ], + "angle": 0, + "content": "Rooms are the bases of our study. For modeling a room, we extract the shape of the space representation which is composed by a box with three measures: length \\((l \\in \\mathbb{R})\\), width \\((w \\in \\mathbb{R})\\), height \\((h \\in \\mathbb{R})\\). Sensors are represented by \\(S = \\{\\mathrm{S}_1, \\dots, \\mathrm{S}_M\\}\\), where \\(M\\) is the number of sensors. Sensors \\(\\mathrm{S}_i (\\mathrm{i} \\in \\{1, \\dots, M\\})\\) are placed on the space on a layer \\(\\mathbf{L} \\in \\mathbb{N}\\) and have a location represented by: \\(\\{\\mathbf{X}_i, \\mathbf{Y}_i, \\mathbf{L}_j\\}\\) with \\(\\mathbf{X}_i \\in \\mathbb{R}\\), \\(\\mathbf{Y}_i \\in \\mathbb{R}\\) and \\(j\\) is the layer used. For modeling the space inside a room, we use a particle system instead of 2D map representations which have some lacks.\\(^{14}\\) Actually 2D map does not allow having a real visualization of space. A particle visualization gives a better efficiency for modeling space. We use a large number of particles to represent the entire space. \\(\\mathbf{N} \\in \\mathbb{N}\\) represents the number of particles in the room. It can be calculated using:" + }, + { + "type": "equation", + "bbox": [ + 0.181, + 0.279, + 0.525, + 0.318 + ], + "angle": 0, + "content": "\\[\nN = \\frac {\\left(\\left(l + 1\\right) \\times (h + 1) \\times (w + 1)\\right)}{\\delta^ {3}} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.33, + 0.842, + 0.396 + ], + "angle": 0, + "content": "where \\(\\delta \\in \\mathbb{R}\\) is the space between particles. The particle grid is regular. In this model, three layers of temperature sensors compose rooms. They are defined according to their real locations in the data center. Figure ?? presents the different layers of sensors in the data center." + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.399, + 0.837, + 0.434 + ], + "angle": 0, + "content": "Particles carry information, and flow motion can be simulated if needed by changing the value of particles and the computational cost is inferior." + }, + { + "type": "title", + "bbox": [ + 0.142, + 0.449, + 0.419, + 0.468 + ], + "angle": 0, + "content": "3.2 Segmentation algorithms" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.478, + 0.836, + 0.528 + ], + "angle": 0, + "content": "In our solution, each sensors has an influence on surrounding particules. To calculate the set of particles in the sensor range, we use two methods: Voronoi cells extraction and Delaunay triangulation." + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.529, + 0.856, + 0.769 + ], + "angle": 0, + "content": "Voronoi cells is a method to extract a partition of space \\(^{15}\\). This method is available for \\(\\phi\\) dimensions where \\(\\phi \\in [1, +\\infty]\\), but most of implementations are done in 2D. Tools for extracting 3D Voronoi diagrams exist: Voro++ and QHull but particles are discrete and these solutions are not suitable because they extract Voronoi diagram in a continuous way. Then we designed our own method based on sphere expansion. We search nearest sensors for each particle. This part allows to weight particles outside the sensors mesh. A second method to weight the interior of the sensors mesh is used. We extract the mesh tetrahedron of sensors using the Delaunay triangulation implemented in QHull. This method was used to analyze the location of particle. We compute the exact location using ray tracing on the soup of tetrahedron. First, we search the nearest particles inside the hull of each tetrahedron. We extract the normal of each face of tetrahedron and we apply these normals on each particle. If the ray cuts three faces or more, the particle is inside the tetrahedron. This method is cost expensive and done in preprocessing. Moreover, particles are static and position didn't need to be update." + }, + { + "type": "title", + "bbox": [ + 0.142, + 0.783, + 0.4, + 0.803 + ], + "angle": 0, + "content": "3.3 Client server paradigm" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.812, + 0.851, + 0.933 + ], + "angle": 0, + "content": "To improve computation, a client server paradigm is used. We define a low cost communication protocol to transfer data from a server to a client. Server computes the modification of particles and the client displays the results. This protocol works in five steps. These steps are: sending header, sending sensor data, sending particle data, sending footer and receiving acknowledgment/language command from client. At each step, the server waits the acknowledgment from the client. We develop two ways to send data. The first sends the entire point cloud (sensors and particles). The biggest problem of this method is the" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.97, + 0.518, + 0.981 + ], + "angle": 0, + "content": "3/10" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.14, + 0.066, + 0.831, + 0.168 + ], + "angle": 0, + "content": "transmission of data. Sensors are sent with their coordinates and their value. We encode these data in bit words. For the particles data, the same method was used. The footer was sent for closing the communication. The second method is used to reduce efficiently the communication cost. We only send modified sensors and particles. The id and the new value is sent instead of coordinates. The last step is the command sent by the client. It allows the user to interact with the server. We use it to modify the camera viewpoint." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.184, + 0.436, + 0.202 + ], + "angle": 0, + "content": "3.4 Level of detail for particles" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.212, + 0.849, + 0.364 + ], + "angle": 0, + "content": "Level of detail (LOD) is one of the most important methods in computer graphics. It allows to solve rendering problems or performance problems. This method consists by producing several resolution of a 3D object. In our works, we use some features to define the object resolution: hardware and viewpoint. Hardware and viewpoint do not need the same data structure and we need to recompute it for each modification of the viewpoint or when hardware changes. LOD was defined by two problems statement. The first one uses a sample of original points, the second one uses a new point data set. In this part, we define six methods to produce LOD. The four first methods are for the client, the other are for the server." + }, + { + "type": "title", + "bbox": [ + 0.141, + 0.379, + 0.308, + 0.393 + ], + "angle": 0, + "content": "Problems statement:" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.394, + 0.856, + 0.482 + ], + "angle": 0, + "content": "For this two approaches, we have a set \\(\\omega\\) of Vertices \\(V\\), \\(V = \\{V_1, \\ldots, V_\\omega\\}\\). Each vertex is defined in \\(\\mathbb{R}^3\\). Simplify a mesh using a sample vertex means \\(\\omega > \\omega 2\\), where \\(\\omega 2\\) is the size of the second data set. For approach 1, we obtain a new object \\(\\mathrm{V}2 = \\{\\mathrm{V}2_1, \\ldots, \\mathrm{V}2_\\omega\\}\\) with fewer points than V but V 2 is a subset of V. For approach 2, we obtain a new object \\(\\mathrm{V}3 = \\{\\mathrm{V}3_1, \\ldots, \\mathrm{V}3_\\omega\\}\\) with fewer points than V but each point in V 3 is a new vertex." + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.494, + 0.849, + 0.648 + ], + "angle": 0, + "content": "In Section 2 we have presented methods to produce simplification. A few were designed for volumetric simplification. In this section, we propose several methods to produce different volumetric simplifications on our client. We develop four approaches to simplify 3D objects: clustering, neighbor simplification and two approaches based on server. Clustering method was based on He et al. \\(^{9}\\) works, it consists of clustering particles using a 3D grid. Cells sizes of grid are set depending to the viewpoint of the camera. Clusters were being weight with the average of the different values of particles. The position is the barycenter of these particles. Figures 1(a)-1(e) give some examples of simplification using clustering solution. Figure 1(a) present the original point of cloud mesh. Figure" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.659, + 0.851, + 0.693 + ], + "angle": 0, + "content": "1(b) and 1(d) give two different methods for clustering. And finally, Figure 1(c) and 1(e) give the results of clustering methods." + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.697, + 0.851, + 0.822 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.843, + 0.593, + 0.859 + ], + "angle": 0, + "content": "Figure 1. Clustering method for simplification point cloud." + }, + { + "type": "image_footnote", + "bbox": [ + 0.139, + 0.86, + 0.854, + 0.929 + ], + "angle": 0, + "content": "The second solution used is based on neighborhood extraction. Before runtime, we extract all neighbors of a particle. We measure the distance between each particle. Some optimization can help to decrease complexity: we can estimate easily in our structure which particle is closer to another one (using the fact that particle grid is regular). After this," + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.97, + 0.518, + 0.98 + ], + "angle": 0, + "content": "4/10" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.141, + 0.066, + 0.845, + 0.168 + ], + "angle": 0, + "content": "we extract the main value of particles. We explore each neighbor of particles and we keep the most important. In some cases, the most important can be the high values, in other the low values and in other both of them. This solution is able to produce a low resolution model with the most important information structure. Several low resolution models are created by exploring deeper in neighborhood. Figures 2(a)-2(c) illustrate a neighbor, and two simplifications of this mesh." + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.174, + 0.38, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.341, + 0.296, + 0.372 + ], + "angle": 0, + "content": "(a) Neighborhood cloud." + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.174, + 0.613, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.384, + 0.341, + 0.532, + 0.373 + ], + "angle": 0, + "content": "(b) Simplification neighborhood of 1." + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.174, + 0.848, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.341, + 0.766, + 0.373 + ], + "angle": 0, + "content": "(c) Simplification neighborhood of 2." + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.393, + 0.492, + 0.409 + ], + "angle": 0, + "content": "Figure 2. Neighbor method for simplification." + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.41, + 0.854, + 0.493 + ], + "angle": 0, + "content": "Other methods were based on server instead of client. Client sent via TCP connection his viewpoint. The server recomputes the particles structure and recreates the entire structure. With this solution, it is possible to produce a point cloud resolution depending on hardware. Figure 3(a) presents particles rendering with a distance of 2 from the camera. Figure 3(b) is the decimation produced with a distance of 3 and Figure 3(c) is a distance of 1." + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.507, + 0.857, + 0.643 + ], + "angle": 0, + "content": "Another method was based on Voronoi diffusion of temperature. The bandwidth for transmitting data is limited. We developed Voronoi temperature diffusion to solve this communication. In this approach, we update data using sphere expansion. Each time, we update particles depending on their distance from sensors. The more particles are distant from sensors the later they will be refreshed. This method sends only modified particles. The bandwidth is saved and the visualization gives a flow effect. Figure 4(a) represents values at time 0. At time 1, values of sensors change, 4(b). After time 2, we update a first range of particles 4(c) and finally the second range 4(d)." + }, + { + "type": "image", + "bbox": [ + 0.157, + 0.651, + 0.382, + 0.816 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.817, + 0.277, + 0.849 + ], + "angle": 0, + "content": "(a) Particles server \\((\\mathrm{D} = 2)\\)" + }, + { + "type": "image", + "bbox": [ + 0.389, + 0.651, + 0.614, + 0.816 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.389, + 0.818, + 0.577, + 0.849 + ], + "angle": 0, + "content": "(b) Particles produce server \\((\\mathrm{D} = 3)\\)" + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.651, + 0.846, + 0.816 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.818, + 0.848, + 0.849 + ], + "angle": 0, + "content": "(c) Particles produce by server \\((\\mathrm{D} = 1)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.868, + 0.595, + 0.884 + ], + "angle": 0, + "content": "Figure 3. Particle simplification using server and distance." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.97, + 0.516, + 0.98 + ], + "angle": 0, + "content": "5/10" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.151, + 0.068, + 0.323, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.196, + 0.325, + 0.22 + ], + "angle": 0, + "content": "(a) Particles and sensors (T = 0)." + }, + { + "type": "image", + "bbox": [ + 0.329, + 0.068, + 0.497, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.332, + 0.196, + 0.493, + 0.207 + ], + "angle": 0, + "content": "(b) Sensors update \\((\\mathrm{T} = 1)\\)." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.069, + 0.671, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.517, + 0.196, + 0.658, + 0.208 + ], + "angle": 0, + "content": "(c) First range \\((\\mathrm{T} = 2)\\)." + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.069, + 0.849, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.685, + 0.196, + 0.84, + 0.208 + ], + "angle": 0, + "content": "(d) Second range \\((\\mathrm{T} = 3)\\)." + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.238, + 0.496, + 0.255 + ], + "angle": 0, + "content": "Figure 4. Simplification using bandwidth size." + }, + { + "type": "title", + "bbox": [ + 0.142, + 0.288, + 0.491, + 0.308 + ], + "angle": 0, + "content": "4. EXPERIMENTAL RESULTS" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.322, + 0.807, + 0.372 + ], + "angle": 0, + "content": "The data are extracted from two rooms of the IBM data center. Firstly, we present our method for rendering the room, and later we present our results using Level Of Detail methods." + }, + { + "type": "title", + "bbox": [ + 0.142, + 0.39, + 0.348, + 0.407 + ], + "angle": 0, + "content": "4.1 Data visualization" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.419, + 0.849, + 0.572 + ], + "angle": 0, + "content": "We want to visualize and manage the consumption of a data center. For the visualization, we want to use an IFC viewer. But the IFC model for GDC is not available yet. Data center extraction of the room space is for the moment done by hand. The room is empty and was represent by a simple shape a box with 4 meters length, 3 meters width and 2.5 meters height. We use point cloud visualization based on particle paradigm. We use the two rooms of the data center and we put the same number of particles (30000) and 35 sensors distributed on three layers at 1 meter; 2 meter and on the ground. We define high and low temperature regarding the real sensors value. Figure 5(a) presents temperature color scale, Figure 5(b) and Figure 5(c) present data center sensors." + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.585, + 0.854, + 0.756 + ], + "angle": 0, + "content": "The next step is to interpolate data from sensors. For this, we extract the sensor mesh. We use QHULL to produce a soup of tetrahedrons. Particles need to be located. We can determine which tetrahedron is the nearest, we extract the box hull of tetrahedron and we apply for each particle the norms of each tetrahedron face. If these rays cut three or more faces, then particle is inside the tetrahedron. With this method, we can determine exactly the location of each particles regarding to the tetrahedrons, a weight is given to them easily. It was used to apply a coefficient to the value of each vertex of tetrahedron. For the outside particles, another solution was used: Voronoi cells. This method is based on a discrete extraction of Voronoi cells. We use our own method because other method like Voro ++ or QHull extract Voronoi diagram in a continuous way." + }, + { + "type": "image", + "bbox": [ + 0.153, + 0.879, + 0.368, + 0.923 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.399, + 0.765, + 0.607, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.438, + 0.907, + 0.547, + 0.922 + ], + "angle": 0, + "content": "(b) Room one." + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.766, + 0.851, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.692, + 0.907, + 0.8, + 0.922 + ], + "angle": 0, + "content": "(c) Room two." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.97, + 0.516, + 0.98 + ], + "angle": 0, + "content": "6/10" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.066, + 0.445, + 0.083 + ], + "angle": 0, + "content": "Figure 5. Data use to model the system." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.099, + 0.326, + 0.117 + ], + "angle": 0, + "content": "4.2 Level of details" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.127, + 0.859, + 0.368 + ], + "angle": 0, + "content": "In the earlier days of this project, first solution proposed gives a low frame rates, about 15 FPS (Frame Per Second): visualization was not in real-time (real-time is about 24 FPS). For solving this problem, we define a client server paradigm. This solution allows to produce a real-time rendering on the client. Figure ?? gives an example of LOD for particles. We use Openscenegraph \\(^{20}\\) as a 3D engine. It owns several features useful in LOD. A special object is defined to manage multi-resolution model. It calculates the distance of the object from the camera. For our experimentation we use five resolutions of mesh. The first mesh was the original mesh, it is set at 0 to 500. The next mesh was set at 500 to 1000, the next at 1000 to 1500 and the other at 1500 to 2000. These three meshes were constructed by specific LOD methods: clustering and significant vertices. Clustering defines a 3D grid inside the room. The size of each cell depends on the viewpoint location. The size of the cluster depends on the visibility of the clustered particles. First results are given Figure 6(a) and 6(b). Value of cluster is an average of clustered value. The number of points of the final mesh depends on the grid size. Table 1 shows the results at several distances." + }, + { + "type": "table", + "bbox": [ + 0.145, + 0.376, + 0.855, + 0.451 + ], + "angle": 0, + "content": "
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X30000390024036
" + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.484, + 0.482, + 0.501 + ], + "angle": 0, + "content": "Table 1. Results of clustering simplification." + }, + { + "type": "image", + "bbox": [ + 0.159, + 0.51, + 0.501, + 0.706 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.236, + 0.706, + 0.425, + 0.722 + ], + "angle": 0, + "content": "(a) \\(\\mathrm{D} = 500\\) to 1000." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.51, + 0.848, + 0.706 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.706, + 0.776, + 0.721 + ], + "angle": 0, + "content": "(b) \\(D = 1000\\) to 1500." + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.74, + 0.492, + 0.757 + ], + "angle": 0, + "content": "Figure 6. Clustering visualization algorithms." + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.757, + 0.844, + 0.86 + ], + "angle": 0, + "content": "Significant points method extracts the neighbors for each particle. We extract the highest and lowest temperatures, by exploring the neighborhood of a particle, in order to have significant vertices of the model. For the first step of simplified model we explore neighbor. For the second model, we explore neighbor and neighbor of neighbor, etc. This solution simplifies drastically the model. First results are given Figure ??-??. Table 2 shows the number of vertices at several distance." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.97, + 0.517, + 0.98 + ], + "angle": 0, + "content": "7/10" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.145, + 0.063, + 0.855, + 0.138 + ], + "angle": 0, + "content": "
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X300002295045543524
" + }, + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.171, + 0.474, + 0.187 + ], + "angle": 0, + "content": "Table 2. Results of neighbor simplification." + }, + { + "type": "image", + "bbox": [ + 0.154, + 0.196, + 0.497, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.403, + 0.422, + 0.42 + ], + "angle": 0, + "content": "(a) Neighborhood 1." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.196, + 0.844, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.403, + 0.769, + 0.42 + ], + "angle": 0, + "content": "(b) Neighborhood 2." + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.441, + 0.607, + 0.459 + ], + "angle": 0, + "content": "Figure 7. Clustering visualization algorithms using neighbor." + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.471, + 0.845, + 0.556 + ], + "angle": 0, + "content": "The first server solution receives orders from client as presented Section 3.4. We calculate the viewpoint distance and we send data according to it. A new structure is recalculated if the camera is too far from the object. After the recomputing, we send the new data. This solution allows the user to receive more or less data according to its distance to the object. Table 3 shows some different resolutions produced with this method." + }, + { + "type": "table", + "bbox": [ + 0.145, + 0.567, + 0.855, + 0.641 + ], + "angle": 0, + "content": "
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X1200003000075001875
" + }, + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.675, + 0.425, + 0.689 + ], + "angle": 0, + "content": "Table 3. Several resolution of model." + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.692, + 0.854, + 0.776 + ], + "angle": 0, + "content": "Another solution is to use bandwidth latency. We send data at several times, we do not send the entire set of data but only modified particles. We send at first time the sensors data, and subsequently we send a range of data (the nearest). After few minutes, all data are sent. This solution gives good results, and simulates a thermal diffusion in the whole structure of particles. Figure 8(a)-8(c) illustrate this method." + }, + { + "type": "image", + "bbox": [ + 0.15, + 0.78, + 0.382, + 0.913 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.235, + 0.912, + 0.299, + 0.924 + ], + "angle": 0, + "content": "(a) \\(\\mathrm{T} = 0\\)" + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.78, + 0.617, + 0.913 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.468, + 0.912, + 0.532, + 0.924 + ], + "angle": 0, + "content": "(b) \\(\\mathrm{T} = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.78, + 0.851, + 0.913 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.912, + 0.766, + 0.924 + ], + "angle": 0, + "content": "(c) \\(\\mathrm{T} = 4\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.97, + 0.516, + 0.98 + ], + "angle": 0, + "content": "8/10" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.141, + 0.066, + 0.415, + 0.082 + ], + "angle": 0, + "content": "Figure 8. Bandwidth simplification." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.115, + 0.341, + 0.136 + ], + "angle": 0, + "content": "5. CONCLUSION" + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.15, + 0.851, + 0.252 + ], + "angle": 0, + "content": "In this paper, we have presented a method to visualize sensors data extracted from a Green Data Center. This approach produces interpolation visualization for managing and visualizing data. This interpolation used a Delaunay triangulation and a cell extraction based on Voronoi. An unusual way of use particles helps to process data. First results present the solution proposed to visualize the inside of a GDC space. The second results proposed in this paper aim to improve the rendering." + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.253, + 0.854, + 0.372 + ], + "angle": 0, + "content": "For this, first step introduces a client/server protocol a second step illustrates methods to simplify the model. With these different approaches we improve the rendering time, preserving most important data are kept. In future works, we will work on data \"dressing\". We want to find a way to improve rendering of the scene using meatballs or marching cube algorithms. A main constraint of this work is real-time computation. Future work also concern to add rooms to the visualization. At present, we only visualize a single room. We want to visualize building, and complex form, by using an IFC loader." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.404, + 0.421, + 0.424 + ], + "angle": 0, + "content": "ACKNOWLEDGMENTS" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.439, + 0.838, + 0.507 + ], + "angle": 0, + "content": "We want to thanks the PSSC (Products and Solutions Support Center) team of IBM Montpellier for having provided the necessary equipment and data need for this experimentation. And we thank the FUI (Fonds Unique Interministriel) for their financial support." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.54, + 0.311, + 0.559 + ], + "angle": 0, + "content": "REFERENCES" + }, + { + "type": "ref_text", + "bbox": [ + 0.142, + 0.574, + 0.744, + 0.606 + ], + "angle": 0, + "content": "[1] Clark, J. H., \"Hierarchical geometric models for visible surface algorithms,\" Communications of the ACM 19(10), 547-554 (1976)." + }, + { + "type": "ref_text", + "bbox": [ + 0.143, + 0.609, + 0.81, + 0.641 + ], + "angle": 0, + "content": "[2] Damon, M., Kameyama, M., Knox, M., Porter, D., Yuen, D., and Sevre, E., \"Interactive visualization of 3d mantle convection,\" Visual Geosciences (2008)." + }, + { + "type": "ref_text", + "bbox": [ + 0.143, + 0.643, + 0.831, + 0.675 + ], + "angle": 0, + "content": "[3] Jordan, K. E., Yuen, D. A., Reuteler, D. M., Zhang, S., and Haimes, R., \"Parallel interactive visualization of 3d mantle convection,\" IEEE Comput. Sci. 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M. and Barr, A. H., \"Ray tracing complex models containing surface tessellations,\" SIGGRAPH Comput. Graph. 21(4), 119-128 (1987)." + }, + { + "type": "ref_text", + "bbox": [ + 0.144, + 0.305, + 0.836, + 0.336 + ], + "angle": 0, + "content": "[19] Hoppe, H., \"Progressive meshes. computer graphics,\" SIGGRAPH96 Proceedings, 99108 (1996)." + }, + { + "type": "ref_text", + "bbox": [ + 0.143, + 0.339, + 0.774, + 0.372 + ], + "angle": 0, + "content": "[20] Burns, D. and Osfield, R., \"Open scene graph a: Introduction, b: Examples and applications,\" 265 (2004)." + }, + { + "type": "list", + "bbox": [ + 0.143, + 0.066, + 0.851, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.394, + 0.39, + 0.409 + ], + "angle": 0, + "content": "Further author information:" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.412, + 0.482, + 0.427 + ], + "angle": 0, + "content": "Lange B.: E-mail: benoit.lange@lirmm.fr" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.429, + 0.544, + 0.444 + ], + "angle": 0, + "content": "Rodriguez N.: E-mail: nancy.rodriguez@lirmm.fr" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.446, + 0.498, + 0.46 + ], + "angle": 0, + "content": "Puech W.: E-mail: william.puech@lirmm.fr" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.463, + 0.468, + 0.478 + ], + "angle": 0, + "content": "Rey H.: E-mail:REYHERVE@fr.ibm.com" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.48, + 0.529, + 0.495 + ], + "angle": 0, + "content": "Vasques X.: E-mail: xaviervasques@fr.ibm.com" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.97, + 0.519, + 0.98 + ], + "angle": 0, + "content": "10/10" + } + ] +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_origin.pdf b/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b18d64ddc3337469734d990e27fd93b7953a6ad3 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09198/ef3c6a72-d844-464a-90c5-502ddc16df65_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1ccb0b38b36e023702ff1726eaa2bd337a2762c59724e11e0f0dfcd4402cebf8 +size 964405 diff --git a/data/2025/2503_09xxx/2503.09198/full.md b/data/2025/2503_09xxx/2503.09198/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5f43bb263267fc8297fe4185d5003b9afd722dc6 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09198/full.md @@ -0,0 +1,222 @@ +# A 3D particle visualization system for temperature management + +Lange B. $^{a}$ , Rodriguez N. $^{a}$ , Puech W. $^{a}$ , Rey H. $^{b}$ and Vasques X. $^{b}$ + +$^{a}$ LIRMM, 141 rue ADA, Montpellier, France; + +b IBM, Rue de la vieille poste, Montpellier, + +France + +# Abstract + +This paper deals with a 3D visualization technique proposed to analyze and manage energy efficiency from a data center. Data are extracted from sensors located in the IBM Green Data Center in Montpellier France. These sensors measure different information such as hygrometry, pressure and temperature. We want to visualize in real-time the large among of data produced by these sensors. A visualization engine has been designed, based on particles system and a client server paradigm. In order to solve performance problems, a Level Of Detail solution has been developed. These methods are based on the earlier work introduced by J. Clark in $1976^{1}$ . In this paper we introduce a particle method used for this work and subsequently we explain different simplification methods applied to improve our solution. + +Keywords: 3D Visualization, Sensors, Particles, Client/Server, Level Of Details + +# 1. INTRODUCTION + +In this paper, we present a method to produce a 3D visualization for analyzing and managing temperature. Data are extracted from sensors located in the IBM Green Data Center in Montpellier, which provides many different types of information like temperature, pressure or hygrometry. In our system, sensors are placed in a virtual room and the internal space is modeled using particles. The main constraint here is to produce a real-time rendering. However, latency appears du to the number of vertices. In this paper, we use a solution called LOD (Level Of Detail) to produce multi resolution 3D objects. This solution has been introduced in 1976 by J. Clark1. In this paper, J. Clark introduces the use of several mesh resolutions to simplify the 3D scene complexity. In our work, we use various simplification methods to provide interactive rendering and allows rendering the most important part of data extracted from sensors. In this paper, we describe how we create a room, and the methods used to produce different resolution visualization. In Section 2, we introduce related work on particles systems and LOD. In Section 3, we expose our solution to simplify particles system. In Section 4 we give some results and finally, in Section 5 we present our conclusions and future work. + +# 2. RELATED WORK + +In this section we present several previous works concerning data visualization, particle systems and level of detail methods. + +Some previous work present solutions to visualize large data flow extracted from mantle convection. M. Damon et al. $^{2}$ and K. E. Jordan et al. $^{3}$ present interactive viewers for this kind of data. These data are computed by using Hight Performance Computing (HPC) and visualized on a large display. The rendering is calculated by using another HPC. The data flow is very important and a real-time 3D simulation is hard to obtain. W. Kapfer and + +T. Riser6 introduce how to use particle system to visualize astronomic simulation, particles representing space objects. The number of particles is extremely important for computing motion in real-time. GPU computing is preferred to render instead of a common HPC solution. To display their data, they have developed their own 3D graphical engine. The space objects are represented by point sprite instead of sphere. Lights are used to give a spherical aspect to the point sprite. This solution allows to render more stars than spherical object method. The 3D engine provides different rendering methods to group space objects: cell simplification or extraction of isosurface. The use of GPU seems quite well for a particle solution, parallel processing allows to render large data; the astrological data seems to be well suited. + +In 1976, J. Clark introduces Level Of Detail (LOD) concept1. LOD consists of several resolution meshes for using them at different distances from the camera. Firstly, designer produces these meshes. First algorithms, in 1992 Schroeder et al. developed a method by decimation for simplify the mesh7. It analyses mesh geometry and evaluates the complexity of triangles. Vertices are removed if only constraints set by the user are respected. Vertices are removed and gaps are filled using triangulation. These algorithms of simplification are not enough to simplify mesh efficiently because shape is not always totally respected. D. Luebke, in 1997, has proposed a taxonomy of mesh simplification8. He presented the most used algorithms. He extracted different ways to use each algorithm. But in this paper, only one solution works with volumetric mesh9. T. He et al. propose a method based on voxel simplification by using a grid for clustering voxels. A marching cube10 algorithm was applied to produce a surface mesh. But this simplification algorithm did not preserve the shape of the mesh. In our work, we look for point cloud simplification. Indeed, previous methods which deal with simplification for surface point cloud like11-13 are not adapted to our case. All of these methods produce LOD for surface mesh and point cloud is extracted from scanner. + +# 3. PROPOSED APPROACH + +This section presents the different methods that are used to visualize a kind of data from Green Data Center (GDC). The main goal is to be able to visualize in real-time the evolution of temperature in the data center. For this, we use a special particle method. Particles are located using a segmentation algorithm based on Voronoi cell extraction and Delaunay triangulation. The latency due to the large flow of particles is avoided by using a client server paradigm. We improve our solution by using LOD methods to simplify rendering. + +# 3.1 Particle systems + +Rooms are the bases of our study. For modeling a room, we extract the shape of the space representation which is composed by a box with three measures: length $(l \in \mathbb{R})$ , width $(w \in \mathbb{R})$ , height $(h \in \mathbb{R})$ . Sensors are represented by $S = \{\mathrm{S}_1, \dots, \mathrm{S}_M\}$ , where $M$ is the number of sensors. Sensors $\mathrm{S}_i (\mathrm{i} \in \{1, \dots, M\})$ are placed on the space on a layer $\mathbf{L} \in \mathbb{N}$ and have a location represented by: $\{\mathbf{X}_i, \mathbf{Y}_i, \mathbf{L}_j\}$ with $\mathbf{X}_i \in \mathbb{R}$ , $\mathbf{Y}_i \in \mathbb{R}$ and $j$ is the layer used. For modeling the space inside a room, we use a particle system instead of 2D map representations which have some lacks. $^{14}$ Actually 2D map does not allow having a real visualization of space. A particle visualization gives a better efficiency for modeling space. We use a large number of particles to represent the entire space. $\mathbf{N} \in \mathbb{N}$ represents the number of particles in the room. It can be calculated using: + +$$ +N = \frac {\left(\left(l + 1\right) \times (h + 1) \times (w + 1)\right)}{\delta^ {3}} \tag {1} +$$ + +where $\delta \in \mathbb{R}$ is the space between particles. The particle grid is regular. In this model, three layers of temperature sensors compose rooms. They are defined according to their real locations in the data center. Figure ?? presents the different layers of sensors in the data center. + +Particles carry information, and flow motion can be simulated if needed by changing the value of particles and the computational cost is inferior. + +# 3.2 Segmentation algorithms + +In our solution, each sensors has an influence on surrounding particules. To calculate the set of particles in the sensor range, we use two methods: Voronoi cells extraction and Delaunay triangulation. + +Voronoi cells is a method to extract a partition of space $^{15}$ . This method is available for $\phi$ dimensions where $\phi \in [1, +\infty]$ , but most of implementations are done in 2D. Tools for extracting 3D Voronoi diagrams exist: Voro++ and QHull but particles are discrete and these solutions are not suitable because they extract Voronoi diagram in a continuous way. Then we designed our own method based on sphere expansion. We search nearest sensors for each particle. This part allows to weight particles outside the sensors mesh. A second method to weight the interior of the sensors mesh is used. We extract the mesh tetrahedron of sensors using the Delaunay triangulation implemented in QHull. This method was used to analyze the location of particle. We compute the exact location using ray tracing on the soup of tetrahedron. First, we search the nearest particles inside the hull of each tetrahedron. We extract the normal of each face of tetrahedron and we apply these normals on each particle. If the ray cuts three faces or more, the particle is inside the tetrahedron. This method is cost expensive and done in preprocessing. Moreover, particles are static and position didn't need to be update. + +# 3.3 Client server paradigm + +To improve computation, a client server paradigm is used. We define a low cost communication protocol to transfer data from a server to a client. Server computes the modification of particles and the client displays the results. This protocol works in five steps. These steps are: sending header, sending sensor data, sending particle data, sending footer and receiving acknowledgment/language command from client. At each step, the server waits the acknowledgment from the client. We develop two ways to send data. The first sends the entire point cloud (sensors and particles). The biggest problem of this method is the + +transmission of data. Sensors are sent with their coordinates and their value. We encode these data in bit words. For the particles data, the same method was used. The footer was sent for closing the communication. The second method is used to reduce efficiently the communication cost. We only send modified sensors and particles. The id and the new value is sent instead of coordinates. The last step is the command sent by the client. It allows the user to interact with the server. We use it to modify the camera viewpoint. + +# 3.4 Level of detail for particles + +Level of detail (LOD) is one of the most important methods in computer graphics. It allows to solve rendering problems or performance problems. This method consists by producing several resolution of a 3D object. In our works, we use some features to define the object resolution: hardware and viewpoint. Hardware and viewpoint do not need the same data structure and we need to recompute it for each modification of the viewpoint or when hardware changes. LOD was defined by two problems statement. The first one uses a sample of original points, the second one uses a new point data set. In this part, we define six methods to produce LOD. The four first methods are for the client, the other are for the server. + +# Problems statement: + +For this two approaches, we have a set $\omega$ of Vertices $V$ , $V = \{V_1, \ldots, V_\omega\}$ . Each vertex is defined in $\mathbb{R}^3$ . Simplify a mesh using a sample vertex means $\omega > \omega 2$ , where $\omega 2$ is the size of the second data set. For approach 1, we obtain a new object $\mathrm{V}2 = \{\mathrm{V}2_1, \ldots, \mathrm{V}2_\omega\}$ with fewer points than V but V 2 is a subset of V. For approach 2, we obtain a new object $\mathrm{V}3 = \{\mathrm{V}3_1, \ldots, \mathrm{V}3_\omega\}$ with fewer points than V but each point in V 3 is a new vertex. + +In Section 2 we have presented methods to produce simplification. A few were designed for volumetric simplification. In this section, we propose several methods to produce different volumetric simplifications on our client. We develop four approaches to simplify 3D objects: clustering, neighbor simplification and two approaches based on server. Clustering method was based on He et al. $^{9}$ works, it consists of clustering particles using a 3D grid. Cells sizes of grid are set depending to the viewpoint of the camera. Clusters were being weight with the average of the different values of particles. The position is the barycenter of these particles. Figures 1(a)-1(e) give some examples of simplification using clustering solution. Figure 1(a) present the original point of cloud mesh. Figure + +1(b) and 1(d) give two different methods for clustering. And finally, Figure 1(c) and 1(e) give the results of clustering methods. + +Figure 1. Clustering method for simplification point cloud. +![](images/ae6cbd294176dc493b50c73240c504ea8c9fc09c9e3151fba6f0be709b525025.jpg) +The second solution used is based on neighborhood extraction. Before runtime, we extract all neighbors of a particle. We measure the distance between each particle. Some optimization can help to decrease complexity: we can estimate easily in our structure which particle is closer to another one (using the fact that particle grid is regular). After this, + +we extract the main value of particles. We explore each neighbor of particles and we keep the most important. In some cases, the most important can be the high values, in other the low values and in other both of them. This solution is able to produce a low resolution model with the most important information structure. Several low resolution models are created by exploring deeper in neighborhood. Figures 2(a)-2(c) illustrate a neighbor, and two simplifications of this mesh. + +![](images/23944f9963b290146f2ac445e8970545bcf00b2949e999067a13468653d749cc.jpg) +(a) Neighborhood cloud. + +![](images/0e41ba0aeddc8af5f2b6664c64abea63f9b32bfd4692c38f916d07f501d537e5.jpg) +(b) Simplification neighborhood of 1. + +![](images/c01c12cfcf72e187db35ff49ad4d5edb57331b8d93efa4c1f20941ebf580a3d7.jpg) +(c) Simplification neighborhood of 2. +Figure 2. Neighbor method for simplification. + +Other methods were based on server instead of client. Client sent via TCP connection his viewpoint. The server recomputes the particles structure and recreates the entire structure. With this solution, it is possible to produce a point cloud resolution depending on hardware. Figure 3(a) presents particles rendering with a distance of 2 from the camera. Figure 3(b) is the decimation produced with a distance of 3 and Figure 3(c) is a distance of 1. + +Another method was based on Voronoi diffusion of temperature. The bandwidth for transmitting data is limited. We developed Voronoi temperature diffusion to solve this communication. In this approach, we update data using sphere expansion. Each time, we update particles depending on their distance from sensors. The more particles are distant from sensors the later they will be refreshed. This method sends only modified particles. The bandwidth is saved and the visualization gives a flow effect. Figure 4(a) represents values at time 0. At time 1, values of sensors change, 4(b). After time 2, we update a first range of particles 4(c) and finally the second range 4(d). + +![](images/7eac2440a2fedd66d943c82b390c3a9df5d95d019d523a29c7a3e2f9c7218928.jpg) +(a) Particles server $(\mathrm{D} = 2)$ +Figure 3. Particle simplification using server and distance. + +![](images/c4777a0507eee1c1beaa13c04e351827098bc588e6ced9d8de6cff01430e3df5.jpg) +(b) Particles produce server $(\mathrm{D} = 3)$ + +![](images/5dabdfa6b0129921b2abb27785be9608573a25f26e4646d20c6b92250fad1414.jpg) +(c) Particles produce by server $(\mathrm{D} = 1)$ + +![](images/e340d9807d4ed601eee3bd74351618a9adfda026a8dbd720f9d2aa40857dad26.jpg) +(a) Particles and sensors (T = 0). + +![](images/92c09c0b767ea453098777786fb815e8c2f833a8abc790807397f42e9a6f6887.jpg) +(b) Sensors update $(\mathrm{T} = 1)$ . + +![](images/416dbc943d118d6834e80c8c5ad759b34f940700b96fd0b87bb23c082f10cf10.jpg) +(c) First range $(\mathrm{T} = 2)$ . +Figure 4. Simplification using bandwidth size. + +![](images/a79e8f2104ab8c32df4137808fc6b4ce9b7465bfa15c2080bd3aabb2c58986d0.jpg) +(d) Second range $(\mathrm{T} = 3)$ . + +# 4. EXPERIMENTAL RESULTS + +The data are extracted from two rooms of the IBM data center. Firstly, we present our method for rendering the room, and later we present our results using Level Of Detail methods. + +# 4.1 Data visualization + +We want to visualize and manage the consumption of a data center. For the visualization, we want to use an IFC viewer. But the IFC model for GDC is not available yet. Data center extraction of the room space is for the moment done by hand. The room is empty and was represent by a simple shape a box with 4 meters length, 3 meters width and 2.5 meters height. We use point cloud visualization based on particle paradigm. We use the two rooms of the data center and we put the same number of particles (30000) and 35 sensors distributed on three layers at 1 meter; 2 meter and on the ground. We define high and low temperature regarding the real sensors value. Figure 5(a) presents temperature color scale, Figure 5(b) and Figure 5(c) present data center sensors. + +The next step is to interpolate data from sensors. For this, we extract the sensor mesh. We use QHULL to produce a soup of tetrahedrons. Particles need to be located. We can determine which tetrahedron is the nearest, we extract the box hull of tetrahedron and we apply for each particle the norms of each tetrahedron face. If these rays cut three or more faces, then particle is inside the tetrahedron. With this method, we can determine exactly the location of each particles regarding to the tetrahedrons, a weight is given to them easily. It was used to apply a coefficient to the value of each vertex of tetrahedron. For the outside particles, another solution was used: Voronoi cells. This method is based on a discrete extraction of Voronoi cells. We use our own method because other method like Voro ++ or QHull extract Voronoi diagram in a continuous way. + +![](images/7c729f1706460b0bf0adde7a8dbd071f9ae77f611ef3f85b3d951fb62795016c.jpg) + +![](images/8c16ad7a59f34e5974a4322466cec0149f8905a1a1b1cfadff910a3fec50d004.jpg) +(b) Room one. + +![](images/2eb0e7b79700cbbd72a8a244992163f567dbbd68f9d3db6bad3e5808cda4dabb.jpg) +(c) Room two. + +# 4.2 Level of details + +In the earlier days of this project, first solution proposed gives a low frame rates, about 15 FPS (Frame Per Second): visualization was not in real-time (real-time is about 24 FPS). For solving this problem, we define a client server paradigm. This solution allows to produce a real-time rendering on the client. Figure ?? gives an example of LOD for particles. We use Openscenegraph $^{20}$ as a 3D engine. It owns several features useful in LOD. A special object is defined to manage multi-resolution model. It calculates the distance of the object from the camera. For our experimentation we use five resolutions of mesh. The first mesh was the original mesh, it is set at 0 to 500. The next mesh was set at 500 to 1000, the next at 1000 to 1500 and the other at 1500 to 2000. These three meshes were constructed by specific LOD methods: clustering and significant vertices. Clustering defines a 3D grid inside the room. The size of each cell depends on the viewpoint location. The size of the cluster depends on the visibility of the clustered particles. First results are given Figure 6(a) and 6(b). Value of cluster is an average of clustered value. The number of points of the final mesh depends on the grid size. Table 1 shows the results at several distances. + +
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X30000390024036
+ +![](images/9fbe1142edda7eab13f0abb9592b84e63d1611257e7426d7d569a68b9df82b38.jpg) +Figure 5. Data use to model the system. +(a) $\mathrm{D} = 500$ to 1000. +Figure 6. Clustering visualization algorithms. + +![](images/69ae709df8988787ff641b5b6eb5a608ca0636bba7110a3a4735064168d117da.jpg) +Table 1. Results of clustering simplification. +(b) $D = 1000$ to 1500. + +Significant points method extracts the neighbors for each particle. We extract the highest and lowest temperatures, by exploring the neighborhood of a particle, in order to have significant vertices of the model. For the first step of simplified model we explore neighbor. For the second model, we explore neighbor and neighbor of neighbor, etc. This solution simplifies drastically the model. First results are given Figure ??-??. Table 2 shows the number of vertices at several distance. + +
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X300002295045543524
+ +![](images/4050e8f862ac40be7bc6d5c239997192325936e244911b8d69fe60a4ab8810b8.jpg) +(a) Neighborhood 1. +Figure 7. Clustering visualization algorithms using neighbor. + +![](images/dafb2130c8265a91a7faed53db3de1181cd524770896acda68d5a953df004f87.jpg) +(b) Neighborhood 2. + +The first server solution receives orders from client as presented Section 3.4. We calculate the viewpoint distance and we send data according to it. A new structure is recalculated if the camera is too far from the object. After the recomputing, we send the new data. This solution allows the user to receive more or less data according to its distance to the object. Table 3 shows some different resolutions produced with this method. + +Table 2. Results of neighbor simplification. + +
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X1200003000075001875
+ +Table 3. Several resolution of model. + +Another solution is to use bandwidth latency. We send data at several times, we do not send the entire set of data but only modified particles. We send at first time the sensors data, and subsequently we send a range of data (the nearest). After few minutes, all data are sent. This solution gives good results, and simulates a thermal diffusion in the whole structure of particles. Figure 8(a)-8(c) illustrate this method. + +![](images/2fcee6efa3b1d3c44144e2639f3857a15c4079f838c4f9132953fd427a8b1be9.jpg) +(a) $\mathrm{T} = 0$ + +![](images/b2be70bd4cc7d261ac38e8bc653a0c09c537d49d2a5612ed5c067058a98ef463.jpg) +(b) $\mathrm{T} = 1$ + +![](images/0d4e22f04d3ea25761125c93fc6d70fe856bf840ef353c043f32d21c9633724e.jpg) +(c) $\mathrm{T} = 4$ + +# 5. CONCLUSION + +In this paper, we have presented a method to visualize sensors data extracted from a Green Data Center. This approach produces interpolation visualization for managing and visualizing data. This interpolation used a Delaunay triangulation and a cell extraction based on Voronoi. An unusual way of use particles helps to process data. First results present the solution proposed to visualize the inside of a GDC space. The second results proposed in this paper aim to improve the rendering. + +For this, first step introduces a client/server protocol a second step illustrates methods to simplify the model. With these different approaches we improve the rendering time, preserving most important data are kept. In future works, we will work on data "dressing". We want to find a way to improve rendering of the scene using meatballs or marching cube algorithms. A main constraint of this work is real-time computation. Future work also concern to add rooms to the visualization. At present, we only visualize a single room. We want to visualize building, and complex form, by using an IFC loader. + +# ACKNOWLEDGMENTS + +We want to thanks the PSSC (Products and Solutions Support Center) team of IBM Montpellier for having provided the necessary equipment and data need for this experimentation. And we thank the FUI (Fonds Unique Interministriel) for their financial support. + +# REFERENCES + +[1] Clark, J. H., "Hierarchical geometric models for visible surface algorithms," Communications of the ACM 19(10), 547-554 (1976). +[2] Damon, M., Kameyama, M., Knox, M., Porter, D., Yuen, D., and Sevre, E., "Interactive visualization of 3d mantle convection," Visual Geosciences (2008). +[3] Jordan, K. E., Yuen, D. A., Reuteler, D. M., Zhang, S., and Haimes, R., "Parallel interactive visualization of 3d mantle convection," IEEE Comput. Sci. Eng. 3(4), 29-37 (1996). +[4] Reeves, W. 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H., "Ray tracing complex models containing surface tessellations," SIGGRAPH Comput. Graph. 21(4), 119-128 (1987). +[19] Hoppe, H., "Progressive meshes. computer graphics," SIGGRAPH96 Proceedings, 99108 (1996). +[20] Burns, D. and Osfield, R., "Open scene graph a: Introduction, b: Examples and applications," 265 (2004). + +Further author information: + +Lange B.: E-mail: benoit.lange@lirmm.fr + +Rodriguez N.: E-mail: nancy.rodriguez@lirmm.fr + +Puech W.: E-mail: william.puech@lirmm.fr + +Rey H.: E-mail:REYHERVE@fr.ibm.com + +Vasques X.: E-mail: xaviervasques@fr.ibm.com \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09198/images/0d4e22f04d3ea25761125c93fc6d70fe856bf840ef353c043f32d21c9633724e.jpg b/data/2025/2503_09xxx/2503.09198/images/0d4e22f04d3ea25761125c93fc6d70fe856bf840ef353c043f32d21c9633724e.jpg new file mode 100644 index 0000000000000000000000000000000000000000..5def2780305cf01e1e03ab140e1d88418bc6b996 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09198/images/0d4e22f04d3ea25761125c93fc6d70fe856bf840ef353c043f32d21c9633724e.jpg @@ -0,0 +1,3 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Data are extracted from sensors located in the IBM Green Data Center in Montpellier France. These sensors measure different information such as hygrometry, pressure and temperature. We want to visualize in real-time the large among of data produced by these sensors. A visualization engine has been designed, based on particles system and a client server paradigm. In order to solve performance problems, a Level Of Detail solution has been developed. These methods are based on the earlier work introduced by J. Clark in " + }, + { + "bbox": [ + 131, + 267, + 481, + 407 + ], + "type": "inline_equation", + "content": "1976^{1}" + }, + { + "bbox": [ + 131, + 267, + 481, + 407 + ], + "type": "text", + "content": ". In this paper we introduce a particle method used for this work and subsequently we explain different simplification methods applied to improve our solution." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 417, + 449, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 417, + 449, + 429 + ], + "spans": [ + { + "bbox": [ + 88, + 417, + 449, + 429 + ], + "type": "text", + "content": "Keywords: 3D Visualization, Sensors, Particles, Client/Server, Level Of Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 89, + 456, + 227, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 456, + 227, + 472 + ], + "spans": [ + { + "bbox": [ + 89, + 456, + 227, + 472 + ], + "type": "text", + "content": "1. INTRODUCTION" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 87, + 483, + 515, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 483, + 515, + 685 + ], + "spans": [ + { + "bbox": [ + 87, + 483, + 515, + 685 + ], + "type": "text", + "content": "In this paper, we present a method to produce a 3D visualization for analyzing and managing temperature. Data are extracted from sensors located in the IBM Green Data Center in Montpellier, which provides many different types of information like temperature, pressure or hygrometry. In our system, sensors are placed in a virtual room and the internal space is modeled using particles. The main constraint here is to produce a real-time rendering. However, latency appears du to the number of vertices. In this paper, we use a solution called LOD (Level Of Detail) to produce multi resolution 3D objects. This solution has been introduced in 1976 by J. Clark1. In this paper, J. Clark introduces the use of several mesh resolutions to simplify the 3D scene complexity. In our work, we use various simplification methods to provide interactive rendering and allows rendering the most important part of data extracted from sensors. In this paper, we describe how we create a room, and the methods used to produce different resolution visualization. In Section 2, we introduce related work on particles systems and LOD. In Section 3, we expose our solution to simplify particles system. In Section 4 we give some results and finally, in Section 5 we present our conclusions and future work." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 769, + 315, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 769, + 315, + 776 + ], + "spans": [ + { + "bbox": [ + 296, + 769, + 315, + 776 + ], + "type": "text", + "content": "1/10" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 89, + 55, + 230, + 70 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 55, + 230, + 70 + ], + "spans": [ + { + "bbox": [ + 89, + 55, + 230, + 70 + ], + "type": "text", + "content": "2. RELATED WORK" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 88, + 83, + 507, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 83, + 507, + 108 + ], + "spans": [ + { + "bbox": [ + 88, + 83, + 507, + 108 + ], + "type": "text", + "content": "In this section we present several previous works concerning data visualization, particle systems and level of detail methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 88, + 110, + 512, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 110, + 512, + 176 + ], + "spans": [ + { + "bbox": [ + 88, + 110, + 512, + 176 + ], + "type": "text", + "content": "Some previous work present solutions to visualize large data flow extracted from mantle convection. M. Damon et al. " + }, + { + "bbox": [ + 88, + 110, + 512, + 176 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 88, + 110, + 512, + 176 + ], + "type": "text", + "content": " and K. E. Jordan et al. " + }, + { + "bbox": [ + 88, + 110, + 512, + 176 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 88, + 110, + 512, + 176 + ], + "type": "text", + "content": " present interactive viewers for this kind of data. These data are computed by using Hight Performance Computing (HPC) and visualized on a large display. The rendering is calculated by using another HPC. The data flow is very important and a real-time 3D simulation is hard to obtain. W. Kapfer and" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 88, + 186, + 521, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 186, + 521, + 320 + ], + "spans": [ + { + "bbox": [ + 88, + 186, + 521, + 320 + ], + "type": "text", + "content": "T. Riser6 introduce how to use particle system to visualize astronomic simulation, particles representing space objects. The number of particles is extremely important for computing motion in real-time. GPU computing is preferred to render instead of a common HPC solution. To display their data, they have developed their own 3D graphical engine. The space objects are represented by point sprite instead of sphere. Lights are used to give a spherical aspect to the point sprite. This solution allows to render more stars than spherical object method. The 3D engine provides different rendering methods to group space objects: cell simplification or extraction of isosurface. The use of GPU seems quite well for a particle solution, parallel processing allows to render large data; the astrological data seems to be well suited." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 322, + 521, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 322, + 521, + 536 + ], + "spans": [ + { + "bbox": [ + 88, + 322, + 521, + 536 + ], + "type": "text", + "content": "In 1976, J. Clark introduces Level Of Detail (LOD) concept1. LOD consists of several resolution meshes for using them at different distances from the camera. Firstly, designer produces these meshes. First algorithms, in 1992 Schroeder et al. developed a method by decimation for simplify the mesh7. It analyses mesh geometry and evaluates the complexity of triangles. Vertices are removed if only constraints set by the user are respected. Vertices are removed and gaps are filled using triangulation. These algorithms of simplification are not enough to simplify mesh efficiently because shape is not always totally respected. D. Luebke, in 1997, has proposed a taxonomy of mesh simplification8. He presented the most used algorithms. He extracted different ways to use each algorithm. But in this paper, only one solution works with volumetric mesh9. T. He et al. propose a method based on voxel simplification by using a grid for clustering voxels. A marching cube10 algorithm was applied to produce a surface mesh. But this simplification algorithm did not preserve the shape of the mesh. In our work, we look for point cloud simplification. Indeed, previous methods which deal with simplification for surface point cloud like11-13 are not adapted to our case. All of these methods produce LOD for surface mesh and point cloud is extracted from scanner." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 89, + 563, + 277, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 563, + 277, + 578 + ], + "spans": [ + { + "bbox": [ + 89, + 563, + 277, + 578 + ], + "type": "text", + "content": "3. PROPOSED APPROACH" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 88, + 590, + 517, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 590, + 517, + 671 + ], + "spans": [ + { + "bbox": [ + 88, + 590, + 517, + 671 + ], + "type": "text", + "content": "This section presents the different methods that are used to visualize a kind of data from Green Data Center (GDC). The main goal is to be able to visualize in real-time the evolution of temperature in the data center. For this, we use a special particle method. Particles are located using a segmentation algorithm based on Voronoi cell extraction and Delaunay triangulation. The latency due to the large flow of particles is avoided by using a client server paradigm. We improve our solution by using LOD methods to simplify rendering." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 769, + 315, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 769, + 315, + 776 + ], + "spans": [ + { + "bbox": [ + 296, + 769, + 315, + 776 + ], + "type": "text", + "content": "2/10" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 87, + 54, + 204, + 68 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 54, + 204, + 68 + ], + "spans": [ + { + "bbox": [ + 87, + 54, + 204, + 68 + ], + "type": "text", + "content": "3.1 Particle systems" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "spans": [ + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": "Rooms are the bases of our study. For modeling a room, we extract the shape of the space representation which is composed by a box with three measures: length " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "(l \\in \\mathbb{R})" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": ", width " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "(w \\in \\mathbb{R})" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": ", height " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "(h \\in \\mathbb{R})" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": ". Sensors are represented by " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "S = \\{\\mathrm{S}_1, \\dots, \\mathrm{S}_M\\}" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": " is the number of sensors. Sensors " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "\\mathrm{S}_i (\\mathrm{i} \\in \\{1, \\dots, M\\})" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": " are placed on the space on a layer " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "\\mathbf{L} \\in \\mathbb{N}" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": " and have a location represented by: " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}_i, \\mathbf{Y}_i, \\mathbf{L}_j\\}" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_i \\in \\mathbb{R}" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_i \\in \\mathbb{R}" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": " is the layer used. For modeling the space inside a room, we use a particle system instead of 2D map representations which have some lacks." + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "^{14}" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": " Actually 2D map does not allow having a real visualization of space. A particle visualization gives a better efficiency for modeling space. We use a large number of particles to represent the entire space. " + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "inline_equation", + "content": "\\mathbf{N} \\in \\mathbb{N}" + }, + { + "bbox": [ + 85, + 77, + 517, + 214 + ], + "type": "text", + "content": " represents the number of particles in the room. It can be calculated using:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 110, + 220, + 321, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 220, + 321, + 251 + ], + "spans": [ + { + "bbox": [ + 110, + 220, + 321, + 251 + ], + "type": "interline_equation", + "content": "N = \\frac {\\left(\\left(l + 1\\right) \\times (h + 1) \\times (w + 1)\\right)}{\\delta^ {3}} \\tag {1}", + "image_path": "96bce3148486d00ea374e73aeb6caf0bb16a8ee9cc4e78a0b161de5fdfe93db0.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 261, + 515, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 261, + 515, + 313 + ], + "spans": [ + { + "bbox": [ + 85, + 261, + 515, + 313 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 85, + 261, + 515, + 313 + ], + "type": "inline_equation", + "content": "\\delta \\in \\mathbb{R}" + }, + { + "bbox": [ + 85, + 261, + 515, + 313 + ], + "type": "text", + "content": " is the space between particles. The particle grid is regular. In this model, three layers of temperature sensors compose rooms. They are defined according to their real locations in the data center. Figure ?? presents the different layers of sensors in the data center." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 85, + 316, + 512, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 316, + 512, + 343 + ], + "spans": [ + { + "bbox": [ + 85, + 316, + 512, + 343 + ], + "type": "text", + "content": "Particles carry information, and flow motion can be simulated if needed by changing the value of particles and the computational cost is inferior." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 355, + 256, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 355, + 256, + 370 + ], + "spans": [ + { + "bbox": [ + 86, + 355, + 256, + 370 + ], + "type": "text", + "content": "3.2 Segmentation algorithms" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 378, + 511, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 378, + 511, + 418 + ], + "spans": [ + { + "bbox": [ + 85, + 378, + 511, + 418 + ], + "type": "text", + "content": "In our solution, each sensors has an influence on surrounding particules. To calculate the set of particles in the sensor range, we use two methods: Voronoi cells extraction and Delaunay triangulation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "spans": [ + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "type": "text", + "content": "Voronoi cells is a method to extract a partition of space " + }, + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "type": "inline_equation", + "content": "^{15}" + }, + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "type": "text", + "content": ". This method is available for " + }, + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "type": "text", + "content": " dimensions where " + }, + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "type": "inline_equation", + "content": "\\phi \\in [1, +\\infty]" + }, + { + "bbox": [ + 85, + 418, + 523, + 609 + ], + "type": "text", + "content": ", but most of implementations are done in 2D. Tools for extracting 3D Voronoi diagrams exist: Voro++ and QHull but particles are discrete and these solutions are not suitable because they extract Voronoi diagram in a continuous way. Then we designed our own method based on sphere expansion. We search nearest sensors for each particle. This part allows to weight particles outside the sensors mesh. A second method to weight the interior of the sensors mesh is used. We extract the mesh tetrahedron of sensors using the Delaunay triangulation implemented in QHull. This method was used to analyze the location of particle. We compute the exact location using ray tracing on the soup of tetrahedron. First, we search the nearest particles inside the hull of each tetrahedron. We extract the normal of each face of tetrahedron and we apply these normals on each particle. If the ray cuts three faces or more, the particle is inside the tetrahedron. This method is cost expensive and done in preprocessing. Moreover, particles are static and position didn't need to be update." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 620, + 244, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 620, + 244, + 635 + ], + "spans": [ + { + "bbox": [ + 86, + 620, + 244, + 635 + ], + "type": "text", + "content": "3.3 Client server paradigm" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 85, + 643, + 520, + 738 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 643, + 520, + 738 + ], + "spans": [ + { + "bbox": [ + 85, + 643, + 520, + 738 + ], + "type": "text", + "content": "To improve computation, a client server paradigm is used. We define a low cost communication protocol to transfer data from a server to a client. Server computes the modification of particles and the client displays the results. This protocol works in five steps. These steps are: sending header, sending sensor data, sending particle data, sending footer and receiving acknowledgment/language command from client. At each step, the server waits the acknowledgment from the client. We develop two ways to send data. The first sends the entire point cloud (sensors and particles). The biggest problem of this method is the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "spans": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "type": "text", + "content": "3/10" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 85, + 52, + 508, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 52, + 508, + 133 + ], + "spans": [ + { + "bbox": [ + 85, + 52, + 508, + 133 + ], + "type": "text", + "content": "transmission of data. Sensors are sent with their coordinates and their value. We encode these data in bit words. For the particles data, the same method was used. The footer was sent for closing the communication. The second method is used to reduce efficiently the communication cost. We only send modified sensors and particles. The id and the new value is sent instead of coordinates. The last step is the command sent by the client. It allows the user to interact with the server. We use it to modify the camera viewpoint." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 87, + 145, + 266, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 145, + 266, + 159 + ], + "spans": [ + { + "bbox": [ + 87, + 145, + 266, + 159 + ], + "type": "text", + "content": "3.4 Level of detail for particles" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 85, + 167, + 519, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 167, + 519, + 288 + ], + "spans": [ + { + "bbox": [ + 85, + 167, + 519, + 288 + ], + "type": "text", + "content": "Level of detail (LOD) is one of the most important methods in computer graphics. It allows to solve rendering problems or performance problems. This method consists by producing several resolution of a 3D object. In our works, we use some features to define the object resolution: hardware and viewpoint. Hardware and viewpoint do not need the same data structure and we need to recompute it for each modification of the viewpoint or when hardware changes. LOD was defined by two problems statement. The first one uses a sample of original points, the second one uses a new point data set. In this part, we define six methods to produce LOD. The four first methods are for the client, the other are for the server." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 300, + 188, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 300, + 188, + 311 + ], + "spans": [ + { + "bbox": [ + 86, + 300, + 188, + 311 + ], + "type": "text", + "content": "Problems statement:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "spans": [ + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": "For this two approaches, we have a set " + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": " of Vertices " + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "inline_equation", + "content": "V = \\{V_1, \\ldots, V_\\omega\\}" + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": ". Each vertex is defined in " + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3" + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": ". Simplify a mesh using a sample vertex means " + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "inline_equation", + "content": "\\omega > \\omega 2" + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "inline_equation", + "content": "\\omega 2" + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": " is the size of the second data set. For approach 1, we obtain a new object " + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "inline_equation", + "content": "\\mathrm{V}2 = \\{\\mathrm{V}2_1, \\ldots, \\mathrm{V}2_\\omega\\}" + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": " with fewer points than V but V 2 is a subset of V. For approach 2, we obtain a new object " + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "inline_equation", + "content": "\\mathrm{V}3 = \\{\\mathrm{V}3_1, \\ldots, \\mathrm{V}3_\\omega\\}" + }, + { + "bbox": [ + 85, + 312, + 523, + 381 + ], + "type": "text", + "content": " with fewer points than V but each point in V 3 is a new vertex." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 85, + 391, + 519, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 391, + 519, + 513 + ], + "spans": [ + { + "bbox": [ + 85, + 391, + 519, + 513 + ], + "type": "text", + "content": "In Section 2 we have presented methods to produce simplification. A few were designed for volumetric simplification. In this section, we propose several methods to produce different volumetric simplifications on our client. We develop four approaches to simplify 3D objects: clustering, neighbor simplification and two approaches based on server. Clustering method was based on He et al. " + }, + { + "bbox": [ + 85, + 391, + 519, + 513 + ], + "type": "inline_equation", + "content": "^{9}" + }, + { + "bbox": [ + 85, + 391, + 519, + 513 + ], + "type": "text", + "content": " works, it consists of clustering particles using a 3D grid. Cells sizes of grid are set depending to the viewpoint of the camera. Clusters were being weight with the average of the different values of particles. The position is the barycenter of these particles. Figures 1(a)-1(e) give some examples of simplification using clustering solution. Figure 1(a) present the original point of cloud mesh. Figure" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 521, + 520, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 521, + 520, + 548 + ], + "spans": [ + { + "bbox": [ + 85, + 521, + 520, + 548 + ], + "type": "text", + "content": "1(b) and 1(d) give two different methods for clustering. And finally, Figure 1(c) and 1(e) give the results of clustering methods." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 91, + 552, + 520, + 651 + ], + "blocks": [ + { + "bbox": [ + 91, + 552, + 520, + 651 + ], + "lines": [ + { + "bbox": [ + 91, + 552, + 520, + 651 + ], + "spans": [ + { + "bbox": [ + 91, + 552, + 520, + 651 + ], + "type": "image", + "image_path": "ae6cbd294176dc493b50c73240c504ea8c9fc09c9e3151fba6f0be709b525025.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 85, + 667, + 362, + 680 + ], + "lines": [ + { + "bbox": [ + 85, + 667, + 362, + 680 + ], + "spans": [ + { + "bbox": [ + 85, + 667, + 362, + 680 + ], + "type": "text", + "content": "Figure 1. Clustering method for simplification point cloud." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 85, + 681, + 522, + 735 + ], + "lines": [ + { + "bbox": [ + 85, + 681, + 522, + 735 + ], + "spans": [ + { + "bbox": [ + 85, + 681, + 522, + 735 + ], + "type": "text", + "content": "The second solution used is based on neighborhood extraction. Before runtime, we extract all neighbors of a particle. We measure the distance between each particle. Some optimization can help to decrease complexity: we can estimate easily in our structure which particle is closer to another one (using the fact that particle grid is regular). After this," + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "spans": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "type": "text", + "content": "4/10" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 86, + 52, + 517, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 52, + 517, + 133 + ], + "spans": [ + { + "bbox": [ + 86, + 52, + 517, + 133 + ], + "type": "text", + "content": "we extract the main value of particles. We explore each neighbor of particles and we keep the most important. In some cases, the most important can be the high values, in other the low values and in other both of them. This solution is able to produce a low resolution model with the most important information structure. Several low resolution models are created by exploring deeper in neighborhood. Figures 2(a)-2(c) illustrate a neighbor, and two simplifications of this mesh." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 91, + 137, + 232, + 269 + ], + "blocks": [ + { + "bbox": [ + 91, + 137, + 232, + 269 + ], + "lines": [ + { + "bbox": [ + 91, + 137, + 232, + 269 + ], + "spans": [ + { + "bbox": [ + 91, + 137, + 232, + 269 + ], + "type": "image", + "image_path": "23944f9963b290146f2ac445e8970545bcf00b2949e999067a13468653d749cc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 91, + 270, + 181, + 294 + ], + "lines": [ + { + "bbox": [ + 91, + 270, + 181, + 294 + ], + "spans": [ + { + "bbox": [ + 91, + 270, + 181, + 294 + ], + "type": "text", + "content": "(a) Neighborhood cloud." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 235, + 137, + 375, + 267 + ], + "blocks": [ + { + "bbox": [ + 235, + 137, + 375, + 267 + ], + "lines": [ + { + "bbox": [ + 235, + 137, + 375, + 267 + ], + "spans": [ + { + "bbox": [ + 235, + 137, + 375, + 267 + ], + "type": "image", + "image_path": "0e41ba0aeddc8af5f2b6664c64abea63f9b32bfd4692c38f916d07f501d537e5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 235, + 270, + 325, + 295 + ], + "lines": [ + { + "bbox": [ + 235, + 270, + 325, + 295 + ], + "spans": [ + { + "bbox": [ + 235, + 270, + 325, + 295 + ], + "type": "text", + "content": "(b) Simplification neighborhood of 1." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 378, + 137, + 518, + 268 + ], + "blocks": [ + { + "bbox": [ + 378, + 137, + 518, + 268 + ], + "lines": [ + { + "bbox": [ + 378, + 137, + 518, + 268 + ], + "spans": [ + { + "bbox": [ + 378, + 137, + 518, + 268 + ], + "type": "image", + "image_path": "c01c12cfcf72e187db35ff49ad4d5edb57331b8d93efa4c1f20941ebf580a3d7.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 378, + 270, + 468, + 295 + ], + "lines": [ + { + "bbox": [ + 378, + 270, + 468, + 295 + ], + "spans": [ + { + "bbox": [ + 378, + 270, + 468, + 295 + ], + "type": "text", + "content": "(c) Simplification neighborhood of 2." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 86, + 311, + 301, + 323 + ], + "lines": [ + { + "bbox": [ + 86, + 311, + 301, + 323 + ], + "spans": [ + { + "bbox": [ + 86, + 311, + 301, + 323 + ], + "type": "text", + "content": "Figure 2. Neighbor method for simplification." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 324, + 522, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 324, + 522, + 390 + ], + "spans": [ + { + "bbox": [ + 85, + 324, + 522, + 390 + ], + "type": "text", + "content": "Other methods were based on server instead of client. Client sent via TCP connection his viewpoint. The server recomputes the particles structure and recreates the entire structure. With this solution, it is possible to produce a point cloud resolution depending on hardware. Figure 3(a) presents particles rendering with a distance of 2 from the camera. Figure 3(b) is the decimation produced with a distance of 3 and Figure 3(c) is a distance of 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 85, + 401, + 524, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 401, + 524, + 509 + ], + "spans": [ + { + "bbox": [ + 85, + 401, + 524, + 509 + ], + "type": "text", + "content": "Another method was based on Voronoi diffusion of temperature. The bandwidth for transmitting data is limited. We developed Voronoi temperature diffusion to solve this communication. In this approach, we update data using sphere expansion. Each time, we update particles depending on their distance from sensors. The more particles are distant from sensors the later they will be refreshed. This method sends only modified particles. The bandwidth is saved and the visualization gives a flow effect. Figure 4(a) represents values at time 0. At time 1, values of sensors change, 4(b). After time 2, we update a first range of particles 4(c) and finally the second range 4(d)." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 96, + 515, + 233, + 646 + ], + "blocks": [ + { + "bbox": [ + 96, + 515, + 233, + 646 + ], + "lines": [ + { + "bbox": [ + 96, + 515, + 233, + 646 + ], + "spans": [ + { + "bbox": [ + 96, + 515, + 233, + 646 + ], + "type": "image", + "image_path": "7eac2440a2fedd66d943c82b390c3a9df5d95d019d523a29c7a3e2f9c7218928.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 95, + 647, + 169, + 672 + ], + "lines": [ + { + "bbox": [ + 95, + 647, + 169, + 672 + ], + "spans": [ + { + "bbox": [ + 95, + 647, + 169, + 672 + ], + "type": "text", + "content": "(a) Particles server " + }, + { + "bbox": [ + 95, + 647, + 169, + 672 + ], + "type": "inline_equation", + "content": "(\\mathrm{D} = 2)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 86, + 687, + 364, + 700 + ], + "lines": [ + { + "bbox": [ + 86, + 687, + 364, + 700 + ], + "spans": [ + { + "bbox": [ + 86, + 687, + 364, + 700 + ], + "type": "text", + "content": "Figure 3. Particle simplification using server and distance." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 238, + 515, + 375, + 646 + ], + "blocks": [ + { + "bbox": [ + 238, + 515, + 375, + 646 + ], + "lines": [ + { + "bbox": [ + 238, + 515, + 375, + 646 + ], + "spans": [ + { + "bbox": [ + 238, + 515, + 375, + 646 + ], + "type": "image", + "image_path": "c4777a0507eee1c1beaa13c04e351827098bc588e6ced9d8de6cff01430e3df5.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 238, + 647, + 353, + 672 + ], + "lines": [ + { + "bbox": [ + 238, + 647, + 353, + 672 + ], + "spans": [ + { + "bbox": [ + 238, + 647, + 353, + 672 + ], + "type": "text", + "content": "(b) Particles produce server " + }, + { + "bbox": [ + 238, + 647, + 353, + 672 + ], + "type": "inline_equation", + "content": "(\\mathrm{D} = 3)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 380, + 515, + 517, + 646 + ], + "blocks": [ + { + "bbox": [ + 380, + 515, + 517, + 646 + ], + "lines": [ + { + "bbox": [ + 380, + 515, + 517, + 646 + ], + "spans": [ + { + "bbox": [ + 380, + 515, + 517, + 646 + ], + "type": "image", + "image_path": "5dabdfa6b0129921b2abb27785be9608573a25f26e4646d20c6b92250fad1414.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 378, + 647, + 518, + 672 + ], + "lines": [ + { + "bbox": [ + 378, + 647, + 518, + 672 + ], + "spans": [ + { + "bbox": [ + 378, + 647, + 518, + 672 + ], + "type": "text", + "content": "(c) Particles produce by server " + }, + { + "bbox": [ + 378, + 647, + 518, + 672 + ], + "type": "inline_equation", + "content": "(\\mathrm{D} = 1)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "spans": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "type": "text", + "content": "5/10" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 92, + 53, + 197, + 153 + ], + "blocks": [ + { + "bbox": [ + 92, + 53, + 197, + 153 + ], + "lines": [ + { + "bbox": [ + 92, + 53, + 197, + 153 + ], + "spans": [ + { + "bbox": [ + 92, + 53, + 197, + 153 + ], + "type": "image", + "image_path": "e340d9807d4ed601eee3bd74351618a9adfda026a8dbd720f9d2aa40857dad26.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 91, + 155, + 198, + 174 + ], + "lines": [ + { + "bbox": [ + 91, + 155, + 198, + 174 + ], + "spans": [ + { + "bbox": [ + 91, + 155, + 198, + 174 + ], + "type": "text", + "content": "(a) Particles and sensors (T = 0)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 201, + 53, + 304, + 154 + ], + "blocks": [ + { + "bbox": [ + 201, + 53, + 304, + 154 + ], + "lines": [ + { + "bbox": [ + 201, + 53, + 304, + 154 + ], + "spans": [ + { + "bbox": [ + 201, + 53, + 304, + 154 + ], + "type": "image", + "image_path": "92c09c0b767ea453098777786fb815e8c2f833a8abc790807397f42e9a6f6887.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 203, + 155, + 301, + 163 + ], + "lines": [ + { + "bbox": [ + 203, + 155, + 301, + 163 + ], + "spans": [ + { + "bbox": [ + 203, + 155, + 301, + 163 + ], + "type": "text", + "content": "(b) Sensors update " + }, + { + "bbox": [ + 203, + 155, + 301, + 163 + ], + "type": "inline_equation", + "content": "(\\mathrm{T} = 1)" + }, + { + "bbox": [ + 203, + 155, + 301, + 163 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 308, + 54, + 410, + 154 + ], + "blocks": [ + { + "bbox": [ + 308, + 54, + 410, + 154 + ], + "lines": [ + { + "bbox": [ + 308, + 54, + 410, + 154 + ], + "spans": [ + { + "bbox": [ + 308, + 54, + 410, + 154 + ], + "type": "image", + "image_path": "416dbc943d118d6834e80c8c5ad759b34f940700b96fd0b87bb23c082f10cf10.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 316, + 155, + 402, + 164 + ], + "lines": [ + { + "bbox": [ + 316, + 155, + 402, + 164 + ], + "spans": [ + { + "bbox": [ + 316, + 155, + 402, + 164 + ], + "type": "text", + "content": "(c) First range " + }, + { + "bbox": [ + 316, + 155, + 402, + 164 + ], + "type": "inline_equation", + "content": "(\\mathrm{T} = 2)" + }, + { + "bbox": [ + 316, + 155, + 402, + 164 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 85, + 188, + 303, + 201 + ], + "lines": [ + { + "bbox": [ + 85, + 188, + 303, + 201 + ], + "spans": [ + { + "bbox": [ + 85, + 188, + 303, + 201 + ], + "type": "text", + "content": "Figure 4. Simplification using bandwidth size." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 413, + 54, + 519, + 154 + ], + "blocks": [ + { + "bbox": [ + 413, + 54, + 519, + 154 + ], + "lines": [ + { + "bbox": [ + 413, + 54, + 519, + 154 + ], + "spans": [ + { + "bbox": [ + 413, + 54, + 519, + 154 + ], + "type": "image", + "image_path": "a79e8f2104ab8c32df4137808fc6b4ce9b7465bfa15c2080bd3aabb2c58986d0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 419, + 155, + 514, + 164 + ], + "lines": [ + { + "bbox": [ + 419, + 155, + 514, + 164 + ], + "spans": [ + { + "bbox": [ + 419, + 155, + 514, + 164 + ], + "type": "text", + "content": "(d) Second range " + }, + { + "bbox": [ + 419, + 155, + 514, + 164 + ], + "type": "inline_equation", + "content": "(\\mathrm{T} = 3)" + }, + { + "bbox": [ + 419, + 155, + 514, + 164 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 228, + 300, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 228, + 300, + 243 + ], + "spans": [ + { + "bbox": [ + 86, + 228, + 300, + 243 + ], + "type": "text", + "content": "4. EXPERIMENTAL RESULTS" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 85, + 255, + 493, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 255, + 493, + 294 + ], + "spans": [ + { + "bbox": [ + 85, + 255, + 493, + 294 + ], + "type": "text", + "content": "The data are extracted from two rooms of the IBM data center. Firstly, we present our method for rendering the room, and later we present our results using Level Of Detail methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 308, + 212, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 308, + 212, + 322 + ], + "spans": [ + { + "bbox": [ + 86, + 308, + 212, + 322 + ], + "type": "text", + "content": "4.1 Data visualization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 85, + 331, + 519, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 331, + 519, + 453 + ], + "spans": [ + { + "bbox": [ + 85, + 331, + 519, + 453 + ], + "type": "text", + "content": "We want to visualize and manage the consumption of a data center. For the visualization, we want to use an IFC viewer. But the IFC model for GDC is not available yet. Data center extraction of the room space is for the moment done by hand. The room is empty and was represent by a simple shape a box with 4 meters length, 3 meters width and 2.5 meters height. We use point cloud visualization based on particle paradigm. We use the two rooms of the data center and we put the same number of particles (30000) and 35 sensors distributed on three layers at 1 meter; 2 meter and on the ground. We define high and low temperature regarding the real sensors value. Figure 5(a) presents temperature color scale, Figure 5(b) and Figure 5(c) present data center sensors." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 85, + 463, + 522, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 463, + 522, + 598 + ], + "spans": [ + { + "bbox": [ + 85, + 463, + 522, + 598 + ], + "type": "text", + "content": "The next step is to interpolate data from sensors. For this, we extract the sensor mesh. We use QHULL to produce a soup of tetrahedrons. Particles need to be located. We can determine which tetrahedron is the nearest, we extract the box hull of tetrahedron and we apply for each particle the norms of each tetrahedron face. If these rays cut three or more faces, then particle is inside the tetrahedron. With this method, we can determine exactly the location of each particles regarding to the tetrahedrons, a weight is given to them easily. It was used to apply a coefficient to the value of each vertex of tetrahedron. For the outside particles, another solution was used: Voronoi cells. This method is based on a discrete extraction of Voronoi cells. We use our own method because other method like Voro ++ or QHull extract Voronoi diagram in a continuous way." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 93, + 696, + 225, + 731 + ], + "blocks": [ + { + "bbox": [ + 93, + 696, + 225, + 731 + ], + "lines": [ + { + "bbox": [ + 93, + 696, + 225, + 731 + ], + "spans": [ + { + "bbox": [ + 93, + 696, + 225, + 731 + ], + "type": "image", + "image_path": "7c729f1706460b0bf0adde7a8dbd071f9ae77f611ef3f85b3d951fb62795016c.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 244, + 605, + 371, + 712 + ], + "blocks": [ + { + "bbox": [ + 244, + 605, + 371, + 712 + ], + "lines": [ + { + "bbox": [ + 244, + 605, + 371, + 712 + ], + "spans": [ + { + "bbox": [ + 244, + 605, + 371, + 712 + ], + "type": "image", + "image_path": "8c16ad7a59f34e5974a4322466cec0149f8905a1a1b1cfadff910a3fec50d004.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 268, + 718, + 334, + 730 + ], + "lines": [ + { + "bbox": [ + 268, + 718, + 334, + 730 + ], + "spans": [ + { + "bbox": [ + 268, + 718, + 334, + 730 + ], + "type": "text", + "content": "(b) Room one." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 394, + 606, + 520, + 712 + ], + "blocks": [ + { + "bbox": [ + 394, + 606, + 520, + 712 + ], + "lines": [ + { + "bbox": [ + 394, + 606, + 520, + 712 + ], + "spans": [ + { + "bbox": [ + 394, + 606, + 520, + 712 + ], + "type": "image", + "image_path": "2eb0e7b79700cbbd72a8a244992163f567dbbd68f9d3db6bad3e5808cda4dabb.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 423, + 718, + 489, + 730 + ], + "lines": [ + { + "bbox": [ + 423, + 718, + 489, + 730 + ], + "spans": [ + { + "bbox": [ + 423, + 718, + 489, + 730 + ], + "type": "text", + "content": "(c) Room two." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "spans": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "type": "text", + "content": "6/10" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 87, + 78, + 199, + 92 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 78, + 199, + 92 + ], + "spans": [ + { + "bbox": [ + 87, + 78, + 199, + 92 + ], + "type": "text", + "content": "4.2 Level of details" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 85, + 100, + 525, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 100, + 525, + 291 + ], + "spans": [ + { + "bbox": [ + 85, + 100, + 525, + 291 + ], + "type": "text", + "content": "In the earlier days of this project, first solution proposed gives a low frame rates, about 15 FPS (Frame Per Second): visualization was not in real-time (real-time is about 24 FPS). For solving this problem, we define a client server paradigm. This solution allows to produce a real-time rendering on the client. Figure ?? gives an example of LOD for particles. We use Openscenegraph " + }, + { + "bbox": [ + 85, + 100, + 525, + 291 + ], + "type": "inline_equation", + "content": "^{20}" + }, + { + "bbox": [ + 85, + 100, + 525, + 291 + ], + "type": "text", + "content": " as a 3D engine. It owns several features useful in LOD. A special object is defined to manage multi-resolution model. It calculates the distance of the object from the camera. For our experimentation we use five resolutions of mesh. The first mesh was the original mesh, it is set at 0 to 500. The next mesh was set at 500 to 1000, the next at 1000 to 1500 and the other at 1500 to 2000. These three meshes were constructed by specific LOD methods: clustering and significant vertices. Clustering defines a 3D grid inside the room. The size of each cell depends on the viewpoint location. The size of the cluster depends on the visibility of the clustered particles. First results are given Figure 6(a) and 6(b). Value of cluster is an average of clustered value. The number of points of the final mesh depends on the grid size. Table 1 shows the results at several distances." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 88, + 297, + 523, + 357 + ], + "blocks": [ + { + "bbox": [ + 88, + 297, + 523, + 357 + ], + "lines": [ + { + "bbox": [ + 88, + 297, + 523, + 357 + ], + "spans": [ + { + "bbox": [ + 88, + 297, + 523, + 357 + ], + "type": "table", + "html": "
D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
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D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
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D = 0 to 500D = 500 to 1000D = 1000 to 1500D = 1500 to 2000
C = X1200003000075001875
", + "image_path": "9434d9911bf9b1660b16b84b9672b9a68ac66eec53e61ed383a2c752f12025a2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 85, + 534, + 260, + 545 + ], + "lines": [ + { + "bbox": [ + 85, + 534, + 260, + 545 + ], + "spans": [ + { + "bbox": [ + 85, + 534, + 260, + 545 + ], + "type": "text", + "content": "Table 3. Several resolution of model." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 85, + 548, + 522, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 548, + 522, + 614 + ], + "spans": [ + { + "bbox": [ + 85, + 548, + 522, + 614 + ], + "type": "text", + "content": "Another solution is to use bandwidth latency. We send data at several times, we do not send the entire set of data but only modified particles. We send at first time the sensors data, and subsequently we send a range of data (the nearest). After few minutes, all data are sent. This solution gives good results, and simulates a thermal diffusion in the whole structure of particles. Figure 8(a)-8(c) illustrate this method." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 91, + 617, + 233, + 723 + ], + "blocks": [ + { + "bbox": [ + 91, + 617, + 233, + 723 + ], + "lines": [ + { + "bbox": [ + 91, + 617, + 233, + 723 + ], + "spans": [ + { + "bbox": [ + 91, + 617, + 233, + 723 + ], + "type": "image", + "image_path": "2fcee6efa3b1d3c44144e2639f3857a15c4079f838c4f9132953fd427a8b1be9.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 143, + 722, + 182, + 731 + ], + "lines": [ + { + "bbox": [ + 143, + 722, + 182, + 731 + ], + "spans": [ + { + "bbox": [ + 143, + 722, + 182, + 731 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 143, + 722, + 182, + 731 + ], + "type": "inline_equation", + "content": "\\mathrm{T} = 0" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 235, + 617, + 377, + 723 + ], + "blocks": [ + { + "bbox": [ + 235, + 617, + 377, + 723 + ], + "lines": [ + { + "bbox": [ + 235, + 617, + 377, + 723 + ], + "spans": [ + { + "bbox": [ + 235, + 617, + 377, + 723 + ], + "type": "image", + "image_path": "b2be70bd4cc7d261ac38e8bc653a0c09c537d49d2a5612ed5c067058a98ef463.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 286, + 722, + 325, + 731 + ], + "lines": [ + { + "bbox": [ + 286, + 722, + 325, + 731 + ], + "spans": [ + { + "bbox": [ + 286, + 722, + 325, + 731 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 286, + 722, + 325, + 731 + ], + "type": "inline_equation", + "content": "\\mathrm{T} = 1" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 378, + 617, + 520, + 723 + ], + "blocks": [ + { + "bbox": [ + 378, + 617, + 520, + 723 + ], + "lines": [ + { + "bbox": [ + 378, + 617, + 520, + 723 + ], + "spans": [ + { + "bbox": [ + 378, + 617, + 520, + 723 + ], + "type": "image", + "image_path": "0d4e22f04d3ea25761125c93fc6d70fe856bf840ef353c043f32d21c9633724e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 430, + 722, + 468, + 731 + ], + "lines": [ + { + "bbox": [ + 430, + 722, + 468, + 731 + ], + "spans": [ + { + "bbox": [ + 430, + 722, + 468, + 731 + ], + "type": "text", + "content": "(c) " + }, + { + "bbox": [ + 430, + 722, + 468, + 731 + ], + "type": "inline_equation", + "content": "\\mathrm{T} = 4" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "spans": [ + { + "bbox": [ + 295, + 768, + 315, + 776 + ], + "type": "text", + "content": "8/10" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 87, + 91, + 208, + 107 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 91, + 208, + 107 + ], + "spans": [ + { + "bbox": [ + 87, + 91, + 208, + 107 + ], + "type": "text", + "content": "5. CONCLUSION" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 86, + 118, + 520, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 118, + 520, + 199 + ], + "spans": [ + { + "bbox": [ + 86, + 118, + 520, + 199 + ], + "type": "text", + "content": "In this paper, we have presented a method to visualize sensors data extracted from a Green Data Center. This approach produces interpolation visualization for managing and visualizing data. This interpolation used a Delaunay triangulation and a cell extraction based on Voronoi. An unusual way of use particles helps to process data. First results present the solution proposed to visualize the inside of a GDC space. The second results proposed in this paper aim to improve the rendering." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 200, + 522, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 200, + 522, + 294 + ], + "spans": [ + { + "bbox": [ + 86, + 200, + 522, + 294 + ], + "type": "text", + "content": "For this, first step introduces a client/server protocol a second step illustrates methods to simplify the model. With these different approaches we improve the rendering time, preserving most important data are kept. In future works, we will work on data \"dressing\". We want to find a way to improve rendering of the scene using meatballs or marching cube algorithms. A main constraint of this work is real-time computation. Future work also concern to add rooms to the visualization. At present, we only visualize a single room. We want to visualize building, and complex form, by using an IFC loader." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 87, + 319, + 257, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 319, + 257, + 335 + ], + "spans": [ + { + "bbox": [ + 87, + 319, + 257, + 335 + ], + "type": "text", + "content": "ACKNOWLEDGMENTS" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 85, + 347, + 512, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 347, + 512, + 401 + ], + "spans": [ + { + "bbox": [ + 85, + 347, + 512, + 401 + ], + "type": "text", + "content": "We want to thanks the PSSC (Products and Solutions Support Center) team of IBM Montpellier for having provided the necessary equipment and data need for this experimentation. And we thank the FUI (Fonds Unique Interministriel) for their financial support." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 87, + 427, + 190, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 427, + 190, + 442 + ], + "spans": [ + { + "bbox": [ + 87, + 427, + 190, + 442 + ], + "type": "text", + "content": "REFERENCES" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 454, + 522, + 738 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 86, + 454, + 455, + 479 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 454, + 455, + 479 + ], + "spans": [ + { + "bbox": [ + 86, + 454, + 455, + 479 + ], + "type": "text", + "content": "[1] Clark, J. 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P., \"Efficient simplification of point-sampled surfaces,\" (2002)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 87, + 725, + 516, + 738 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 725, + 516, + 738 + ], + "spans": [ + { + "bbox": [ + 87, + 725, + 516, + 738 + ], + "type": "text", + "content": "[12] Moenning, C., , Moenning, C., and Dodgson, N. A., \"Intrinsic point cloud simplification,\"" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 86, + 52, + 253, + 64 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 52, + 253, + 64 + ], + "spans": [ + { + "bbox": [ + 86, + 52, + 253, + 64 + ], + "type": "text", + "content": "Figure 8. Bandwidth simplification." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 768, + 315, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 768, + 315, + 776 + ], + "spans": [ + { + "bbox": [ + 294, + 768, + 315, + 776 + ], + "type": "text", + "content": "9/10" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 87, + 52, + 520, + 294 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 87, + 52, + 119, + 63 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 52, + 119, + 63 + ], + "spans": [ + { + "bbox": [ + 87, + 52, + 119, + 63 + ], + "type": "text", + "content": "(2004)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 87, + 65, + 488, + 104 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 65, + 488, + 104 + ], + "spans": [ + { + "bbox": [ + 87, + 65, + 488, + 104 + ], + "type": "text", + "content": "[13] Song, H. and Feng, H.-Y., \"A progressive point cloud simplification algorithm with preserved sharp edge data,\" The International Journal of Advanced Manufacturing Technology 45, 583-592 (November 2009)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 87, + 106, + 514, + 131 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 106, + 514, + 131 + ], + "spans": [ + { + "bbox": [ + 87, + 106, + 514, + 131 + ], + "type": "text", + "content": "[14] Buschmann, C., Pfisterer, D., Fischer, S., Fekete, S. P., and Kröller, A., \"Spyglass: a wireless sensor network visualizer,\" SIGBED Rev. 2(1), 1-6 (2005)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 87, + 133, + 488, + 158 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 133, + 488, + 158 + ], + "spans": [ + { + "bbox": [ + 87, + 133, + 488, + 158 + ], + "type": "text", + "content": "[15] Avis, D. and Bhattacharya, B., \"Algorithms for computing d-dimensional voronoi diagrams and their duals,\" 1, 159-180 (1983)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 159, + 520, + 186 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 159, + 520, + 186 + ], + "spans": [ + { + "bbox": [ + 88, + 159, + 520, + 186 + ], + "type": "text", + "content": "[16] Rycroft, C. H., \"Voro++: a three-dimensional voronoi cell library in " + }, + { + "bbox": [ + 88, + 159, + 520, + 186 + ], + "type": "inline_equation", + "content": "c++" + }, + { + "bbox": [ + 88, + 159, + 520, + 186 + ], + "type": "text", + "content": ",\" Chaos 19 (2009). Lawrence Berkeley National Laboratory." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 87, + 187, + 501, + 212 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 187, + 501, + 212 + ], + "spans": [ + { + "bbox": [ + 87, + 187, + 501, + 212 + ], + "type": "text", + "content": "[17] Barber, C. B., Dobkin, D. P., and Huhdanpaa, H., \"The quickhull algorithm for convex hulls,\" ACM Trans. Math. Softw. 22(4), 469-483 (1996)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 87, + 214, + 473, + 239 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 214, + 473, + 239 + ], + "spans": [ + { + "bbox": [ + 87, + 214, + 473, + 239 + ], + "type": "text", + "content": "[18] Snyder, J. M. and Barr, A. H., \"Ray tracing complex models containing surface tessellations,\" SIGGRAPH Comput. Graph. 21(4), 119-128 (1987)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 241, + 511, + 266 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 241, + 511, + 266 + ], + "spans": [ + { + "bbox": [ + 88, + 241, + 511, + 266 + ], + "type": "text", + "content": "[19] Hoppe, H., \"Progressive meshes. computer graphics,\" SIGGRAPH96 Proceedings, 99108 (1996)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 87, + 268, + 473, + 294 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 268, + 473, + 294 + ], + "spans": [ + { + "bbox": [ + 87, + 268, + 473, + 294 + ], + "type": "text", + "content": "[20] Burns, D. and Osfield, R., \"Open scene graph a: Introduction, b: Examples and applications,\" 265 (2004)." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 102, + 312, + 238, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 312, + 238, + 323 + ], + "spans": [ + { + "bbox": [ + 102, + 312, + 238, + 323 + ], + "type": "text", + "content": "Further author information:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 102, + 326, + 294, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 326, + 294, + 338 + ], + "spans": [ + { + "bbox": [ + 102, + 326, + 294, + 338 + ], + "type": "text", + "content": "Lange B.: E-mail: benoit.lange@lirmm.fr" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 102, + 339, + 332, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 339, + 332, + 351 + ], + "spans": [ + { + "bbox": [ + 102, + 339, + 332, + 351 + ], + "type": "text", + "content": "Rodriguez N.: E-mail: nancy.rodriguez@lirmm.fr" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 102, + 353, + 304, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 353, + 304, + 364 + ], + "spans": [ + { + "bbox": [ + 102, + 353, + 304, + 364 + ], + "type": "text", + "content": "Puech W.: E-mail: william.puech@lirmm.fr" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 102, + 366, + 286, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 366, + 286, + 378 + ], + "spans": [ + { + "bbox": [ + 102, + 366, + 286, + 378 + ], + "type": "text", + "content": "Rey H.: E-mail:REYHERVE@fr.ibm.com" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 102, + 380, + 323, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 380, + 323, + 392 + ], + "spans": [ + { + "bbox": [ + 102, + 380, + 323, + 392 + ], + "type": "text", + "content": "Vasques X.: E-mail: xaviervasques@fr.ibm.com" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "spans": [ + { + "bbox": [ + 294, + 768, + 317, + 776 + ], + "type": "text", + "content": "10/10" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_content_list.json b/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b405f0da66db10cb3e2fb23117aa4614922f68d3 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_content_list.json @@ -0,0 +1,1878 @@ +[ + { + "type": "text", + "text": "UniCombine: Unified Multi-Conditional Combination with Diffusion Transformer", + "text_level": 1, + "bbox": [ + 225, + 130, + 772, + 172 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haoxuan Wang $^{1\\dagger}$ , Jinlong Peng $^{2\\dagger}$ , Qingdong He $^{2}$ , Hao Yang $^{3}$ , Ying Jin $^{1}$ , Jiafu Wu $^{2}$ , Xiaobin Hu $^{2}$ , Yanjie Pan $^{1}$ , Zhenye Gan $^{2}$ , Mingmin Chi $^{1*}$ , Bo Peng $^{4*}$ , Yabiao Wang $^{2,5*}$", + "bbox": [ + 156, + 189, + 836, + 226 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Fudan University, $^{2}$ Tencent Youtu Lab, $^{3}$ Shanghai Jiao Tong University, $^{4}$ Shanghai Ocean University $^{5}$ Zhejiang University", + "bbox": [ + 132, + 227, + 864, + 244 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://github.com/Xuan-World/UniCombine", + "bbox": [ + 256, + 262, + 732, + 279 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2c8007f4046d1a3e78dbaf014b7a491dbbbf9b78ef27cf90ee2c58035b246a98.jpg", + "image_caption": [ + "Figure 1. Fantastic results of our proposed UniCombine on multi-conditional controllable generation: (a) Subject-Insertion task. (b) and (c) Subject-Spatial task. (d) Multi-Spatial task. Our unified framework effectively handles any combination of input conditions and achieves remarkable alignment with all of them, including but not limited to text prompts, spatial maps, and subject images." + ], + "image_footnote": [], + "bbox": [ + 96, + 292, + 898, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 248, + 747, + 326, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rapid development of diffusion models in image generation, the demand for more powerful and flexible controllable frameworks is increasing. Although existing methods can guide generation beyond text prompts, the challenge of effectively combining multiple conditional inputs", + "bbox": [ + 89, + 781, + 482, + 857 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "while maintaining consistency with all of them remains unsolved. To address this, we introduce UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Specifically, we introduce a novel Conditional MMDiT Attention mechanism and incorporate a trainable LoRA module to build both the training-free and training-based versions. Additionally, we propose a new pipeline to construct SubjectSpatial200K, the first dataset", + "bbox": [ + 511, + 748, + 906, + 900 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2503.09277v2 [cs.CV] 8 Jul 2025", + "bbox": [ + 22, + 287, + 57, + 709 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Equal contribution.", + "bbox": [ + 114, + 875, + 227, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author.", + "bbox": [ + 114, + 888, + 245, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1", + "bbox": [ + 493, + 924, + 503, + 935 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "designed for multi-conditional generative tasks covering both the subject-driven and spatially-aligned conditions. Extensive experimental results on multi-conditional generation demonstrate the outstanding universality and powerful capability of our approach with state-of-the-art performance.", + "bbox": [ + 88, + 90, + 480, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 89, + 210, + 222, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the advancement of diffusion-based [13, 42] text-to-image generative technology, a series of single-conditional controllable generative frameworks like ControlNet [59], T2I-Adapter [31], IP-Adapter [58], and InstantID [47] have expanded the scope of the control signals from text prompts to image conditions. It allows users to control more plentiful aspects of the generated images, such as layout, style, characteristics, etc. These conventional approaches are specifically designed for the UNet [38] backbone of Latent Diffusion Models (LDM) [37] with dedicated control networks. Besides, some recent approaches, such as Omini-Control [45], integrate control signals into the Diffusion Transformer (DiT) [7, 23] architecture, which demonstrates superior performance compared to the UNet in LDM.", + "bbox": [ + 91, + 234, + 483, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although the methods mentioned above have achieved a promising single-conditional performance, the challenge of multi-conditional controllable generation is still unsolved. Previous multi-conditional generative methods like UniControl [35] and UniControlNet [60] are generally restricted to handling spatial conditions like Canny or Depth maps and fail to accommodate subject conditions, resulting in limited applicable scenarios. Despite the recently proposed Ctrl-X [27] features controlling structure and appearance together, its performance is unsatisfactory and supports only a limited combination of conditions.", + "bbox": [ + 91, + 448, + 483, + 613 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, we assume that many existing generative tasks can be viewed as a multi-conditional generation, such as virtual try-on [5, 17], object insertion [3, 51], style transfer [15, 33, 52], spatially-aligned customization [20, 21, 25, 27], etc. Consequently, there is a need for a unified framework to encompass these generative tasks in a way of multi-conditional generation. This framework should ensure consistency with all input constraints, including subject ID preservation, spatial structural alignment, background coherence, and style uniformity.", + "bbox": [ + 91, + 614, + 483, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve this, we propose UniCombine, a powerful and universal framework that offers several key advantages: Firstly, our framework is capable of simultaneously handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Specifically, we introduce a novel Conditional MMDiT Attention mechanism and incorporate a trainable Denoising-LoRA module to build both the training-free and training-based versions. By integrating multiple pre", + "bbox": [ + 89, + 765, + 480, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "trained Condition-LoRA module weights into the conditional branches, UniCombine achieves excellent training-free performance, which can be improved further after training on the task-specific multi-conditional dataset. Secondly, due to the lack of a publicly available dataset for multi-conditional generative tasks, we build the SubjectSpatial200K dataset to serve as the training dataset and the testing benchmark. Specifically, we generate the subject grounding annotations and spatial map annotations for all the data samples from Subjects200K [45] and therefore formulate our SubjectSpatial200K dataset. Thirdly, our UniCombine can achieve many unprecedented multi-conditional combinations, as shown in Fig. 1, such as combining a reference subject image with the inpainting area of a background image or with the layout guidance of a depth (or canny) map while imposing precise control via text prompt. Furthermore, extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generation demonstrate the outstanding universality and powerful capability of our method against other existing specialized approaches.", + "bbox": [ + 511, + 90, + 903, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we highlight our contributions as follows:", + "bbox": [ + 529, + 411, + 893, + 426 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images.", + "- We construct the SubjectSpatial200K dataset, which encompasses both subject-driven and spatially-aligned conditions for all text-image sample pairs. It addresses the absence of a publicly available dataset for training and testing multi-conditional controllable generative models.", + "- We conduct extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generative tasks. The experimental results demonstrate the state-of-the-art performance of our UniCombine, which effectively aligns with all conditions harmoniously." + ], + "bbox": [ + 513, + 430, + 903, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 513, + 665, + 653, + 681 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Diffusion-Based Models", + "text_level": 1, + "bbox": [ + 513, + 693, + 733, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion-based [13, 42] models have demonstrated superior performance than GAN-based [9] ones across various domains, including controllable generation [18, 31, 47, 58, 59], image editing [11, 30, 39], customized generation [8, 22, 40], object insertion [4, 43, 56], mask-guided inpainting [19, 48, 61], and so on. These breakthroughs begin with the LDM [37] and are further advanced with the DiT [32] architecture. The latest text-to-image generative models, SD3 [7] and FLUX [23], have attained state-of-the-art results by employing the Rectified Flow [28, 29] training strategy, the RPE [44] positional embedding and the MultiModal Diffusion Transformer (MMDiT) [7] architecture.", + "bbox": [ + 511, + 719, + 903, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 493, + 924, + 504, + 935 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e21e3bf9a4a78294b155fc81f3e6b7e3e4251e119c112d81fb0f47a4822439d5.jpg", + "image_caption": [ + "(a) Overall Framework" + ], + "image_footnote": [], + "bbox": [ + 93, + 87, + 321, + 335 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3162d24f03eacb746bd4ecce492028784582c1beb179bc5cf91d96a185a56eec.jpg", + "image_caption": [ + "(b) Single-Conditional Setting" + ], + "image_footnote": [], + "bbox": [ + 328, + 87, + 545, + 335 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7fa892b46091963fb1ee53c8e239a5cf468404dfb70774813a489096638da93b.jpg", + "image_caption": [ + "(c) Multi-Conditional Setting", + "Figure 2. Overview of our proposed UniCombine. (a) The overall framework. We regard the MMDiT-based diffusion models as consisting of the text branch and the denoising branch. Based on it, our UniCombine introduces multiple conditional branches to process the input conditions. (b) The single-conditional setting of our UniCombine. It is equivalent to OminiControl [45] which is a special case of our proposed UniCombine framework under a single-conditional setting. (c) The multi-conditional setting of our UniCombine. Our LoRA Switching module adaptively activates the pre-trained Condition-LoRA modules on the weights of the denoising branch according to the conditional types. The proposed Conditional MMDiT Attention mechanism is used to replace the original MMDiT Attention mechanism for handling the unified multi-conditional input sequence. Whether to load the optional Denoising-LoRA module is the difference between the training-free and training-based versions." + ], + "image_footnote": [], + "bbox": [ + 552, + 88, + 905, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Controllable Generation", + "text_level": 1, + "bbox": [ + 89, + 484, + 313, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Controllable generation allows for customizing the desired spatial layout, filter style, or subject appearance in the generated images. A series of methods such as ControlNet [59], T2I-Adapter [31], GLIGEN [26], and ZestGuide [6] successfully introduce the spatial conditions into controllable generation, enabling models to control the spatial layout of generated images. Another series of methods, such as IP-Adapter [58], InstantID [47], BLIP-Diffusion [24], and StyleDrop [41] incorporate the subject conditions into controllable generation, ensuring consistency between generated images and reference images in style, characteristics, subject appearance, etc. To unify these two tasks, OminiControl [45] proposes a novel MMDiT-based controllable framework to handle various conditions with a unified pipeline. Unfortunately, it lacks the capability to control generation with multiple conditions. To this end, we propose UniCombine, which successfully extends this framework to multi-conditional scenarios.", + "bbox": [ + 91, + 506, + 483, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Multi-Conditional Controllable Generation", + "text_level": 1, + "bbox": [ + 89, + 787, + 459, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As controllable generation advances, merely providing a single condition to guide the image generation no longer satisfies the needs. As a result, research on multi-conditional controllable generation has emerged. Existing methods like UniControl [35], UniControlNet [60] and Cocktail [14] exhibit acceptable performance when simul", + "bbox": [ + 89, + 810, + 483, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "taneously leveraging multiple spatial conditions for image generation. However, there is a lack of multi-conditional generative models that support utilizing both spatial conditions and subject conditions to guide the generative process together. Although the recently proposed method Ctrl-X [27] features controlling the appearance and structure simultaneously, its performance remains unsatisfactory with a limited combination of conditions and it is not compatible with the Diffusion Transformer architecture. To address the aforementioned limitations, we propose UniCombine to enable the flexible combination of various control signals.", + "bbox": [ + 511, + 484, + 906, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 513, + 678, + 604, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 511, + 708, + 640, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we mainly explore the latest generative models that utilize the Rectified Flow (RF) [28, 29] training strategy and the MMDiT [7] backbone architecture, like FLUX [23] and SD3 [7]. For the source noise distribution $X_0 \\sim p_{\\mathrm{noise}}$ and the target image distribution $X_1 \\sim p_{\\mathrm{data}}$ , the RF defines a linear interpolation between them as $X_t = (1 - t)X_0 + tX_1$ for $t \\in [0,1]$ . The training objective is to learn a time-dependent vector field $v_t(X_t, t; \\theta)$ that describes the trajectory of the ODE $dX_t = v_t(X_t, t; \\theta)dt$ . Specifically, $v_t(X_t, t; \\theta)$ is optimized to approximate the constant velocity $X_1 - X_0$ , leading to the loss function as Eq. (1).", + "bbox": [ + 511, + 734, + 906, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 493, + 924, + 503, + 935 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {R F}} (\\theta) = \\mathbb {E} _ {X _ {1} \\sim p _ {\\text {d a t a}}, X _ {0} \\sim p _ {\\text {n o i s e}}, t \\sim U [ 0, 1 ]} \\left[ \\| (X _ {1} - X _ {0}) - v _ {t} (X _ {t}, t; \\theta) \\| ^ {2} \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 107, + 483, + 138 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, we propose a concept of branch to differentiate the processing flows of input embeddings from different modalities in MMDiT-based models. As shown in Fig. 2 (a), instead of the single-branch architecture [37] where the text prompt is injected into the denoising branch via crossattention, MMDiT uses two independent transformers to construct the text branch and the denoising branch. Based on it, OminiControl [45] incorporates a Condition-LoRA module onto the weights of the denoising branch to process the input conditional embedding, thus forming its Conditional Branch, as depicted in Fig. 2 (b). It is worth noting that, OminiControl [45] can be regarded as a special case of our proposed UniCombine framework under the single-conditional setting. It provides the pre-trained Condition-LoRA modules to meet the need for our multi-conditional settings. In the single-conditional setting, the text branch embedding $T$ , the denoising branch embedding $X$ , and the conditional branch embedding $C$ are concatenated to form a unified sequence $[T;X;C]$ to be processed in the MMDiT Attention mechanism.", + "bbox": [ + 89, + 138, + 483, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. UniCombine", + "text_level": 1, + "bbox": [ + 89, + 450, + 225, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Building upon the MMDiT-based text-to-image generative model FLUX [23], we propose UniCombine, a multi-conditional controllable generative framework consisting of various conditional branches. Each conditional branch is in charge of processing one conditional embedding, thus forming a unified embedding sequence $S$ as presented in Eq. (2).", + "bbox": [ + 89, + 470, + 483, + 564 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS = [ T; X; C _ {1}; \\dots ; C _ {N} ] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 566, + 480, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given that the single-conditional setting of our UniCombine is equivalent to OmniControl [45], we only focus on the multi-conditional setting in this section. Firstly, we introduce a LoRA Switching module to manage multiple conditional branches effectively. Secondly, we introduce a novel Conditional MMDiT Attention mechanism to process the unified sequence $S$ in the multi-conditional setting. Thirdly, we present an insight analysis of our training-free strategy, which leverages the pre-trained Condition-LoRA module weights to perform a training-free multi-conditional controllable generation. Lastly, we present a feasible training-based strategy, which utilizes a trainable Denoising-LoRA module to enhance the performance further after training on a task-specific multi-conditional dataset.", + "bbox": [ + 89, + 584, + 483, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LoRA Switching Module. Before denoising with multiple input conditions, the Condition-LoRA modules pre-trained under single-conditional settings should be loaded onto the weights of the denoising branch, like $[CondLoRA_1, CondLoRA_2, \\ldots]$ . Then the LoRA Switching module determines which one of them should be", + "bbox": [ + 89, + 810, + 483, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "activated according to the type of input conditions, forming a one-hot gating mechanism $[0,1,0,\\dots,0]$ , as shown in Fig. 2 (c). Subsequently, different conditional branches with different activated Condition-LoRA modules are used for processing different conditional embeddings, resulting in a minimal number of additional parameters introduced for different conditions. Unlike the single-conditional setting in Fig. 2 (b), which only needs loading LoRA modules, the LoRA Switching module in Fig. 2 (c) enables adaptive selection among multiple LoRA modules to provide the matching conditional branches for each conditional embeddings, granting our framework greater flexibility and adaptability to handle diverse conditional combinations.", + "bbox": [ + 511, + 90, + 903, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conditional MMDiT Attention. After concatenating the output embeddings from these $N$ conditional branches, the unified sequence $S$ cannot be processed through the original MMDiT Attention mechanism due to two major challenges: (1) The computational complexity scales quadratically as $O(N^2)$ with respect to the number of conditions, which becomes especially problematic when handling multiple high-resolution conditions. (2) When performing MMDiT Attention on the unified sequence $S$ , different condition signals interfere with each other during the attention calculation, making it difficult to effectively utilize the pre-trained Condition-LoRA module weights for the denoising process.", + "bbox": [ + 511, + 287, + 903, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address these challenges, we introduce a novel Conditional MMDiT Attention mechanism (CMMDiT Attention) as depicted in Fig. 2 (c) to replace the original MMDiT Attention. Instead of feeding the entire unified sequence $S$ into the MMDiT Attention at once, CMMDiT Attention follows distinct computational mechanisms according to which branch is serving as queries. The core idea is that the branch serving as a query aggregates the information from different scopes of the unified sequence $S$ depending on its type. Specifically, when the denoising branch $X$ and the text branch $T$ serve as queries, their scope of keys and values correspond to the entire unified sequence $S$ , granting them a global receptive field and the ability to aggregate information from all conditional branches. In contrast, when the conditional branches $C_i$ serve as queries, their receptive fields do not encompass one another. Their scope of keys and values are restricted to the subsequence $S_i$ as presented in Eq. (3), which prevents feature exchange and avoids information entanglement between different conditions.", + "bbox": [ + 511, + 469, + 903, + 755 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i} = [ T; X; C _ {i} ] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 661, + 760, + 903, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, the CMMDiT Attention reduces computational complexity from $O(N^2)$ to $O(N)$ as the number of conditions increases, making it more scalable.", + "bbox": [ + 511, + 779, + 906, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training-free Strategy. The following analyses provide a detailed explanation of why our UniCombine is capable of seamlessly integrating and effectively reusing the pretrained Condition-LoRA module weights to tackle multi-conditional challenges in a training-free manner.", + "bbox": [ + 511, + 825, + 903, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 493, + 924, + 504, + 935 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8c57a3c424f01738f8a53f6d6f0c8688e8016cc7a73bf6ea21df63ffdafe3eaa.jpg", + "image_caption": [ + "Figure 3. Average $\\mathrm{X} \\rightarrow$ Subject cross-attention map of the insertion area." + ], + "image_footnote": [], + "bbox": [ + 94, + 87, + 482, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the one hand, when the conditional embeddings $C_i$ serve as queries in CMMDiT, they follow the same attention computational paradigm as in the MMDiT of single-conditional settings, as indicated in Eq. (4).", + "bbox": [ + 89, + 215, + 483, + 277 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {C M M D i T} \\left(Q = C _ {i} ^ {q}, K = \\left[ T ^ {k}, X ^ {k}, C _ {i} ^ {k} \\right], V = \\left[ T ^ {v}, X ^ {v}, C _ {i} ^ {v} \\right]\\right) \\\\ = \\operatorname {M M D i T} (Q = C ^ {q}, K = [ T ^ {k}, X ^ {k}, C ^ {k} ], V = [ T ^ {v}, X ^ {v}, C ^ {v} ]) \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 280, + 480, + 314 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This consistent computational paradigm enables the conditional branches to share the same feature extraction capability between the multi-conditional setting and the single-conditional setting.", + "bbox": [ + 89, + 321, + 483, + 381 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the other hand, when the denoising embedding $X$ and the text prompt embedding $T$ serve as queries in CMMDiT, their attention computational paradigm diverges from the single-conditional settings. As illustrated in Eq. (5), when the denoising embedding $X$ is used as a query for attention computation with multiple conditional embeddings in CMMDiT, the attention score matrix is computed between $X$ and all the conditional embeddings.", + "bbox": [ + 89, + 381, + 483, + 502 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathrm {C M M D i T} (Q = X ^ {q}, K / V = [ X ^ {k / v}, T ^ {k / v}, C _ {1} ^ {k / v}, \\dots , C _ {N} ^ {k / v} ]) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {1}{\\sqrt {d i m}} X ^ {q} \\left[ X ^ {k}, T ^ {k}, C _ {1} ^ {k}, \\dots , C _ {N} ^ {k} \\right] ^ {\\top}\\right) \\left[ X ^ {v}, T ^ {v}, C _ {1} ^ {v}, \\dots , C _ {N} ^ {v} \\right] \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 503, + 488, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It allows $X$ to extract and integrate information from each of the conditional embeddings separately and fusion them. This divide-and-conquer computational paradigm enables the text branch and denoising branch to fuse the conditional features effectively.", + "bbox": [ + 89, + 568, + 483, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By leveraging the computational paradigms mentioned above, our UniCombine is able to perform a training-free multi-conditional controllable generation with the pretrained Condition-LoRA modules.", + "bbox": [ + 89, + 643, + 483, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training-based Strategy. However, due to the lack of training, solely relying on the softmax operation in Eq. (5) to balance the attention score distribution across multiple conditional embeddings may result in an undesirable feature fusion result, making our training-free version unsatisfactory in some cases. To address this issue, we introduce a trainable Denoising-LoRA module within the denoising branch to rectify the distribution of attention scores in Eq. (5). During training, we keep all the Condition-LoRA modules frozen to preserve the conditional extracting capability and train the Denoising-LoRA module solely on the task-specific multi-conditional dataset, as shown in Fig. 2 (c). After training, the denoising embedding $X$ learns to", + "bbox": [ + 89, + 704, + 483, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d04a32c8e874aab106f9fa111d4a7b255e65e731a4acd2452f053c1c30949d06.jpg", + "image_caption": [ + "Figure 4. SubjectSpatial200K dataset construction pipeline." + ], + "image_footnote": [], + "bbox": [ + 519, + 88, + 901, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "better aggregate the appropriate information during the CM-MDiT Attention operation. As presented in Fig. 3, the average $\\mathrm{X} \\rightarrow$ Subject attention map within the inpainting area is more concentrated on the subject area in the training-based version.", + "bbox": [ + 511, + 323, + 906, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. SubjectSpatial200K dataset", + "text_level": 1, + "bbox": [ + 511, + 409, + 761, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our SubjectSpatial200K dataset aims to address the lack of a publicly available dataset for multi-conditional generative tasks. Existing datasets fail to include both the subject-driven and spatially-aligned annotations. Recently, the Subjects200K [45] dataset provides a publicly accessible dataset for subject-driven generation. Based on it, we introduce the SubjectSpatial200K dataset, which is a unified high-quality dataset designed for training and testing multi-conditional controllable generative models. This dataset includes comprehensive annotations as elaborated below. Besides, the construction pipeline is detailed in Fig. 4.", + "bbox": [ + 511, + 431, + 906, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Subject Grounding Annotation. The subject grounding annotation is significantly necessary for many generative tasks like instance-level inpainting [19, 61], instance-level controllable generation [26, 49], and object insertion [4, 43]. By leveraging the open-vocabulary object detection model Mamba-YOLO-World [46] on Subjects200K, we detect bounding boxes for all subjects according to their category descriptions and subsequently derive the corresponding mask regions.", + "bbox": [ + 511, + 598, + 905, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spatial Map Annotation. The spatial map annotation further extends the applicable scope of our dataset to spatially-aligned synthesis tasks. Specifically, we employ the Depth-Anything [57] model and the OpenCV [1] library on Subjects200K to derive the Depth and Canny maps.", + "bbox": [ + 511, + 734, + 905, + 810 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 511, + 823, + 637, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 511, + 848, + 594, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation. We use the FLUX.1-schnell [23] as our base model and the weights provided by OminiControl [45]", + "bbox": [ + 511, + 869, + 905, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 493, + 924, + 503, + 935 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a34bbcb900321fe501a520855202f376e6664d9faf88390dd30b55aa8d6f1b53.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TaskMethodGenerative QualityControllabilitySubject ConsistencyText Consistency
FID ↓SSIM ↑F1 ↑MSE ↓CLIP-I ↑DINO ↑CLIP-T ↑
Multi-SpatialUniControl44.170.320.071346.02--30.28
UniControlNet20.960.280.091231.06--32.74
UniCombine (training-free)10.350.540.18519.53--33.70
UniCombine (training-based)6.820.640.24165.90--33.45
Subject-InsertionObjectStitch26.860.37--93.0582.3432.25
AnyDoor26.070.37--94.8886.0432.55
UniCombine (training-free)6.370.76--95.6089.0133.11
UniCombine (training-based)4.550.81--97.1492.9633.08
Subject-DepthControlNet w. IP-Adapter29.930.34-1295.8080.4162.2632.94
Ctrl-X52.370.36-2644.9078.0850.8330.20
UniCombine (training-free)10.030.48-507.4091.1585.7333.41
UniCombine (training-based)6.660.55-196.6594.4790.3133.30
Subject-CannyControlNet w. IP-Adapter30.380.380.09-79.8060.1932.85
Ctrl-X47.890.360.05-79.3554.3130.34
UniCombine (training-free)10.220.490.17-91.8486.8833.21
UniCombine (training-based)6.010.610.24-95.2692.5933.30
", + "bbox": [ + 120, + 88, + 874, + 338 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison of our method with existing approaches on Multi-Spatial, Subject-Insertion, Subject-Depth, and Subject-Canny conditional generative tasks. The bold and underlined figures represent the optimal and sub-optimal results, respectively.", + "bbox": [ + 89, + 344, + 903, + 375 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1e06b7a6c1ae6b58e94df98cc9be3d1764e9ac9f480e954299aa319606949d55.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison on Multi-Spatial generation." + ], + "image_footnote": [], + "bbox": [ + 93, + 387, + 480, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "as our pre-trained Condition-LoRA module weights. During the training of our Denoising-LoRA module, we use a rank of 4, consistent with the Condition-LoRA. We choose the Adam optimizer with a learning rate of $1e^{-4}$ and set the weight decay to 0.01. Our models are trained for 30,000 steps on 16 NVIDIA V100 GPUs at a resolution of $512 \\times 512$ .", + "bbox": [ + 89, + 715, + 482, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "**Benchmarks.** We evaluate the performance of our method in both training-free and training-based versions. The training and testing datasets are partitioned from the SubjectSpatial200K dataset based on image quality assessment scores evaluated by ChatGPT-4o, with details provided in Sec. A1.", + "bbox": [ + 89, + 824, + 483, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d60c55bfaeeeedfd5aefc1bba87bd491b67f9a1c54a3f0b04bece1daafa5fa08.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison on Subject-Insertion generation." + ], + "image_footnote": [], + "bbox": [ + 514, + 387, + 903, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Importantly, the dataset partitioning scheme remains consistent in all experiments.", + "bbox": [ + 511, + 717, + 903, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. To evaluate the subject consistency, we calculate the CLIP-I [36] score and DINO [2] score between the generated images and the ground truth images. To assess the generative quality, we compute the FID [12] and SSIM [50] between the generated image set and the ground truth image set. To measure the controllability, we compute the F1 Score for edge conditions and the MSE score for depth conditions between the extracted maps from generated images and the original conditions. Additionally, we adopt the CLIP-T [36] score to estimate the text consistency between", + "bbox": [ + 511, + 750, + 906, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 493, + 925, + 503, + 935 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/506fe3547ab1943e7faa90d0f349eb3f11dc59ed4a47d7cf36007f74a6ca38f0.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison on Subject-Depth generation." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 480, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the generated images and the text prompts.", + "bbox": [ + 89, + 412, + 374, + 428 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Main Result", + "text_level": 1, + "bbox": [ + 89, + 435, + 220, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct extensive and comprehensive comparative experiments on the Multi-Spatial, Subject-Insertion, and Subject-Spatial conditional generative tasks.", + "bbox": [ + 89, + 457, + 482, + 502 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.1. Multi-Spatial Conditional Generation", + "text_level": 1, + "bbox": [ + 89, + 508, + 398, + 523 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Multi-Spatial conditional generation aims to generate images adhering to the collective layout constraints of diverse spatial conditions. This requires the model to achieve a more comprehensive layout control based on input conditions in a complementary manner. The comparative results in Tab. 1 and Fig. 5 demonstrate that our method outperforms existing multi-spatial conditional generation approaches in generative quality and controllability.", + "bbox": [ + 89, + 527, + 482, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.2. Subject-Insertion Conditional Generation", + "text_level": 1, + "bbox": [ + 89, + 655, + 426, + 670 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Subject-Insertion conditional generation requires the model to generate images where the reference subject is inserted into the masked region of the target background. As illustrated in Tab. 1 and Fig. 6, our UniCombine demonstrates superior performance compared to previous methods with three advantages: Firstly, our method ensures that the reference subject is inserted into the background with high consistency and harmonious integration. Secondly, our method excels in open-world object insertion without requiring test-time tuning, unlike conventional customization methods [22, 40]. Finally, our method demonstrates strong semantic comprehension capabilities, enabling it to extract the desired object from a complex subject image with a non-white background, rather than simply pasting the entire subject image into the masked region.", + "bbox": [ + 89, + 674, + 482, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44ebde2dd6cfbcb637ef99847a469c9c5e74ddeb4368792fe3d6809b1e91856e.jpg", + "image_caption": [ + "Figure 8. Qualitative comparison on Subject-Canny generation." + ], + "image_footnote": [], + "bbox": [ + 516, + 87, + 903, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.3. Subject-Spatial Conditional Generation", + "text_level": 1, + "bbox": [ + 511, + 414, + 834, + 429 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Subject-Spatial conditional generation focuses on generating images of the reference subject while ensuring the layout aligns with specified spatial conditions. We compare our method with Ctrl-X [27] and a simple baseline model. Ctrl-X is a recently proposed model based on SDXL [34] that simultaneously controls structure and appearance. The baseline model is constructed by integrating the FLUX ControlNet [53, 54] and FLUX IP-Adapter [55] into the FLUX.1-dev [23] base model. Specifically, we divided the Subject-Spatial generative task into different experimental groups based on the type of spatial conditions, referred to as Subject-Depth and Subject-Canny, respectively. As presented in Fig. 7, Fig. 8, and Tab. 1, the experimental results demonstrate the superior performance of our UniCombine: Firstly, our method exhibits stronger semantic comprehension capability, generating the reference subject in the accurate localization of the spatial conditions without confusing appearance features. Secondly, our method demonstrates greater adaptability, generating the reference subject with reasonable morphological transformations to align with the guidance of spatial conditions and text prompts. Lastly, our method achieves superior subject consistency while maintaining excellent spatial coherence.", + "bbox": [ + 511, + 434, + 906, + 781 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.4. Textual Guidance", + "text_level": 1, + "bbox": [ + 511, + 790, + 684, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Fig. 1 and Tab. 1, our method not only allows for controllable generation by combining multiple conditions but also enables precise textual guidance simultaneously. By utilizing a unified input sequence $S = [T; X; C_1; \\ldots; C_N]$ during the denoising process, our UniCombine effectively aligns the descriptive words in $T$ with", + "bbox": [ + 511, + 809, + 906, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 493, + 924, + 503, + 935 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8b5b9183e06014b6e81f79d2b0e6e78e929ba4f810448e1f8a953e9f0afcf401.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑AttnOps ↓
Ours w/o CMMDiT95.4788.4233.10732.17M
Ours w/ CMMDiT95.6089.0133.11612.63M
", + "bbox": [ + 91, + 88, + 493, + 141 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2a92bbe800381328c2717f661d17a8523810856178e0fb0febb65310f9baa364.jpg", + "table_caption": [ + "Table 2. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Insertion task. AttnOps is short for the number of attention operations." + ], + "table_footnote": [], + "table_body": "
Background\nSubjectTraining-free\nw/o CMMDiTTraining-free\nw/ CMMDiTBackground\nSubjectTraining-free\nw/o CMMDiTTraining-free\nw/ CMMDiT
inconsistentsuccessinconsistentsuccess
failsuccessfailsuccess
", + "bbox": [ + 91, + 198, + 480, + 335 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b5701621428ee2941e72b32e1a85040f321539ed97d657923eef29882e89bdfd.jpg", + "table_caption": [ + "Figure 9. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Insertion task." + ], + "table_footnote": [], + "table_body": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑
Ours w/ Text-LoRA96.9792.3233.10
Ours w/ Denoising-LoRA97.1492.9633.08
", + "bbox": [ + 106, + 378, + 465, + 431 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fc8bc88e1ec09551aeba8132d1ccff2d2a1eb574ea62259a59e0357472255443.jpg", + "image_caption": [ + "Figure 10. Qualitative ablation of trainable LoRA on training-based Subject-Insertion task." + ], + "image_footnote": [], + "bbox": [ + 91, + 473, + 480, + 612 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the relevant features in $C_i$ and the corresponding patches in $X$ , thereby achieving a remarkable text-guided multi-conditional controllable generation.", + "bbox": [ + 89, + 657, + 482, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 89, + 712, + 243, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We exhibit the ablation study results conducted on the Subject-Insertion task in this section, while more results on the other tasks are provided in Sec. A2.", + "bbox": [ + 89, + 734, + 482, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Conditional MMDiT Attention. To evaluate the effectiveness of our proposed Conditional MMDiT Attention mechanism, we replace the CMMDiT Attention with the original MMDiT Attention and test its training-free performance to avoid the influence of training data. As shown in Tab. 2 and Fig. 9, our framework attains superior performance with fewer attention operations when employing the CMMDiT Attention mechanism.", + "bbox": [ + 89, + 779, + 482, + 898 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3618030c54b9a80305073bef94f2394a26e7580cbe554afe3dc981094168e421.jpg", + "table_caption": [ + "Table 3. Quantitative ablation of trainable LoRA on training-based Subject-Insertion task." + ], + "table_footnote": [], + "table_body": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑
Ours w/ DSB only96.8592.3833.07
Ours w/ DSB and SSB97.1492.9633.08
", + "bbox": [ + 537, + 88, + 879, + 141 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e87e6f8b3e137a3f2fcae475f15efcbe2b56a7113615b229b8cb075304866a5d.jpg", + "table_caption": [ + "Table 4. Quantitative ablation of training strategy on training-based Subject-Insertion task. DSB: Dual-Stream Blocks. SSB: Single-Stream Blocks." + ], + "table_footnote": [], + "table_body": "
Background\nSubjectTraining-based\nw/ DSB onlyTraining-based\nw/ DSB + SSBBackground\nSubjectTraining-based\nw/ DSB onlyTraining-based\nw/ DSB + SSB
inconsistentsuccessinconsistentsuccessinconsistentsuccess
inconsistentsuccessfailsuccessinconsistentinconsistent
", + "bbox": [ + 514, + 199, + 903, + 335 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a4f5c4fc9d8ce66afbdd123ab7fca8f063e5af00acb1254be7e07f83f23cd544.jpg", + "table_caption": [ + "Figure 11. Qualitative ablation of training strategy on training-based Subject-Insertion task. DSB: Dual-Stream Blocks. SSB: Single-Stream Blocks." + ], + "table_footnote": [], + "table_body": "
ModelGPU Memory ↓Add Params ↓
FLUX (bf16, base model)32933M-
CN, 1 cond35235M744M
IP, 1 cond35325M918M
CN + IP, 2 cond36753M1662M
Ours (training-free), 2 cond33323M29M
Ours (training-based), 2 cond33349M44M
", + "bbox": [ + 521, + 396, + 895, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Comparison of inference GPU memory cost and additionally introduced parameters. CN: ControlNet. IP: IP-Adapter.", + "bbox": [ + 511, + 503, + 903, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different Options for Trainable LoRA. To evaluate whether the trainable LoRA module can be applied to the text branch instead of the denoising branch, we load a Text-LoRA in the text branch, with a configuration identical to that of the Denoising-LoRA. The Tab. 3 and Fig. 10 indicate that applying the trainable LoRA module to the denoising branch better modulates the feature aggregation operation across multiple conditional branches.", + "bbox": [ + 511, + 550, + 906, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Training Strategy. As the parameter scale of the base model increases, the FLUX adaptations of ControlNet [53, 54] and IP-adapter [55] provided by the HuggingFace [16] community inject conditional features only into the dual-stream MMDiT blocks, rather than the entire network, to save memory. In contrast, since our Denoising-LoRA module introduces only a small number of parameters, we incorporate it into both the dual-stream and single-stream blocks to achieve better performance. The results in Tab. 4 and Fig. 11 confirm the validity of our choice.", + "bbox": [ + 511, + 672, + 906, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Computational Cost. The overheads of our approach in terms of inference GPU memory cost and additionally introduced parameters are minimal. The comparison results against the FLUX ControlNet [53, 54] and FLUX IP-Adapter [55] are shown in Tab. 5.", + "bbox": [ + 511, + 824, + 903, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 493, + 924, + 503, + 935 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "More Conditional Branches. Our model places no restrictions on the number of supported conditions. The results shown in Fig. 12 demonstrate our model's strong scalability. As the number of conditional branches increases, the level of control becomes finer.", + "bbox": [ + 89, + 90, + 480, + 165 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/a621a99e80843ff5996990493bd8940b3ce3197ae924350ffd10503c3b7c6b1c.jpg", + "image_caption": [ + "Figure 12. From left to right are training-free multi-conditional combination tasks under: $1/2/3/4$ conditions." + ], + "image_footnote": [], + "bbox": [ + 94, + 181, + 478, + 344 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "More Application Scenarios. Our UniCombine can be easily extended to new scenarios, such as reference-based image stylization. After training a new Condition-LoRA on StyleBooth [10] dataset, our UniCombine is able to integrate the style of the reference image with other conditions successfully, as demonstrated in Fig. 13.", + "bbox": [ + 89, + 396, + 483, + 488 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/697b9a0d3b2d71d9ac73a42626a46546416d486f912cfdb2949db0c5a79882ad.jpg", + "image_caption": [ + "Figure 13. Training-free Spatial-Style combination task." + ], + "image_footnote": [], + "bbox": [ + 94, + 503, + 478, + 635 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 89, + 691, + 209, + 707 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We present UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generative tasks demonstrate the state-of-the-art performance of our UniCombine in both training-free and training-based versions. Additionally, we propose the SubjectSpatial200K dataset to address the lack of a publicly available dataset for training and testing multi-conditional generative models. 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Dataset Partitioning Scheme", + "text_level": 1, + "bbox": [ + 89, + 178, + 367, + 195 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In our proposed SubjectSpatial200K dataset, we utilize the ChatGPT-4o assessment scores provided by Subjects200K [45] on Subject Consistency, Composition Structure, and Image Quality to guide the dataset partitioning in our experiments.", + "bbox": [ + 89, + 203, + 483, + 277 + ], + "page_idx": 11 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Subject Consistency: Ensuring the identity of the subject image is consistent with that of the ground truth image.", + "- Composition Structure: Verifying a reasonable composition of the subject and ground truth images.", + "- Image Quality: Confirming each image pair maintains high resolution and visual fidelity." + ], + "bbox": [ + 89, + 279, + 482, + 369 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "We partition the dataset into 139,403 training samples and 5,827 testing samples through Algorithm 1.", + "bbox": [ + 89, + 369, + 482, + 400 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/081e7579449455ce9a0a6c20f089187297d01d022d3027a0bfa4afb2c5a31aa9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Algorithm 1: Dataset Partitioning Scheme
Input: example
Output: train or test
cs← example["Composite Structure"]
iq← example["Image Quality"]
sc← example["Subject Consistency"]
scores← [cs, iq, sc]
if all(s==5 for s in scores) then
return train;
else if cs≥3 and iq==5 and sc==5 then
return test;
", + "bbox": [ + 93, + 404, + 480, + 588 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "A2. More Ablation on CMMDiT Attention", + "text_level": 1, + "bbox": [ + 89, + 609, + 450, + 625 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "More quantitative and qualitative ablation results on the other multi-conditional generative tasks are provided here. The comprehensive ablation results in Tab. A1, Tab. A2, Tab. A3, Fig. A1, Fig. A2, and Fig. A3 demonstrate that the UniCombine performs better with our proposed CMMDiT Attention.", + "bbox": [ + 89, + 633, + 483, + 724 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/7780b4ae3fc30805750b62e7bb1b1c2e1322a555efcac56b2f8f7632150cf53d.jpg", + "table_caption": [], + "table_footnote": [ + "Table A1. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Canny task" + ], + "table_body": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑F1 ↑
Ours w/o CMMDiT91.5186.3133.200.16
Ours w/ CMMDiT91.8486.8833.210.17
", + "bbox": [ + 99, + 734, + 470, + 792 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "A3. More Qualitative Results", + "text_level": 1, + "bbox": [ + 89, + 844, + 339, + 861 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "More qualitative results are presented in Fig. A4 and Fig. A5.", + "bbox": [ + 89, + 869, + 482, + 901 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/c8c9030826d874847297d6aad99732ff7992fa1efed8eaf2d42146029239dcfe.jpg", + "image_caption": [ + "Figure A1. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Canny task" + ], + "image_footnote": [], + "bbox": [ + 516, + 181, + 903, + 321 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/719ea07bb1cd1e89b41905beec203585fbe544e5a1ee5e9ab3f601d287ad2795.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑MSE ↓
Ours w/o CMMDiT90.8385.3833.38547.63
Ours w/ CMMDiT91.1585.7333.41507.40
", + "bbox": [ + 516, + 362, + 900, + 421 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/eec53f0d14c8df15f39c097595e64b40514c9c785b2e319a4f3ff0334abfd869.jpg", + "image_caption": [ + "Table A2. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Depth task", + "Figure A2. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Depth task" + ], + "image_footnote": [], + "bbox": [ + 516, + 458, + 903, + 595 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/825bdf58c053f99cc780532dc82a60487da430bb38579c85ad77eb49436315d5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCLIP-T ↑F1 ↑MSE ↓
Ours w/o CMMDiT33.700.17524.04
Ours w/ CMMDiT33.700.18519.53
", + "bbox": [ + 558, + 638, + 857, + 698 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Table A3. Quantitative ablation of CMMDiT Attention mechanism on training-free Multi-Spatial task", + "bbox": [ + 511, + 699, + 903, + 727 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/4009d7abc995632fbc8e9c0c98b070e0d250aff3285f29dd8f899b9c93e1e20e.jpg", + "image_caption": [ + "Figure A3. Qualitative ablation of CMMDiT Attention mechanism on training-free Multi-Spatial task" + ], + "image_footnote": [], + "bbox": [ + 516, + 736, + 903, + 875 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12", + "bbox": [ + 490, + 924, + 508, + 936 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/adfac4a9eebfdf05d1126a0a351b1aaafa113e3c17e6ad1d0d3ccee8c001ec91.jpg", + "image_caption": [ + "Figure A4. More qualitative results on Multi-Spatial and Subject-Insertion tasks." + ], + "image_footnote": [], + "bbox": [ + 93, + 97, + 475, + 858 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/721139a8e4ed891aeab8a9eecb8d33d046e4e4574b78dabb5cd359d3ae06e6b6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 97, + 903, + 858 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "13", + "bbox": [ + 490, + 924, + 508, + 936 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/179cb411321ca8ecf6e101c92a53a0ef8cbc9728a7f08f18d3c37f263493e513.jpg", + "image_caption": [ + "Figure A5. More qualitative results on Subject-Depth and Subject-Canny tasks." + ], + "image_footnote": [], + "bbox": [ + 89, + 97, + 475, + 859 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/6cc95ee7d4dc5bf05bbb25255f5081767689dccf861e6597d6fd8d83a62792f9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 97, + 903, + 859 + ], + "page_idx": 13 + }, + { + "type": "page_number", + "text": "14", + "bbox": [ + 490, + 924, + 508, + 936 + ], + "page_idx": 13 + } +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_model.json b/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2c5367ed245beba45df157301f2d59ea1e0942fe --- /dev/null +++ b/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_model.json @@ -0,0 +1,2736 @@ +[ + [ + { + "type": "aside_text", + "bbox": [ + 0.023, + 0.288, + 0.058, + 0.71 + ], + "angle": 270, + "content": "arXiv:2503.09277v2 [cs.CV] 8 Jul 2025" + }, + { + "type": "title", + "bbox": [ + 0.226, + 0.131, + 0.773, + 0.174 + ], + "angle": 0, + "content": "UniCombine: Unified Multi-Conditional Combination with Diffusion Transformer" + }, + { + "type": "text", + "bbox": [ + 0.158, + 0.19, + 0.837, + 0.227 + ], + "angle": 0, + "content": "Haoxuan Wang\\(^{1\\dagger}\\), Jinlong Peng\\(^{2\\dagger}\\), Qingdong He\\(^{2}\\), Hao Yang\\(^{3}\\), Ying Jin\\(^{1}\\), Jiafu Wu\\(^{2}\\), Xiaobin Hu\\(^{2}\\), Yanjie Pan\\(^{1}\\), Zhenye Gan\\(^{2}\\), Mingmin Chi\\(^{1*}\\), Bo Peng\\(^{4*}\\), Yabiao Wang\\(^{2,5*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.228, + 0.866, + 0.245 + ], + "angle": 0, + "content": "\\(^{1}\\)Fudan University, \\(^{2}\\)Tencent Youtu Lab, \\(^{3}\\)Shanghai Jiao Tong University, \\(^{4}\\)Shanghai Ocean University \\(^{5}\\)Zhejiang University" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.263, + 0.733, + 0.28 + ], + "angle": 0, + "content": "https://github.com/Xuan-World/UniCombine" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.293, + 0.9, + 0.685 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.693, + 0.908, + 0.737 + ], + "angle": 0, + "content": "Figure 1. Fantastic results of our proposed UniCombine on multi-conditional controllable generation: (a) Subject-Insertion task. (b) and (c) Subject-Spatial task. (d) Multi-Spatial task. Our unified framework effectively handles any combination of input conditions and achieves remarkable alignment with all of them, including but not limited to text prompts, spatial maps, and subject images." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.748, + 0.327, + 0.763 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.782, + 0.483, + 0.858 + ], + "angle": 0, + "content": "With the rapid development of diffusion models in image generation, the demand for more powerful and flexible controllable frameworks is increasing. Although existing methods can guide generation beyond text prompts, the challenge of effectively combining multiple conditional inputs" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.749, + 0.907, + 0.901 + ], + "angle": 0, + "content": "while maintaining consistency with all of them remains unsolved. To address this, we introduce UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Specifically, we introduce a novel Conditional MMDiT Attention mechanism and incorporate a trainable LoRA module to build both the training-free and training-based versions. Additionally, we propose a new pipeline to construct SubjectSpatial200K, the first dataset" + }, + { + "type": "page_footnote", + "bbox": [ + 0.115, + 0.876, + 0.228, + 0.888 + ], + "angle": 0, + "content": "\\(\\dagger\\) Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.116, + 0.889, + 0.246, + 0.9 + ], + "angle": 0, + "content": "* Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.115, + 0.876, + 0.246, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.495, + 0.925, + 0.504, + 0.936 + ], + "angle": 0, + "content": "1" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.089, + 0.092, + 0.482, + 0.182 + ], + "angle": 0, + "content": "designed for multi-conditional generative tasks covering both the subject-driven and spatially-aligned conditions. Extensive experimental results on multi-conditional generation demonstrate the outstanding universality and powerful capability of our approach with state-of-the-art performance." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.211, + 0.223, + 0.227 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.236, + 0.485, + 0.447 + ], + "angle": 0, + "content": "With the advancement of diffusion-based [13, 42] text-to-image generative technology, a series of single-conditional controllable generative frameworks like ControlNet [59], T2I-Adapter [31], IP-Adapter [58], and InstantID [47] have expanded the scope of the control signals from text prompts to image conditions. It allows users to control more plentiful aspects of the generated images, such as layout, style, characteristics, etc. These conventional approaches are specifically designed for the UNet [38] backbone of Latent Diffusion Models (LDM) [37] with dedicated control networks. Besides, some recent approaches, such as Omini-Control [45], integrate control signals into the Diffusion Transformer (DiT) [7, 23] architecture, which demonstrates superior performance compared to the UNet in LDM." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.449, + 0.485, + 0.614 + ], + "angle": 0, + "content": "Although the methods mentioned above have achieved a promising single-conditional performance, the challenge of multi-conditional controllable generation is still unsolved. Previous multi-conditional generative methods like UniControl [35] and UniControlNet [60] are generally restricted to handling spatial conditions like Canny or Depth maps and fail to accommodate subject conditions, resulting in limited applicable scenarios. Despite the recently proposed Ctrl-X [27] features controlling structure and appearance together, its performance is unsatisfactory and supports only a limited combination of conditions." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.615, + 0.485, + 0.765 + ], + "angle": 0, + "content": "Moreover, we assume that many existing generative tasks can be viewed as a multi-conditional generation, such as virtual try-on [5, 17], object insertion [3, 51], style transfer [15, 33, 52], spatially-aligned customization [20, 21, 25, 27], etc. Consequently, there is a need for a unified framework to encompass these generative tasks in a way of multi-conditional generation. This framework should ensure consistency with all input constraints, including subject ID preservation, spatial structural alignment, background coherence, and style uniformity." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.766, + 0.482, + 0.902 + ], + "angle": 0, + "content": "To achieve this, we propose UniCombine, a powerful and universal framework that offers several key advantages: Firstly, our framework is capable of simultaneously handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Specifically, we introduce a novel Conditional MMDiT Attention mechanism and incorporate a trainable Denoising-LoRA module to build both the training-free and training-based versions. By integrating multiple pre" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.41 + ], + "angle": 0, + "content": "trained Condition-LoRA module weights into the conditional branches, UniCombine achieves excellent training-free performance, which can be improved further after training on the task-specific multi-conditional dataset. Secondly, due to the lack of a publicly available dataset for multi-conditional generative tasks, we build the SubjectSpatial200K dataset to serve as the training dataset and the testing benchmark. Specifically, we generate the subject grounding annotations and spatial map annotations for all the data samples from Subjects200K [45] and therefore formulate our SubjectSpatial200K dataset. Thirdly, our UniCombine can achieve many unprecedented multi-conditional combinations, as shown in Fig. 1, such as combining a reference subject image with the inpainting area of a background image or with the layout guidance of a depth (or canny) map while imposing precise control via text prompt. Furthermore, extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generation demonstrate the outstanding universality and powerful capability of our method against other existing specialized approaches." + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.412, + 0.895, + 0.427 + ], + "angle": 0, + "content": "In summary, we highlight our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.431, + 0.905, + 0.491 + ], + "angle": 0, + "content": "- We present UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.491, + 0.905, + 0.567 + ], + "angle": 0, + "content": "- We construct the SubjectSpatial200K dataset, which encompasses both subject-driven and spatially-aligned conditions for all text-image sample pairs. It addresses the absence of a publicly available dataset for training and testing multi-conditional controllable generative models." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.567, + 0.905, + 0.643 + ], + "angle": 0, + "content": "- We conduct extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generative tasks. The experimental results demonstrate the state-of-the-art performance of our UniCombine, which effectively aligns with all conditions harmoniously." + }, + { + "type": "list", + "bbox": [ + 0.514, + 0.431, + 0.905, + 0.643 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.666, + 0.655, + 0.682 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.694, + 0.734, + 0.71 + ], + "angle": 0, + "content": "2.1. Diffusion-Based Models" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Diffusion-based [13, 42] models have demonstrated superior performance than GAN-based [9] ones across various domains, including controllable generation [18, 31, 47, 58, 59], image editing [11, 30, 39], customized generation [8, 22, 40], object insertion [4, 43, 56], mask-guided inpainting [19, 48, 61], and so on. These breakthroughs begin with the LDM [37] and are further advanced with the DiT [32] architecture. The latest text-to-image generative models, SD3 [7] and FLUX [23], have attained state-of-the-art results by employing the Rectified Flow [28, 29] training strategy, the RPE [44] positional embedding and the MultiModal Diffusion Transformer (MMDiT) [7] architecture." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.925, + 0.505, + 0.936 + ], + "angle": 0, + "content": "2" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.088, + 0.322, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.34, + 0.271, + 0.352 + ], + "angle": 0, + "content": "(a) Overall Framework" + }, + { + "type": "image", + "bbox": [ + 0.329, + 0.088, + 0.547, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.34, + 0.522, + 0.353 + ], + "angle": 0, + "content": "(b) Single-Conditional Setting" + }, + { + "type": "image", + "bbox": [ + 0.553, + 0.089, + 0.906, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.34, + 0.811, + 0.353 + ], + "angle": 0, + "content": "(c) Multi-Conditional Setting" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.36, + 0.907, + 0.472 + ], + "angle": 0, + "content": "Figure 2. Overview of our proposed UniCombine. (a) The overall framework. We regard the MMDiT-based diffusion models as consisting of the text branch and the denoising branch. Based on it, our UniCombine introduces multiple conditional branches to process the input conditions. (b) The single-conditional setting of our UniCombine. It is equivalent to OminiControl [45] which is a special case of our proposed UniCombine framework under a single-conditional setting. (c) The multi-conditional setting of our UniCombine. Our LoRA Switching module adaptively activates the pre-trained Condition-LoRA modules on the weights of the denoising branch according to the conditional types. The proposed Conditional MMDiT Attention mechanism is used to replace the original MMDiT Attention mechanism for handling the unified multi-conditional input sequence. Whether to load the optional Denoising-LoRA module is the difference between the training-free and training-based versions." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.485, + 0.315, + 0.499 + ], + "angle": 0, + "content": "2.2. Controllable Generation" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.507, + 0.485, + 0.778 + ], + "angle": 0, + "content": "Controllable generation allows for customizing the desired spatial layout, filter style, or subject appearance in the generated images. A series of methods such as ControlNet [59], T2I-Adapter [31], GLIGEN [26], and ZestGuide [6] successfully introduce the spatial conditions into controllable generation, enabling models to control the spatial layout of generated images. Another series of methods, such as IP-Adapter [58], InstantID [47], BLIP-Diffusion [24], and StyleDrop [41] incorporate the subject conditions into controllable generation, ensuring consistency between generated images and reference images in style, characteristics, subject appearance, etc. To unify these two tasks, OminiControl [45] proposes a novel MMDiT-based controllable framework to handle various conditions with a unified pipeline. Unfortunately, it lacks the capability to control generation with multiple conditions. To this end, we propose UniCombine, which successfully extends this framework to multi-conditional scenarios." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.789, + 0.46, + 0.803 + ], + "angle": 0, + "content": "2.3. Multi-Conditional Controllable Generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.902 + ], + "angle": 0, + "content": "As controllable generation advances, merely providing a single condition to guide the image generation no longer satisfies the needs. As a result, research on multi-conditional controllable generation has emerged. Existing methods like UniControl [35], UniControlNet [60] and Cocktail [14] exhibit acceptable performance when simul" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.485, + 0.907, + 0.652 + ], + "angle": 0, + "content": "taneously leveraging multiple spatial conditions for image generation. However, there is a lack of multi-conditional generative models that support utilizing both spatial conditions and subject conditions to guide the generative process together. Although the recently proposed method Ctrl-X [27] features controlling the appearance and structure simultaneously, its performance remains unsatisfactory with a limited combination of conditions and it is not compatible with the Diffusion Transformer architecture. To address the aforementioned limitations, we propose UniCombine to enable the flexible combination of various control signals." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.679, + 0.605, + 0.695 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.709, + 0.642, + 0.724 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.907, + 0.903 + ], + "angle": 0, + "content": "In this work, we mainly explore the latest generative models that utilize the Rectified Flow (RF) [28, 29] training strategy and the MMDiT [7] backbone architecture, like FLUX [23] and SD3 [7]. For the source noise distribution \\(X_0 \\sim p_{\\mathrm{noise}}\\) and the target image distribution \\(X_1 \\sim p_{\\mathrm{data}}\\), the RF defines a linear interpolation between them as \\(X_t = (1 - t)X_0 + tX_1\\) for \\(t \\in [0,1]\\). The training objective is to learn a time-dependent vector field \\(v_t(X_t, t; \\theta)\\) that describes the trajectory of the ODE \\(dX_t = v_t(X_t, t; \\theta)dt\\). Specifically, \\(v_t(X_t, t; \\theta)\\) is optimized to approximate the constant velocity \\(X_1 - X_0\\), leading to the loss function as Eq. (1)." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.925, + 0.504, + 0.936 + ], + "angle": 0, + "content": "3" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.091, + 0.108, + 0.484, + 0.139 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {R F}} (\\theta) = \\mathbb {E} _ {X _ {1} \\sim p _ {\\text {d a t a}}, X _ {0} \\sim p _ {\\text {n o i s e}}, t \\sim U [ 0, 1 ]} \\left[ \\| (X _ {1} - X _ {0}) - v _ {t} (X _ {t}, t; \\theta) \\| ^ {2} \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.14, + 0.484, + 0.442 + ], + "angle": 0, + "content": "In this paper, we propose a concept of branch to differentiate the processing flows of input embeddings from different modalities in MMDiT-based models. As shown in Fig. 2 (a), instead of the single-branch architecture [37] where the text prompt is injected into the denoising branch via crossattention, MMDiT uses two independent transformers to construct the text branch and the denoising branch. Based on it, OminiControl [45] incorporates a Condition-LoRA module onto the weights of the denoising branch to process the input conditional embedding, thus forming its Conditional Branch, as depicted in Fig. 2 (b). It is worth noting that, OminiControl [45] can be regarded as a special case of our proposed UniCombine framework under the single-conditional setting. It provides the pre-trained Condition-LoRA modules to meet the need for our multi-conditional settings. In the single-conditional setting, the text branch embedding \\( T \\), the denoising branch embedding \\( X \\), and the conditional branch embedding \\( C \\) are concatenated to form a unified sequence \\( [T;X;C] \\) to be processed in the MMDiT Attention mechanism." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.451, + 0.226, + 0.465 + ], + "angle": 0, + "content": "3.2. UniCombine" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.472, + 0.484, + 0.565 + ], + "angle": 0, + "content": "Building upon the MMDiT-based text-to-image generative model FLUX [23], we propose UniCombine, a multi-conditional controllable generative framework consisting of various conditional branches. Each conditional branch is in charge of processing one conditional embedding, thus forming a unified embedding sequence \\( S \\) as presented in Eq. (2)." + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.567, + 0.482, + 0.582 + ], + "angle": 0, + "content": "\\[\nS = [ T; X; C _ {1}; \\dots ; C _ {N} ] \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.585, + 0.484, + 0.809 + ], + "angle": 0, + "content": "Given that the single-conditional setting of our UniCombine is equivalent to OmniControl [45], we only focus on the multi-conditional setting in this section. Firstly, we introduce a LoRA Switching module to manage multiple conditional branches effectively. Secondly, we introduce a novel Conditional MMDiT Attention mechanism to process the unified sequence \\( S \\) in the multi-conditional setting. Thirdly, we present an insight analysis of our training-free strategy, which leverages the pre-trained Condition-LoRA module weights to perform a training-free multi-conditional controllable generation. Lastly, we present a feasible training-based strategy, which utilizes a trainable Denoising-LoRA module to enhance the performance further after training on a task-specific multi-conditional dataset." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.811, + 0.484, + 0.901 + ], + "angle": 0, + "content": "LoRA Switching Module. Before denoising with multiple input conditions, the Condition-LoRA modules pre-trained under single-conditional settings should be loaded onto the weights of the denoising branch, like \\([CondLoRA_1, CondLoRA_2, \\ldots]\\). Then the LoRA Switching module determines which one of them should be" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.905, + 0.287 + ], + "angle": 0, + "content": "activated according to the type of input conditions, forming a one-hot gating mechanism \\([0,1,0,\\dots,0]\\), as shown in Fig. 2 (c). Subsequently, different conditional branches with different activated Condition-LoRA modules are used for processing different conditional embeddings, resulting in a minimal number of additional parameters introduced for different conditions. Unlike the single-conditional setting in Fig. 2 (b), which only needs loading LoRA modules, the LoRA Switching module in Fig. 2 (c) enables adaptive selection among multiple LoRA modules to provide the matching conditional branches for each conditional embeddings, granting our framework greater flexibility and adaptability to handle diverse conditional combinations." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.288, + 0.905, + 0.47 + ], + "angle": 0, + "content": "Conditional MMDiT Attention. After concatenating the output embeddings from these \\(N\\) conditional branches, the unified sequence \\(S\\) cannot be processed through the original MMDiT Attention mechanism due to two major challenges: (1) The computational complexity scales quadratically as \\(O(N^2)\\) with respect to the number of conditions, which becomes especially problematic when handling multiple high-resolution conditions. (2) When performing MMDiT Attention on the unified sequence \\(S\\), different condition signals interfere with each other during the attention calculation, making it difficult to effectively utilize the pre-trained Condition-LoRA module weights for the denoising process." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.905, + 0.756 + ], + "angle": 0, + "content": "To address these challenges, we introduce a novel Conditional MMDiT Attention mechanism (CMMDiT Attention) as depicted in Fig. 2 (c) to replace the original MMDiT Attention. Instead of feeding the entire unified sequence \\( S \\) into the MMDiT Attention at once, CMMDiT Attention follows distinct computational mechanisms according to which branch is serving as queries. The core idea is that the branch serving as a query aggregates the information from different scopes of the unified sequence \\( S \\) depending on its type. Specifically, when the denoising branch \\( X \\) and the text branch \\( T \\) serve as queries, their scope of keys and values correspond to the entire unified sequence \\( S \\), granting them a global receptive field and the ability to aggregate information from all conditional branches. In contrast, when the conditional branches \\( C_i \\) serve as queries, their receptive fields do not encompass one another. Their scope of keys and values are restricted to the subsequence \\( S_i \\) as presented in Eq. (3), which prevents feature exchange and avoids information entanglement between different conditions." + }, + { + "type": "equation", + "bbox": [ + 0.662, + 0.761, + 0.905, + 0.776 + ], + "angle": 0, + "content": "\\[\nS _ {i} = [ T; X; C _ {i} ] \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.78, + 0.907, + 0.825 + ], + "angle": 0, + "content": "Furthermore, the CMMDiT Attention reduces computational complexity from \\( O(N^2) \\) to \\( O(N) \\) as the number of conditions increases, making it more scalable." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.826, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Training-free Strategy. The following analyses provide a detailed explanation of why our UniCombine is capable of seamlessly integrating and effectively reusing the pretrained Condition-LoRA module weights to tackle multi-conditional challenges in a training-free manner." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.925, + 0.505, + 0.936 + ], + "angle": 0, + "content": "4" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.088, + 0.483, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.175, + 0.483, + 0.202 + ], + "angle": 0, + "content": "Figure 3. Average \\( \\mathrm{X} \\rightarrow \\) Subject cross-attention map of the insertion area." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.217, + 0.484, + 0.278 + ], + "angle": 0, + "content": "On the one hand, when the conditional embeddings \\( C_i \\) serve as queries in CMMDiT, they follow the same attention computational paradigm as in the MMDiT of single-conditional settings, as indicated in Eq. (4)." + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.281, + 0.482, + 0.315 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {C M M D i T} \\left(Q = C _ {i} ^ {q}, K = \\left[ T ^ {k}, X ^ {k}, C _ {i} ^ {k} \\right], V = \\left[ T ^ {v}, X ^ {v}, C _ {i} ^ {v} \\right]\\right) \\\\ = \\operatorname {M M D i T} (Q = C ^ {q}, K = [ T ^ {k}, X ^ {k}, C ^ {k} ], V = [ T ^ {v}, X ^ {v}, C ^ {v} ]) \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.322, + 0.484, + 0.382 + ], + "angle": 0, + "content": "This consistent computational paradigm enables the conditional branches to share the same feature extraction capability between the multi-conditional setting and the single-conditional setting." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.382, + 0.484, + 0.503 + ], + "angle": 0, + "content": "On the other hand, when the denoising embedding \\( X \\) and the text prompt embedding \\( T \\) serve as queries in CMMDiT, their attention computational paradigm diverges from the single-conditional settings. As illustrated in Eq. (5), when the denoising embedding \\( X \\) is used as a query for attention computation with multiple conditional embeddings in CMMDiT, the attention score matrix is computed between \\( X \\) and all the conditional embeddings." + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.505, + 0.49, + 0.564 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathrm {C M M D i T} (Q = X ^ {q}, K / V = [ X ^ {k / v}, T ^ {k / v}, C _ {1} ^ {k / v}, \\dots , C _ {N} ^ {k / v} ]) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {1}{\\sqrt {d i m}} X ^ {q} \\left[ X ^ {k}, T ^ {k}, C _ {1} ^ {k}, \\dots , C _ {N} ^ {k} \\right] ^ {\\top}\\right) \\left[ X ^ {v}, T ^ {v}, C _ {1} ^ {v}, \\dots , C _ {N} ^ {v} \\right] \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.569, + 0.484, + 0.645 + ], + "angle": 0, + "content": "It allows \\( X \\) to extract and integrate information from each of the conditional embeddings separately and fusion them. This divide-and-conquer computational paradigm enables the text branch and denoising branch to fuse the conditional features effectively." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.645, + 0.484, + 0.704 + ], + "angle": 0, + "content": "By leveraging the computational paradigms mentioned above, our UniCombine is able to perform a training-free multi-conditional controllable generation with the pretrained Condition-LoRA modules." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.705, + 0.484, + 0.902 + ], + "angle": 0, + "content": "Training-based Strategy. However, due to the lack of training, solely relying on the softmax operation in Eq. (5) to balance the attention score distribution across multiple conditional embeddings may result in an undesirable feature fusion result, making our training-free version unsatisfactory in some cases. To address this issue, we introduce a trainable Denoising-LoRA module within the denoising branch to rectify the distribution of attention scores in Eq. (5). During training, we keep all the Condition-LoRA modules frozen to preserve the conditional extracting capability and train the Denoising-LoRA module solely on the task-specific multi-conditional dataset, as shown in Fig. 2 (c). After training, the denoising embedding \\( X \\) learns to" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.089, + 0.903, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.296, + 0.887, + 0.311 + ], + "angle": 0, + "content": "Figure 4. SubjectSpatial200K dataset construction pipeline." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.324, + 0.907, + 0.4 + ], + "angle": 0, + "content": "better aggregate the appropriate information during the CM-MDiT Attention operation. As presented in Fig. 3, the average \\(\\mathrm{X} \\rightarrow\\) Subject attention map within the inpainting area is more concentrated on the subject area in the training-based version." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.41, + 0.763, + 0.426 + ], + "angle": 0, + "content": "3.3. SubjectSpatial200K dataset" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.432, + 0.907, + 0.599 + ], + "angle": 0, + "content": "Our SubjectSpatial200K dataset aims to address the lack of a publicly available dataset for multi-conditional generative tasks. Existing datasets fail to include both the subject-driven and spatially-aligned annotations. Recently, the Subjects200K [45] dataset provides a publicly accessible dataset for subject-driven generation. Based on it, we introduce the SubjectSpatial200K dataset, which is a unified high-quality dataset designed for training and testing multi-conditional controllable generative models. This dataset includes comprehensive annotations as elaborated below. Besides, the construction pipeline is detailed in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.599, + 0.906, + 0.734 + ], + "angle": 0, + "content": "Subject Grounding Annotation. The subject grounding annotation is significantly necessary for many generative tasks like instance-level inpainting [19, 61], instance-level controllable generation [26, 49], and object insertion [4, 43]. By leveraging the open-vocabulary object detection model Mamba-YOLO-World [46] on Subjects200K, we detect bounding boxes for all subjects according to their category descriptions and subsequently derive the corresponding mask regions." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.906, + 0.811 + ], + "angle": 0, + "content": "Spatial Map Annotation. The spatial map annotation further extends the applicable scope of our dataset to spatially-aligned synthesis tasks. Specifically, we employ the Depth-Anything [57] model and the OpenCV [1] library on Subjects200K to derive the Depth and Canny maps." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.824, + 0.638, + 0.841 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.849, + 0.596, + 0.865 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.906, + 0.902 + ], + "angle": 0, + "content": "Implementation. We use the FLUX.1-schnell [23] as our base model and the weights provided by OminiControl [45]" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.925, + 0.504, + 0.936 + ], + "angle": 0, + "content": "5" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.122, + 0.089, + 0.875, + 0.339 + ], + "angle": 0, + "content": "
TaskMethodGenerative QualityControllabilitySubject ConsistencyText Consistency
FID ↓SSIM ↑F1 ↑MSE ↓CLIP-I ↑DINO ↑CLIP-T ↑
Multi-SpatialUniControl44.170.320.071346.02--30.28
UniControlNet20.960.280.091231.06--32.74
UniCombine (training-free)10.350.540.18519.53--33.70
UniCombine (training-based)6.820.640.24165.90--33.45
Subject-InsertionObjectStitch26.860.37--93.0582.3432.25
AnyDoor26.070.37--94.8886.0432.55
UniCombine (training-free)6.370.76--95.6089.0133.11
UniCombine (training-based)4.550.81--97.1492.9633.08
Subject-DepthControlNet w. IP-Adapter29.930.34-1295.8080.4162.2632.94
Ctrl-X52.370.36-2644.9078.0850.8330.20
UniCombine (training-free)10.030.48-507.4091.1585.7333.41
UniCombine (training-based)6.660.55-196.6594.4790.3133.30
Subject-CannyControlNet w. IP-Adapter30.380.380.09-79.8060.1932.85
Ctrl-X47.890.360.05-79.3554.3130.34
UniCombine (training-free)10.220.490.17-91.8486.8833.21
UniCombine (training-based)6.010.610.24-95.2692.5933.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.345, + 0.905, + 0.375 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of our method with existing approaches on Multi-Spatial, Subject-Insertion, Subject-Depth, and Subject-Canny conditional generative tasks. The bold and underlined figures represent the optimal and sub-optimal results, respectively." + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.388, + 0.481, + 0.677 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.684, + 0.472, + 0.699 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison on Multi-Spatial generation." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.717, + 0.483, + 0.822 + ], + "angle": 0, + "content": "as our pre-trained Condition-LoRA module weights. During the training of our Denoising-LoRA module, we use a rank of 4, consistent with the Condition-LoRA. We choose the Adam optimizer with a learning rate of \\(1e^{-4}\\) and set the weight decay to 0.01. Our models are trained for 30,000 steps on 16 NVIDIA V100 GPUs at a resolution of \\(512 \\times 512\\)." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.825, + 0.484, + 0.903 + ], + "angle": 0, + "content": "**Benchmarks.** We evaluate the performance of our method in both training-free and training-based versions. The training and testing datasets are partitioned from the SubjectSpatial200K dataset based on image quality assessment scores evaluated by ChatGPT-4o, with details provided in Sec. A1." + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.388, + 0.905, + 0.677 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.685, + 0.905, + 0.7 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison on Subject-Insertion generation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.718, + 0.905, + 0.748 + ], + "angle": 0, + "content": "Importantly, the dataset partitioning scheme remains consistent in all experiments." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.75, + 0.907, + 0.901 + ], + "angle": 0, + "content": "Metrics. To evaluate the subject consistency, we calculate the CLIP-I [36] score and DINO [2] score between the generated images and the ground truth images. To assess the generative quality, we compute the FID [12] and SSIM [50] between the generated image set and the ground truth image set. To measure the controllability, we compute the F1 Score for edge conditions and the MSE score for depth conditions between the extracted maps from generated images and the original conditions. Additionally, we adopt the CLIP-T [36] score to estimate the text consistency between" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.926, + 0.504, + 0.936 + ], + "angle": 0, + "content": "6" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.482, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.386, + 0.474, + 0.401 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison on Subject-Depth generation." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.413, + 0.375, + 0.429 + ], + "angle": 0, + "content": "the generated images and the text prompts." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.436, + 0.222, + 0.451 + ], + "angle": 0, + "content": "4.2. Main Result" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.458, + 0.483, + 0.503 + ], + "angle": 0, + "content": "We conduct extensive and comprehensive comparative experiments on the Multi-Spatial, Subject-Insertion, and Subject-Spatial conditional generative tasks." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.51, + 0.4, + 0.525 + ], + "angle": 0, + "content": "4.2.1. Multi-Spatial Conditional Generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.528, + 0.483, + 0.65 + ], + "angle": 0, + "content": "The Multi-Spatial conditional generation aims to generate images adhering to the collective layout constraints of diverse spatial conditions. This requires the model to achieve a more comprehensive layout control based on input conditions in a complementary manner. The comparative results in Tab. 1 and Fig. 5 demonstrate that our method outperforms existing multi-spatial conditional generation approaches in generative quality and controllability." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.656, + 0.428, + 0.671 + ], + "angle": 0, + "content": "4.2.2. Subject-Insertion Conditional Generation" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.675, + 0.483, + 0.901 + ], + "angle": 0, + "content": "The Subject-Insertion conditional generation requires the model to generate images where the reference subject is inserted into the masked region of the target background. As illustrated in Tab. 1 and Fig. 6, our UniCombine demonstrates superior performance compared to previous methods with three advantages: Firstly, our method ensures that the reference subject is inserted into the background with high consistency and harmonious integration. Secondly, our method excels in open-world object insertion without requiring test-time tuning, unlike conventional customization methods [22, 40]. Finally, our method demonstrates strong semantic comprehension capabilities, enabling it to extract the desired object from a complex subject image with a non-white background, rather than simply pasting the entire subject image into the masked region." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.088, + 0.905, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.385, + 0.898, + 0.4 + ], + "angle": 0, + "content": "Figure 8. Qualitative comparison on Subject-Canny generation." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.415, + 0.836, + 0.43 + ], + "angle": 0, + "content": "4.2.3. Subject-Spatial Conditional Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.435, + 0.907, + 0.782 + ], + "angle": 0, + "content": "The Subject-Spatial conditional generation focuses on generating images of the reference subject while ensuring the layout aligns with specified spatial conditions. We compare our method with Ctrl-X [27] and a simple baseline model. Ctrl-X is a recently proposed model based on SDXL [34] that simultaneously controls structure and appearance. The baseline model is constructed by integrating the FLUX ControlNet [53, 54] and FLUX IP-Adapter [55] into the FLUX.1-dev [23] base model. Specifically, we divided the Subject-Spatial generative task into different experimental groups based on the type of spatial conditions, referred to as Subject-Depth and Subject-Canny, respectively. As presented in Fig. 7, Fig. 8, and Tab. 1, the experimental results demonstrate the superior performance of our UniCombine: Firstly, our method exhibits stronger semantic comprehension capability, generating the reference subject in the accurate localization of the spatial conditions without confusing appearance features. Secondly, our method demonstrates greater adaptability, generating the reference subject with reasonable morphological transformations to align with the guidance of spatial conditions and text prompts. Lastly, our method achieves superior subject consistency while maintaining excellent spatial coherence." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.791, + 0.685, + 0.805 + ], + "angle": 0, + "content": "4.2.4. Textual Guidance" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.81, + 0.907, + 0.901 + ], + "angle": 0, + "content": "As shown in Fig. 1 and Tab. 1, our method not only allows for controllable generation by combining multiple conditions but also enables precise textual guidance simultaneously. By utilizing a unified input sequence \\( S = [T; X; C_1; \\ldots; C_N] \\) during the denoising process, our UniCombine effectively aligns the descriptive words in \\( T \\) with" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.925, + 0.504, + 0.936 + ], + "angle": 0, + "content": "7" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.495, + 0.142 + ], + "angle": 0, + "content": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑AttnOps ↓
Ours w/o CMMDiT95.4788.4233.10732.17M
Ours w/ CMMDiT95.6089.0133.11612.63M
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.143, + 0.486, + 0.186 + ], + "angle": 0, + "content": "Table 2. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Insertion task. AttnOps is short for the number of attention operations." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.199, + 0.482, + 0.337 + ], + "angle": 0, + "content": "
Background\nSubjectTraining-free\nw/o CMMDiTTraining-free\nw/ CMMDiTBackground\nSubjectTraining-free\nw/o CMMDiTTraining-free\nw/ CMMDiT
inconsistentsuccessinconsistentsuccess
failsuccessfailsuccess
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.339, + 0.483, + 0.368 + ], + "angle": 0, + "content": "Figure 9. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Insertion task." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.38, + 0.466, + 0.433 + ], + "angle": 0, + "content": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑
Ours w/ Text-LoRA96.9792.3233.10
Ours w/ Denoising-LoRA97.1492.9633.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.434, + 0.483, + 0.462 + ], + "angle": 0, + "content": "Table 3. Quantitative ablation of trainable LoRA on training-based Subject-Insertion task." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.474, + 0.482, + 0.613 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.616, + 0.483, + 0.645 + ], + "angle": 0, + "content": "Figure 10. Qualitative ablation of trainable LoRA on training-based Subject-Insertion task." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.658, + 0.483, + 0.705 + ], + "angle": 0, + "content": "the relevant features in \\( C_i \\) and the corresponding patches in \\( X \\), thereby achieving a remarkable text-guided multi-conditional controllable generation." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.713, + 0.245, + 0.73 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.735, + 0.483, + 0.78 + ], + "angle": 0, + "content": "We exhibit the ablation study results conducted on the Subject-Insertion task in this section, while more results on the other tasks are provided in Sec. A2." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.78, + 0.483, + 0.9 + ], + "angle": 0, + "content": "Effect of Conditional MMDiT Attention. To evaluate the effectiveness of our proposed Conditional MMDiT Attention mechanism, we replace the CMMDiT Attention with the original MMDiT Attention and test its training-free performance to avoid the influence of training data. As shown in Tab. 2 and Fig. 9, our framework attains superior performance with fewer attention operations when employing the CMMDiT Attention mechanism." + }, + { + "type": "table", + "bbox": [ + 0.539, + 0.089, + 0.88, + 0.142 + ], + "angle": 0, + "content": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑
Ours w/ DSB only96.8592.3833.07
Ours w/ DSB and SSB97.1492.9633.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.143, + 0.905, + 0.184 + ], + "angle": 0, + "content": "Table 4. Quantitative ablation of training strategy on training-based Subject-Insertion task. DSB: Dual-Stream Blocks. SSB: Single-Stream Blocks." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.2, + 0.905, + 0.337 + ], + "angle": 0, + "content": "
Background\nSubjectTraining-based\nw/ DSB onlyTraining-based\nw/ DSB + SSBBackground\nSubjectTraining-based\nw/ DSB onlyTraining-based\nw/ DSB + SSB
inconsistentsuccessinconsistentsuccessinconsistentsuccess
inconsistentsuccessfailsuccessinconsistentinconsistent
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.339, + 0.905, + 0.38 + ], + "angle": 0, + "content": "Figure 11. Qualitative ablation of training strategy on training-based Subject-Insertion task. DSB: Dual-Stream Blocks. SSB: Single-Stream Blocks." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.397, + 0.897, + 0.503 + ], + "angle": 0, + "content": "
ModelGPU Memory ↓Add Params ↓
FLUX (bf16, base model)32933M-
CN, 1 cond35235M744M
IP, 1 cond35325M918M
CN + IP, 2 cond36753M1662M
Ours (training-free), 2 cond33323M29M
Ours (training-based), 2 cond33349M44M
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.504, + 0.905, + 0.533 + ], + "angle": 0, + "content": "Table 5. Comparison of inference GPU memory cost and additionally introduced parameters. CN: ControlNet. IP: IP-Adapter." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.551, + 0.907, + 0.672 + ], + "angle": 0, + "content": "Different Options for Trainable LoRA. To evaluate whether the trainable LoRA module can be applied to the text branch instead of the denoising branch, we load a Text-LoRA in the text branch, with a configuration identical to that of the Denoising-LoRA. The Tab. 3 and Fig. 10 indicate that applying the trainable LoRA module to the denoising branch better modulates the feature aggregation operation across multiple conditional branches." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.673, + 0.907, + 0.824 + ], + "angle": 0, + "content": "Training Strategy. As the parameter scale of the base model increases, the FLUX adaptations of ControlNet [53, 54] and IP-adapter [55] provided by the HuggingFace [16] community inject conditional features only into the dual-stream MMDiT blocks, rather than the entire network, to save memory. In contrast, since our Denoising-LoRA module introduces only a small number of parameters, we incorporate it into both the dual-stream and single-stream blocks to achieve better performance. The results in Tab. 4 and Fig. 11 confirm the validity of our choice." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.825, + 0.905, + 0.901 + ], + "angle": 0, + "content": "Computational Cost. The overheads of our approach in terms of inference GPU memory cost and additionally introduced parameters are minimal. The comparison results against the FLUX ControlNet [53, 54] and FLUX IP-Adapter [55] are shown in Tab. 5." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.925, + 0.504, + 0.936 + ], + "angle": 0, + "content": "8" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.482, + 0.166 + ], + "angle": 0, + "content": "More Conditional Branches. Our model places no restrictions on the number of supported conditions. The results shown in Fig. 12 demonstrate our model's strong scalability. As the number of conditional branches increases, the level of control becomes finer." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.182, + 0.48, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.346, + 0.483, + 0.372 + ], + "angle": 0, + "content": "Figure 12. From left to right are training-free multi-conditional combination tasks under: \\(1/2/3/4\\) conditions." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.397, + 0.484, + 0.489 + ], + "angle": 0, + "content": "More Application Scenarios. Our UniCombine can be easily extended to new scenarios, such as reference-based image stylization. After training a new Condition-LoRA on StyleBooth [10] dataset, our UniCombine is able to integrate the style of the reference image with other conditions successfully, as demonstrated in Fig. 13." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.504, + 0.48, + 0.636 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.639, + 0.454, + 0.653 + ], + "angle": 0, + "content": "Figure 13. Training-free Spatial-Style combination task." + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.692, + 0.21, + 0.708 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.72, + 0.484, + 0.901 + ], + "angle": 0, + "content": "We present UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generative tasks demonstrate the state-of-the-art performance of our UniCombine in both training-free and training-based versions. Additionally, we propose the SubjectSpatial200K dataset to address the lack of a publicly available dataset for training and testing multi-conditional generative models. 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Springer, 2025. 2, 5" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.093, + 0.905, + 0.673 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.925, + 0.508, + 0.937 + ], + "angle": 0, + "content": "11" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.227, + 0.086, + 0.773, + 0.13 + ], + "angle": 0, + "content": "UniCombine: Unified Multi-Conditional Combination with Diffusion Transformer" + }, + { + "type": "text", + "bbox": [ + 0.382, + 0.142, + 0.615, + 0.163 + ], + "angle": 0, + "content": "Supplementary Material" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.179, + 0.368, + 0.196 + ], + "angle": 0, + "content": "A1. Dataset Partitioning Scheme" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.204, + 0.484, + 0.279 + ], + "angle": 0, + "content": "In our proposed SubjectSpatial200K dataset, we utilize the ChatGPT-4o assessment scores provided by Subjects200K [45] on Subject Consistency, Composition Structure, and Image Quality to guide the dataset partitioning in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.28, + 0.483, + 0.31 + ], + "angle": 0, + "content": "- Subject Consistency: Ensuring the identity of the subject image is consistent with that of the ground truth image." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.311, + 0.482, + 0.34 + ], + "angle": 0, + "content": "- Composition Structure: Verifying a reasonable composition of the subject and ground truth images." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.341, + 0.482, + 0.37 + ], + "angle": 0, + "content": "- Image Quality: Confirming each image pair maintains high resolution and visual fidelity." + }, + { + "type": "list", + "bbox": [ + 0.091, + 0.28, + 0.483, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.371, + 0.483, + 0.401 + ], + "angle": 0, + "content": "We partition the dataset into 139,403 training samples and 5,827 testing samples through Algorithm 1." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.405, + 0.482, + 0.589 + ], + "angle": 0, + "content": "
Algorithm 1: Dataset Partitioning Scheme
Input: example
Output: train or test
cs← example["Composite Structure"]
iq← example["Image Quality"]
sc← example["Subject Consistency"]
scores← [cs, iq, sc]
if all(s==5 for s in scores) then
return train;
else if cs≥3 and iq==5 and sc==5 then
return test;
" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.61, + 0.451, + 0.626 + ], + "angle": 0, + "content": "A2. More Ablation on CMMDiT Attention" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.635, + 0.484, + 0.725 + ], + "angle": 0, + "content": "More quantitative and qualitative ablation results on the other multi-conditional generative tasks are provided here. The comprehensive ablation results in Tab. A1, Tab. A2, Tab. A3, Fig. A1, Fig. A2, and Fig. A3 demonstrate that the UniCombine performs better with our proposed CMMDiT Attention." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.735, + 0.472, + 0.794 + ], + "angle": 0, + "content": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑F1 ↑
Ours w/o CMMDiT91.5186.3133.200.16
Ours w/ CMMDiT91.8486.8833.210.17
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.091, + 0.795, + 0.482, + 0.823 + ], + "angle": 0, + "content": "Table A1. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Canny task" + }, + { + "type": "title", + "bbox": [ + 0.091, + 0.845, + 0.34, + 0.862 + ], + "angle": 0, + "content": "A3. More Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.483, + 0.902 + ], + "angle": 0, + "content": "More qualitative results are presented in Fig. A4 and Fig. A5." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.182, + 0.905, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.323, + 0.905, + 0.351 + ], + "angle": 0, + "content": "Figure A1. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Canny task" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.363, + 0.901, + 0.422 + ], + "angle": 0, + "content": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑MSE ↓
Ours w/o CMMDiT90.8385.3833.38547.63
Ours w/ CMMDiT91.1585.7333.41507.40
" + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.424, + 0.905, + 0.451 + ], + "angle": 0, + "content": "Table A2. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Depth task" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.459, + 0.905, + 0.597 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.599, + 0.905, + 0.627 + ], + "angle": 0, + "content": "Figure A2. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Depth task" + }, + { + "type": "table", + "bbox": [ + 0.56, + 0.64, + 0.858, + 0.699 + ], + "angle": 0, + "content": "
MethodCLIP-T ↑F1 ↑MSE ↓
Ours w/o CMMDiT33.700.17524.04
Ours w/ CMMDiT33.700.18519.53
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.7, + 0.905, + 0.728 + ], + "angle": 0, + "content": "Table A3. Quantitative ablation of CMMDiT Attention mechanism on training-free Multi-Spatial task" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.737, + 0.905, + 0.875 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.877, + 0.905, + 0.904 + ], + "angle": 0, + "content": "Figure A3. Qualitative ablation of CMMDiT Attention mechanism on training-free Multi-Spatial task" + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.925, + 0.509, + 0.937 + ], + "angle": 0, + "content": "12" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.098, + 0.476, + 0.859 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.098, + 0.905, + 0.859 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.873, + 0.737, + 0.888 + ], + "angle": 0, + "content": "Figure A4. More qualitative results on Multi-Spatial and Subject-Insertion tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.925, + 0.509, + 0.937 + ], + "angle": 0, + "content": "13" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.098, + 0.477, + 0.86 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.098, + 0.905, + 0.86 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.263, + 0.873, + 0.733, + 0.888 + ], + "angle": 0, + "content": "Figure A5. More qualitative results on Subject-Depth and Subject-Canny tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.925, + 0.509, + 0.937 + ], + "angle": 0, + "content": "14" + } + ] +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_origin.pdf b/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..519edcf50614af3b35ddfb40b1d5136bc27b4c97 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09277/39fed2ad-9645-4fde-a1c3-86b0c99b7b36_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4ccdc8108a290b385b2525b036f451b5dca21e11515c65ae490b08bb29254142 +size 13732806 diff --git a/data/2025/2503_09xxx/2503.09277/full.md b/data/2025/2503_09xxx/2503.09277/full.md new file mode 100644 index 0000000000000000000000000000000000000000..37c85a9e8e29e19ff0ed5b1e6707600f9d1cc941 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09277/full.md @@ -0,0 +1,380 @@ +# UniCombine: Unified Multi-Conditional Combination with Diffusion Transformer + +Haoxuan Wang $^{1\dagger}$ , Jinlong Peng $^{2\dagger}$ , Qingdong He $^{2}$ , Hao Yang $^{3}$ , Ying Jin $^{1}$ , Jiafu Wu $^{2}$ , Xiaobin Hu $^{2}$ , Yanjie Pan $^{1}$ , Zhenye Gan $^{2}$ , Mingmin Chi $^{1*}$ , Bo Peng $^{4*}$ , Yabiao Wang $^{2,5*}$ + +$^{1}$ Fudan University, $^{2}$ Tencent Youtu Lab, $^{3}$ Shanghai Jiao Tong University, $^{4}$ Shanghai Ocean University $^{5}$ Zhejiang University + +https://github.com/Xuan-World/UniCombine + +![](images/2c8007f4046d1a3e78dbaf014b7a491dbbbf9b78ef27cf90ee2c58035b246a98.jpg) +Figure 1. Fantastic results of our proposed UniCombine on multi-conditional controllable generation: (a) Subject-Insertion task. (b) and (c) Subject-Spatial task. (d) Multi-Spatial task. Our unified framework effectively handles any combination of input conditions and achieves remarkable alignment with all of them, including but not limited to text prompts, spatial maps, and subject images. + +# Abstract + +With the rapid development of diffusion models in image generation, the demand for more powerful and flexible controllable frameworks is increasing. Although existing methods can guide generation beyond text prompts, the challenge of effectively combining multiple conditional inputs + +while maintaining consistency with all of them remains unsolved. To address this, we introduce UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Specifically, we introduce a novel Conditional MMDiT Attention mechanism and incorporate a trainable LoRA module to build both the training-free and training-based versions. Additionally, we propose a new pipeline to construct SubjectSpatial200K, the first dataset + +designed for multi-conditional generative tasks covering both the subject-driven and spatially-aligned conditions. Extensive experimental results on multi-conditional generation demonstrate the outstanding universality and powerful capability of our approach with state-of-the-art performance. + +# 1. Introduction + +With the advancement of diffusion-based [13, 42] text-to-image generative technology, a series of single-conditional controllable generative frameworks like ControlNet [59], T2I-Adapter [31], IP-Adapter [58], and InstantID [47] have expanded the scope of the control signals from text prompts to image conditions. It allows users to control more plentiful aspects of the generated images, such as layout, style, characteristics, etc. These conventional approaches are specifically designed for the UNet [38] backbone of Latent Diffusion Models (LDM) [37] with dedicated control networks. Besides, some recent approaches, such as Omini-Control [45], integrate control signals into the Diffusion Transformer (DiT) [7, 23] architecture, which demonstrates superior performance compared to the UNet in LDM. + +Although the methods mentioned above have achieved a promising single-conditional performance, the challenge of multi-conditional controllable generation is still unsolved. Previous multi-conditional generative methods like UniControl [35] and UniControlNet [60] are generally restricted to handling spatial conditions like Canny or Depth maps and fail to accommodate subject conditions, resulting in limited applicable scenarios. Despite the recently proposed Ctrl-X [27] features controlling structure and appearance together, its performance is unsatisfactory and supports only a limited combination of conditions. + +Moreover, we assume that many existing generative tasks can be viewed as a multi-conditional generation, such as virtual try-on [5, 17], object insertion [3, 51], style transfer [15, 33, 52], spatially-aligned customization [20, 21, 25, 27], etc. Consequently, there is a need for a unified framework to encompass these generative tasks in a way of multi-conditional generation. This framework should ensure consistency with all input constraints, including subject ID preservation, spatial structural alignment, background coherence, and style uniformity. + +To achieve this, we propose UniCombine, a powerful and universal framework that offers several key advantages: Firstly, our framework is capable of simultaneously handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Specifically, we introduce a novel Conditional MMDiT Attention mechanism and incorporate a trainable Denoising-LoRA module to build both the training-free and training-based versions. By integrating multiple pre + +trained Condition-LoRA module weights into the conditional branches, UniCombine achieves excellent training-free performance, which can be improved further after training on the task-specific multi-conditional dataset. Secondly, due to the lack of a publicly available dataset for multi-conditional generative tasks, we build the SubjectSpatial200K dataset to serve as the training dataset and the testing benchmark. Specifically, we generate the subject grounding annotations and spatial map annotations for all the data samples from Subjects200K [45] and therefore formulate our SubjectSpatial200K dataset. Thirdly, our UniCombine can achieve many unprecedented multi-conditional combinations, as shown in Fig. 1, such as combining a reference subject image with the inpainting area of a background image or with the layout guidance of a depth (or canny) map while imposing precise control via text prompt. Furthermore, extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generation demonstrate the outstanding universality and powerful capability of our method against other existing specialized approaches. + +In summary, we highlight our contributions as follows: + +- We present UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. +- We construct the SubjectSpatial200K dataset, which encompasses both subject-driven and spatially-aligned conditions for all text-image sample pairs. It addresses the absence of a publicly available dataset for training and testing multi-conditional controllable generative models. +- We conduct extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generative tasks. The experimental results demonstrate the state-of-the-art performance of our UniCombine, which effectively aligns with all conditions harmoniously. + +# 2. Related Work + +# 2.1. Diffusion-Based Models + +Diffusion-based [13, 42] models have demonstrated superior performance than GAN-based [9] ones across various domains, including controllable generation [18, 31, 47, 58, 59], image editing [11, 30, 39], customized generation [8, 22, 40], object insertion [4, 43, 56], mask-guided inpainting [19, 48, 61], and so on. These breakthroughs begin with the LDM [37] and are further advanced with the DiT [32] architecture. The latest text-to-image generative models, SD3 [7] and FLUX [23], have attained state-of-the-art results by employing the Rectified Flow [28, 29] training strategy, the RPE [44] positional embedding and the MultiModal Diffusion Transformer (MMDiT) [7] architecture. + +![](images/e21e3bf9a4a78294b155fc81f3e6b7e3e4251e119c112d81fb0f47a4822439d5.jpg) +(a) Overall Framework + +![](images/3162d24f03eacb746bd4ecce492028784582c1beb179bc5cf91d96a185a56eec.jpg) +(b) Single-Conditional Setting + +![](images/7fa892b46091963fb1ee53c8e239a5cf468404dfb70774813a489096638da93b.jpg) +(c) Multi-Conditional Setting +Figure 2. Overview of our proposed UniCombine. (a) The overall framework. We regard the MMDiT-based diffusion models as consisting of the text branch and the denoising branch. Based on it, our UniCombine introduces multiple conditional branches to process the input conditions. (b) The single-conditional setting of our UniCombine. It is equivalent to OminiControl [45] which is a special case of our proposed UniCombine framework under a single-conditional setting. (c) The multi-conditional setting of our UniCombine. Our LoRA Switching module adaptively activates the pre-trained Condition-LoRA modules on the weights of the denoising branch according to the conditional types. The proposed Conditional MMDiT Attention mechanism is used to replace the original MMDiT Attention mechanism for handling the unified multi-conditional input sequence. Whether to load the optional Denoising-LoRA module is the difference between the training-free and training-based versions. + +# 2.2. Controllable Generation + +Controllable generation allows for customizing the desired spatial layout, filter style, or subject appearance in the generated images. A series of methods such as ControlNet [59], T2I-Adapter [31], GLIGEN [26], and ZestGuide [6] successfully introduce the spatial conditions into controllable generation, enabling models to control the spatial layout of generated images. Another series of methods, such as IP-Adapter [58], InstantID [47], BLIP-Diffusion [24], and StyleDrop [41] incorporate the subject conditions into controllable generation, ensuring consistency between generated images and reference images in style, characteristics, subject appearance, etc. To unify these two tasks, OminiControl [45] proposes a novel MMDiT-based controllable framework to handle various conditions with a unified pipeline. Unfortunately, it lacks the capability to control generation with multiple conditions. To this end, we propose UniCombine, which successfully extends this framework to multi-conditional scenarios. + +# 2.3. Multi-Conditional Controllable Generation + +As controllable generation advances, merely providing a single condition to guide the image generation no longer satisfies the needs. As a result, research on multi-conditional controllable generation has emerged. Existing methods like UniControl [35], UniControlNet [60] and Cocktail [14] exhibit acceptable performance when simul + +taneously leveraging multiple spatial conditions for image generation. However, there is a lack of multi-conditional generative models that support utilizing both spatial conditions and subject conditions to guide the generative process together. Although the recently proposed method Ctrl-X [27] features controlling the appearance and structure simultaneously, its performance remains unsatisfactory with a limited combination of conditions and it is not compatible with the Diffusion Transformer architecture. To address the aforementioned limitations, we propose UniCombine to enable the flexible combination of various control signals. + +# 3. Method + +# 3.1. Preliminary + +In this work, we mainly explore the latest generative models that utilize the Rectified Flow (RF) [28, 29] training strategy and the MMDiT [7] backbone architecture, like FLUX [23] and SD3 [7]. For the source noise distribution $X_0 \sim p_{\mathrm{noise}}$ and the target image distribution $X_1 \sim p_{\mathrm{data}}$ , the RF defines a linear interpolation between them as $X_t = (1 - t)X_0 + tX_1$ for $t \in [0,1]$ . The training objective is to learn a time-dependent vector field $v_t(X_t, t; \theta)$ that describes the trajectory of the ODE $dX_t = v_t(X_t, t; \theta)dt$ . Specifically, $v_t(X_t, t; \theta)$ is optimized to approximate the constant velocity $X_1 - X_0$ , leading to the loss function as Eq. (1). + +$$ +\mathcal {L} _ {\mathrm {R F}} (\theta) = \mathbb {E} _ {X _ {1} \sim p _ {\text {d a t a}}, X _ {0} \sim p _ {\text {n o i s e}}, t \sim U [ 0, 1 ]} \left[ \| (X _ {1} - X _ {0}) - v _ {t} (X _ {t}, t; \theta) \| ^ {2} \right] \tag {1} +$$ + +In this paper, we propose a concept of branch to differentiate the processing flows of input embeddings from different modalities in MMDiT-based models. As shown in Fig. 2 (a), instead of the single-branch architecture [37] where the text prompt is injected into the denoising branch via crossattention, MMDiT uses two independent transformers to construct the text branch and the denoising branch. Based on it, OminiControl [45] incorporates a Condition-LoRA module onto the weights of the denoising branch to process the input conditional embedding, thus forming its Conditional Branch, as depicted in Fig. 2 (b). It is worth noting that, OminiControl [45] can be regarded as a special case of our proposed UniCombine framework under the single-conditional setting. It provides the pre-trained Condition-LoRA modules to meet the need for our multi-conditional settings. In the single-conditional setting, the text branch embedding $T$ , the denoising branch embedding $X$ , and the conditional branch embedding $C$ are concatenated to form a unified sequence $[T;X;C]$ to be processed in the MMDiT Attention mechanism. + +# 3.2. UniCombine + +Building upon the MMDiT-based text-to-image generative model FLUX [23], we propose UniCombine, a multi-conditional controllable generative framework consisting of various conditional branches. Each conditional branch is in charge of processing one conditional embedding, thus forming a unified embedding sequence $S$ as presented in Eq. (2). + +$$ +S = [ T; X; C _ {1}; \dots ; C _ {N} ] \tag {2} +$$ + +Given that the single-conditional setting of our UniCombine is equivalent to OmniControl [45], we only focus on the multi-conditional setting in this section. Firstly, we introduce a LoRA Switching module to manage multiple conditional branches effectively. Secondly, we introduce a novel Conditional MMDiT Attention mechanism to process the unified sequence $S$ in the multi-conditional setting. Thirdly, we present an insight analysis of our training-free strategy, which leverages the pre-trained Condition-LoRA module weights to perform a training-free multi-conditional controllable generation. Lastly, we present a feasible training-based strategy, which utilizes a trainable Denoising-LoRA module to enhance the performance further after training on a task-specific multi-conditional dataset. + +LoRA Switching Module. Before denoising with multiple input conditions, the Condition-LoRA modules pre-trained under single-conditional settings should be loaded onto the weights of the denoising branch, like $[CondLoRA_1, CondLoRA_2, \ldots]$ . Then the LoRA Switching module determines which one of them should be + +activated according to the type of input conditions, forming a one-hot gating mechanism $[0,1,0,\dots,0]$ , as shown in Fig. 2 (c). Subsequently, different conditional branches with different activated Condition-LoRA modules are used for processing different conditional embeddings, resulting in a minimal number of additional parameters introduced for different conditions. Unlike the single-conditional setting in Fig. 2 (b), which only needs loading LoRA modules, the LoRA Switching module in Fig. 2 (c) enables adaptive selection among multiple LoRA modules to provide the matching conditional branches for each conditional embeddings, granting our framework greater flexibility and adaptability to handle diverse conditional combinations. + +Conditional MMDiT Attention. After concatenating the output embeddings from these $N$ conditional branches, the unified sequence $S$ cannot be processed through the original MMDiT Attention mechanism due to two major challenges: (1) The computational complexity scales quadratically as $O(N^2)$ with respect to the number of conditions, which becomes especially problematic when handling multiple high-resolution conditions. (2) When performing MMDiT Attention on the unified sequence $S$ , different condition signals interfere with each other during the attention calculation, making it difficult to effectively utilize the pre-trained Condition-LoRA module weights for the denoising process. + +To address these challenges, we introduce a novel Conditional MMDiT Attention mechanism (CMMDiT Attention) as depicted in Fig. 2 (c) to replace the original MMDiT Attention. Instead of feeding the entire unified sequence $S$ into the MMDiT Attention at once, CMMDiT Attention follows distinct computational mechanisms according to which branch is serving as queries. The core idea is that the branch serving as a query aggregates the information from different scopes of the unified sequence $S$ depending on its type. Specifically, when the denoising branch $X$ and the text branch $T$ serve as queries, their scope of keys and values correspond to the entire unified sequence $S$ , granting them a global receptive field and the ability to aggregate information from all conditional branches. In contrast, when the conditional branches $C_i$ serve as queries, their receptive fields do not encompass one another. Their scope of keys and values are restricted to the subsequence $S_i$ as presented in Eq. (3), which prevents feature exchange and avoids information entanglement between different conditions. + +$$ +S _ {i} = [ T; X; C _ {i} ] \tag {3} +$$ + +Furthermore, the CMMDiT Attention reduces computational complexity from $O(N^2)$ to $O(N)$ as the number of conditions increases, making it more scalable. + +Training-free Strategy. The following analyses provide a detailed explanation of why our UniCombine is capable of seamlessly integrating and effectively reusing the pretrained Condition-LoRA module weights to tackle multi-conditional challenges in a training-free manner. + +![](images/8c57a3c424f01738f8a53f6d6f0c8688e8016cc7a73bf6ea21df63ffdafe3eaa.jpg) +Figure 3. Average $\mathrm{X} \rightarrow$ Subject cross-attention map of the insertion area. + +On the one hand, when the conditional embeddings $C_i$ serve as queries in CMMDiT, they follow the same attention computational paradigm as in the MMDiT of single-conditional settings, as indicated in Eq. (4). + +$$ +\begin{array}{l} \operatorname {C M M D i T} \left(Q = C _ {i} ^ {q}, K = \left[ T ^ {k}, X ^ {k}, C _ {i} ^ {k} \right], V = \left[ T ^ {v}, X ^ {v}, C _ {i} ^ {v} \right]\right) \\ = \operatorname {M M D i T} (Q = C ^ {q}, K = [ T ^ {k}, X ^ {k}, C ^ {k} ], V = [ T ^ {v}, X ^ {v}, C ^ {v} ]) \tag {4} \\ \end{array} +$$ + +This consistent computational paradigm enables the conditional branches to share the same feature extraction capability between the multi-conditional setting and the single-conditional setting. + +On the other hand, when the denoising embedding $X$ and the text prompt embedding $T$ serve as queries in CMMDiT, their attention computational paradigm diverges from the single-conditional settings. As illustrated in Eq. (5), when the denoising embedding $X$ is used as a query for attention computation with multiple conditional embeddings in CMMDiT, the attention score matrix is computed between $X$ and all the conditional embeddings. + +$$ +\begin{array}{l} \mathrm {C M M D i T} (Q = X ^ {q}, K / V = [ X ^ {k / v}, T ^ {k / v}, C _ {1} ^ {k / v}, \dots , C _ {N} ^ {k / v} ]) \\ = \operatorname {s o f t m a x} \left(\frac {1}{\sqrt {d i m}} X ^ {q} \left[ X ^ {k}, T ^ {k}, C _ {1} ^ {k}, \dots , C _ {N} ^ {k} \right] ^ {\top}\right) \left[ X ^ {v}, T ^ {v}, C _ {1} ^ {v}, \dots , C _ {N} ^ {v} \right] \tag {5} \\ \end{array} +$$ + +It allows $X$ to extract and integrate information from each of the conditional embeddings separately and fusion them. This divide-and-conquer computational paradigm enables the text branch and denoising branch to fuse the conditional features effectively. + +By leveraging the computational paradigms mentioned above, our UniCombine is able to perform a training-free multi-conditional controllable generation with the pretrained Condition-LoRA modules. + +Training-based Strategy. However, due to the lack of training, solely relying on the softmax operation in Eq. (5) to balance the attention score distribution across multiple conditional embeddings may result in an undesirable feature fusion result, making our training-free version unsatisfactory in some cases. To address this issue, we introduce a trainable Denoising-LoRA module within the denoising branch to rectify the distribution of attention scores in Eq. (5). During training, we keep all the Condition-LoRA modules frozen to preserve the conditional extracting capability and train the Denoising-LoRA module solely on the task-specific multi-conditional dataset, as shown in Fig. 2 (c). After training, the denoising embedding $X$ learns to + +![](images/d04a32c8e874aab106f9fa111d4a7b255e65e731a4acd2452f053c1c30949d06.jpg) +Figure 4. SubjectSpatial200K dataset construction pipeline. + +better aggregate the appropriate information during the CM-MDiT Attention operation. As presented in Fig. 3, the average $\mathrm{X} \rightarrow$ Subject attention map within the inpainting area is more concentrated on the subject area in the training-based version. + +# 3.3. SubjectSpatial200K dataset + +Our SubjectSpatial200K dataset aims to address the lack of a publicly available dataset for multi-conditional generative tasks. Existing datasets fail to include both the subject-driven and spatially-aligned annotations. Recently, the Subjects200K [45] dataset provides a publicly accessible dataset for subject-driven generation. Based on it, we introduce the SubjectSpatial200K dataset, which is a unified high-quality dataset designed for training and testing multi-conditional controllable generative models. This dataset includes comprehensive annotations as elaborated below. Besides, the construction pipeline is detailed in Fig. 4. + +Subject Grounding Annotation. The subject grounding annotation is significantly necessary for many generative tasks like instance-level inpainting [19, 61], instance-level controllable generation [26, 49], and object insertion [4, 43]. By leveraging the open-vocabulary object detection model Mamba-YOLO-World [46] on Subjects200K, we detect bounding boxes for all subjects according to their category descriptions and subsequently derive the corresponding mask regions. + +Spatial Map Annotation. The spatial map annotation further extends the applicable scope of our dataset to spatially-aligned synthesis tasks. Specifically, we employ the Depth-Anything [57] model and the OpenCV [1] library on Subjects200K to derive the Depth and Canny maps. + +# 4. Experiment + +# 4.1. Setup + +Implementation. We use the FLUX.1-schnell [23] as our base model and the weights provided by OminiControl [45] + +
TaskMethodGenerative QualityControllabilitySubject ConsistencyText Consistency
FID ↓SSIM ↑F1 ↑MSE ↓CLIP-I ↑DINO ↑CLIP-T ↑
Multi-SpatialUniControl44.170.320.071346.02--30.28
UniControlNet20.960.280.091231.06--32.74
UniCombine (training-free)10.350.540.18519.53--33.70
UniCombine (training-based)6.820.640.24165.90--33.45
Subject-InsertionObjectStitch26.860.37--93.0582.3432.25
AnyDoor26.070.37--94.8886.0432.55
UniCombine (training-free)6.370.76--95.6089.0133.11
UniCombine (training-based)4.550.81--97.1492.9633.08
Subject-DepthControlNet w. IP-Adapter29.930.34-1295.8080.4162.2632.94
Ctrl-X52.370.36-2644.9078.0850.8330.20
UniCombine (training-free)10.030.48-507.4091.1585.7333.41
UniCombine (training-based)6.660.55-196.6594.4790.3133.30
Subject-CannyControlNet w. IP-Adapter30.380.380.09-79.8060.1932.85
Ctrl-X47.890.360.05-79.3554.3130.34
UniCombine (training-free)10.220.490.17-91.8486.8833.21
UniCombine (training-based)6.010.610.24-95.2692.5933.30
+ +Table 1. Quantitative comparison of our method with existing approaches on Multi-Spatial, Subject-Insertion, Subject-Depth, and Subject-Canny conditional generative tasks. The bold and underlined figures represent the optimal and sub-optimal results, respectively. + +![](images/1e06b7a6c1ae6b58e94df98cc9be3d1764e9ac9f480e954299aa319606949d55.jpg) +Figure 5. Qualitative comparison on Multi-Spatial generation. + +as our pre-trained Condition-LoRA module weights. During the training of our Denoising-LoRA module, we use a rank of 4, consistent with the Condition-LoRA. We choose the Adam optimizer with a learning rate of $1e^{-4}$ and set the weight decay to 0.01. Our models are trained for 30,000 steps on 16 NVIDIA V100 GPUs at a resolution of $512 \times 512$ . + +**Benchmarks.** We evaluate the performance of our method in both training-free and training-based versions. The training and testing datasets are partitioned from the SubjectSpatial200K dataset based on image quality assessment scores evaluated by ChatGPT-4o, with details provided in Sec. A1. + +![](images/d60c55bfaeeeedfd5aefc1bba87bd491b67f9a1c54a3f0b04bece1daafa5fa08.jpg) +Figure 6. Qualitative comparison on Subject-Insertion generation. + +Importantly, the dataset partitioning scheme remains consistent in all experiments. + +Metrics. To evaluate the subject consistency, we calculate the CLIP-I [36] score and DINO [2] score between the generated images and the ground truth images. To assess the generative quality, we compute the FID [12] and SSIM [50] between the generated image set and the ground truth image set. To measure the controllability, we compute the F1 Score for edge conditions and the MSE score for depth conditions between the extracted maps from generated images and the original conditions. Additionally, we adopt the CLIP-T [36] score to estimate the text consistency between + +![](images/506fe3547ab1943e7faa90d0f349eb3f11dc59ed4a47d7cf36007f74a6ca38f0.jpg) +Figure 7. Qualitative comparison on Subject-Depth generation. + +the generated images and the text prompts. + +# 4.2. Main Result + +We conduct extensive and comprehensive comparative experiments on the Multi-Spatial, Subject-Insertion, and Subject-Spatial conditional generative tasks. + +# 4.2.1. Multi-Spatial Conditional Generation + +The Multi-Spatial conditional generation aims to generate images adhering to the collective layout constraints of diverse spatial conditions. This requires the model to achieve a more comprehensive layout control based on input conditions in a complementary manner. The comparative results in Tab. 1 and Fig. 5 demonstrate that our method outperforms existing multi-spatial conditional generation approaches in generative quality and controllability. + +# 4.2.2. Subject-Insertion Conditional Generation + +The Subject-Insertion conditional generation requires the model to generate images where the reference subject is inserted into the masked region of the target background. As illustrated in Tab. 1 and Fig. 6, our UniCombine demonstrates superior performance compared to previous methods with three advantages: Firstly, our method ensures that the reference subject is inserted into the background with high consistency and harmonious integration. Secondly, our method excels in open-world object insertion without requiring test-time tuning, unlike conventional customization methods [22, 40]. Finally, our method demonstrates strong semantic comprehension capabilities, enabling it to extract the desired object from a complex subject image with a non-white background, rather than simply pasting the entire subject image into the masked region. + +![](images/44ebde2dd6cfbcb637ef99847a469c9c5e74ddeb4368792fe3d6809b1e91856e.jpg) +Figure 8. Qualitative comparison on Subject-Canny generation. + +# 4.2.3. Subject-Spatial Conditional Generation + +The Subject-Spatial conditional generation focuses on generating images of the reference subject while ensuring the layout aligns with specified spatial conditions. We compare our method with Ctrl-X [27] and a simple baseline model. Ctrl-X is a recently proposed model based on SDXL [34] that simultaneously controls structure and appearance. The baseline model is constructed by integrating the FLUX ControlNet [53, 54] and FLUX IP-Adapter [55] into the FLUX.1-dev [23] base model. Specifically, we divided the Subject-Spatial generative task into different experimental groups based on the type of spatial conditions, referred to as Subject-Depth and Subject-Canny, respectively. As presented in Fig. 7, Fig. 8, and Tab. 1, the experimental results demonstrate the superior performance of our UniCombine: Firstly, our method exhibits stronger semantic comprehension capability, generating the reference subject in the accurate localization of the spatial conditions without confusing appearance features. Secondly, our method demonstrates greater adaptability, generating the reference subject with reasonable morphological transformations to align with the guidance of spatial conditions and text prompts. Lastly, our method achieves superior subject consistency while maintaining excellent spatial coherence. + +# 4.2.4. Textual Guidance + +As shown in Fig. 1 and Tab. 1, our method not only allows for controllable generation by combining multiple conditions but also enables precise textual guidance simultaneously. By utilizing a unified input sequence $S = [T; X; C_1; \ldots; C_N]$ during the denoising process, our UniCombine effectively aligns the descriptive words in $T$ with + +
MethodCLIP-I ↑DINO ↑CLIP-T ↑AttnOps ↓
Ours w/o CMMDiT95.4788.4233.10732.17M
Ours w/ CMMDiT95.6089.0133.11612.63M
+ +Table 2. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Insertion task. AttnOps is short for the number of attention operations. + +
Background +SubjectTraining-free +w/o CMMDiTTraining-free +w/ CMMDiTBackground +SubjectTraining-free +w/o CMMDiTTraining-free +w/ CMMDiT
inconsistentsuccessinconsistentsuccess
failsuccessfailsuccess
+ +Figure 9. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Insertion task. + +
MethodCLIP-I ↑DINO ↑CLIP-T ↑
Ours w/ Text-LoRA96.9792.3233.10
Ours w/ Denoising-LoRA97.1492.9633.08
+ +![](images/fc8bc88e1ec09551aeba8132d1ccff2d2a1eb574ea62259a59e0357472255443.jpg) +Figure 10. Qualitative ablation of trainable LoRA on training-based Subject-Insertion task. + +the relevant features in $C_i$ and the corresponding patches in $X$ , thereby achieving a remarkable text-guided multi-conditional controllable generation. + +# 4.3. Ablation Study + +We exhibit the ablation study results conducted on the Subject-Insertion task in this section, while more results on the other tasks are provided in Sec. A2. + +Effect of Conditional MMDiT Attention. To evaluate the effectiveness of our proposed Conditional MMDiT Attention mechanism, we replace the CMMDiT Attention with the original MMDiT Attention and test its training-free performance to avoid the influence of training data. As shown in Tab. 2 and Fig. 9, our framework attains superior performance with fewer attention operations when employing the CMMDiT Attention mechanism. + +Table 3. Quantitative ablation of trainable LoRA on training-based Subject-Insertion task. + +
MethodCLIP-I ↑DINO ↑CLIP-T ↑
Ours w/ DSB only96.8592.3833.07
Ours w/ DSB and SSB97.1492.9633.08
+ +Table 4. Quantitative ablation of training strategy on training-based Subject-Insertion task. DSB: Dual-Stream Blocks. SSB: Single-Stream Blocks. + +
Background +SubjectTraining-based +w/ DSB onlyTraining-based +w/ DSB + SSBBackground +SubjectTraining-based +w/ DSB onlyTraining-based +w/ DSB + SSB
inconsistentsuccessinconsistentsuccessinconsistentsuccess
inconsistentsuccessfailsuccessinconsistentinconsistent
+ +Figure 11. Qualitative ablation of training strategy on training-based Subject-Insertion task. DSB: Dual-Stream Blocks. SSB: Single-Stream Blocks. + +
ModelGPU Memory ↓Add Params ↓
FLUX (bf16, base model)32933M-
CN, 1 cond35235M744M
IP, 1 cond35325M918M
CN + IP, 2 cond36753M1662M
Ours (training-free), 2 cond33323M29M
Ours (training-based), 2 cond33349M44M
+ +Table 5. Comparison of inference GPU memory cost and additionally introduced parameters. CN: ControlNet. IP: IP-Adapter. + +Different Options for Trainable LoRA. To evaluate whether the trainable LoRA module can be applied to the text branch instead of the denoising branch, we load a Text-LoRA in the text branch, with a configuration identical to that of the Denoising-LoRA. The Tab. 3 and Fig. 10 indicate that applying the trainable LoRA module to the denoising branch better modulates the feature aggregation operation across multiple conditional branches. + +Training Strategy. As the parameter scale of the base model increases, the FLUX adaptations of ControlNet [53, 54] and IP-adapter [55] provided by the HuggingFace [16] community inject conditional features only into the dual-stream MMDiT blocks, rather than the entire network, to save memory. In contrast, since our Denoising-LoRA module introduces only a small number of parameters, we incorporate it into both the dual-stream and single-stream blocks to achieve better performance. The results in Tab. 4 and Fig. 11 confirm the validity of our choice. + +Computational Cost. The overheads of our approach in terms of inference GPU memory cost and additionally introduced parameters are minimal. The comparison results against the FLUX ControlNet [53, 54] and FLUX IP-Adapter [55] are shown in Tab. 5. + +More Conditional Branches. Our model places no restrictions on the number of supported conditions. The results shown in Fig. 12 demonstrate our model's strong scalability. As the number of conditional branches increases, the level of control becomes finer. + +![](images/a621a99e80843ff5996990493bd8940b3ce3197ae924350ffd10503c3b7c6b1c.jpg) +Figure 12. From left to right are training-free multi-conditional combination tasks under: $1/2/3/4$ conditions. + +More Application Scenarios. Our UniCombine can be easily extended to new scenarios, such as reference-based image stylization. After training a new Condition-LoRA on StyleBooth [10] dataset, our UniCombine is able to integrate the style of the reference image with other conditions successfully, as demonstrated in Fig. 13. + +![](images/697b9a0d3b2d71d9ac73a42626a46546416d486f912cfdb2949db0c5a79882ad.jpg) +Figure 13. Training-free Spatial-Style combination task. + +# 5. Conclusion + +We present UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generative tasks demonstrate the state-of-the-art performance of our UniCombine in both training-free and training-based versions. 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Advances in Neural Information Processing Systems, 36, 2024. 2, 3 +[61] Junhao Zhuang, Yanhong Zeng, Wenran Liu, Chun Yuan, and Kai Chen. A task is worth one word: Learning with task prompts for high-quality versatile image inpainting. In European Conference on Computer Vision, pages 195-211. Springer, 2025. 2, 5 + +# UniCombine: Unified Multi-Conditional Combination with Diffusion Transformer + +Supplementary Material + +# A1. Dataset Partitioning Scheme + +In our proposed SubjectSpatial200K dataset, we utilize the ChatGPT-4o assessment scores provided by Subjects200K [45] on Subject Consistency, Composition Structure, and Image Quality to guide the dataset partitioning in our experiments. + +- Subject Consistency: Ensuring the identity of the subject image is consistent with that of the ground truth image. +- Composition Structure: Verifying a reasonable composition of the subject and ground truth images. +- Image Quality: Confirming each image pair maintains high resolution and visual fidelity. + +We partition the dataset into 139,403 training samples and 5,827 testing samples through Algorithm 1. + +
Algorithm 1: Dataset Partitioning Scheme
Input: example
Output: train or test
cs← example["Composite Structure"]
iq← example["Image Quality"]
sc← example["Subject Consistency"]
scores← [cs, iq, sc]
if all(s==5 for s in scores) then
return train;
else if cs≥3 and iq==5 and sc==5 then
return test;
+ +# A2. More Ablation on CMMDiT Attention + +More quantitative and qualitative ablation results on the other multi-conditional generative tasks are provided here. The comprehensive ablation results in Tab. A1, Tab. A2, Tab. A3, Fig. A1, Fig. A2, and Fig. A3 demonstrate that the UniCombine performs better with our proposed CMMDiT Attention. + +
MethodCLIP-I ↑DINO ↑CLIP-T ↑F1 ↑
Ours w/o CMMDiT91.5186.3133.200.16
Ours w/ CMMDiT91.8486.8833.210.17
+ +Table A1. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Canny task + +# A3. More Qualitative Results + +More qualitative results are presented in Fig. A4 and Fig. A5. + +![](images/c8c9030826d874847297d6aad99732ff7992fa1efed8eaf2d42146029239dcfe.jpg) +Figure A1. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Canny task + +
MethodCLIP-I ↑DINO ↑CLIP-T ↑MSE ↓
Ours w/o CMMDiT90.8385.3833.38547.63
Ours w/ CMMDiT91.1585.7333.41507.40
+ +![](images/eec53f0d14c8df15f39c097595e64b40514c9c785b2e319a4f3ff0334abfd869.jpg) +Table A2. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Depth task +Figure A2. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Depth task + +
MethodCLIP-T ↑F1 ↑MSE ↓
Ours w/o CMMDiT33.700.17524.04
Ours w/ CMMDiT33.700.18519.53
+ +Table A3. Quantitative ablation of CMMDiT Attention mechanism on training-free Multi-Spatial task + +![](images/4009d7abc995632fbc8e9c0c98b070e0d250aff3285f29dd8f899b9c93e1e20e.jpg) +Figure A3. Qualitative ablation of CMMDiT Attention mechanism on training-free Multi-Spatial task + +![](images/adfac4a9eebfdf05d1126a0a351b1aaafa113e3c17e6ad1d0d3ccee8c001ec91.jpg) +Figure A4. More qualitative results on Multi-Spatial and Subject-Insertion tasks. + +![](images/721139a8e4ed891aeab8a9eecb8d33d046e4e4574b78dabb5cd359d3ae06e6b6.jpg) + +![](images/179cb411321ca8ecf6e101c92a53a0ef8cbc9728a7f08f18d3c37f263493e513.jpg) +Figure A5. 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+ "type": "image_body" + }, + { + "bbox": [ + 55, + 548, + 555, + 583 + ], + "lines": [ + { + "bbox": [ + 55, + 548, + 555, + 583 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 555, + 583 + ], + "type": "text", + "content": "Figure 1. Fantastic results of our proposed UniCombine on multi-conditional controllable generation: (a) Subject-Insertion task. (b) and (c) Subject-Spatial task. (d) Multi-Spatial task. Our unified framework effectively handles any combination of input conditions and achieves remarkable alignment with all of them, including but not limited to text prompts, spatial maps, and subject images." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 152, + 592, + 200, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 592, + 200, + 604 + ], + "spans": [ + { + "bbox": [ + 152, + 592, + 200, + 604 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 619, + 295, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 619, + 295, + 679 + ], + "spans": [ + { + "bbox": [ + 55, + 619, + 295, + 679 + ], + "type": "text", + "content": "With the rapid development of diffusion models in image generation, the demand for more powerful and flexible controllable frameworks is increasing. Although existing methods can guide generation beyond text prompts, the challenge of effectively combining multiple conditional inputs" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 593, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 593, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 593, + 555, + 713 + ], + "type": "text", + "content": "while maintaining consistency with all of them remains unsolved. To address this, we introduce UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Specifically, we introduce a novel Conditional MMDiT Attention mechanism and incorporate a trainable LoRA module to build both the training-free and training-based versions. Additionally, we propose a new pipeline to construct SubjectSpatial200K, the first dataset" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 14, + 228, + 35, + 562 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 14, + 228, + 35, + 562 + ], + "spans": [ + { + "bbox": [ + 14, + 228, + 35, + 562 + ], + "type": "text", + "content": "arXiv:2503.09277v2 [cs.CV] 8 Jul 2025" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 693, + 139, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 693, + 139, + 703 + ], + "spans": [ + { + "bbox": [ + 70, + 693, + 139, + 703 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 70, + 693, + 139, + 703 + ], + "type": "text", + "content": " Equal contribution." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 70, + 704, + 150, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 704, + 150, + 712 + ], + "spans": [ + { + "bbox": [ + 70, + 704, + 150, + 712 + ], + "type": "text", + "content": "* Corresponding author." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "spans": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "text", + "content": "1" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 72, + 294, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 72, + 294, + 144 + ], + "spans": [ + { + "bbox": [ + 54, + 72, + 294, + 144 + ], + "type": "text", + "content": "designed for multi-conditional generative tasks covering both the subject-driven and spatially-aligned conditions. Extensive experimental results on multi-conditional generation demonstrate the outstanding universality and powerful capability of our approach with state-of-the-art performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 167, + 136, + 179 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 167, + 136, + 179 + ], + "spans": [ + { + "bbox": [ + 55, + 167, + 136, + 179 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 186, + 296, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 186, + 296, + 354 + ], + "spans": [ + { + "bbox": [ + 56, + 186, + 296, + 354 + ], + "type": "text", + "content": "With the advancement of diffusion-based [13, 42] text-to-image generative technology, a series of single-conditional controllable generative frameworks like ControlNet [59], T2I-Adapter [31], IP-Adapter [58], and InstantID [47] have expanded the scope of the control signals from text prompts to image conditions. It allows users to control more plentiful aspects of the generated images, such as layout, style, characteristics, etc. These conventional approaches are specifically designed for the UNet [38] backbone of Latent Diffusion Models (LDM) [37] with dedicated control networks. Besides, some recent approaches, such as Omini-Control [45], integrate control signals into the Diffusion Transformer (DiT) [7, 23] architecture, which demonstrates superior performance compared to the UNet in LDM." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 355, + 296, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 355, + 296, + 486 + ], + "spans": [ + { + "bbox": [ + 56, + 355, + 296, + 486 + ], + "type": "text", + "content": "Although the methods mentioned above have achieved a promising single-conditional performance, the challenge of multi-conditional controllable generation is still unsolved. Previous multi-conditional generative methods like UniControl [35] and UniControlNet [60] are generally restricted to handling spatial conditions like Canny or Depth maps and fail to accommodate subject conditions, resulting in limited applicable scenarios. Despite the recently proposed Ctrl-X [27] features controlling structure and appearance together, its performance is unsatisfactory and supports only a limited combination of conditions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 487, + 296, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 487, + 296, + 605 + ], + "spans": [ + { + "bbox": [ + 56, + 487, + 296, + 605 + ], + "type": "text", + "content": "Moreover, we assume that many existing generative tasks can be viewed as a multi-conditional generation, such as virtual try-on [5, 17], object insertion [3, 51], style transfer [15, 33, 52], spatially-aligned customization [20, 21, 25, 27], etc. Consequently, there is a need for a unified framework to encompass these generative tasks in a way of multi-conditional generation. This framework should ensure consistency with all input constraints, including subject ID preservation, spatial structural alignment, background coherence, and style uniformity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 606, + 294, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 606, + 294, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 606, + 294, + 714 + ], + "type": "text", + "content": "To achieve this, we propose UniCombine, a powerful and universal framework that offers several key advantages: Firstly, our framework is capable of simultaneously handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Specifically, we introduce a novel Conditional MMDiT Attention mechanism and incorporate a trainable Denoising-LoRA module to build both the training-free and training-based versions. By integrating multiple pre" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 324 + ], + "type": "text", + "content": "trained Condition-LoRA module weights into the conditional branches, UniCombine achieves excellent training-free performance, which can be improved further after training on the task-specific multi-conditional dataset. Secondly, due to the lack of a publicly available dataset for multi-conditional generative tasks, we build the SubjectSpatial200K dataset to serve as the training dataset and the testing benchmark. Specifically, we generate the subject grounding annotations and spatial map annotations for all the data samples from Subjects200K [45] and therefore formulate our SubjectSpatial200K dataset. Thirdly, our UniCombine can achieve many unprecedented multi-conditional combinations, as shown in Fig. 1, such as combining a reference subject image with the inpainting area of a background image or with the layout guidance of a depth (or canny) map while imposing precise control via text prompt. Furthermore, extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generation demonstrate the outstanding universality and powerful capability of our method against other existing specialized approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 324, + 326, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 326, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 324, + 326, + 547, + 338 + ], + "type": "text", + "content": "In summary, we highlight our contributions as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 341, + 553, + 509 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 314, + 341, + 553, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 341, + 553, + 388 + ], + "spans": [ + { + "bbox": [ + 314, + 341, + 553, + 388 + ], + "type": "text", + "content": "- We present UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 388, + 553, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 388, + 553, + 449 + ], + "spans": [ + { + "bbox": [ + 314, + 388, + 553, + 449 + ], + "type": "text", + "content": "- We construct the SubjectSpatial200K dataset, which encompasses both subject-driven and spatially-aligned conditions for all text-image sample pairs. It addresses the absence of a publicly available dataset for training and testing multi-conditional controllable generative models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 314, + 449, + 553, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 449, + 553, + 509 + ], + "spans": [ + { + "bbox": [ + 314, + 449, + 553, + 509 + ], + "type": "text", + "content": "- We conduct extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generative tasks. The experimental results demonstrate the state-of-the-art performance of our UniCombine, which effectively aligns with all conditions harmoniously." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 314, + 527, + 400, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 527, + 400, + 540 + ], + "spans": [ + { + "bbox": [ + 314, + 527, + 400, + 540 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 549, + 449, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 549, + 449, + 562 + ], + "spans": [ + { + "bbox": [ + 314, + 549, + 449, + 562 + ], + "type": "text", + "content": "2.1. Diffusion-Based Models" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 553, + 713 + ], + "type": "text", + "content": "Diffusion-based [13, 42] models have demonstrated superior performance than GAN-based [9] ones across various domains, including controllable generation [18, 31, 47, 58, 59], image editing [11, 30, 39], customized generation [8, 22, 40], object insertion [4, 43, 56], mask-guided inpainting [19, 48, 61], and so on. These breakthroughs begin with the LDM [37] and are further advanced with the DiT [32] architecture. The latest text-to-image generative models, SD3 [7] and FLUX [23], have attained state-of-the-art results by employing the Rectified Flow [28, 29] training strategy, the RPE [44] positional embedding and the MultiModal Diffusion Transformer (MMDiT) [7] architecture." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 732, + 309, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 732, + 309, + 741 + ], + "spans": [ + { + "bbox": [ + 302, + 732, + 309, + 741 + ], + "type": "text", + "content": "2" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 69, + 197, + 266 + ], + "blocks": [ + { + "bbox": [ + 57, + 69, + 197, + 266 + ], + "lines": [ + { + "bbox": [ + 57, + 69, + 197, + 266 + ], + "spans": [ + { + "bbox": [ + 57, + 69, + 197, + 266 + ], + "type": "image", + "image_path": "e21e3bf9a4a78294b155fc81f3e6b7e3e4251e119c112d81fb0f47a4822439d5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 87, + 269, + 165, + 278 + ], + "lines": [ + { + "bbox": [ + 87, + 269, + 165, + 278 + ], + "spans": [ + { + "bbox": [ + 87, + 269, + 165, + 278 + ], + "type": "text", + "content": "(a) Overall Framework" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 201, + 69, + 334, + 266 + ], + "blocks": [ + { + "bbox": [ + 201, + 69, + 334, + 266 + ], + "lines": [ + { + "bbox": [ + 201, + 69, + 334, + 266 + ], + "spans": [ + { + "bbox": [ + 201, + 69, + 334, + 266 + ], + "type": "image", + "image_path": "3162d24f03eacb746bd4ecce492028784582c1beb179bc5cf91d96a185a56eec.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 216, + 269, + 319, + 279 + ], + "lines": [ + { + "bbox": [ + 216, + 269, + 319, + 279 + ], + "spans": [ + { + "bbox": [ + 216, + 269, + 319, + 279 + ], + "type": "text", + "content": "(b) Single-Conditional Setting" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 338, + 70, + 554, + 266 + ], + "blocks": [ + { + "bbox": [ + 338, + 70, + 554, + 266 + ], + "lines": [ + { + "bbox": [ + 338, + 70, + 554, + 266 + ], + "spans": [ + { + "bbox": [ + 338, + 70, + 554, + 266 + ], + "type": "image", + "image_path": "7fa892b46091963fb1ee53c8e239a5cf468404dfb70774813a489096638da93b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 269, + 496, + 279 + ], + "lines": [ + { + "bbox": [ + 397, + 269, + 496, + 279 + ], + "spans": [ + { + "bbox": [ + 397, + 269, + 496, + 279 + ], + "type": "text", + "content": "(c) Multi-Conditional Setting" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 285, + 555, + 373 + ], + "lines": [ + { + "bbox": [ + 54, + 285, + 555, + 373 + ], + "spans": [ + { + "bbox": [ + 54, + 285, + 555, + 373 + ], + "type": "text", + "content": "Figure 2. Overview of our proposed UniCombine. (a) The overall framework. We regard the MMDiT-based diffusion models as consisting of the text branch and the denoising branch. Based on it, our UniCombine introduces multiple conditional branches to process the input conditions. (b) The single-conditional setting of our UniCombine. It is equivalent to OminiControl [45] which is a special case of our proposed UniCombine framework under a single-conditional setting. (c) The multi-conditional setting of our UniCombine. Our LoRA Switching module adaptively activates the pre-trained Condition-LoRA modules on the weights of the denoising branch according to the conditional types. The proposed Conditional MMDiT Attention mechanism is used to replace the original MMDiT Attention mechanism for handling the unified multi-conditional input sequence. Whether to load the optional Denoising-LoRA module is the difference between the training-free and training-based versions." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 384, + 192, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 384, + 192, + 395 + ], + "spans": [ + { + "bbox": [ + 55, + 384, + 192, + 395 + ], + "type": "text", + "content": "2.2. Controllable Generation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 401, + 296, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 401, + 296, + 616 + ], + "spans": [ + { + "bbox": [ + 56, + 401, + 296, + 616 + ], + "type": "text", + "content": "Controllable generation allows for customizing the desired spatial layout, filter style, or subject appearance in the generated images. A series of methods such as ControlNet [59], T2I-Adapter [31], GLIGEN [26], and ZestGuide [6] successfully introduce the spatial conditions into controllable generation, enabling models to control the spatial layout of generated images. Another series of methods, such as IP-Adapter [58], InstantID [47], BLIP-Diffusion [24], and StyleDrop [41] incorporate the subject conditions into controllable generation, ensuring consistency between generated images and reference images in style, characteristics, subject appearance, etc. To unify these two tasks, OminiControl [45] proposes a novel MMDiT-based controllable framework to handle various conditions with a unified pipeline. Unfortunately, it lacks the capability to control generation with multiple conditions. To this end, we propose UniCombine, which successfully extends this framework to multi-conditional scenarios." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 624, + 281, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 624, + 281, + 635 + ], + "spans": [ + { + "bbox": [ + 55, + 624, + 281, + 635 + ], + "type": "text", + "content": "2.3. Multi-Conditional Controllable Generation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 714 + ], + "type": "text", + "content": "As controllable generation advances, merely providing a single condition to guide the image generation no longer satisfies the needs. As a result, research on multi-conditional controllable generation has emerged. Existing methods like UniControl [35], UniControlNet [60] and Cocktail [14] exhibit acceptable performance when simul" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 384, + 555, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 555, + 516 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 555, + 516 + ], + "type": "text", + "content": "taneously leveraging multiple spatial conditions for image generation. However, there is a lack of multi-conditional generative models that support utilizing both spatial conditions and subject conditions to guide the generative process together. Although the recently proposed method Ctrl-X [27] features controlling the appearance and structure simultaneously, its performance remains unsatisfactory with a limited combination of conditions and it is not compatible with the Diffusion Transformer architecture. To address the aforementioned limitations, we propose UniCombine to enable the flexible combination of various control signals." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 537, + 370, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 537, + 370, + 550 + ], + "spans": [ + { + "bbox": [ + 314, + 537, + 370, + 550 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 561, + 392, + 573 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 561, + 392, + 573 + ], + "spans": [ + { + "bbox": [ + 313, + 561, + 392, + 573 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": "In this work, we mainly explore the latest generative models that utilize the Rectified Flow (RF) [28, 29] training strategy and the MMDiT [7] backbone architecture, like FLUX [23] and SD3 [7]. For the source noise distribution " + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "inline_equation", + "content": "X_0 \\sim p_{\\mathrm{noise}}" + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": " and the target image distribution " + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "inline_equation", + "content": "X_1 \\sim p_{\\mathrm{data}}" + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": ", the RF defines a linear interpolation between them as " + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "inline_equation", + "content": "X_t = (1 - t)X_0 + tX_1" + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": ". The training objective is to learn a time-dependent vector field " + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "inline_equation", + "content": "v_t(X_t, t; \\theta)" + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": " that describes the trajectory of the ODE " + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "inline_equation", + "content": "dX_t = v_t(X_t, t; \\theta)dt" + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "inline_equation", + "content": "v_t(X_t, t; \\theta)" + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": " is optimized to approximate the constant velocity " + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "inline_equation", + "content": "X_1 - X_0" + }, + { + "bbox": [ + 313, + 582, + 555, + 715 + ], + "type": "text", + "content": ", leading to the loss function as Eq. (1)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "spans": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "text", + "content": "3" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 85, + 296, + 110 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 85, + 296, + 110 + ], + "spans": [ + { + "bbox": [ + 55, + 85, + 296, + 110 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {R F}} (\\theta) = \\mathbb {E} _ {X _ {1} \\sim p _ {\\text {d a t a}}, X _ {0} \\sim p _ {\\text {n o i s e}}, t \\sim U [ 0, 1 ]} \\left[ \\| (X _ {1} - X _ {0}) - v _ {t} (X _ {t}, t; \\theta) \\| ^ {2} \\right] \\tag {1}", + "image_path": "99512443b31f1e244aae53591cf61ea45942f31984f52b9e648e6112280d77e4.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "text", + "content": "In this paper, we propose a concept of branch to differentiate the processing flows of input embeddings from different modalities in MMDiT-based models. As shown in Fig. 2 (a), instead of the single-branch architecture [37] where the text prompt is injected into the denoising branch via crossattention, MMDiT uses two independent transformers to construct the text branch and the denoising branch. Based on it, OminiControl [45] incorporates a Condition-LoRA module onto the weights of the denoising branch to process the input conditional embedding, thus forming its Conditional Branch, as depicted in Fig. 2 (b). It is worth noting that, OminiControl [45] can be regarded as a special case of our proposed UniCombine framework under the single-conditional setting. It provides the pre-trained Condition-LoRA modules to meet the need for our multi-conditional settings. In the single-conditional setting, the text branch embedding " + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "text", + "content": ", the denoising branch embedding " + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "text", + "content": ", and the conditional branch embedding " + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "text", + "content": " are concatenated to form a unified sequence " + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "inline_equation", + "content": "[T;X;C]" + }, + { + "bbox": [ + 55, + 110, + 296, + 350 + ], + "type": "text", + "content": " to be processed in the MMDiT Attention mechanism." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 357, + 138, + 368 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 357, + 138, + 368 + ], + "spans": [ + { + "bbox": [ + 55, + 357, + 138, + 368 + ], + "type": "text", + "content": "3.2. UniCombine" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 373, + 296, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 373, + 296, + 447 + ], + "spans": [ + { + "bbox": [ + 55, + 373, + 296, + 447 + ], + "type": "text", + "content": "Building upon the MMDiT-based text-to-image generative model FLUX [23], we propose UniCombine, a multi-conditional controllable generative framework consisting of various conditional branches. Each conditional branch is in charge of processing one conditional embedding, thus forming a unified embedding sequence " + }, + { + "bbox": [ + 55, + 373, + 296, + 447 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 373, + 296, + 447 + ], + "type": "text", + "content": " as presented in Eq. (2)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 131, + 449, + 294, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 449, + 294, + 460 + ], + "spans": [ + { + "bbox": [ + 131, + 449, + 294, + 460 + ], + "type": "interline_equation", + "content": "S = [ T; X; C _ {1}; \\dots ; C _ {N} ] \\tag {2}", + "image_path": "93282f189196c23bdfd799eb8a46475b81447637d02f5a79af7f94e82a528bc4.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 463, + 296, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 463, + 296, + 640 + ], + "spans": [ + { + "bbox": [ + 55, + 463, + 296, + 640 + ], + "type": "text", + "content": "Given that the single-conditional setting of our UniCombine is equivalent to OmniControl [45], we only focus on the multi-conditional setting in this section. Firstly, we introduce a LoRA Switching module to manage multiple conditional branches effectively. Secondly, we introduce a novel Conditional MMDiT Attention mechanism to process the unified sequence " + }, + { + "bbox": [ + 55, + 463, + 296, + 640 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 55, + 463, + 296, + 640 + ], + "type": "text", + "content": " in the multi-conditional setting. Thirdly, we present an insight analysis of our training-free strategy, which leverages the pre-trained Condition-LoRA module weights to perform a training-free multi-conditional controllable generation. Lastly, we present a feasible training-based strategy, which utilizes a trainable Denoising-LoRA module to enhance the performance further after training on a task-specific multi-conditional dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": "LoRA Switching Module. Before denoising with multiple input conditions, the Condition-LoRA modules pre-trained under single-conditional settings should be loaded onto the weights of the denoising branch, like " + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "inline_equation", + "content": "[CondLoRA_1, CondLoRA_2, \\ldots]" + }, + { + "bbox": [ + 55, + 642, + 296, + 713 + ], + "type": "text", + "content": ". Then the LoRA Switching module determines which one of them should be" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "content": "activated according to the type of input conditions, forming a one-hot gating mechanism " + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "inline_equation", + "content": "[0,1,0,\\dots,0]" + }, + { + "bbox": [ + 313, + 72, + 553, + 227 + ], + "type": "text", + "content": ", as shown in Fig. 2 (c). Subsequently, different conditional branches with different activated Condition-LoRA modules are used for processing different conditional embeddings, resulting in a minimal number of additional parameters introduced for different conditions. Unlike the single-conditional setting in Fig. 2 (b), which only needs loading LoRA modules, the LoRA Switching module in Fig. 2 (c) enables adaptive selection among multiple LoRA modules to provide the matching conditional branches for each conditional embeddings, granting our framework greater flexibility and adaptability to handle diverse conditional combinations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "text", + "content": "Conditional MMDiT Attention. After concatenating the output embeddings from these " + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "text", + "content": " conditional branches, the unified sequence " + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "text", + "content": " cannot be processed through the original MMDiT Attention mechanism due to two major challenges: (1) The computational complexity scales quadratically as " + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "inline_equation", + "content": "O(N^2)" + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "text", + "content": " with respect to the number of conditions, which becomes especially problematic when handling multiple high-resolution conditions. (2) When performing MMDiT Attention on the unified sequence " + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 228, + 553, + 372 + ], + "type": "text", + "content": ", different condition signals interfere with each other during the attention calculation, making it difficult to effectively utilize the pre-trained Condition-LoRA module weights for the denoising process." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "content": "To address these challenges, we introduce a novel Conditional MMDiT Attention mechanism (CMMDiT Attention) as depicted in Fig. 2 (c) to replace the original MMDiT Attention. Instead of feeding the entire unified sequence " + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "content": " into the MMDiT Attention at once, CMMDiT Attention follows distinct computational mechanisms according to which branch is serving as queries. The core idea is that the branch serving as a query aggregates the information from different scopes of the unified sequence " + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "content": " depending on its type. Specifically, when the denoising branch " + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "content": " and the text branch " + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "content": " serve as queries, their scope of keys and values correspond to the entire unified sequence " + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "content": ", granting them a global receptive field and the ability to aggregate information from all conditional branches. In contrast, when the conditional branches " + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "content": " serve as queries, their receptive fields do not encompass one another. Their scope of keys and values are restricted to the subsequence " + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "inline_equation", + "content": "S_i" + }, + { + "bbox": [ + 313, + 372, + 553, + 598 + ], + "type": "text", + "content": " as presented in Eq. (3), which prevents feature exchange and avoids information entanglement between different conditions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 405, + 602, + 553, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 602, + 553, + 614 + ], + "spans": [ + { + "bbox": [ + 405, + 602, + 553, + 614 + ], + "type": "interline_equation", + "content": "S _ {i} = [ T; X; C _ {i} ] \\tag {3}", + "image_path": "3661792d048303c132e0cc107e11197e07793e4fd697e499d3481bbdc763b8c7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 617, + 555, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 617, + 555, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 617, + 555, + 653 + ], + "type": "text", + "content": "Furthermore, the CMMDiT Attention reduces computational complexity from " + }, + { + "bbox": [ + 313, + 617, + 555, + 653 + ], + "type": "inline_equation", + "content": "O(N^2)" + }, + { + "bbox": [ + 313, + 617, + 555, + 653 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 313, + 617, + 555, + 653 + ], + "type": "inline_equation", + "content": "O(N)" + }, + { + "bbox": [ + 313, + 617, + 555, + 653 + ], + "type": "text", + "content": " as the number of conditions increases, making it more scalable." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 654, + 553, + 713 + ], + "type": "text", + "content": "Training-free Strategy. The following analyses provide a detailed explanation of why our UniCombine is capable of seamlessly integrating and effectively reusing the pretrained Condition-LoRA module weights to tackle multi-conditional challenges in a training-free manner." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 732, + 309, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 732, + 309, + 741 + ], + "spans": [ + { + "bbox": [ + 302, + 732, + 309, + 741 + ], + "type": "text", + "content": "4" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 69, + 295, + 133 + ], + "blocks": [ + { + "bbox": [ + 58, + 69, + 295, + 133 + ], + "lines": [ + { + "bbox": [ + 58, + 69, + 295, + 133 + ], + "spans": [ + { + "bbox": [ + 58, + 69, + 295, + 133 + ], + "type": "image", + "image_path": "8c57a3c424f01738f8a53f6d6f0c8688e8016cc7a73bf6ea21df63ffdafe3eaa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 138, + 295, + 159 + ], + "lines": [ + { + "bbox": [ + 55, + 138, + 295, + 159 + ], + "spans": [ + { + "bbox": [ + 55, + 138, + 295, + 159 + ], + "type": "text", + "content": "Figure 3. Average " + }, + { + "bbox": [ + 55, + 138, + 295, + 159 + ], + "type": "inline_equation", + "content": "\\mathrm{X} \\rightarrow" + }, + { + "bbox": [ + 55, + 138, + 295, + 159 + ], + "type": "text", + "content": " Subject cross-attention map of the insertion area." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 171, + 296, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 171, + 296, + 220 + ], + "spans": [ + { + "bbox": [ + 55, + 171, + 296, + 220 + ], + "type": "text", + "content": "On the one hand, when the conditional embeddings " + }, + { + "bbox": [ + 55, + 171, + 296, + 220 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 55, + 171, + 296, + 220 + ], + "type": "text", + "content": " serve as queries in CMMDiT, they follow the same attention computational paradigm as in the MMDiT of single-conditional settings, as indicated in Eq. (4)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 222, + 294, + 249 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 222, + 294, + 249 + ], + "spans": [ + { + "bbox": [ + 66, + 222, + 294, + 249 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {C M M D i T} \\left(Q = C _ {i} ^ {q}, K = \\left[ T ^ {k}, X ^ {k}, C _ {i} ^ {k} \\right], V = \\left[ T ^ {v}, X ^ {v}, C _ {i} ^ {v} \\right]\\right) \\\\ = \\operatorname {M M D i T} (Q = C ^ {q}, K = [ T ^ {k}, X ^ {k}, C ^ {k} ], V = [ T ^ {v}, X ^ {v}, C ^ {v} ]) \\tag {4} \\\\ \\end{array}", + "image_path": "21b0e5e13ae17e5a1c0fc46b9ae2bd7c1ae40e8754d83e2afe15c56a0a886ccc.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 255, + 296, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 255, + 296, + 302 + ], + "spans": [ + { + "bbox": [ + 55, + 255, + 296, + 302 + ], + "type": "text", + "content": "This consistent computational paradigm enables the conditional branches to share the same feature extraction capability between the multi-conditional setting and the single-conditional setting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "spans": [ + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "text", + "content": "On the other hand, when the denoising embedding " + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "text", + "content": " and the text prompt embedding " + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "text", + "content": " serve as queries in CMMDiT, their attention computational paradigm diverges from the single-conditional settings. As illustrated in Eq. (5), when the denoising embedding " + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "text", + "content": " is used as a query for attention computation with multiple conditional embeddings in CMMDiT, the attention score matrix is computed between " + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 55, + 302, + 296, + 398 + ], + "type": "text", + "content": " and all the conditional embeddings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 399, + 299, + 446 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 399, + 299, + 446 + ], + "spans": [ + { + "bbox": [ + 56, + 399, + 299, + 446 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathrm {C M M D i T} (Q = X ^ {q}, K / V = [ X ^ {k / v}, T ^ {k / v}, C _ {1} ^ {k / v}, \\dots , C _ {N} ^ {k / v} ]) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {1}{\\sqrt {d i m}} X ^ {q} \\left[ X ^ {k}, T ^ {k}, C _ {1} ^ {k}, \\dots , C _ {N} ^ {k} \\right] ^ {\\top}\\right) \\left[ X ^ {v}, T ^ {v}, C _ {1} ^ {v}, \\dots , C _ {N} ^ {v} \\right] \\tag {5} \\\\ \\end{array}", + "image_path": "366bfb556eb7348d43c9ba6eb176249717e1ac12f3b91c45a0204d9d3b46b469.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 450, + 296, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 450, + 296, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 450, + 296, + 510 + ], + "type": "text", + "content": "It allows " + }, + { + "bbox": [ + 55, + 450, + 296, + 510 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 55, + 450, + 296, + 510 + ], + "type": "text", + "content": " to extract and integrate information from each of the conditional embeddings separately and fusion them. This divide-and-conquer computational paradigm enables the text branch and denoising branch to fuse the conditional features effectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 510, + 296, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 510, + 296, + 557 + ], + "spans": [ + { + "bbox": [ + 55, + 510, + 296, + 557 + ], + "type": "text", + "content": "By leveraging the computational paradigms mentioned above, our UniCombine is able to perform a training-free multi-conditional controllable generation with the pretrained Condition-LoRA modules." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "type": "text", + "content": "Training-based Strategy. However, due to the lack of training, solely relying on the softmax operation in Eq. (5) to balance the attention score distribution across multiple conditional embeddings may result in an undesirable feature fusion result, making our training-free version unsatisfactory in some cases. To address this issue, we introduce a trainable Denoising-LoRA module within the denoising branch to rectify the distribution of attention scores in Eq. (5). During training, we keep all the Condition-LoRA modules frozen to preserve the conditional extracting capability and train the Denoising-LoRA module solely on the task-specific multi-conditional dataset, as shown in Fig. 2 (c). After training, the denoising embedding " + }, + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 55, + 558, + 296, + 714 + ], + "type": "text", + "content": " learns to" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 70, + 552, + 228 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 552, + 228 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 552, + 228 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 552, + 228 + ], + "type": "image", + "image_path": "d04a32c8e874aab106f9fa111d4a7b255e65e731a4acd2452f053c1c30949d06.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 234, + 542, + 246 + ], + "lines": [ + { + "bbox": [ + 324, + 234, + 542, + 246 + ], + "spans": [ + { + "bbox": [ + 324, + 234, + 542, + 246 + ], + "type": "text", + "content": "Figure 4. SubjectSpatial200K dataset construction pipeline." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 256, + 555, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 256, + 555, + 316 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 555, + 316 + ], + "type": "text", + "content": "better aggregate the appropriate information during the CM-MDiT Attention operation. As presented in Fig. 3, the average " + }, + { + "bbox": [ + 313, + 256, + 555, + 316 + ], + "type": "inline_equation", + "content": "\\mathrm{X} \\rightarrow" + }, + { + "bbox": [ + 313, + 256, + 555, + 316 + ], + "type": "text", + "content": " Subject attention map within the inpainting area is more concentrated on the subject area in the training-based version." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 324, + 466, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 324, + 466, + 337 + ], + "spans": [ + { + "bbox": [ + 313, + 324, + 466, + 337 + ], + "type": "text", + "content": "3.3. SubjectSpatial200K dataset" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 342, + 555, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 555, + 474 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 555, + 474 + ], + "type": "text", + "content": "Our SubjectSpatial200K dataset aims to address the lack of a publicly available dataset for multi-conditional generative tasks. Existing datasets fail to include both the subject-driven and spatially-aligned annotations. Recently, the Subjects200K [45] dataset provides a publicly accessible dataset for subject-driven generation. Based on it, we introduce the SubjectSpatial200K dataset, which is a unified high-quality dataset designed for training and testing multi-conditional controllable generative models. This dataset includes comprehensive annotations as elaborated below. Besides, the construction pipeline is detailed in Fig. 4." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 474, + 554, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 474, + 554, + 581 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 554, + 581 + ], + "type": "text", + "content": "Subject Grounding Annotation. The subject grounding annotation is significantly necessary for many generative tasks like instance-level inpainting [19, 61], instance-level controllable generation [26, 49], and object insertion [4, 43]. By leveraging the open-vocabulary object detection model Mamba-YOLO-World [46] on Subjects200K, we detect bounding boxes for all subjects according to their category descriptions and subsequently derive the corresponding mask regions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 582, + 554, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 554, + 642 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 554, + 642 + ], + "type": "text", + "content": "Spatial Map Annotation. The spatial map annotation further extends the applicable scope of our dataset to spatially-aligned synthesis tasks. Specifically, we employ the Depth-Anything [57] model and the OpenCV [1] library on Subjects200K to derive the Depth and Canny maps." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 652, + 390, + 666 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 652, + 390, + 666 + ], + "spans": [ + { + "bbox": [ + 313, + 652, + 390, + 666 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 672, + 364, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 672, + 364, + 685 + ], + "spans": [ + { + "bbox": [ + 313, + 672, + 364, + 685 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 554, + 714 + ], + "type": "text", + "content": "Implementation. We use the FLUX.1-schnell [23] as our base model and the weights provided by OminiControl [45]" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "spans": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "text", + "content": "5" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 70, + 535, + 268 + ], + "blocks": [ + { + "bbox": [ + 74, + 70, + 535, + 268 + ], + "lines": [ + { + "bbox": [ + 74, + 70, + 535, + 268 + ], + "spans": [ + { + "bbox": [ + 74, + 70, + 535, + 268 + ], + "type": "table", + "html": "
TaskMethodGenerative QualityControllabilitySubject ConsistencyText Consistency
FID ↓SSIM ↑F1 ↑MSE ↓CLIP-I ↑DINO ↑CLIP-T ↑
Multi-SpatialUniControl44.170.320.071346.02--30.28
UniControlNet20.960.280.091231.06--32.74
UniCombine (training-free)10.350.540.18519.53--33.70
UniCombine (training-based)6.820.640.24165.90--33.45
Subject-InsertionObjectStitch26.860.37--93.0582.3432.25
AnyDoor26.070.37--94.8886.0432.55
UniCombine (training-free)6.370.76--95.6089.0133.11
UniCombine (training-based)4.550.81--97.1492.9633.08
Subject-DepthControlNet w. IP-Adapter29.930.34-1295.8080.4162.2632.94
Ctrl-X52.370.36-2644.9078.0850.8330.20
UniCombine (training-free)10.030.48-507.4091.1585.7333.41
UniCombine (training-based)6.660.55-196.6594.4790.3133.30
Subject-CannyControlNet w. IP-Adapter30.380.380.09-79.8060.1932.85
Ctrl-X47.890.360.05-79.3554.3130.34
UniCombine (training-free)10.220.490.17-91.8486.8833.21
UniCombine (training-based)6.010.610.24-95.2692.5933.30
", + "image_path": "a34bbcb900321fe501a520855202f376e6664d9faf88390dd30b55aa8d6f1b53.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 273, + 553, + 297 + ], + "lines": [ + { + "bbox": [ + 55, + 273, + 553, + 297 + ], + "spans": [ + { + "bbox": [ + 55, + 273, + 553, + 297 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of our method with existing approaches on Multi-Spatial, Subject-Insertion, Subject-Depth, and Subject-Canny conditional generative tasks. The bold and underlined figures represent the optimal and sub-optimal results, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 57, + 307, + 294, + 536 + ], + "blocks": [ + { + "bbox": [ + 57, + 307, + 294, + 536 + ], + "lines": [ + { + "bbox": [ + 57, + 307, + 294, + 536 + ], + "spans": [ + { + "bbox": [ + 57, + 307, + 294, + 536 + ], + "type": "image", + "image_path": "1e06b7a6c1ae6b58e94df98cc9be3d1764e9ac9f480e954299aa319606949d55.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 62, + 541, + 288, + 553 + ], + "lines": [ + { + "bbox": [ + 62, + 541, + 288, + 553 + ], + "spans": [ + { + "bbox": [ + 62, + 541, + 288, + 553 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison on Multi-Spatial generation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "text", + "content": "as our pre-trained Condition-LoRA module weights. During the training of our Denoising-LoRA module, we use a rank of 4, consistent with the Condition-LoRA. We choose the Adam optimizer with a learning rate of " + }, + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "text", + "content": " and set the weight decay to 0.01. Our models are trained for 30,000 steps on 16 NVIDIA V100 GPUs at a resolution of " + }, + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 55, + 567, + 295, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "spans": [ + { + "bbox": [ + 55, + 653, + 296, + 715 + ], + "type": "text", + "content": "**Benchmarks.** We evaluate the performance of our method in both training-free and training-based versions. The training and testing datasets are partitioned from the SubjectSpatial200K dataset based on image quality assessment scores evaluated by ChatGPT-4o, with details provided in Sec. A1." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 315, + 307, + 553, + 536 + ], + "blocks": [ + { + "bbox": [ + 315, + 307, + 553, + 536 + ], + "lines": [ + { + "bbox": [ + 315, + 307, + 553, + 536 + ], + "spans": [ + { + "bbox": [ + 315, + 307, + 553, + 536 + ], + "type": "image", + "image_path": "d60c55bfaeeeedfd5aefc1bba87bd491b67f9a1c54a3f0b04bece1daafa5fa08.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 542, + 553, + 554 + ], + "lines": [ + { + "bbox": [ + 313, + 542, + 553, + 554 + ], + "spans": [ + { + "bbox": [ + 313, + 542, + 553, + 554 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison on Subject-Insertion generation." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 568, + 553, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 568, + 553, + 592 + ], + "spans": [ + { + "bbox": [ + 313, + 568, + 553, + 592 + ], + "type": "text", + "content": "Importantly, the dataset partitioning scheme remains consistent in all experiments." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 594, + 555, + 713 + ], + "type": "text", + "content": "Metrics. To evaluate the subject consistency, we calculate the CLIP-I [36] score and DINO [2] score between the generated images and the ground truth images. To assess the generative quality, we compute the FID [12] and SSIM [50] between the generated image set and the ground truth image set. To measure the controllability, we compute the F1 Score for edge conditions and the MSE score for depth conditions between the extracted maps from generated images and the original conditions. Additionally, we adopt the CLIP-T [36] score to estimate the text consistency between" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 733, + 308, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 733, + 308, + 741 + ], + "spans": [ + { + "bbox": [ + 302, + 733, + 308, + 741 + ], + "type": "text", + "content": "6" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 294, + 299 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 294, + 299 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 294, + 299 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 294, + 299 + ], + "type": "image", + "image_path": "506fe3547ab1943e7faa90d0f349eb3f11dc59ed4a47d7cf36007f74a6ca38f0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 305, + 290, + 317 + ], + "lines": [ + { + "bbox": [ + 59, + 305, + 290, + 317 + ], + "spans": [ + { + "bbox": [ + 59, + 305, + 290, + 317 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison on Subject-Depth generation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 327, + 229, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 327, + 229, + 339 + ], + "spans": [ + { + "bbox": [ + 55, + 327, + 229, + 339 + ], + "type": "text", + "content": "the generated images and the text prompts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 345, + 135, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 345, + 135, + 357 + ], + "spans": [ + { + "bbox": [ + 55, + 345, + 135, + 357 + ], + "type": "text", + "content": "4.2. Main Result" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 362, + 295, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 362, + 295, + 398 + ], + "spans": [ + { + "bbox": [ + 55, + 362, + 295, + 398 + ], + "type": "text", + "content": "We conduct extensive and comprehensive comparative experiments on the Multi-Spatial, Subject-Insertion, and Subject-Spatial conditional generative tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 403, + 244, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 403, + 244, + 415 + ], + "spans": [ + { + "bbox": [ + 55, + 403, + 244, + 415 + ], + "type": "text", + "content": "4.2.1. Multi-Spatial Conditional Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 418, + 295, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 418, + 295, + 514 + ], + "spans": [ + { + "bbox": [ + 55, + 418, + 295, + 514 + ], + "type": "text", + "content": "The Multi-Spatial conditional generation aims to generate images adhering to the collective layout constraints of diverse spatial conditions. This requires the model to achieve a more comprehensive layout control based on input conditions in a complementary manner. The comparative results in Tab. 1 and Fig. 5 demonstrate that our method outperforms existing multi-spatial conditional generation approaches in generative quality and controllability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 519, + 261, + 531 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 519, + 261, + 531 + ], + "spans": [ + { + "bbox": [ + 55, + 519, + 261, + 531 + ], + "type": "text", + "content": "4.2.2. Subject-Insertion Conditional Generation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 534, + 295, + 713 + ], + "type": "text", + "content": "The Subject-Insertion conditional generation requires the model to generate images where the reference subject is inserted into the masked region of the target background. As illustrated in Tab. 1 and Fig. 6, our UniCombine demonstrates superior performance compared to previous methods with three advantages: Firstly, our method ensures that the reference subject is inserted into the background with high consistency and harmonious integration. Secondly, our method excels in open-world object insertion without requiring test-time tuning, unlike conventional customization methods [22, 40]. Finally, our method demonstrates strong semantic comprehension capabilities, enabling it to extract the desired object from a complex subject image with a non-white background, rather than simply pasting the entire subject image into the masked region." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 69, + 553, + 299 + ], + "blocks": [ + { + "bbox": [ + 316, + 69, + 553, + 299 + ], + "lines": [ + { + "bbox": [ + 316, + 69, + 553, + 299 + ], + "spans": [ + { + "bbox": [ + 316, + 69, + 553, + 299 + ], + "type": "image", + "image_path": "44ebde2dd6cfbcb637ef99847a469c9c5e74ddeb4368792fe3d6809b1e91856e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 304, + 549, + 316 + ], + "lines": [ + { + "bbox": [ + 318, + 304, + 549, + 316 + ], + "spans": [ + { + "bbox": [ + 318, + 304, + 549, + 316 + ], + "type": "text", + "content": "Figure 8. Qualitative comparison on Subject-Canny generation." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 328, + 511, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 328, + 511, + 340 + ], + "spans": [ + { + "bbox": [ + 313, + 328, + 511, + 340 + ], + "type": "text", + "content": "4.2.3. Subject-Spatial Conditional Generation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 344, + 555, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 344, + 555, + 619 + ], + "spans": [ + { + "bbox": [ + 313, + 344, + 555, + 619 + ], + "type": "text", + "content": "The Subject-Spatial conditional generation focuses on generating images of the reference subject while ensuring the layout aligns with specified spatial conditions. We compare our method with Ctrl-X [27] and a simple baseline model. Ctrl-X is a recently proposed model based on SDXL [34] that simultaneously controls structure and appearance. The baseline model is constructed by integrating the FLUX ControlNet [53, 54] and FLUX IP-Adapter [55] into the FLUX.1-dev [23] base model. Specifically, we divided the Subject-Spatial generative task into different experimental groups based on the type of spatial conditions, referred to as Subject-Depth and Subject-Canny, respectively. As presented in Fig. 7, Fig. 8, and Tab. 1, the experimental results demonstrate the superior performance of our UniCombine: Firstly, our method exhibits stronger semantic comprehension capability, generating the reference subject in the accurate localization of the spatial conditions without confusing appearance features. Secondly, our method demonstrates greater adaptability, generating the reference subject with reasonable morphological transformations to align with the guidance of spatial conditions and text prompts. Lastly, our method achieves superior subject consistency while maintaining excellent spatial coherence." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 626, + 419, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 626, + 419, + 637 + ], + "spans": [ + { + "bbox": [ + 313, + 626, + 419, + 637 + ], + "type": "text", + "content": "4.2.4. Textual Guidance" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 641, + 555, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 641, + 555, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 641, + 555, + 713 + ], + "type": "text", + "content": "As shown in Fig. 1 and Tab. 1, our method not only allows for controllable generation by combining multiple conditions but also enables precise textual guidance simultaneously. By utilizing a unified input sequence " + }, + { + "bbox": [ + 313, + 641, + 555, + 713 + ], + "type": "inline_equation", + "content": "S = [T; X; C_1; \\ldots; C_N]" + }, + { + "bbox": [ + 313, + 641, + 555, + 713 + ], + "type": "text", + "content": " during the denoising process, our UniCombine effectively aligns the descriptive words in " + }, + { + "bbox": [ + 313, + 641, + 555, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 641, + 555, + 713 + ], + "type": "text", + "content": " with" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "spans": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "text", + "content": "7" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 302, + 112 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 302, + 112 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 302, + 112 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 302, + 112 + ], + "type": "table", + "html": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑AttnOps ↓
Ours w/o CMMDiT95.4788.4233.10732.17M
Ours w/ CMMDiT95.6089.0133.11612.63M
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Background\nSubjectTraining-free\nw/o CMMDiTTraining-free\nw/ CMMDiTBackground\nSubjectTraining-free\nw/o CMMDiTTraining-free\nw/ CMMDiT
inconsistentsuccessinconsistentsuccess
failsuccessfailsuccess
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MethodCLIP-I ↑DINO ↑CLIP-T ↑
Ours w/ Text-LoRA96.9792.3233.10
Ours w/ Denoising-LoRA97.1492.9633.08
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MethodCLIP-I ↑DINO ↑CLIP-T ↑
Ours w/ DSB only96.8592.3833.07
Ours w/ DSB and SSB97.1492.9633.08
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Background\nSubjectTraining-based\nw/ DSB onlyTraining-based\nw/ DSB + SSBBackground\nSubjectTraining-based\nw/ DSB onlyTraining-based\nw/ DSB + SSB
inconsistentsuccessinconsistentsuccessinconsistentsuccess
inconsistentsuccessfailsuccessinconsistentinconsistent
", + "image_path": "e87e6f8b3e137a3f2fcae475f15efcbe2b56a7113615b229b8cb075304866a5d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 319, + 314, + 548, + 398 + ], + "blocks": [ + { + "bbox": [ + 313, + 268, + 553, + 300 + ], + "lines": [ + { + "bbox": [ + 313, + 268, + 553, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 268, + 553, + 300 + ], + "type": "text", + "content": "Figure 11. Qualitative ablation of training strategy on training-based Subject-Insertion task. DSB: Dual-Stream Blocks. SSB: Single-Stream Blocks." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 314, + 548, + 398 + ], + "lines": [ + { + "bbox": [ + 319, + 314, + 548, + 398 + ], + "spans": [ + { + "bbox": [ + 319, + 314, + 548, + 398 + ], + "type": "table", + "html": "
ModelGPU Memory ↓Add Params ↓
FLUX (bf16, base model)32933M-
CN, 1 cond35235M744M
IP, 1 cond35325M918M
CN + IP, 2 cond36753M1662M
Ours (training-free), 2 cond33323M29M
Ours (training-based), 2 cond33349M44M
", + "image_path": "a4f5c4fc9d8ce66afbdd123ab7fca8f063e5af00acb1254be7e07f83f23cd544.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 399, + 553, + 422 + ], + "lines": [ + { + "bbox": [ + 313, + 399, + 553, + 422 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 553, + 422 + ], + "type": "text", + "content": "Table 5. Comparison of inference GPU memory cost and additionally introduced parameters. CN: ControlNet. IP: IP-Adapter." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 436, + 555, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 436, + 555, + 532 + ], + "spans": [ + { + "bbox": [ + 313, + 436, + 555, + 532 + ], + "type": "text", + "content": "Different Options for Trainable LoRA. To evaluate whether the trainable LoRA module can be applied to the text branch instead of the denoising branch, we load a Text-LoRA in the text branch, with a configuration identical to that of the Denoising-LoRA. The Tab. 3 and Fig. 10 indicate that applying the trainable LoRA module to the denoising branch better modulates the feature aggregation operation across multiple conditional branches." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 533, + 555, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 533, + 555, + 652 + ], + "spans": [ + { + "bbox": [ + 313, + 533, + 555, + 652 + ], + "type": "text", + "content": "Training Strategy. As the parameter scale of the base model increases, the FLUX adaptations of ControlNet [53, 54] and IP-adapter [55] provided by the HuggingFace [16] community inject conditional features only into the dual-stream MMDiT blocks, rather than the entire network, to save memory. In contrast, since our Denoising-LoRA module introduces only a small number of parameters, we incorporate it into both the dual-stream and single-stream blocks to achieve better performance. The results in Tab. 4 and Fig. 11 confirm the validity of our choice." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 653, + 553, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 653, + 553, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 653, + 553, + 713 + ], + "type": "text", + "content": "Computational Cost. The overheads of our approach in terms of inference GPU memory cost and additionally introduced parameters are minimal. The comparison results against the FLUX ControlNet [53, 54] and FLUX IP-Adapter [55] are shown in Tab. 5." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "spans": [ + { + "bbox": [ + 302, + 732, + 308, + 741 + ], + "type": "text", + "content": "8" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 294, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 294, + 131 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 294, + 131 + ], + "type": "text", + "content": "More Conditional Branches. Our model places no restrictions on the number of supported conditions. The results shown in Fig. 12 demonstrate our model's strong scalability. As the number of conditional branches increases, the level of control becomes finer." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 144, + 293, + 273 + ], + "blocks": [ + { + "bbox": [ + 58, + 144, + 293, + 273 + ], + "lines": [ + { + "bbox": [ + 58, + 144, + 293, + 273 + ], + "spans": [ + { + "bbox": [ + 58, + 144, + 293, + 273 + ], + "type": "image", + "image_path": "a621a99e80843ff5996990493bd8940b3ce3197ae924350ffd10503c3b7c6b1c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 274, + 295, + 294 + ], + "lines": [ + { + "bbox": [ + 55, + 274, + 295, + 294 + ], + "spans": [ + { + "bbox": [ + 55, + 274, + 295, + 294 + ], + "type": "text", + "content": "Figure 12. From left to right are training-free multi-conditional combination tasks under: " + }, + { + "bbox": [ + 55, + 274, + 295, + 294 + ], + "type": "inline_equation", + "content": "1/2/3/4" + }, + { + "bbox": [ + 55, + 274, + 295, + 294 + ], + "type": "text", + "content": " conditions." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 314, + 296, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 314, + 296, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 296, + 387 + ], + "type": "text", + "content": "More Application Scenarios. Our UniCombine can be easily extended to new scenarios, such as reference-based image stylization. After training a new Condition-LoRA on StyleBooth [10] dataset, our UniCombine is able to integrate the style of the reference image with other conditions successfully, as demonstrated in Fig. 13." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 58, + 399, + 293, + 503 + ], + "blocks": [ + { + "bbox": [ + 58, + 399, + 293, + 503 + ], + "lines": [ + { + "bbox": [ + 58, + 399, + 293, + 503 + ], + "spans": [ + { + "bbox": [ + 58, + 399, + 293, + 503 + ], + "type": "image", + "image_path": "697b9a0d3b2d71d9ac73a42626a46546416d486f912cfdb2949db0c5a79882ad.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 506, + 277, + 517 + ], + "lines": [ + { + "bbox": [ + 72, + 506, + 277, + 517 + ], + "spans": [ + { + "bbox": [ + 72, + 506, + 277, + 517 + ], + "type": "text", + "content": "Figure 13. Training-free Spatial-Style combination task." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 548, + 128, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 548, + 128, + 560 + ], + "spans": [ + { + "bbox": [ + 55, + 548, + 128, + 560 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 570, + 296, + 713 + ], + "type": "text", + "content": "We present UniCombine, a DiT-based multi-conditional controllable generative framework capable of handling any combination of conditions, including but not limited to text prompts, spatial maps, and subject images. Extensive experiments on Subject-Insertion, Subject-Spatial, and Multi-Spatial conditional generative tasks demonstrate the state-of-the-art performance of our UniCombine in both training-free and training-based versions. Additionally, we propose the SubjectSpatial200K dataset to address the lack of a publicly available dataset for training and testing multi-conditional generative models. 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Springer, 2025. 2, 5" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 732, + 310, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 732, + 310, + 742 + ], + "spans": [ + { + "bbox": [ + 300, + 732, + 310, + 742 + ], + "type": "text", + "content": "11" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + }, + { + "para_blocks": [ + { + "bbox": [ + 138, + 68, + 473, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 68, + 473, + 102 + ], + "spans": [ + { + "bbox": [ + 138, + 68, + 473, + 102 + ], + "type": "text", + "content": "UniCombine: Unified Multi-Conditional Combination with Diffusion Transformer" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 233, + 112, + 376, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 233, + 112, + 376, + 129 + ], + "spans": [ + { + "bbox": [ + 233, + 112, + 376, + 129 + ], + "type": "text", + "content": "Supplementary Material" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 141, + 225, + 155 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 141, + 225, + 155 + ], + "spans": [ + { + "bbox": [ + 55, + 141, + 225, + 155 + ], + "type": "text", + "content": "A1. Dataset Partitioning Scheme" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 161, + 296, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 161, + 296, + 220 + ], + "spans": [ + { + "bbox": [ + 55, + 161, + 296, + 220 + ], + "type": "text", + "content": "In our proposed SubjectSpatial200K dataset, we utilize the ChatGPT-4o assessment scores provided by Subjects200K [45] on Subject Consistency, Composition Structure, and Image Quality to guide the dataset partitioning in our experiments." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 221, + 295, + 293 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 55, + 221, + 295, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 221, + 295, + 245 + ], + "spans": [ + { + "bbox": [ + 55, + 221, + 295, + 245 + ], + "type": "text", + "content": "- Subject Consistency: Ensuring the identity of the subject image is consistent with that of the ground truth image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 246, + 294, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 246, + 294, + 269 + ], + "spans": [ + { + "bbox": [ + 56, + 246, + 294, + 269 + ], + "type": "text", + "content": "- Composition Structure: Verifying a reasonable composition of the subject and ground truth images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 270, + 294, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 270, + 294, + 293 + ], + "spans": [ + { + "bbox": [ + 56, + 270, + 294, + 293 + ], + "type": "text", + "content": "- Image Quality: Confirming each image pair maintains high resolution and visual fidelity." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 55, + 293, + 295, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 293, + 295, + 317 + ], + "spans": [ + { + "bbox": [ + 55, + 293, + 295, + 317 + ], + "type": "text", + "content": "We partition the dataset into 139,403 training samples and 5,827 testing samples through Algorithm 1." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 57, + 320, + 294, + 466 + ], + "blocks": [ + { + "bbox": [ + 57, + 320, + 294, + 466 + ], + "lines": [ + { + "bbox": [ + 57, + 320, + 294, + 466 + ], + "spans": [ + { + "bbox": [ + 57, + 320, + 294, + 466 + ], + "type": "table", + "html": "
Algorithm 1: Dataset Partitioning Scheme
Input: example
Output: train or test
cs← example["Composite Structure"]
iq← example["Image Quality"]
sc← example["Subject Consistency"]
scores← [cs, iq, sc]
if all(s==5 for s in scores) then
return train;
else if cs≥3 and iq==5 and sc==5 then
return test;
", + "image_path": "081e7579449455ce9a0a6c20f089187297d01d022d3027a0bfa4afb2c5a31aa9.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 483, + 276, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 483, + 276, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 483, + 276, + 495 + ], + "type": "text", + "content": "A2. More Ablation on CMMDiT Attention" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 55, + 502, + 296, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 296, + 574 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 296, + 574 + ], + "type": "text", + "content": "More quantitative and qualitative ablation results on the other multi-conditional generative tasks are provided here. The comprehensive ablation results in Tab. A1, Tab. A2, Tab. A3, Fig. A1, Fig. A2, and Fig. A3 demonstrate that the UniCombine performs better with our proposed CMMDiT Attention." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 61, + 582, + 288, + 628 + ], + "blocks": [ + { + "bbox": [ + 61, + 582, + 288, + 628 + ], + "lines": [ + { + "bbox": [ + 61, + 582, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 61, + 582, + 288, + 628 + ], + "type": "table", + "html": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑F1 ↑
Ours w/o CMMDiT91.5186.3133.200.16
Ours w/ CMMDiT91.8486.8833.210.17
", + "image_path": "7780b4ae3fc30805750b62e7bb1b1c2e1322a555efcac56b2f8f7632150cf53d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 629, + 294, + 651 + ], + "lines": [ + { + "bbox": [ + 55, + 629, + 294, + 651 + ], + "spans": [ + { + "bbox": [ + 55, + 629, + 294, + 651 + ], + "type": "text", + "content": "Table A1. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Canny task" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 669, + 208, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 669, + 208, + 682 + ], + "spans": [ + { + "bbox": [ + 55, + 669, + 208, + 682 + ], + "type": "text", + "content": "A3. More Qualitative Results" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 295, + 714 + ], + "type": "text", + "content": "More qualitative results are presented in Fig. A4 and Fig. A5." + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 316, + 144, + 553, + 255 + ], + "blocks": [ + { + "bbox": [ + 316, + 144, + 553, + 255 + ], + "lines": [ + { + "bbox": [ + 316, + 144, + 553, + 255 + ], + "spans": [ + { + "bbox": [ + 316, + 144, + 553, + 255 + ], + "type": "image", + "image_path": "c8c9030826d874847297d6aad99732ff7992fa1efed8eaf2d42146029239dcfe.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 314, + 255, + 553, + 277 + ], + "lines": [ + { + "bbox": [ + 314, + 255, + 553, + 277 + ], + "spans": [ + { + "bbox": [ + 314, + 255, + 553, + 277 + ], + "type": "text", + "content": "Figure A1. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Canny task" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 316, + 287, + 551, + 334 + ], + "blocks": [ + { + "bbox": [ + 316, + 287, + 551, + 334 + ], + "lines": [ + { + "bbox": [ + 316, + 287, + 551, + 334 + ], + "spans": [ + { + "bbox": [ + 316, + 287, + 551, + 334 + ], + "type": "table", + "html": "
MethodCLIP-I ↑DINO ↑CLIP-T ↑MSE ↓
Ours w/o CMMDiT90.8385.3833.38547.63
Ours w/ CMMDiT91.1585.7333.41507.40
", + "image_path": "719ea07bb1cd1e89b41905beec203585fbe544e5a1ee5e9ab3f601d287ad2795.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 316, + 363, + 553, + 472 + ], + "blocks": [ + { + "bbox": [ + 314, + 335, + 553, + 357 + ], + "lines": [ + { + "bbox": [ + 314, + 335, + 553, + 357 + ], + "spans": [ + { + "bbox": [ + 314, + 335, + 553, + 357 + ], + "type": "text", + "content": "Table A2. Quantitative ablation of CMMDiT Attention mechanism on training-free Subject-Depth task" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 316, + 363, + 553, + 472 + ], + "lines": [ + { + "bbox": [ + 316, + 363, + 553, + 472 + ], + "spans": [ + { + "bbox": [ + 316, + 363, + 553, + 472 + ], + "type": "image", + "image_path": "eec53f0d14c8df15f39c097595e64b40514c9c785b2e319a4f3ff0334abfd869.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 474, + 553, + 496 + ], + "lines": [ + { + "bbox": [ + 313, + 474, + 553, + 496 + ], + "spans": [ + { + "bbox": [ + 313, + 474, + 553, + 496 + ], + "type": "text", + "content": "Figure A2. Qualitative ablation of CMMDiT Attention mechanism on training-free Subject-Depth task" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "table", + "bbox": [ + 342, + 506, + 525, + 553 + ], + "blocks": [ + { + "bbox": [ + 342, + 506, + 525, + 553 + ], + "lines": [ + { + "bbox": [ + 342, + 506, + 525, + 553 + ], + "spans": [ + { + "bbox": [ + 342, + 506, + 525, + 553 + ], + "type": "table", + "html": "
MethodCLIP-T ↑F1 ↑MSE ↓
Ours w/o CMMDiT33.700.17524.04
Ours w/ CMMDiT33.700.18519.53
", + "image_path": "825bdf58c053f99cc780532dc82a60487da430bb38579c85ad77eb49436315d5.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 554, + 553, + 576 + ], + "lines": [ + { + "bbox": [ + 313, + 554, + 553, + 576 + ], + "spans": [ + { + "bbox": [ + 313, + 554, + 553, + 576 + ], + "type": "text", + "content": "Table A3. Quantitative ablation of CMMDiT Attention mechanism on training-free Multi-Spatial task" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 316, + 583, + 553, + 693 + ], + "blocks": [ + { + "bbox": [ + 316, + 583, + 553, + 693 + ], + "lines": [ + { + "bbox": [ + 316, + 583, + 553, + 693 + ], + "spans": [ + { + "bbox": [ + 316, + 583, + 553, + 693 + ], + "type": "image", + "image_path": "4009d7abc995632fbc8e9c0c98b070e0d250aff3285f29dd8f899b9c93e1e20e.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 694, + 553, + 715 + ], + "lines": [ + { + "bbox": [ + 313, + 694, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 313, + 694, + 553, + 715 + ], + "type": "text", + "content": "Figure A3. Qualitative ablation of CMMDiT Attention mechanism on training-free Multi-Spatial task" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "spans": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "type": "text", + "content": "12" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 77, + 291, + 680 + ], + "blocks": [ + { + "bbox": [ + 57, + 77, + 291, + 680 + ], + "lines": [ + { + "bbox": [ + 57, + 77, + 291, + 680 + ], + "spans": [ + { + "bbox": [ + 57, + 77, + 291, + 680 + ], + "type": "image", + "image_path": "adfac4a9eebfdf05d1126a0a351b1aaafa113e3c17e6ad1d0d3ccee8c001ec91.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 159, + 691, + 451, + 703 + ], + "lines": [ + { + "bbox": [ + 159, + 691, + 451, + 703 + ], + "spans": [ + { + "bbox": [ + 159, + 691, + 451, + 703 + ], + "type": "text", + "content": "Figure A4. More qualitative results on Multi-Spatial and Subject-Insertion tasks." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 319, + 77, + 553, + 680 + ], + "blocks": [ + { + "bbox": [ + 319, + 77, + 553, + 680 + ], + "lines": [ + { + "bbox": [ + 319, + 77, + 553, + 680 + ], + "spans": [ + { + "bbox": [ + 319, + 77, + 553, + 680 + ], + "type": "image", + "image_path": "721139a8e4ed891aeab8a9eecb8d33d046e4e4574b78dabb5cd359d3ae06e6b6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "spans": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "type": "text", + "content": "13" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 77, + 291, + 681 + ], + "blocks": [ + { + "bbox": [ + 55, + 77, + 291, + 681 + ], + "lines": [ + { + "bbox": [ + 55, + 77, + 291, + 681 + ], + "spans": [ + { + "bbox": [ + 55, + 77, + 291, + 681 + ], + "type": "image", + "image_path": "179cb411321ca8ecf6e101c92a53a0ef8cbc9728a7f08f18d3c37f263493e513.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 160, + 691, + 448, + 703 + ], + "lines": [ + { + "bbox": [ + 160, + 691, + 448, + 703 + ], + "spans": [ + { + "bbox": [ + 160, + 691, + 448, + 703 + ], + "type": "text", + "content": "Figure A5. More qualitative results on Subject-Depth and Subject-Canny tasks." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 319, + 77, + 553, + 681 + ], + "blocks": [ + { + "bbox": [ + 319, + 77, + 553, + 681 + ], + "lines": [ + { + "bbox": [ + 319, + 77, + 553, + 681 + ], + "spans": [ + { + "bbox": [ + 319, + 77, + 553, + 681 + ], + "type": "image", + "image_path": "6cc95ee7d4dc5bf05bbb25255f5081767689dccf861e6597d6fd8d83a62792f9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "spans": [ + { + "bbox": [ + 300, + 732, + 311, + 742 + ], + "type": "text", + "content": "14" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 13 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_content_list.json b/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9d74bc60b10a87f4315148a9baecb66eca334464 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_content_list.json @@ -0,0 +1,6351 @@ +[ + { + "type": "text", + "text": "ReMA: Learning to Meta-think for LLMs with Multi-agent Reinforcement Learning", + "text_level": 1, + "bbox": [ + 214, + 122, + 782, + 172 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ziyu Wan $^{1,2*}$ , Yunxiang Li $^{3*}$ , Xiaoyu Wen $^{1,2}$ , Yan Song $^{4}$ , Hanjing Wang $^{1}$ , Linyi Yang $^{4}$ , Mark Schmidt $^{3}$ , Jun Wang $^{4}$ , Weinan Zhang $^{1}$ , Shuyue Hu $^{2\\ddagger}$ , Ying Wen $^{1\\ddagger}$", + "bbox": [ + 200, + 223, + 795, + 256 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1 Shanghai Jiao Tong University", + "$^{2}$ Shanghai Artificial Intelligence Laboratory", + "3 University of British Columbia", + "4 University College London" + ], + "bbox": [ + 351, + 268, + 643, + 328 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 459, + 363, + 537, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent research on Reasoning of Large Language Models (LLMs) has sought to further enhance their performance by integrating meta-thinking—enabling models to monitor, evaluate, and control their reasoning processes for more adaptive and effective problem-solving. However, current single-agent work lacks a specialized design for acquiring meta-thinking, resulting in low efficacy. To address this challenge, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages Multi-Agent Reinforcement Learning (MARL) to elicit meta-thinking behaviors, encouraging LLMs to think about thinking. ReMA decouples the reasoning process into two hierarchical agents: a high-level meta-thinking agent responsible for generating strategic oversight and plans, and a low-level reasoning agent for detailed executions. Through iterative reinforcement learning with aligned objectives, these agents explore and learn collaboration, leading to improved generalization and robustness. Empirical results from single-turn experiments demonstrate that ReMA outperforms single-agent RL baselines on complex reasoning tasks, including competitive-level mathematical benchmarks and LLM-as-a-Judge benchmarks. Additionally, we further extend ReMA to multi-turn interaction settings, leveraging turn-level ratio and parameter sharing to improve efficiency. Comprehensive ablation studies further illustrate the evolving dynamics of each distinct agent, providing valuable insights into how the meta-thinking reasoning process enhances the reasoning capabilities of LLMs. Our code can be found in https://github.com/ziyuwan/ReMA-public", + "bbox": [ + 228, + 393, + 766, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction", + "text_level": 1, + "bbox": [ + 171, + 709, + 313, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large language models (LLMs) have demonstrated remarkable capabilities in knowledge understanding and complex reasoning tasks [Chowdhery et al., 2023, Achiam et al., 2023, Anil et al., 2023, Dubey et al., 2024]. The paradigm in developing LLM-based reasoning models is shifting from scaling training-time computation towards scaling test-time computation [Snell et al., 2024]. Recent advancements, such as OpenAI-o1 [OpenAI, 2024], Deepseek R1 [DeepSeek-AI et al., 2025], and Gemini 2.0 Flash Thinking [DeepMind, 2025], have demonstrated that allowing LLMs to think before generating answers can significantly enhance performance and lead to the emergence of human-like reasoning patterns. These patterns like \"Wait, hold on.\" or \"Let's break this down.\"", + "bbox": [ + 169, + 739, + 826, + 852 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2503.09501v3 [cs.AI] 27 May 2025", + "bbox": [ + 22, + 263, + 60, + 705 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 189, + 859, + 315, + 873 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{\\dagger}$ Work done during internship at Shanghai Artificial Intelligence Laboratory", + "bbox": [ + 192, + 873, + 640, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Corresponding Author", + "bbox": [ + 192, + 887, + 334, + 901 + ], + "page_idx": 0 + }, + { + "type": "footer", + "text": "Preprint. Under review.", + "bbox": [ + 171, + 922, + 313, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Question: $T = 9.5$ . If $\\log_2 x^T - \\log_4 x = \\log_8 x^k$ is an identity for all $x > 0$ , compute the value of $k$ .", + "bbox": [ + 305, + 93, + 691, + 106 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/fd5b40d644792636991a20db79d8c4202f072f2e023bbd6106c186898b906286.jpg", + "image_caption": [ + "Figure 1: Left: A construction-based method that fine-tunes LLMs using rejection sampling, searching among combinations of pre-defined templates. Middle: R1-like method learns to mix meta-thinking and detailed reasoning steps during training. Right: Our method ReMA separates the meta-thinking and reasoning steps in a multi-agent system and updated by reinforcement learning." + ], + "image_footnote": [], + "bbox": [ + 178, + 108, + 823, + 296 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "indicate that LLMs can develop a form of meta-thinking abilities that can generalize well to out-of-distribution (OOD) tasks [Xiang et al., 2025]. Meta-thinking, also known as metacognitive skills [Flavell, 1979], is an ability traditionally considered uniquely human [Didolkar et al., 2024].", + "bbox": [ + 169, + 380, + 823, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To cultivate meta-thinking patterns from LLMs themselves, recent construction-based supervised approaches leverage supervised finetuning on structured reasoning trajectories. Specifically, these methods sampling reasoning trajectories from predefined meta-thinking templates and then use supervised finetuning (SFT) or direct preference optimization (DPO) [Rafailov et al., 2023] to teach LLMs imitate these patterns [Qi et al., 2024, Yue et al., Xi et al., 2024, Yang et al., 2025, Muenighoff et al., 2025, Ye et al., 2025c]. However, such methods lack sufficient flexibility for LLMs to explore suitable meta-thinking patterns. Thus, they often fail to generalize to out-of-distribution (OOD) problems, leading to unstable performance on unseen data [Kirk et al., Chu et al., 2025]. Besides construction-based methods, R1-like single-agent reinforcement learning (SARL) has also been adopted for meta-thinking in reasoning [DeepSeek-AI et al., 2025, Xie et al., 2025]. However, these SARL attempts typically rely on strong foundational models for easier exploration or extensive task-specific fine-tuning for stable training [Xu et al., 2025, Gandhi et al., 2025]. Furthermore, SARL needs to learn meta-thinking and reasoning within a single forward pass, seeking to capture complex reasoning structures purely in an autoregressive manner [Xie et al., 2025]. This can potentially lead to issues such as inefficient exploration as well as reduced readability and early convergence to local optima [DeepSeek-AI et al., 2025, Xiang et al., 2025].", + "bbox": [ + 169, + 429, + 826, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these limitations, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages multi-agent reinforcement learning (MARL) to encourage LLMs to think about thinking. Our approach employs a multi-agent system (MAS) composed of a high-level meta-thinking agent, responsible for strategic oversight and instruction generation, and a low-level reasoning agent tasked with detailed executing processes based on provided guidance. We compare the inference process among the construction-based method, R1-like method, and ReMA in Fig. 1. Since MAS distributes the exploration space of SARL into multiple agents, it enables each agent to explore more structurally and efficiently during training. Then we apply reinforcement learning on each agent with aligned reward functions. In this way, ReMA effectively balances the trade-off between generalization capability and exploration efficiency. As a result, they can learn to play the best of their role (either to meta-think or to follow instructions), at the present of the other agent.", + "bbox": [ + 169, + 656, + 826, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To our knowledge, we are the first to formally define and optimize a multi-agent meta-thinking reasoning process (MAMRP) through multi-agent reinforcement learning. Our extensive experiments span both math reasoning and LLM-as-a-Judge tasks, where ReMA consistently achieves the highest average performance across three backbone pretrained models. We further extend ReMA to multi-turn interaction settings on math reasoning tasks, implementing turn-level ratio to optimize trajectory returns and stabilize training. Through comprehensive ablation studies, we illustrate the evolving dynamics between agents, revealing unexpected interaction patterns such as role reversals", + "bbox": [ + 169, + 814, + 823, + 912 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "under different reward settings. These findings provide valuable insights into how meta-thinking processes enhance the reasoning capabilities of LLMs.", + "bbox": [ + 169, + 90, + 823, + 122 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2 Preliminaries", + "text_level": 1, + "bbox": [ + 171, + 140, + 320, + 157 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we outline the formulation of the vanilla reasoning process (Sec. 2.1) and the representative training methods (Sec. 2.2) along with the notation used throughout the paper.", + "bbox": [ + 169, + 172, + 823, + 202 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1 Vanilla Reasoning Process (VRP)", + "text_level": 1, + "bbox": [ + 171, + 218, + 444, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The probability of generating a response $\\mathbf{y}$ equals the product of its stepwise probabilities. Given a model $\\pi_{\\theta}$ and a prompt $\\mathbf{x} = (x_1, \\ldots, x_N)$ , the vanilla reasoning process (VRP) autoregressively produces a response $\\mathbf{y} = (y_1, \\ldots, y_L)$ with", + "bbox": [ + 169, + 244, + 823, + 289 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\pi_ {\\theta} (\\mathbf {y} | \\mathbf {x}) = \\prod_ {l = 1} ^ {L} \\pi_ {\\theta} (y _ {l} | x _ {1}, x _ {2}, \\dots x _ {N}, y _ {1}, \\dots , y _ {l - 1}) = \\prod_ {l = 1} ^ {L} \\pi_ {\\theta} (\\mathbf {y} _ {l} | \\mathbf {x}, \\mathbf {y} _ {< l})\n$$\n", + "text_format": "latex", + "bbox": [ + 263, + 296, + 730, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The response usually contains intermediate reasoning steps before arriving at the final answer, this process is also known as chain-of-thought (CoT) [Wei et al., 2022], which can be represented as:", + "bbox": [ + 169, + 345, + 823, + 377 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} \\xrightarrow {\\text {r e a s o n i n g s t e p s}} \\mathbf {y} \\sim \\mathbf {a}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 421, + 385, + 823, + 406 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{a}$ is the extracted final answer, which is included in the answer $\\mathbf{y}$ .", + "bbox": [ + 171, + 412, + 645, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2 Training VRP via Reinforcement Learning", + "text_level": 1, + "bbox": [ + 171, + 445, + 511, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "RL frames VRP decoding process as a deterministic, token-level Markov Decision process (MDP) [Wang et al., 2024a]. Its objective is", + "bbox": [ + 169, + 470, + 823, + 501 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {J} (\\theta) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\mathbf {y} \\sim \\pi_ {\\theta}} \\left[ R (\\mathbf {y}, \\mathbf {y} ^ {*}) \\right].\n$$\n", + "text_format": "latex", + "bbox": [ + 372, + 508, + 620, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $R(\\cdot, \\cdot)$ represents a reward function comparing generated answer $\\mathbf{y}$ with the golden answer $\\mathbf{y}^*$ for any question $\\mathbf{x}$ sampled from dataset $\\mathcal{D}$ .", + "bbox": [ + 169, + 534, + 823, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To compute the gradient $\\nabla_{\\theta}\\mathcal{J}(\\theta)$ , computationally efficient algorithms GRPO [Shao et al., 2024] and REINFORCE++ [Hu, 2025] are widely adopted. Take GRPO as an example, given a question-answer pair $\\mathbf{x},\\mathbf{y}^*$ and a group of $G$ generated responses $\\mathbf{y}_i$ , denote $\\mathbf{y}_{i,j}$ as the $j$ -th token of the $i$ -th response, it optimizes the following token-level objective:", + "bbox": [ + 169, + 566, + 823, + 621 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {J} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\{\\mathbf {y} _ {i} \\} _ {i = 1} ^ {G} \\sim \\pi_ {\\boldsymbol {\\theta} _ {\\mathrm {o l d}}} (\\cdot | \\mathbf {x})} \\\\ \\left[ \\frac {1}{G} \\sum_ {i = 1} ^ {G} \\frac {1}{| \\mathbf {y} _ {i} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i} |} \\left(\\min \\left(r _ {i, j} (\\theta) \\hat {A} _ {i, j}, \\operatorname {c l i p} \\left(r _ {i, j} (\\theta), 1 - \\epsilon , 1 + \\epsilon\\right) \\hat {A} _ {i, j}\\right) - \\beta D _ {\\mathrm {K L}} \\left(\\pi_ {\\theta} \\| \\pi_ {\\text {r e f}}\\right)\\right) \\right], \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 627, + 823, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the token-level ratio $r_{i,j}(\\theta)$ and the group-normalized advantage $\\hat{A}_{i,j}$ are defined as:", + "bbox": [ + 174, + 696, + 776, + 715 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i, j} (\\theta) = \\frac {\\pi_ {\\theta} \\left(\\mathbf {y} _ {i , j} \\mid \\mathbf {x} , \\mathbf {y} _ {i , < j}\\right)}{\\pi_ {\\theta_ {\\mathrm {o l d}}} \\left(\\mathbf {y} _ {i , j} \\mid \\mathbf {x} , \\mathbf {y} _ {i , < j}\\right)}, \\hat {A} _ {i, j} = \\frac {R _ {i} - \\operatorname {m e a n} \\left(\\left\\{R _ {i} \\right\\} _ {i = 1} ^ {G}\\right)}{\\operatorname {s t d} \\left(\\left\\{R _ {i} \\right\\} _ {i = 1} ^ {G}\\right)}.\n$$\n", + "text_format": "latex", + "bbox": [ + 285, + 722, + 709, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, RL on base LLMs that haven't been well-aligned may suffer from issues like poor readability and language mixing, preventing researchers from verifying, understanding, and further developing their LLMs. And huge searching space makes efficient learning of meta-thinking daunting.", + "bbox": [ + 169, + 773, + 823, + 818 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 Method", + "text_level": 1, + "bbox": [ + 171, + 837, + 272, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present Reinforced Meta-thinking Agents (ReMA), a RL method integrating meta-thinking into the reasoning process of LLM under multi-agent settings (Sec. 3.1), then describe the learning process enabled by MARL of single- and multi-turn LLM setting (Secs. 3.2.1 and 3.2.2).", + "bbox": [ + 169, + 869, + 825, + 912 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 Deploying Meta-Thinking Reasoning Process for LLMs", + "text_level": 1, + "bbox": [ + 171, + 90, + 599, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Beyond VRP (Sec. 2.1), recent studies [Muennighoff et al., 2025, Ye et al., 2025c] have shown that integrating meta-thinking behaviors in reasoning process can largely improve the accuracy of the final answers. By integrating Meta-thinking, ReMA decomposes problem solving into two sequential phases: a meta-thinking phase that plans, monitors, or revises strategy, followed by a reasoning phase that produces the detailed solution. We analyse Meta-thinking Reasoning Process along two orthogonal axes—single- vs. multi-agent and single- vs. multi-turn.", + "bbox": [ + 169, + 116, + 823, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In a single-agent setting, such a process calls LLM once and generates meta-thinking and the following reasoning autoregressively. We formulate the meta-thinking reasoning process (MRP) below:", + "bbox": [ + 169, + 205, + 823, + 234 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} \\sim \\pi_ {\\theta} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\cdot \\pi_ {\\theta} (\\mathbf {m} \\mid \\mathbf {x}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 395, + 242, + 823, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{m}$ and $\\mathbf{y}$ are the output of meta-thinking and reasoning respectively. We present the procedure as shown below:", + "bbox": [ + 169, + 263, + 823, + 290 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} \\xrightarrow {\\text {m e t a - t h i n k i n g}} \\mathbf {m} \\xrightarrow {\\text {r e a s o n i n g s t e p s}} \\mathbf {y} \\sim \\mathbf {a}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 375, + 291, + 823, + 310 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Exploring MRP reasoning through a single-agent approach is often inefficient, as it requires the language model to simultaneously master both meta-thinking and detailed problem-solving within one call. Prior research has demonstrated that activating different model capabilities through specialized agents significantly improves MRP exploration efficiency. To leverage this insight, we decouple meta-thinking and reasoning into two separate LLM agents: a high-level agent dedicated to generating meta-thinking, and a low-level agent focused on executing reasoning steps.", + "bbox": [ + 169, + 313, + 823, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During a conversation, the high-level and low-level agents (i.e., $\\pi_h$ and $\\pi_l$ ) act in an interleaving manner. The high-level agent generates and summarizes meta-thoughts from the prompt and interaction history, while the low-level agent executes detailed problem-solving under those instructions. We formulate the multi-agent meta-thinking reasoning process (MAMRP) as follows:", + "bbox": [ + 169, + 402, + 823, + 458 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} \\sim \\pi_ {l} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\pi_ {h} (\\mathbf {m} \\mid \\mathbf {x}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 400, + 465, + 823, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the single-turn MAMRP offers a straightforward approach, it lacks the ability to perform immediate and fine-grained cognitive switching during the reasoning process, which limits its effectiveness on complex, long-horizon planning tasks. Therefore, we extend Eq. (5) and formulate the multi-turn MAMRP as follows:", + "bbox": [ + 169, + 487, + 823, + 542 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} _ {T} \\sim \\prod_ {t = 1} ^ {T} \\pi_ {l} \\left(\\mathbf {y} _ {t} \\mid \\mathbf {x}, \\{\\mathbf {m}, \\mathbf {y} \\} _ {< t}, \\mathbf {m} _ {t}\\right) \\pi_ {h} \\left(\\mathbf {m} _ {t} \\mid \\mathbf {x}, \\{\\mathbf {m}, \\mathbf {y} \\} _ {< t}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 305, + 549, + 823, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T$ is the number of turns. Similarly, we present the process with a directed graph:", + "bbox": [ + 171, + 595, + 750, + 611 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\mathbf {m} _ {1} \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {1} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\mathbf {m} _ {2} \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {2} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\dots \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {T} \\sim \\mathbf {a}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 619, + 823, + 646 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As a complex reasoning system, MAMRP provides various optimization opportunities in scaling inference-time computation. We leave further discussion of these aspects in Appendix C.1.", + "bbox": [ + 169, + 652, + 823, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 Training MAMRP: A Multi-Agent RL Method", + "text_level": 1, + "bbox": [ + 171, + 696, + 539, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-agent RL, unlike single-agent RL in a deterministic MDP, must contend with stochastic, nonstationary dynamics and rewards, making optimization more challenging. We start by considering an easier case, the optimization of single-turn MAMRP.", + "bbox": [ + 169, + 720, + 823, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Optimizing Single-turn MAMRP", + "text_level": 1, + "bbox": [ + 171, + 777, + 455, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To train the system from Sec. 3.1, we embed it as a Markov Game between the two agents. Suppose the two LLM agents are parameterized by $\\theta_h$ and $\\theta_l$ , respectively. Define a joint hierarchical policy over sequential decisions $\\mathbf{m}$ and $\\mathbf{y}$ :", + "bbox": [ + 169, + 801, + 823, + 844 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} \\sim \\pi_ {\\left(\\theta_ {h}, \\theta_ {l}\\right)} (\\mathbf {y} \\mid \\mathbf {x}) := \\pi_ {\\theta_ {l}} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\cdot \\pi_ {\\theta_ {h}} (\\mathbf {m} \\mid \\mathbf {x}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 328, + 851, + 823, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $R(\\mathbf{y}, \\mathbf{y}^*)$ denote the final reward serves as the objective function $\\mathcal{J}(\\theta_h, \\theta_l)$ for the joint policy:", + "bbox": [ + 169, + 875, + 818, + 890 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {J} \\left(\\theta_ {h}, \\theta_ {l}\\right) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\mathbb {E} _ {\\mathbf {y} \\sim \\pi \\left(\\theta_ {h}, \\theta_ {l}\\right)} R (\\mathbf {y}, \\mathbf {y} ^ {*}). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 367, + 897, + 823, + 915 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f246502d1a54bf77abbf1b84a3d339ae985d445d9515b42b122262754119fa92.jpg", + "image_caption": [ + "RL for VRP & MRP" + ], + "image_footnote": [], + "bbox": [ + 176, + 102, + 344, + 268 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7f3231499e748935cfc4e1cfa6d56049cf9d1cab539e1879a81522875ddbfa66.jpg", + "image_caption": [ + "ReMA with Separate Parameters" + ], + "image_footnote": [], + "bbox": [ + 344, + 103, + 602, + 268 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c1b6f6aaf161ccb2d707eb51858e4b49250221c289f22f7d7fd725b003912a00.jpg", + "image_caption": [ + "ReMA with Shared Parameters", + "Figure 2: Comparison of training pipelines. Left: RL training of VRP and MRP, where a single LM agent is updated either with mixed (VRP) or explicit (MRP) meta-thinking. Middle: ReMA with separate parameters for the high-level (meta-thinking) and low-level (reasoning) agents; training alternates between freezing one agent and updating the other. Right: ReMA with shared parameters and multi-turn interactions: both agents share the same parameters and are distinguished by their system prompts. Training employs a turn-level ratio for stable multi-turn reinforcement learning and efficient updates, ensuring each turn's contribution is controlled to prevent instability." + ], + "image_footnote": [], + "bbox": [ + 602, + 103, + 821, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During optimization procedure, the high-level policy $\\pi_{\\theta_h}$ and low-level policy $\\pi_{\\theta_l}$ aim to maximize their respective rewards independently. The optimization goals for agents are:", + "bbox": [ + 169, + 393, + 823, + 422 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {h} ^ {*} = \\arg \\max _ {\\theta_ {h}} \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\mathbf {m} \\sim \\pi_ {\\theta_ {h}}, \\mathbf {y} \\sim \\pi_ {\\theta_ {l} ^ {*}}} \\left[ R _ {h} (\\mathbf {m}, \\mathbf {y}, \\mathbf {y} ^ {*}) \\right], \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 323, + 429, + 823, + 452 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {l} ^ {*} \\left(\\theta_ {h}\\right) = \\arg \\max _ {\\theta_ {l}} \\mathbb {E} _ {\\left(\\mathbf {x}, \\mathbf {y} ^ {*}\\right) \\sim \\mathcal {D}, \\mathbf {m} \\sim \\pi_ {\\theta_ {h}}, \\mathbf {y} \\sim \\pi_ {\\theta_ {l}}} \\left[ R _ {l} \\left(\\mathbf {m}, \\mathbf {y}, \\mathbf {y} ^ {*}\\right) \\right], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 297, + 454, + 823, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $R_{h}$ and $R_{l}$ are policies' individual reward functions, including $R$ and regularization according to tasks and models, e.g., different format rewards (refer to Appendix C.2 for details). The detailed algorithm is in the Algorithm 1. We illustrate the MAMRP inference procedure and the proposed training method in Fig. 2. We also provide an analysis of different loss functions in Appendix C.5.", + "bbox": [ + 169, + 486, + 823, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Scaling up to Multi-turn MAMRP", + "text_level": 1, + "bbox": [ + 171, + 559, + 465, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To scale up to multi-turn MAMRP, we can still adopt the iterative training strategy in Sec. 3.2.1. However, we make some changes to improve the efficiency of rollout and training.", + "bbox": [ + 169, + 583, + 823, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we implement a parameter-sharing strategy where both high-level and low-level agents utilize identical model weights $\\theta$ , distinguished only by role-specific system prompts $S_{h}$ and $S_{l}$ . Formally, we define $\\pi_h = \\pi_\\theta (\\cdot |S_h,\\cdot)$ and $\\pi_l = \\pi_\\theta (\\cdot |S_l,\\cdot)$ , sharing the same underlying parameters rather than maintaining separate model instances. This approach eliminates the need for frequent model swapping on GPU during rollout, avoiding inefficient wait times, while enabling larger batch sizes during training to simultaneously optimize policies for both meta-thinking and reasoning roles.", + "bbox": [ + 169, + 618, + 823, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Second, we propose a multi-turn GRPO with turn-level ratio to address the challenges of multi-turn MAMRP. The trajectory-level averaged objective with turn-level ratio of $\\pi_{l}$ is defined as (The objective of $\\pi_h$ is the similar but with different system prompt):", + "bbox": [ + 169, + 705, + 823, + 747 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {J} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\{(\\mathbf {m} _ {i}, \\mathbf {y} _ {i}) \\} _ {i = 1} ^ {G} \\sim \\pi_ {\\theta_ {\\mathrm {o l d}}} (\\cdot | \\mathbf {x})\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 753, + 434, + 772 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\left[ \\frac {1}{G} \\sum_ {i = 1} ^ {G} \\frac {1}{T _ {i}} \\sum_ {t = 1} ^ {T _ {i}} \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} \\left(\\min \\left(r _ {i, t} (\\theta) \\hat {A} _ {i, t, j}, \\operatorname {c l i p} \\left(r _ {i, t} (\\theta), 1 - \\epsilon , 1 + \\epsilon\\right) \\hat {A} _ {i, t, j}\\right) - \\beta D _ {\\mathrm {K L}} \\left(\\pi_ {\\theta} \\| \\pi_ {\\text {r e f}}\\right)\\right) \\right] \\right. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 775, + 823, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{y}_{i,t,j}$ is the $j$ -th token at turn $t$ of the reasoning agent of the $i$ -th trajectory. And the turn-level ratio for clipping is defined as:", + "bbox": [ + 171, + 825, + 823, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i, t} (\\theta) = \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} r _ {i, t, j} (\\theta) = \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} \\frac {\\pi_ {\\theta} \\left(\\mathbf {y} _ {i , t , j} \\mid \\mathbf {x} , \\left\\{\\mathbf {m} _ {i , ,} , \\mathbf {y} _ {i ,} \\right\\} _ {< t} , \\mathbf {m} _ {i , t} , \\mathbf {y} _ {i , t , < j}\\right)}{\\pi_ {\\theta_ {\\mathrm {o l d}}} \\left(\\mathbf {y} _ {i , t , j} \\mid \\mathbf {x} , \\left\\{\\mathbf {m} _ {i , ,}, \\mathbf {y} _ {i ,} \\right\\} _ {< t} , \\mathbf {m} _ {i , t} , \\mathbf {y} _ {i , t , < j}\\right)}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 864, + 823, + 907 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The introduction of the turn-level ratio serves two key purposes. First, using a token-level ratio (Eq. (2)) in the objective introduces bias for multi-turn training, as it averages over all tokens in a trajectory. This means that tokens within longer turns (those containing more tokens) can disproportionately influence the overall loss, and averaging at the token level may encourage excessively long single-turn responses. Second, clipping each token independently risks instability during training.", + "bbox": [ + 169, + 90, + 823, + 161 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In contrast, the turn-level ratio aligns more closely with the underlying MDP formulation by treating all tokens within a turn as a single action and applying clipping at the turn level. Intuitively, this approach stabilizes training by preventing the LLM from making unstable updates that could result in extreme outputs, such as overly long repetitions or incoherent text. We conduct experimental verification in subsequent empirical results (Sec. 4.3).", + "bbox": [ + 169, + 167, + 826, + 238 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 Experiments", + "text_level": 1, + "bbox": [ + 171, + 258, + 313, + 275 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the effectiveness and efficiency of ReMA, we conduct experiments on challenging benchmarks for two types of tasks: mathematical reasoning and LLM-as-a-Judge with three different LLMs. Then, we investigate the models' performance in both single- & multi-turn settings. Finally, we provide ablation studies and qualitative analyses of our method.", + "bbox": [ + 169, + 291, + 823, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1 Experiment Settings", + "text_level": 1, + "bbox": [ + 171, + 364, + 356, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first analyze the single-turn case of ReMA, i.e., $T = 1$ . The high-level agent generates a complete meta-thinking trace in one shot, and the low-level agent follows the instructions and outputs the final results. Single-turn ReMA reduces stochasticity and training cost while our experiments show that it still provides meaningful performance gains.", + "bbox": [ + 169, + 391, + 823, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Benchmarks We conduct experiments on two types of tasks: mathematical reasoning and LLM-as-a-Judge. For mathematical reasoning experiments, we train models on 7.5k training samples in MATH [Hendrycks et al., 2021] and use MATH500 [Lightman et al., 2023] as the in-distribution test dataset. Additionally, we test the optimized models on out-of-distribution datasets: GSM8K [Cobbe et al., 2021], AIME24 $^{4}$ , AMC23 $^{5}$ , GaoKao2023En [Zhang et al., 2023], Minerva Math [Lewkowycz et al., 2022], and Olympiad Bench [He et al., 2024].", + "bbox": [ + 169, + 464, + 823, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For LLM-as-a-Judge benchmarks, we train models on RewardBench [Lambert et al., 2024]. Specifically, we convert the original data into a pair-ranking format and split it into a training set of 5k items and a test set of 970 items, denoted as RewardBench970. The models are also tested on JudgeBench [Tan et al., 2024] to assess out-of-distribution performance. We refer to Appendix D.1.2 for detailed comparisons and results.", + "bbox": [ + 169, + 553, + 823, + 623 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines, Models, Training Settings We compare pass@1 performance across the following methods: (1) VRP (CoT, step-by-step prompting, Sec. 3.1); (2) $\\mathbf{VRP}_{\\mathbf{RL}}$ (RL under VRP); (3) $\\mathbf{MRP}_{\\mathbf{RL}}$ (RL under MRP with high-level task analysis, Eq. (4)), and (4) ReMA (ours, RL under MAMRP, Eq. (7)).", + "bbox": [ + 169, + 640, + 823, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train and test Llama-3-8B-Instruct, Llama-3.1-8B-Instruct [Dubey et al., 2024], and Qwen2.5-7B-Instruct [Team, 2024] on mathematical reasoning benchmarks. For LLM-as-a-judge benchmarks, we train and test Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct. We use instruct-tuned LLMs to prompt them to perform VRP, MRP, and MAMRP directly during training. Unless specified, we use two separate copies of the same model for high- and low-level agents in ReMA. We use the base reward setting in Appendix C.2 by default. And for the underlying RL algorithm, we use REINFORCE++ [Hu, 2025]. We refer to Appendix D for detailed training settings.", + "bbox": [ + 169, + 700, + 823, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2 Results of Single-turn ReMA", + "text_level": 1, + "bbox": [ + 171, + 816, + 415, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Question 1. Does single-turn ReMA outperforms baselines on both in-distribution and out-of-distribution test sets?", + "bbox": [ + 169, + 844, + 823, + 872 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "4https://huggingface.co/datasets/AI-MO/aimo-validation-aime", + "bbox": [ + 189, + 883, + 712, + 897 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "5https://huggingface.co/datasets/AI-MO/aimo-validation-amc", + "bbox": [ + 192, + 898, + 704, + 910 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Performance on in-distribution test sets and out-of-distribution test sets. We also report the improvement/degradation w.r.t. basic CoT performance(VRP). On average, ReMA outperforms all baselines. Particularly on out-of-distribution datasets, ReMA achieves the highest performance on most of the benchmarks.", + "bbox": [ + 169, + 99, + 823, + 154 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/032ea026c484b25fb0540e17ead1ad673917359410de718a424734cd30d558a2.jpg", + "table_caption": [ + "(a) Performance on math benchmarks" + ], + "table_footnote": [], + "table_body": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3-8B-InstructMATH50030.8033.40 (+2.60)32.80 (+2.00)33.80 (+3.00)
GSM8K67.4881.80 (+14.32)79.68 (+12.20)79.38 (+11.90)
AIME240.000.00 (+0.00)3.33 (+3.33)0.00 (+0.00)
AMC232.5010.00 (+7.50)12.50 (+10.00)22.50 (+20.00)
Gaokao2023en22.3427.53 (+5.19)23.38 (+1.04)28.57 (+6.23)
Minerva Math8.8216.54 (+7.72)18.01 (+9.19)13.97 (+5.15)
Olympiad Bench8.448.89 (+0.45)9.33 (+0.89)8.89 (+0.45)
Average20.0525.45 (+5.40)25.58 (+5.53)26.73 (+6.68)
Llama3.1-8B-InstructMATH50050.8050.20 (-0.60)48.60 (-2.20)53.20 (+2.40)
GSM8K86.0584.53 (-1.52)85.37 (-0.68)87.26 (+1.21)
AIME2410.003.33 (-6.67)6.67 (-3.33)13.33 (+3.33)
AMC2327.5012.50 (-15.00)30.00 (+2.50)20.00 (-7.50)
Gaokao2023en38.9636.10 (-2.86)37.14 (-1.82)37.14 (-1.82)
Minerva Math22.7926.84 (+4.05)25.37 (+2.58)28.31 (+5.52)
Olympiad Bench15.1119.70 (+4.59)15.70 (+0.59)19.56 (+4.45)
Average35.8933.32 (-2.57)35.55 (-0.34)36.97 (+1.08)
Qwen2.5-7B-InstructMATH50075.0077.20 (+2.20)76.40 (+1.40)74.40 (-0.60)
GSM8K92.0491.36 (-0.68)91.81 (-0.23)90.60 (-1.44)
AIME246.676.67 (+0.00)10.00 (+3.33)20.00 (+13.33)
AMC2347.5050.00 (+2.50)52.50 (+5.00)57.50 (+10.00)
Gaokao2023en56.6254.81 (-1.81)55.06 (-1.56)57.92 (+1.30)
Minerva Math35.6634.93 (-0.73)32.35 (-3.31)34.93 (-0.73)
Olympiad Bench38.2238.37 (+0.15)37.78 (-0.44)36.30 (-1.92)
Average50.2450.48 (+0.24)50.84 (+0.60)53.09 (+2.85)
", + "bbox": [ + 205, + 172, + 792, + 539 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/71aca539c79024c7c54c8b500119e08584e1cf23534f6bae0662ad5dc7fbc4aa.jpg", + "table_caption": [ + "(b) Performance on LLM-as-a-Judge benchmarks" + ], + "table_footnote": [], + "table_body": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3.1-8B-InstructRewardBench97069.4882.89 (+13.41)81.13 (+11.65)83.71 (+14.23)
JudgeBench51.2951.94 (+0.65)52.90 (+1.61)52.90 (+1.61)
Average60.3967.41 (+7.02)67.02 (+6.63)68.31 (+7.92)
Qwen2.5-7B-InstructRewardBench97078.5685.36 (+6.80)86.49 (+7.93)83.51 (+4.95)
JudgeBench58.3956.94 (-1.45)58.39 (+0.00)56.94 (-1.45)
Average68.4771.15 (+2.68)72.44 (+3.97)70.22 (+1.75)
", + "bbox": [ + 202, + 561, + 794, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 compares the greedy decoding performance of ReMA against various RL baselines across mathematical benchmarks (Table 1a) and LLM-as-a-Judge benchmarks (Table 1b). Results across different LLMs indicate that, on average, ReMA outperforms all baselines, achieving a maximum improvement of $6.68\\%$ on mathematical benchmarks and $8.49\\%$ on LLM-as-a-Judge benchmarks.", + "bbox": [ + 169, + 738, + 823, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Notably, ReMA achieves the highest performance on most benchmarks, particularly on out-of-distribution datasets, with a maximum improvement of $20\\%$ on AMC23 for Llama3-8B-Instruct, $13.33\\%$ on AIME24 for Qwen2.5-7B-Instruct, $14.23\\%$ on RewardBench970 for Llama3.1-8B-Instruct. These results demonstrate the superior out-of-distribution generalization ability conferred by the meta-thinking mechanism in ReMA. However, we observe that the accuracy gains from RL training on instruction-tuned LMs are smaller than from base models (Sec. 4.2.1). This may be due to the higher initial performance and the relatively fixed output distribution of instruction-tuned models, which limits the improvement and peak performance in RL.", + "bbox": [ + 169, + 800, + 823, + 911 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/37ed86a4d76064b8e7dc589771be62484945d0a0fbaf36c2bdeedac73830355d.jpg", + "image_caption": [ + "Figure 3: An RL experiment with 3 training schemes. While RL from SFT excels on easier problems, RL under Meta-thinking shows superior generalization to harder problems like AIME24." + ], + "image_footnote": [], + "bbox": [ + 186, + 82, + 808, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7cef31214b1e22f8feceb774c7c2fda0d8822a64668c93c676a445aa329e03c2.jpg", + "image_caption": [ + "Figure 4: Average problem difficulty by action type during training. Left: 1B LM collapses to the EMPTY action. Right: 8B LM adapts to a more complex meta-thinking strategy for harder problems." + ], + "image_footnote": [], + "bbox": [ + 173, + 301, + 485, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8067de4a34648160295745db52239f10161f855ef4f748f78627686ff344515e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 301, + 818, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2.1 Meta-thoughts boost low-level generalization", + "text_level": 1, + "bbox": [ + 171, + 468, + 537, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Question 2. Can Reasoning benefit from Meta-thinking?", + "text_level": 1, + "bbox": [ + 171, + 493, + 545, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here we provide a tiny but motivating example of how ReMA gives better learning dynamics. We use Qwen2.5-Math-7B [Yang et al., 2024] as the starting base model, MATH (level 3-5, about $5.5\\mathrm{K}$ number of instances) as the training dataset, and we compare three reinforcement learning training schemes, in particular: (1) RL from Base: train the base model directly on MATH with binary outcome reward; (2) RL from SFT: SFT the base model with GPT-4o's CoT answers; then RL on train dataset with binary outcome reward; (3) RL under Meta-thinking: SFT the base model with GPT-4o's meta-thinking plans; then RL on train dataset with binary outcome reward.", + "bbox": [ + 169, + 513, + 823, + 612 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The models are evaluated on 3 benchmarks (Fig. 3). SFT brings the best initial accuracy on in-distribution and easier sets, but fails to improve on harder ones. RL from Base yields limited gains. In contrast, RL under Meta-thinking achieves the best learning dynamics and generalizes better to challenging problems (AIME24). See Appendix F.1 for case studies.", + "bbox": [ + 169, + 618, + 823, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2.2 Diverse meta-thinking characteristics of LLMs", + "text_level": 1, + "bbox": [ + 171, + 691, + 550, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Question 3. How well can LLMs learn to meta-think?", + "text_level": 1, + "bbox": [ + 171, + 717, + 529, + 732 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further analyze meta-thinking behaviors, we train models with structured JSON-format actions inspired by Yue et al.. The meta-thinking agent generate two entries in one LM call, first selects from three actions: DECOMPOSE (breaking into subproblems), REWRITE (simplifying the problem), or EMPTY (direct solving), then generates the corresponding text. We compare Llama-3.1-8B-Instruct and Llama-3.2-1B-Instruct to study scale effects (two 1B models vs two 8B models) on meta-thinking agent's training. We use vLLM guided JSON decoding [Dong et al., 2024] for valid formatting and base reward (reasoning agent's solution accuracy with format constraints).", + "bbox": [ + 169, + 738, + 823, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We observe that smaller LMs produce simpler outputs, likely due to limited capacity to maintain valid JSON formatting while exploring diverse reasoning strategies. As Fig. 4 shows, smaller LMs like Llama-3.2-1B-Instruct quickly converge to the simplest EMPTY action to avoid formatting penalties, while larger LMs like Llama-3.1-8B-Instruct can adapt meta-thinking strategies based on problem difficulty. See Appendix F.3 for detailed case studies.", + "bbox": [ + 169, + 842, + 823, + 912 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7be77f52a452cae631a3999a5c1a37f14186bd400761aa6b2200170fc2818d62.jpg", + "image_caption": [ + "Figure 5: Training results of multi-turn Figure 6: Ablations of multi-turn ReMA on a tiny subReMA on MATH-Level3-5-8K under different set of MATH, we only show here the training curves of different training and rollout configurations." + ], + "image_footnote": [], + "bbox": [ + 176, + 78, + 467, + 210 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0a12a930e142fe2cdce1144a9d1bcf93a65808b7f66fd19e01bc8a6c088ffc04.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 78, + 821, + 210 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.3 Extending ReMA to Multi-turn MAMRP", + "text_level": 1, + "bbox": [ + 169, + 287, + 501, + 304 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We further extend ReMA to multi-turn MAMRP settings, enabling multiple rounds of interaction between the meta-thinking agent and the reasoning agent as defined in Eq. (7).", + "bbox": [ + 169, + 321, + 823, + 351 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Unlike the inherent VRP capabilities of most LLMs, multi-turn ReMA requires initial bootstrapping. Thus, we constructed a supervised fine-tuning dataset (about 0.8K samples) from LIMO [Ye et al., 2025c] using GPT-4o to establish the starting point for multi-turn interaction capabilities. Then we finetune Qwen2.5-7B before RL training.", + "bbox": [ + 169, + 356, + 823, + 412 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "As described in Sec.3.2.2, we deploy the proposed GRPO with turn-level ratio clipping and trajectory-level averaging loss during training. And we remove the KL-divergence term to allow more flexible exploration. By default, the agents share the same parameters and are simultaneously updated using their trajectories. We refer to details in Appendix D.2.", + "bbox": [ + 169, + 417, + 823, + 474 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.3.1 Results and Ablations", + "text_level": 1, + "bbox": [ + 171, + 507, + 377, + 522 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Question 4. Can ReMA be scaled to multi-turn settings?", + "text_level": 1, + "bbox": [ + 169, + 537, + 545, + 554 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "There are two key points revealed by our multi-turn ReMA experiments, as shown in Fig. 5. On one hand, the algorithm can demonstrate effective convergence on the training set, with accuracy steadily increasing from approximately $55\\%$ to $70\\%$ during training. It also achieves an average performance gain of about $5\\%$ across all seven test benchmarks, indicating stable improvements on out-of-distribution data. (Experiment with the rollout config of turn30_token512, see Appendix D.2.2 and Fig. 8 for more details.)", + "bbox": [ + 169, + 559, + 823, + 643 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "On the other hand, we observe that the performance of multi-turn ReMA is highly sensitive to hyperparameters such as the maximum response length per turn and the maximum number of turns. For certain configurations, the model either collapses into producing massive repetitions within a single turn or generates empty responses after only a few turns. Similar phenomena have been reported in concurrent works such as RAGEN [Wang et al., 2025], where these issues are attributed to the lack of fine-grained, reasoning-aware guidance. As a result, multi-turn RL becomes susceptible to long-horizon credit assignment challenges and state drift, often leading to reduced exploration diversity—a phenomenon referred to as the \"Echo Trap\". To address this challenge, it is essential to comprehensively explore the training recipe w.r.t. model, data, and algorithm.", + "bbox": [ + 169, + 648, + 825, + 773 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Question 5. How does parameter sharing and turn-level ratio affect multi-turn ReMA?", + "text_level": 1, + "bbox": [ + 169, + 779, + 746, + 795 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "As shown in Fig. 6, we compare different configurations on a smaller dataset consisting of 133 samples—19 from each of the 7 MATH problem types—to evaluate sample efficiency and convergence speed. First, all configurations eventually achieve nearly $100\\%$ accuracy on the training dataset. Notably, the trajectory-level loss with turn-level ratio (Turn-Ratio, Eq. (13)) demonstrates substantially better sample efficiency than its token-level variants (Eq. (2)), reaching higher training rewards with fewer steps. We also present the training curve of separate weight setting, the empirical results show that shared parameters with simultaneous updates converge noticeably faster.", + "bbox": [ + 169, + 800, + 825, + 912 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5 Conclusion", + "text_level": 1, + "bbox": [ + 174, + 90, + 299, + 104 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "In this paper, we introduced ReMA, a novel framework that leverages multi-agent reinforcement learning to elicit meta-thinking in large language models. By explicitly separating meta-thinking and reasoning processes into distinct agents, our approach enhances both exploration during training and the interpretability of model outputs. We tailored RL algorithms and reward functions to ensure reliable performance. Through comprehensive experiments on mathematical reasoning and LLM-as-a-Judge benchmarks, ReMA consistently achieved superior results, particularly on out-of-distribution datasets. We further extend ReMA to multi-turn settings, enabling the framework to handle more complex reasoning scenarios that require more communication between agents. Our ablations demonstrate how effective coordination between agents evolves, highlighting the promise of reinforcement learning and structured agents' collaboration for advancing the capabilities of language models in complex reasoning tasks.", + "bbox": [ + 174, + 119, + 823, + 272 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10", + "bbox": [ + 491, + 935, + 506, + 946 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 173, + 89, + 269, + 106 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023.", + "Elif Akata, Lion Schulz, Julian Coda-Forno, Seong Joon Oh, Matthias Bethge, and Eric Schulz. 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Mindstorms in natural language-based societies of mind. arXiv preprint arXiv:2305.17066, 2023." + ], + "bbox": [ + 171, + 90, + 825, + 710 + ], + "page_idx": 17 + }, + { + "type": "page_number", + "text": "18", + "bbox": [ + 490, + 935, + 508, + 946 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Appendix Table of Contents", + "text_level": 1, + "bbox": [ + 171, + 89, + 410, + 107 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "- A Related work 19", + "bbox": [ + 217, + 114, + 825, + 128 + ], + "page_idx": 18 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "-A.1 Single LLM Reasoning 19", + "-A.2MultipleLLMReasoning 20", + "-A.3 Hierarchical Reasoning 20", + "-A.4RL in LLM 21" + ], + "bbox": [ + 245, + 132, + 823, + 193 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "B Limitation and Future Work 21", + "bbox": [ + 215, + 196, + 823, + 210 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "C Supplementary Materials for Method in Section 3 21", + "bbox": [ + 215, + 215, + 823, + 229 + ], + "page_idx": 18 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- C.1 Inference-time Scaling For ReMA 21", + "- C.2 Detailed reward design 22", + "- C.3 Pseudocode of ReMA 23", + "- C.4 Brief convergence analysis 23", + "- C.5 Learning to reason from the perspective of Leader Follower Game 24" + ], + "bbox": [ + 245, + 233, + 823, + 309 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "D Training Details 26", + "bbox": [ + 215, + 313, + 823, + 327 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "- D.1 Single-turn ReMA 26", + "bbox": [ + 245, + 330, + 823, + 345 + ], + "page_idx": 18 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "\\* D.1.1 Supervised fine-tuning data collection 27", + "\\* D.1.2 Dataset Curation of RewardBench970 27", + "\\*D.1.3 Training on MATH 28", + "\\* D.1.4 Training on Reward Bench 28" + ], + "bbox": [ + 272, + 347, + 823, + 404 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "- D.2 Multi-turn ReMA 28", + "bbox": [ + 245, + 406, + 823, + 419 + ], + "page_idx": 18 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "\\* D.2.1 SFT data collection of multi-turn MAMRP 29", + "\\* D.2.2 Training on MATH 29" + ], + "bbox": [ + 272, + 421, + 823, + 450 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "E Other Experiments 29", + "bbox": [ + 215, + 453, + 823, + 467 + ], + "page_idx": 18 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "-E.1 Reward functions shape cross-agent behaviors 29", + "- E.2 Detailed Training Curves on Different Datasets of Multi-turn ReMA 30" + ], + "bbox": [ + 245, + 470, + 823, + 501 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "F Qualitative results 30", + "bbox": [ + 215, + 505, + 823, + 518 + ], + "page_idx": 18 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- F.1 High-level policy finds better plans 30", + "- F.2 Case study for Experiments of Different Reward Functions in Appendix E.1 .30", + "- F.3 Case study for Adaptive Meta-thinking in Single-Turn ReMA in Section 4.2.2 30" + ], + "bbox": [ + 245, + 522, + 823, + 566 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "G Prompts 31", + "bbox": [ + 215, + 571, + 823, + 585 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "A Related work", + "text_level": 1, + "bbox": [ + 171, + 604, + 321, + 619 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Drawing from the bitter lesson [Sutton, 2019], two methods that appear to scale effectively are searching and learning, aligning with current trends in large language models [Xu et al., 2025]. At present, researchers are leveraging these methods to maximize the capabilities of individual transformers, while other efforts are exploring architectures that involve multiple interacting entities. In this paper, we examine this divergence within the context of LLM reasoning, a capability that allows large language models to solve problems through logical reasoning, step-by-step analysis, and inference [Wang et al., 2024a].", + "bbox": [ + 169, + 633, + 826, + 733 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "A.1 Single LLM Reasoning", + "text_level": 1, + "bbox": [ + 171, + 747, + 377, + 763 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Main research works in reasoning involving a single LLM utilize search-based and post-training methods. The fundamental elements of searching methods are text generation and evaluation. Generation schemes include In-Context Learning [Brown et al., 2020], Beam Search [Graves, 2012], and various tree-based searching [Snell et al., 2024]; Evaluation approaches often use outcome accuracy, self-consistency [Wang et al., 2022], or process reward signal [Lightman et al., 2023] as the criteria to select high-quality responses from the generated texts. Post-training method is another research line in opposition to pre-training. Popular training pipelines often involve specific data construction followed by Supervised Fine-tuning [Qin et al., 2024, Ouyang et al., 2022, Hui et al., 2024, Liu et al., 2024], or reinforcement learning to interactively explore learning patterns [Wang et al., 2024a, Zhang et al., 2024a, DeepSeek-AI et al., 2025, Xu et al., 2025].", + "bbox": [ + 169, + 772, + 826, + 912 + ], + "page_idx": 18 + }, + { + "type": "page_number", + "text": "19", + "bbox": [ + 490, + 935, + 508, + 946 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "A.2 Multiple LLM Reasoning", + "text_level": 1, + "bbox": [ + 174, + 92, + 393, + 104 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Integrating multiple entities can potentially surpass the intelligence of the individual model [Chen et al., 2023]. With the rapid emergence of large language models showing a varying level of abilities, some studies have explored facilitating discussions among multiple off-the-shelf LLMs [Zhang et al., 2025a, Chen et al., 2024a, Wang et al., 2023, Du et al., 2023, Zhuge et al., 2023, Tang et al., 2023, Hao et al., 2025, Akata et al., 2023, Hong et al., 2023, Zhang et al., 2024b], taking the form of free discussion [Du et al., 2023, Liang et al., 2023] or structured role assignments [Hong et al., 2023, Zhang et al., 2024b]. Some have applied routing mechanisms to assign tasks to the most suitable expert models [Hu et al., 2024b, Stripelis et al., 2024, Ding et al., 2024, Yue et al., 2025a, Chen et al., 2024c] or merging mechanisms to develop more versatile models [Yadav et al., 2024, Yu et al., 2024, Zhang et al., 2025b]. Beyond aggregating static knowledge from multiple agents, multi-agent LLM training can also enhance reasoning capabilities. For example, multi-agent debates can generate diverse synthetic data, which can subsequently be used for supervised fine-tuning [Estornell et al., 2024, Li et al., 2024, Motwani et al., 2024, Dong and Ma, 2025, Perez et al., 2022, Ye et al., 2025a, Subramaniam et al., 2025]. Reinforcement learning (RL) methods have also been adopted to improve LLM reasoning in areas such as alignment [Perez et al., 2022, Ma et al., 2023] and legibility [Kirchner et al., 2024]. Motwani et al. [2024] utilize a three-agent system for generation and fine-tune the models using Direct Preference Optimization (DPO). Reinforcement Learning with Generative Reward Models (GenRM) [Mahan et al., 2024, Ye et al., 2025b, Jiao et al., 2024, Wang et al., 2024b] represents another common approach of multi-agent training, where the reward signal is derived from the token probabilities of another LLM, coupled with the reasoning process. While our work aligns with these efforts, it diverges by using an additional tunable LLM to provide metacognitive instructions, guiding the low-level LLM during learning, rather than relying on a static GenRM. The most closely related works to ours are MAPoRL [Park et al., 2025] and COPYR [Ma et al., 2024]. MAPoRL is a multi-agent debating framework that uses multi-agent reinforcement learning (MARL) with a learned verifier to fine-tune each LLM agent. COPYR duplicates an LLM into two agents, training them simultaneously in the roles of pioneer and observer using RL. Shen et al. [2025] trained with a novel Chain-of-Action-Thought (COAT) framework that embeds meta-action tokens for self-reflection and exploration into an autoregressive search process. However, unlike our approach, which explicitly separates metacognition from plan execution, these methods do not decompose the reasoning process but instead focus on improving direct chain-of-thought generation. Furthermore, our experiments are conducted on a larger scale and include more challenging problems.", + "bbox": [ + 174, + 119, + 823, + 561 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "A.3 Hierarchical Reasoning", + "text_level": 1, + "bbox": [ + 174, + 592, + 379, + 604 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Partitioning reasoning into hierarchical processes has been explored in prior research to make biological sense [Ye et al., 2018, Langley et al., 2004]. In the context of language models, a hierarchical structure has been used to facilitate diverse reasoning patterns, including planning [Puerta-Merino et al., 2025, Sun et al., 2024, Song et al., 2023, Rana et al., 2023, Chen et al., 2024d, Yan et al., 2023, Xiao et al., 2024], validation [Haji et al., 2024, Xi et al., 2024] and self-refinement [Madaan et al., 2023, Kumar et al., 2024, Welleck et al., 2022]. For instance, EvalPlanner [Saha et al., 2025b] is a framework that conducts reasoning through plan generation and execution. DOTS [Yue et al., 2024] extends decomposition by integrating a tree-based searching method with Analysis, Solution, and Verification layers. Marco-o1 [Zhao et al., 2024] focuses on open-ended problem-solving and abstract thinking, dynamically adjusting reasoning granularity and incorporating reflection mechanisms to enhance reasoning performance. Beyond these approaches, metacognition [Flavell, 1979] has been identified as another critical component of reasoning, referring to the intuitive understanding of one's own cognitive and reasoning processes [Gao et al., 2024, Wang and Zhao, 2023]. Wang and Zhao [2023] proposed a metacognitive prompting strategy to improve large language model (LLM) capabilities. Didolkar et al. [2024] further developed a prompt-guided method that enables models to label math problems with the required skills and subsequently use these labels to solve new problems. Gao et al. [2024] introduce meta-reasoner which use contextual multi-arm bandit to learn a high-level \"advisor\" over low-level reasoning process. Xiang et al. [2025] provides a Meta-CoT framework to think about its own thinking. They use construction-based methods as well as reinforcement learning to develop meta-cognitive skills. Qingsong et al. [2025] introduces a RL framework for dynamic instruction selection during fine-tuning. In our work, we also value reflect-", + "bbox": [ + 174, + 619, + 823, + 910 + ], + "page_idx": 19 + }, + { + "type": "page_number", + "text": "20", + "bbox": [ + 490, + 936, + 506, + 946 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "ing on reasoning processes, and we enhance metacognitive abilities through two-agent interaction and reinforcement learning at both end.", + "bbox": [ + 169, + 90, + 823, + 122 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "A.4 RL in LLM", + "text_level": 1, + "bbox": [ + 171, + 137, + 302, + 152 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Recent advancements in applying RL to LLMs have enhanced their reasoning and decision-making capabilities. Liu et al. [2025] examines token-level optimization biases by introducing Dr. GRPO to stabilize policy gradients. VAPO [Yue et al., 2025b] enhances PPO with value-aware perturbations and adaptive reward shaping to improve robustness in sparse-reward reasoning tasks. DAPO [Yu et al., 2025] provides a scalable, modular RL framework that integrates distributed rollout collection and dynamic replay buffers for reproducible training at scale. SimpleRL-Zoo [Zeng et al., 2025] conducts zero-shot RL experiments across open-base LLMs to uncover emergent cognitive behaviors under minimal reward signals. Echo Chamber [Zhao et al., 2025] investigates how RL fine-tuning algorithms can amplify pretrained model biases and proposes regularization to mitigate over-amplification. Wen et al. [2024] decomposes high-level language actions into token-level operations to achieve finer-grained credit assignment. Some works push RL training for single-turn to multi-turn. Search-R1 [Jin et al., 2025] trains LLMs to orchestrate multi-turn search strategies with RL-optimized decision policies to improve question-answering accuracy. ArCHer [Zhou et al., 2024] employs a hierarchical, multi-turn RL architecture with manager and worker policies to efficiently handle long-horizon dialogue tasks. RAGEN [Wang et al., 2025] introduces trajectory filtering and critic modules within a multi-turn RL framework to stabilize learning and reduce shallow policy behaviors.", + "bbox": [ + 169, + 162, + 826, + 398 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "B Limitation and Future Work", + "text_level": 1, + "bbox": [ + 171, + 419, + 452, + 435 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "In this work, we only test ReMA on math and LLM-as-a-Judge benchmarks. Though the results show the effectiveness of ReMA, adopting ReMA to tasks where naturally needs multi-turn interaction between several interleaved agents has great potential. Moreover, a comprehensive understanding of the learning dynamics of multi-turn RL and multi-turn MARL for LLMs is needed. Finally, there's still sufficient space to further improve the procedure of multi-turn multi-agent rollout through modern LLM speed up techniques, e.g. prefetch-decode disaggregation and asynchronous rollout.", + "bbox": [ + 169, + 450, + 823, + 547 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "C Supplementary Materials for Method in Section 3", + "text_level": 1, + "bbox": [ + 171, + 568, + 625, + 585 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "C.1 Inference-time Scaling of ReMA", + "text_level": 1, + "bbox": [ + 171, + 599, + 442, + 616 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "In this section, we discuss how to enhance the inference-time computation of our hierarchical system, specifically focusing on the interaction between the high-level and low-level agents. The total number of model samples required for inference is determined by the product of the sampling budget allocated to each agent.", + "bbox": [ + 169, + 626, + 823, + 681 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "For instance, in a simple single-turn setting, if the high-level agent samples $k_{1}$ responses and each of these responses leads to $k_{2}$ samples from the low-level agent, the total number of model calls required is:", + "bbox": [ + 169, + 688, + 823, + 729 + ], + "page_idx": 20 + }, + { + "type": "equation", + "text": "\n$$\n\\text {T o t a l s a m p l e s} = k _ {1} \\times k _ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 411, + 731, + 583, + 746 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Given a fixed computational budget, an important question arises: how should the sampling budget be distributed between the high-level and low-level agents to maximize performance? Allocating more samples to the high-level agent may increase diversity in reasoning strategies while allocating more to the low-level agent may yield more refined solutions for a given metacognitive plan.", + "bbox": [ + 169, + 752, + 823, + 821 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Another crucial consideration is how to perform reranking on the final outputs. Two potential strategies include:", + "bbox": [ + 169, + 828, + 823, + 856 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "- Hierarchical reranking: First, for each high-level response, rank and aggregate the low-level responses under it. Then, rank the aggregated results across different high-level responses.", + "bbox": [ + 215, + 869, + 823, + 912 + ], + "page_idx": 20 + }, + { + "type": "page_number", + "text": "21", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "- Flat reranking: Directly rank all sampled responses together, regardless of the hierarchy of high-level reasoning steps.", + "bbox": [ + 215, + 90, + 823, + 119 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "Balancing sampling allocation and designing an effective reranking strategy are key challenges in efficiently scaling our multi-agent reasoning system. In the next section, we explore empirical results comparing different allocation strategies and ranking methods.", + "bbox": [ + 169, + 131, + 825, + 174 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "C.2 Detailed reward design", + "text_level": 1, + "bbox": [ + 171, + 189, + 377, + 205 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "As described in Sec. 3.2, we update both high-level and low-level agents by assigning rewards based on the low-level policy output. Below, we outline several potential reward designs:", + "bbox": [ + 169, + 214, + 823, + 244 + ], + "page_idx": 21 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Correctness reward: For tasks with explicit ground truth, we assign rewards based on the correctness of the low-level agent's output.", + "- Format reward: For tasks that require a specific output format, we enforce adherence to the prescribed structure by providing a format reward.", + "- To encourage the high-level agent to generate informative and unambiguous meta-thinking, and to stabilize the low-level outputs, we reward the high-level agent when the low-level agent produces consistent responses. Specifically, the consistency reward is defined as" + ], + "bbox": [ + 215, + 253, + 823, + 361 + ], + "page_idx": 21 + }, + { + "type": "equation", + "text": "\n$$\nR _ {h} = \\frac {\\text {m a x o c c u r r e n c e o f a n a n s w e r}}{\\text {t o t a l n u m b e r o f r e s p o n s e s}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 403, + 366, + 651, + 398 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "To examine multi-agent metacognition-integrated reasoning with different reward designs, we experiment with different reward function designs to encourage effective collaboration and structured reasoning. Below, we introduce and justify several reward schemes.", + "bbox": [ + 169, + 406, + 823, + 450 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "1. Correctness and Format-Aware Reward (Base Setting) In our primary reward setting, the system's overall correctness is used as the primary reward signal, supplemented by format-based rewards for both the high-level and low-level agents. Using mathematical problem-solving as an example:", + "bbox": [ + 169, + 462, + 825, + 518 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "- Low-level agent $(\\pi_{\\theta_l})$ : Receives a reward of $+1.0$ for a correct answer. If the answer is incorrect, the agent is further penalized based on format compliance. Specifically:", + "bbox": [ + 215, + 530, + 823, + 560 + ], + "page_idx": 21 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- If the output contains the designated answer-indicating format (e.g., boxed in Latex), it receives $-0.5$ .", + "- Otherwise, it receives $-1.0$ , as a missing format often suggests an incomplete or unstructured response." + ], + "bbox": [ + 243, + 561, + 823, + 619 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "- High-level agent $(\\pi_{\\theta_h})$ : Receives the average correctness of the low-level agent's sampled responses as its reward. Additionally, to prevent the high-level agent from directly generating explicit answers instead of guiding reasoning, a strong penalty of $-1.0$ is applied if it includes an explicit answer format (e.g., boxed).", + "bbox": [ + 215, + 625, + 825, + 681 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "2. Consistency-Based Reward Instead of using correctness as the high-level reward signal, this approach rewards the high-level agent for promoting consistent responses from the low-level agent, regardless of actual correctness. The consistency reward is defined as the proportion of the most frequently occurring answer among all sampled responses:", + "bbox": [ + 169, + 694, + 825, + 752 + ], + "page_idx": 21 + }, + { + "type": "equation", + "text": "\n$$\nR _ {h} = \\frac {\\text {m a x o c c u r r e n c e o f a n a n s w e r}}{\\text {t o t a l n u m b e r o f r e s p o n s e s}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 375, + 767, + 823, + 799 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "If the majority of responses do not contain a definitive answer, the reward is set to zero. We also add the format penalty to the high-level agent if its output contains the designated answer-indicating format. This incentivizes the high-level agent to guide the low-level agent toward more stable, detailed, reproducible outputs rather than erratic reasoning paths.", + "bbox": [ + 169, + 806, + 823, + 864 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "These different reward formulations allow us to investigate various dimensions of metacognitive reasoning: correctness, consistency, etc. We empirically compare their effects on learned metacognitive reasoning patterns in Sec. E.1.", + "bbox": [ + 169, + 869, + 823, + 912 + ], + "page_idx": 21 + }, + { + "type": "page_number", + "text": "22", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/315cafbb1d2055dded17eaabf88749be03cfea772911a86fa7b194d2357e1c64.jpg", + "image_caption": [ + "Figure 7: Our method can be viewed as a combination of practical TRPO and block coordinate ascent, with the high and low-level models treated as distinct components within a larger neural network. Note that the figure does not represent the exact gradient back-propagation flow but rather highlights the key idea that we separate the high- and low-level models. This separation allows for the independent computation of gradients and the independent training of each model." + ], + "image_footnote": [], + "bbox": [ + 200, + 95, + 763, + 306 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "C.3 Pseudocode of ReMA", + "text_level": 1, + "bbox": [ + 171, + 422, + 366, + 435 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "The pseudocode is shown in Algorithm 1.", + "bbox": [ + 171, + 450, + 447, + 465 + ], + "page_idx": 22 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Single turn MAMRP" + ], + "code_body": "Require: High-level policy $\\pi_h$ , Low-level policy $\\pi_l$ , Dataset $\\mathcal{D}$ , Optimizers for $\\pi_h$ and $\\pi_l$ . $\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}$ to filter training dataset \n1: Initialize $\\pi_h$ and $\\pi_l$ \n2: while not converged do \n3: build training dataset $\\mathcal{D}_l$ with $\\pi_h, \\pi_l, \\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}$ \n4: for Sample $(\\mathbf{x}, \\mathbf{m}, \\mathbf{y}^*) \\sim \\mathcal{D}_l$ do \n5: Generate $\\mathbf{y} \\sim \\pi_l(\\mathbf{x}, \\mathbf{m})$ \n6: Compute low-level reward $R_l(\\mathbf{y}, \\mathbf{y}^*)$ \n7: Update $\\pi_l$ using $\\nabla_{\\theta_l} \\mathbb{E}[R_l]$ \n8: end for \n9: build training dataset $\\mathcal{D}_h$ with $\\pi_h, \\pi_l, \\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}$ \n10: for Sample $(\\mathbf{x}, \\mathbf{y}^*) \\sim \\mathcal{D}_h$ do \n11: Generate $\\mathbf{m} \\sim \\pi_h(\\mathbf{x})$ and $\\mathbf{y} \\sim \\pi_l(\\mathbf{x}, \\mathbf{m})$ \n12: Compute high-level reward $R_h(\\mathbf{m}, \\mathbf{y}, \\mathbf{y}^*)$ \n13: Update $\\pi_h$ using $\\nabla_{\\theta_h} \\mathbb{E}[R_h]$ \n14: end for \n15: end while", + "bbox": [ + 173, + 507, + 823, + 743 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "C.4 Brief convergence analysis", + "text_level": 1, + "bbox": [ + 171, + 792, + 401, + 806 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "We reuse the notations from Sec. 3.2, where $\\mathbf{x}$ is task prompt, $\\mathbf{y}$ is generated answer, $\\mathbf{y}^*$ is groundtruth, $\\mathbf{m}$ is metacognition on task solving, $\\pi_{\\theta_h}$ and $\\pi_{\\theta_l}$ are high- and low-level agents with parameters $\\theta_h$ and $\\theta_l$ . We consider the joint hierarchical policy defined in Eq. (8) and update the objective as in Eq. (9).", + "bbox": [ + 169, + 821, + 823, + 878 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "To leverage existing RL and optimization convergence analysis methods, we treat the two models as components of a larger model, as illustrated in Fig. 7. When updating one model, we treat the other", + "bbox": [ + 169, + 883, + 823, + 912 + ], + "page_idx": 22 + }, + { + "type": "page_number", + "text": "23", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "model as part of a stationary environment. The gradients with respect to $\\theta_h$ and $\\theta_l$ are:", + "bbox": [ + 171, + 90, + 740, + 106 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\theta_ {h}} J (\\theta_ {h}, \\theta_ {l}) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\sum_ {\\mathbf {m} \\sim \\pi_ {h} (\\mathbf {m} | \\mathbf {x}; \\theta_ {h})} \\nabla_ {\\theta_ {h}} \\pi_ {h} (\\mathbf {m} | \\mathbf {x}; \\theta_ {h}) \\left[ \\mathbb {E} _ {\\mathbf {y} \\sim \\pi_ {l} (\\mathbf {y} | \\mathbf {x}, \\mathbf {m})} R (\\mathbf {y}, \\mathbf {y} ^ {*}) \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 112, + 767, + 146 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\theta_ {l}} J (\\theta_ {h}, \\theta_ {l}) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\sum_ {\\mathbf {y} \\sim \\pi (\\theta_ {h}, \\theta_ {l})} \\nabla_ {\\theta_ {l}} \\pi_ {l} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}; \\theta_ {h}); \\theta_ {l}) R (\\mathbf {y}, \\mathbf {y} ^ {*}).\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 148, + 671, + 183 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "We can compute the gradients with log trick and estimate $\\mathbb{E}_{\\mathbf{y}\\sim \\pi_l(\\mathbf{y}|\\mathbf{x},\\mathbf{m})}R(\\mathbf{y},\\mathbf{y}^*)$ with Monte Carlo method.", + "bbox": [ + 169, + 188, + 823, + 215 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Equipped with the objective function and gradient computation, we update the models iteratively. Without loss of generality, we analyze the case where the high-level policy is updated first:", + "bbox": [ + 169, + 223, + 823, + 252 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {h} ^ {(t + 1)} = \\arg \\max _ {\\theta_ {h}} J (\\theta_ {h}, \\theta_ {l} ^ {(t)}),\n$$\n", + "text_format": "latex", + "bbox": [ + 388, + 256, + 593, + 282 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {l} ^ {(t + 1)} = \\arg \\max _ {\\theta_ {l}} J \\left(\\theta_ {h} ^ {(t + 1)}, \\theta_ {l}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 392, + 285, + 604, + 310 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Regarding the different regularizations $R_{h}$ and $R_{l}$ in Eqs. (10) and (11) for the different policies, instead of directly integrating them into the loss function, we treat them as constraints, as done in Trust Region Policy Optimization (TRPO) [Schulman et al., 2015]. Note that when one policy is fixed, the other policy operates in a stationary decision process.", + "bbox": [ + 169, + 316, + 823, + 372 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Based on the defined objective and update method, we apply TRPO and block coordinate ascent. First, recall that when updating a single policy, TRPO guarantees monotonic improvement by optimizing a lower bound. Specifically, let $\\pi_{\\mathrm{old}}$ and $\\pi$ represent the old and current policies, respectively. We define a surrogate objective as:", + "bbox": [ + 169, + 378, + 823, + 435 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\pi_ {\\mathrm {o l d}}} (\\pi) = \\mathbb {E} _ {s \\sim \\pi_ {\\mathrm {o l d}}, a \\sim \\pi_ {\\mathrm {o l d}}} \\left[ \\frac {\\pi (a | s)}{\\pi_ {\\mathrm {o l d}} (a | s)} A ^ {\\pi_ {\\mathrm {o l d}}} (s, a) \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 334, + 440, + 661, + 474 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "As shown by Schulman et al. [2015], the true objective of $\\pi$ is lower-bounded by:", + "bbox": [ + 171, + 477, + 707, + 492 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\nJ (\\pi) \\geq L _ {\\pi_ {\\mathrm {o l d}}} (\\pi) - C \\cdot \\max _ {s} \\mathrm {K L} [ \\pi_ {\\mathrm {o l d}} (\\cdot | s), \\pi (\\cdot | s) ],\n$$\n", + "text_format": "latex", + "bbox": [ + 323, + 496, + 671, + 518 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "for some constant $C$ . By optimizing the right-hand side of the above inequality, we are guaranteed to improve the performance of $\\pi$ . Therefore, for policies $\\pi^t$ and $\\pi^{t + 1}$ obtained from iterations $t$ and $t + 1$ using the TRPO method, we have:", + "bbox": [ + 169, + 523, + 823, + 565 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\nJ (\\pi^ {t + 1}) \\geq J (\\pi^ {t}).\n$$\n", + "text_format": "latex", + "bbox": [ + 434, + 569, + 558, + 588 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Now, returning to our updating method, we treat the high- and low-level policies as two blocks of a single agent. The iterative update process can thus be viewed as a cyclic block coordinate ascent, where the two policies are updated in a fixed order. By updating each block using the TRPO method, and improving the surrogate objective within the KL constraint, each block update does not decrease $J$ :", + "bbox": [ + 169, + 598, + 823, + 666 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\nJ \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t}\\right) \\geq J \\left(\\theta_ {h} ^ {t}, \\theta_ {l} ^ {t}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 398, + 672, + 566, + 689 + ], + "page_idx": 23 + }, + { + "type": "equation", + "text": "\n$$\nJ \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t + 1}\\right) \\geq J \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 401, + 691, + 596, + 710 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Thus $J(\\theta_h^{t + 1},\\theta_l^{t + 1})\\geq J(\\theta_h^t,\\theta_l^t)$ . This repeated coordinate maximization converges to a fixed point, where no single coordinate update can further improve $J(\\theta_h,\\theta_l)$ .", + "bbox": [ + 169, + 722, + 823, + 753 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Given the theoretical monotonic improvement with TRPO and block coordinate ascent, we adopt a practical version of TRPO in our experiments, specifically Proximal Policy Optimization (PPO) [Schulman et al., 2017] or GRPO [Shao et al., 2024].", + "bbox": [ + 169, + 758, + 823, + 801 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "C.5 Learning to reason from the perspective of Leader Follower Game", + "text_level": 1, + "bbox": [ + 169, + 816, + 678, + 830 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Besides the loss function in the main part, we also propose to frame the problem as a leader-follower game. By analyzing the equilibria of the leader-follower game, we demonstrate that our framework inherently identifies the optimal sub-tasks aligned with the capabilities of the low-level model. This ensures that the high-level decisions are guided by the low-level model's strengths, leading to more efficient and targeted task decomposition.", + "bbox": [ + 169, + 842, + 825, + 912 + ], + "page_idx": 23 + }, + { + "type": "page_number", + "text": "24", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "C.5.1 Leader-follower game", + "text_level": 1, + "bbox": [ + 171, + 90, + 382, + 107 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "The leader-follower game, also known as the Stackelberg game, models interaction between two agents with parametrized strategies $\\pmb{\\theta} = (\\pmb{\\theta}_1, \\pmb{\\theta}_2)$ and differentiable objective functions $(\\mathcal{L}_1, \\mathcal{L}_2): \\mathbb{R}^d \\to \\mathbb{R}$ . In this framework, the leader announces its strategy first, and the follower observes this decision to respond optimally. This sequential structure enables the leader to anticipate the follower's reaction and adjust its strategy accordingly. A Stackelberg equilibrium occurs when neither agent can unilaterally improve its objective. Denoting $\\pmb{\\theta}_1$ as the leader's strategy and $\\pmb{\\theta}_2$ as the follower's, the loss functions $\\mathcal{L}_1$ and $\\mathcal{L}_2$ are optimized with the following bi-level structure:", + "bbox": [ + 169, + 114, + 823, + 213 + ], + "page_idx": 24 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\theta} _ {1} ^ {*} = \\operatorname {a r g m i n} _ {\\boldsymbol {\\theta} _ {1}} \\mathcal {L} _ {1} (\\boldsymbol {\\theta}, \\boldsymbol {\\theta} _ {2} ^ {*} (\\boldsymbol {\\theta} _ {1})), \\quad \\boldsymbol {w} _ {2} ^ {*} (\\boldsymbol {\\theta} _ {1}) = \\operatorname {a r g m i n} _ {\\boldsymbol {\\theta} _ {2}} \\mathcal {L} _ {2} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}).\n$$\n", + "text_format": "latex", + "bbox": [ + 281, + 218, + 712, + 237 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Anil et al. [2021] apply the leader-follower game to ensure checkable answers in a prover-verifier game (PVG). The objective is a verifier that is both complete (accepts all correct proofs from a verifier) and sound (rejects all incorrect proofs from a verifier). They analyze different scenarios where the verifier acts as the leader, the prover as the follower, and both announce strategies simultaneously, forming a Nash equilibrium. The study concludes that in verifier-led SVG, a Stackelberg equilibrium is both necessary and sufficient for achieving a sound and complete verifier, whereas in other configurations, a Stackelberg equilibrium is not necessary or sufficient for this outcome.", + "bbox": [ + 169, + 246, + 823, + 344 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "C.5.2 Efficacy of LLM", + "text_level": 1, + "bbox": [ + 171, + 358, + 344, + 372 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Because the high-level policy possesses strong generalization capabilities, it is impractical for it to exhaustively explore every potential sub-task for each question. Instead, it naturally focuses on tasks within a feasible range of difficulty, leveraging only a limited set of coarse planning actions. Rather than pinpointing perfectly tailored sub-tasks, the policy searches for general tasks of particular computational complexity, i.e., difficulty, that it can handle reliably. Motivated by this perspective, we incorporate the concept of a reasoning boundary for large language models (LLMs) [Chen et al., 2024b]. Intuitively, the reasoning boundary circumscribes the maximum difficulty of problems a model can solve at a desired accuracy level. Formally, for a model $\\theta$ , a task $t$ , and a predefined threshold $A$ , the reasoning boundary of $\\theta$ represents the maximum problem difficulty $d$ that satisfies:", + "bbox": [ + 169, + 381, + 823, + 518 + ], + "page_idx": 24 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {B} _ {A c c = A} (t | \\theta) = \\sup _ {d} \\{d | A c c (t | d, \\theta) = A \\}.\n$$\n", + "text_format": "latex", + "bbox": [ + 359, + 523, + 635, + 547 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "where $d$ denotes the problem difficulty. By quantifying the difficulty level a model can reliably handle, the reasoning boundary provides a systematic way to align the high-level policy's focus with the model's actual capabilities, gauge the efficacy of the low-level policy, and determine the optimal strategy for solving the question.", + "bbox": [ + 169, + 554, + 823, + 609 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "C.5.3 Leader-follower Game for LLM Reasoning", + "text_level": 1, + "bbox": [ + 169, + 625, + 529, + 640 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Our goal is to find the high-level policy that searches for the sub-task sequence based on the efficacy of the low-level policy to solve the question. We design the loss functions as follows:", + "bbox": [ + 169, + 648, + 823, + 676 + ], + "page_idx": 24 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {h} = \\mathbb {E} _ {(x, y) \\sim p _ {D}, t _ {1: K}} \\left[ - \\log \\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}, y _ {1: K - 1}\\right) \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 313, + 683, + 669, + 699 + ], + "page_idx": 24 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {l} = \\mathbb {E} _ {x \\sim p _ {D}, t _ {1: k} \\sim \\pi_ {h}, \\hat {y} _ {k} \\sim \\pi_ {l}} \\left[ - r \\left(y _ {k}, \\hat {y} _ {k} \\mid x, t _ {1: k}, y _ {1: k - 1}\\right) \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 313, + 702, + 683, + 717 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "where $r(y_k, \\hat{y}_k \\mid x, t_{1:k}, y_{1:k-1})$ represents the step reward for the correctness of $\\hat{y}_k$ derived from the question $x$ , the sub-task sequence $t_{1:k}$ from the high policy and prior intermediate answer $y_{1:k-1}$ . The loss functions can be interpreted as follows: the high-level policy is incentivized to find subtasks that lead to the correct answer based on the capabilities of the low-level policy, while the low-level policy is incentivized to enhance its instruction-following ability.", + "bbox": [ + 169, + 722, + 823, + 792 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "How to minimize the loss functions and whether such minimization leads to the desired results remain questions. To explore this, we consider a simplified case of our method, where the high-level policy plans the complete sub-task sequence at the beginning and the low-level executes the instruction in a single interaction. The corresponding parameterized policies are defined as $\\pi_h((t_1,\\ldots ,t_K)\\mid x)$ and $\\pi_l((\\hat{y}_1,\\dots ,\\hat{y}_K)\\mid x,(t_1,\\dots ,t_K))$ . The corresponding loss functions are:", + "bbox": [ + 169, + 797, + 823, + 869 + ], + "page_idx": 24 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {h} = \\mathbb {E} _ {(x, y) \\sim p _ {D}, t _ {1: K}} \\left[ - \\log \\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}\\right) \\right], \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 313, + 875, + 821, + 888 + ], + "page_idx": 24 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {l} = \\mathbb {E} _ {x \\sim p _ {D}, t _ {1: k} \\sim \\pi_ {h}, \\hat {y} _ {k} \\sim \\pi_ {l}} \\left[ - r \\left(y _ {k}, \\hat {y} _ {k} \\mid x, t _ {1: k}, y _ {1: k - 1}\\right) \\right]. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 313, + 893, + 821, + 907 + ], + "page_idx": 24 + }, + { + "type": "page_number", + "text": "25", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "In this step, the high-level policy generates the entire sub-task sequence without relying on intermediate answers, while the low-level policy follows the sequence to produce answers for the sub-tasks. The low-level policy can still leverage prior intermediate answers to sequentially refine its responses.", + "bbox": [ + 169, + 90, + 823, + 133 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "To analyze the result agents by minimizing the loss functions, we adopt the completeness and soundness properties from the PVG framework for LLM reasoning. Specifically, if the high-level policy generates a sub-task sequence that is executable within the low-level policy's capabilities, the problem must be solved (completeness). Conversely, if the sub-task sequence is incorrect or beyond the low-level policy's capacity, the problem cannot be solved (soundness). To achieve this, we utilize the conclusion from Anil et al. [2021], which positions the low-level policy as the leader and the high-level policy as the follower, equilibria guarantee the complete and sound low-level policy.", + "bbox": [ + 169, + 138, + 823, + 238 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "When the high-level policy takes the lead, the low-level policy is forced to adapt to the specific strategy defined by the high-level policy, which can result in neither complete nor sound low-level policy. For example, if the high-level policy dictates that it will only generate sub-tasks involving addition and subtraction, the low-level policy is constrained to optimize only for these tasks. While they may reach an equilibrium, the low-level policy remains incomplete, and this limitation impacts both policies. In the case of the simultaneous PVG game, convergence to a Nash equilibrium is possible, but it is not sufficient for completeness and soundness. For instance, the low-level policy might disregard the high-level policy entirely (e.g., if the high-level provides incorrect instructions, but the low-level still performs correctly). This approach, however, is challenging to implement due to the significantly larger search space involved.", + "bbox": [ + 169, + 242, + 826, + 381 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "Furthermore, the loss functions we design ensure that, at a Stackelberg equilibrium, the high-level policy identifies sub-task sequences that the low-level policy can execute to solve the problem with the highest probability. With the low-level policy acting as the leader, it establishes its reasoning boundary for tasks. Based on the reasoning boundary, let $\\theta_h$ and $\\theta_l$ represent the policy parameters for the high-level and low-level policies, respectively. The probability that the low-level policy correctly solves the question is defined as:", + "bbox": [ + 169, + 387, + 823, + 470 + ], + "page_idx": 25 + }, + { + "type": "equation", + "text": "\n$$\n\\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}\\right) = \\prod_ {k = 1} ^ {K} \\operatorname {A c c} \\left(t _ {k} \\mid x, \\theta_ {l}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 367, + 476, + 627, + 517 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "where we can compute the difficulty $d_{k}$ from $t_k$ and $x$ . where the difficulty $d_{k}$ can be derived from $t_k$ and $x$ . The loss function in Eq. (15) ensures that the selected sub-tasks are optimal for the low-level policy. Here we provide a theoretical condition under which the most efficient solution strategy can be identified, according to the efficacy of the LLM.", + "bbox": [ + 169, + 523, + 823, + 579 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "This approach can be viewed as a game between a high-level \"prover\" and a low-level \"verifier\". The verifier, representing the low-level policy, adheres the high-level policy's instructions to validate its reasoning. Unlike the classic PVG setting, where the prover has ground-truth labels, the label of our high-level policy depends on the tunable low-level policy. This distinction, where the low-level policy (leader) is inherently more complex, contrasts with traditional PVG setups and adds complexity due to the interdependence between the high- and low-level policies.", + "bbox": [ + 169, + 585, + 823, + 669 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "By framing the problem-solving process as a leader-follower game, with the low-level policy designated as the leader, we can construct a bi-level optimization problem to identify an equilibrium. Following the formulation in Sec. C.5.1, the problem is expressed as:", + "bbox": [ + 169, + 674, + 823, + 717 + ], + "page_idx": 25 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {l} ^ {*} = \\underset {\\theta_ {l}} {\\arg \\min } \\mathcal {L} _ {l} (\\theta_ {h} ^ {*} (\\theta_ {l}), \\theta_ {l}) \\quad \\theta_ {h} ^ {*} (\\theta_ {l}) = \\underset {\\theta_ {l}} {\\arg \\min } \\mathcal {L} _ {h} (\\theta_ {h}, \\theta_ {l}).\n$$\n", + "text_format": "latex", + "bbox": [ + 297, + 720, + 696, + 747 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "Then we can apply bi-level optimization techniques.", + "bbox": [ + 171, + 752, + 517, + 767 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "D Training Details", + "text_level": 1, + "bbox": [ + 171, + 786, + 346, + 803 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "D.1 Single-turn ReMA", + "text_level": 1, + "bbox": [ + 171, + 816, + 346, + 830 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "We refer to Appendix G for prompts we use during training. We implement the training pipeline with OpenRLHF [Hu et al., 2024a] which is a highly efficient codebase and is easy to scale up. We select REINFORCE++ to save resources and for efficient training. All experiments are conducted in a node of 8 NVIDIA A100 GPUs. We use bf16, Zero2, Flash-Attention and gradient checkpointing to run our experiments.", + "bbox": [ + 169, + 840, + 823, + 912 + ], + "page_idx": 25 + }, + { + "type": "page_number", + "text": "26", + "bbox": [ + 488, + 935, + 509, + 946 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "During rollout, we set temperature $= 1.0$ , top_p $= 1.0$ , top_k $= -1$ , and use vLLM for inference acceleration. We set the max generation length to be 2048 and, the rollout batch size to be 1000. The number of samples per prompt is 4. During training, we use Adam Optimizer with a learning rate of 5e-7. We set the mini-batch size to be 500, and the clip ratio to be 0.2. Other hyperparameters, such as KL coefficients and the number of training episodes, were carefully tuned based on validation set performance to ensure robust and reliable results. To align with the hyperparameter in OpenRLHF, we use #Training Episode as the number of reinforcement learning epoch on the entire dataset.", + "bbox": [ + 169, + 90, + 823, + 188 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "In ReMA, during prompt filtering of the high-level model, the high-level agent first samples 10 candidates for each question with $t = 1.0$ , and for each output the low-level agents sample 1 solution with $t = 0.0$ , then we select questions of success rate between $[\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}]$ . And for the low-level agent's prompt filtering, the high-level agent first samples 1 candidate for each question with $t = 0.0$ and for each output the low-level agents sample 10 solutions with $t = 1.0$ , then we select questions of success rate between $[\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}]$ and use the high-level agent to sample 4 meta-thoughts with $t = 1.0$ as the input.", + "bbox": [ + 169, + 194, + 826, + 294 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "D.1.1 Supervised fine-tuning data collection", + "text_level": 1, + "bbox": [ + 171, + 306, + 491, + 321 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "For experiments in Sec. 4.2.1, we collect expert data to enhance the reasoning pattern, i.e. $RL$ from SFT. Specifically, we collect demonstration data from GPT-4o Mini on MATH training dataset (7.5k problems) Hendrycks et al. [2021] and use it to fine-tune the LLMs. The data generation follows these steps: First, we prompt GPT-4o Mini to produce metacognitive reasoning for high-level model training. Specifically, we use different prompts to instruct it to rewrite and decompose a given question without providing a final answer. We collect metacognitive reasoning using two predefined actions, \"rewrite\" and \"decompose\", which align with human approaches to complex problem-solving while preserving answer diversity. Next, we use the generated instructions to prompt GPT-4o Mini to follow the metacognitive steps and solve the question, obtaining SFT data for low-level policy training. Below, we present the prompts used for both high-level and low-level models. Prompts can be found in Appendix G.1.1.", + "bbox": [ + 169, + 329, + 826, + 482 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "D.1.2 Dataset Curation of RewardBench970", + "text_level": 1, + "bbox": [ + 171, + 496, + 493, + 510 + ], + "page_idx": 26 + }, + { + "type": "table", + "img_path": "images/13ee9b755412f0ddda27dfb3a4338a0ead1c5a78cddf2ef644b3f886d89c5815.jpg", + "table_caption": [ + "Table 2: Performance on LLM-as-a-Judge benchmarks, trained on dataset under the loose setting. The two-agent workflow in ReMA" + ], + "table_footnote": [], + "table_body": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3.1-8B-InstructRewardBench97071.2481.86 (+10.62)80.41 (+9.17)86.29 (+15.05)
JudgeBench51.7751.45 (-0.32)50.65 (-1.12)53.71 (+1.94)
Average61.5166.65 (+5.14)65.53 (+4.02)70.00 (+8.49)
Qwen2.5-7B-InstructRewardBench97086.4987.22 (+0.73)80.31 (-6.18)90.72 (+4.23)
JudgeBench58.3954.84 (-3.55)55.81 (-2.58)58.71 (+0.32)
Average72.4471.03 (-1.41)68.06 (-4.38)74.72 (+2.28)
", + "bbox": [ + 179, + 561, + 818, + 702 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "We process the original dataset in RewardBench by splitting it into a training set containing 5,000 tuples of (instruction, response A, response B) and a test set with the remaining 970 tuples.", + "bbox": [ + 169, + 717, + 823, + 747 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "To ensure a meaningful dataset split, we validate two separation strategies:", + "bbox": [ + 171, + 752, + 663, + 767 + ], + "page_idx": 26 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Loose setting: We only ensure that there is no direct overlap of tuples between the training and test sets.", + "- Strict setting: We further enforce that no instruction appears in both the training and test sets. The results for this setting are presented in the main results (Table 1b)." + ], + "bbox": [ + 215, + 777, + 823, + 838 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "Additionally, since the original RewardBench data originates from different subsets, we ensure that all original subsets are evenly represented in both the training and test sets.", + "bbox": [ + 169, + 848, + 823, + 877 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "Table 2 reports the learning performance of various methods under the loose dataset split setting. Compared to the results in Table 1b, ReMA significantly outperforms other RL tuning baselines", + "bbox": [ + 169, + 883, + 823, + 912 + ], + "page_idx": 26 + }, + { + "type": "page_number", + "text": "27", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "across all models, particularly on out-of-distribution (OOD) benchmarks. The consistent improvements on OOD datasets of these two settings suggest that ReMA enhances meta-thinking ability, resulting in better generalization across diverse task distributions.", + "bbox": [ + 169, + 90, + 823, + 133 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "D.1.3 Training on MATH", + "text_level": 1, + "bbox": [ + 171, + 148, + 366, + 162 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "VRP For Llama3-8B-Instruct, Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 12,6,6 for these 3 models respectively. For Llama3-8B-Instruct, we set the learning rate of 2e-7 for stable training.", + "bbox": [ + 169, + 172, + 823, + 214 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "MRP For Llama3-8B-Instruct, Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 10,6,6 for these 3 models respectively.", + "bbox": [ + 169, + 229, + 823, + 258 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "MAMRP We use $\\varepsilon_{\\mathrm{min}} = 0.2, \\varepsilon_{\\mathrm{max}} = 0.8$ for prompt filtering. We use the same #Training Episode=4 for all models, and for #Update Iteration, we use 3 for Llama3-8B-Instruct and Llama3.1-8B-Instruct, 10 for Qwen2.5-7B-Instruct. And we set the KL coefficient to be 1e-2 for all the 3 models.", + "bbox": [ + 169, + 272, + 823, + 328 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "D.1.4 Training on Reward Bench", + "text_level": 1, + "bbox": [ + 171, + 343, + 416, + 358 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "VRP For Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 4,6 for these 2 models respectively.", + "bbox": [ + 169, + 367, + 823, + 397 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "MRP For Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 4,6 for these 2 models respectively.", + "bbox": [ + 169, + 410, + 823, + 439 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "MAMRP We set #Update Iteration=1 for all models. We set the KL coefficient to be 1e-2 for Llama3.1-8B-Instruct and 1e-2 for Qwen2.5-7B-Instruct all models. For Llama3.1-8B-Instruct, we use $\\varepsilon_{\\mathrm{min}} = 0.2$ , $\\varepsilon_{\\mathrm{max}} = 0.8$ for prompt filtering and we use #Training Episode of 2 during training. For Llama3.1-8B-Instruct, we use $\\varepsilon_{\\mathrm{min}} = 0.1$ , $\\varepsilon_{\\mathrm{max}} = 0.9$ for prompt filtering and we use #Training Episode of 1 during training.", + "bbox": [ + 169, + 454, + 823, + 525 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "D.2 Multi-turn ReMA", + "text_level": 1, + "bbox": [ + 171, + 541, + 341, + 555 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "We refer to Appendix G for prompts we use during training. We implement a multi-turn ReMA training pipeline with VeRL [Sheng et al., 2024] since it's easier to implement complex training pipeline with a single centralized controller. Similar to OpenRLHF, VeRL is also a highly efficient and scalable codebase for further development.", + "bbox": [ + 169, + 566, + 823, + 622 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "For the multi-turn ReMA rollout, we use parameter sharing and simultaneous update by default. In details, we maintain two message lists with the system prompt of meta-thinking agent and reasoning agent respectively. During rollout, each agent acts as 'assistant' in its own message list and the other agent acts as 'user'. We use three hyperparameters to control the rollout length: (1) 'max_num_turns': the maximum number of turns for each trajectory. (2) 'max_response_length': the maximum number of tokens for each turn's response. (3) 'max_prompt_length': the maximum number of tokens for each trajectory.", + "bbox": [ + 169, + 628, + 823, + 726 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "During training, we apply the collected message list to Qwen2.5-7B's chat template and build loss masks in order to compute the loss for all turns of one trajectory (message list).", + "bbox": [ + 169, + 731, + 823, + 761 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "Moreover, for multi-turn ReMA rollout, unlike single agent single turn rollout, we need to carefully design the termination logic. Basically, we let the meta-thinking agent automatically decide when to finish the solving procedure, we use a special tag '[FINISH]' to indicate the end of the solving procedure. After we detect this tag, we will terminate trajectory after the reasoning agent generates its output.", + "bbox": [ + 169, + 766, + 823, + 835 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "We also design other termination conditions to ensure the quality of the generated trajectories. If the last agent's response is too long, we will terminate the whole trajectory and setting the reward to 0. We also introduce a different version of format reward: we give a reward of 1.0 only if the reasoning agent's last turn response is correct and the meta-thinking agent's last turn response include '[FINISH]'. We use math_check as the default verifier.", + "bbox": [ + 169, + 842, + 825, + 911 + ], + "page_idx": 27 + }, + { + "type": "page_number", + "text": "28", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "D.2.1 SFT data collection of multi-turn MAMRP", + "text_level": 1, + "bbox": [ + 171, + 90, + 527, + 104 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "We use GPT-4o to translate 817 samples in LIMO [Ye et al., 2025c] by prompting it to wrap each sentence with meta-thinking and reasoning tags. We use a temperature of 0. After filtering, we get 800 conversations for training. The prompt can be found in Appendix G.2.1. For supervised finetuning, we use LlamaFactory as the codebase and train the model for 3 epochs with a learning rate of 1e-5, consine learning rate scheduler, and batch size of 8. Use DeepSpeed Zero2 for distributed training.", + "bbox": [ + 169, + 117, + 823, + 202 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "D.2.2 Training on MATH", + "text_level": 1, + "bbox": [ + 171, + 222, + 366, + 237 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "For training of multi-turn ReMA on MATH, we use GRPO [Shao et al., 2024] as the default learning algorithm. We refer to Appendix G.2.2 for prompts. For experiment in Sec 4.3, we use sample 128 prompts, each with 16 trajectories. During training, we drop the KL loss term to improve the numerical stability. We use a learning rate of 1e-6, bfloat16 precision, FSDP backend for distributed training. We split the rollout data into 4 mini-batches for update. For the sake of numerical stability, we do pre-clip before computing the exponential of log-prob for a upperbound of 3.0.", + "bbox": [ + 169, + 248, + 823, + 333 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "For the main result in Fig 5, we test different rollout configurations with a max_prompt_length of 4096, training for 500 steps. We use 32 NVIDIA A800 GPUs, the longest training cost about 40 hours due to large scale validation per 10 steps.", + "bbox": [ + 169, + 338, + 823, + 380 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "For the ablation results in Fig 6, we use a tiny subset of MATH Level 3-5, training for 300 steps. Specifically, we sample 19 questions for every single type (133 instances in total). We use 8 NVIDIA A800 GPUs, the training cost about 30 hours", + "bbox": [ + 169, + 386, + 823, + 429 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "We test different rollout configurations:", + "bbox": [ + 171, + 435, + 433, + 448 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "(1) max_num_turns=30, max_response_length=256, max_prompt_length=4096 (2) \nmax_num_turns=30, max_response_length=1024, max_prompt_length=3072", + "bbox": [ + 169, + 449, + 823, + 477 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "And for the experiment of separate parameter in multi-turn ReMA, we iteratively train each agent with the same configuration as above, but with a switch interval of 10 steps, starting from the metathinking agent.", + "bbox": [ + 169, + 483, + 823, + 526 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "E Other Experiments", + "text_level": 1, + "bbox": [ + 171, + 551, + 372, + 568 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "E.1 Reward functions shape cross-agent behaviors", + "text_level": 1, + "bbox": [ + 171, + 585, + 539, + 601 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "We also investigate the impact of different reward function designs on ReMA's behavior. In addition to the base reward setting described in Appendix C.2, we evaluate a consistency-based reward function using Qwen2.5-7B-Instruct. This reward function is designed to encourage the high-level agent to generate more detailed guidance. Indeed, we observe that the high-level agent trained in this manner produces more detailed solution steps compared to the one trained with the basic correctness format reward. However, we also find that this approach often leads to jailbreak behavior, where the high-level agent tends to include the final answer within its output, compromising the intended hierarchical reasoning process.", + "bbox": [ + 169, + 614, + 823, + 726 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "Furthermore, we discover an interesting evolution of a pattern during training: although our experimental setup is designed for the high-level agent to provide a solution plan while the lower-level agent executes it, we find that under the consistency-based reward, the lower-level agent significantly increases its attempt of verification rather than straightforward execution. We observed a certain sentence commonly appearing in the low-level agent's responses: \"Let's go through the solution step by step to ensure clarity and correctness.\" To quantify this effect, we track the frequency of it. We analyze this pattern across all mathematical test sets, sampling eight completions per question at a temperature of 0.7. Our empirical results have identified a $30\\mathrm{x}$ increase of such self-verifying patterns in the model trained with the consistency-based reward compared to the one trained with the base reward. Moreover, we also observe additional variations of this pattern, e.g. \"Let's carefully re-evaluate the problem and solution to ensure accuracy and clarity.\" These phrases indicate that the low-level agent is actively exploring to verify the detailed response provided by the high-level agent.", + "bbox": [ + 169, + 731, + 826, + 912 + ], + "page_idx": 28 + }, + { + "type": "page_number", + "text": "29", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "This suggests that (1) meta-thinking can not only emerge and be reinforced in the high-level agent but also in the low-level agent. During reinforcement learning (RL) training, the two agents develop a novel problem-solving pattern characterized by a role reversal. (2) Consistency-based rewards promote a more self-corrective approach at the lower level, potentially disrupting the intended separation of roles between planning and execution. For a detailed case study, refer to Appendix F.2.", + "bbox": [ + 169, + 90, + 823, + 161 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "E.2 Detailed Training Curves on Different Datasets of Multi-turn ReMA", + "text_level": 1, + "bbox": [ + 171, + 176, + 689, + 191 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "We show the detailed training curves of the multi-turn ReMA on different datasets in Fig. 8.", + "bbox": [ + 171, + 202, + 772, + 217 + ], + "page_idx": 29 + }, + { + "type": "image", + "img_path": "images/3a07830c095bd1b0e7d492fba662d270532fb4263b681ea523bd6daaeb0902da.jpg", + "image_caption": [ + "Figure 8: Detailed Training Curves on Different Datasets of Multi-turn ReMA" + ], + "image_footnote": [], + "bbox": [ + 176, + 232, + 823, + 483 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "F Qualitative Results", + "text_level": 1, + "bbox": [ + 171, + 539, + 369, + 556 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "F.1 High-level policy finds better plans", + "text_level": 1, + "bbox": [ + 171, + 569, + 455, + 585 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "Here is an example of how a high-level policy alters the solving method of an LLM, increasing the likelihood of providing correct answers. As we can see from the following example, without the high-level policy, the LLM counts all integer coordinates, including those on the boundary, and then subtracts the boundary coordinates. In contrast, the high-level policy identifies a better approach, directly instructing the LLM to count only the coordinates strictly inside the boundary.", + "bbox": [ + 169, + 595, + 823, + 666 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "F.2 Case study for Experiments in Section E.1", + "text_level": 1, + "bbox": [ + 171, + 681, + 504, + 696 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "Fig. 10 and Fig. 11 show an case study of experiments in Sec. E.1.", + "bbox": [ + 171, + 707, + 609, + 722 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "Although both agents are prompted with the same instructions as in our main results, the consistency reward of the high-level agent significantly alters the learning dynamics. As illustrated in Fig. 10, the high-level agent generates detailed solution attempts rather than a strategic plan. Consequently, the low-level agent evolves to verify the high-level agent's solutions. This suggests that, during reinforcement learning (RL) training, the two agents develop a novel problem-solving pattern characterized by a role reversal, where one agent generates an answer while the other verifies it.", + "bbox": [ + 169, + 727, + 823, + 811 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "F.3 Case study for Experiments in Section 4.2.2", + "text_level": 1, + "bbox": [ + 171, + 827, + 516, + 842 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "Fig. 12 shows the detailed outputs of the two groups of LLMs trained in JSON action. The outputs finally converge to relative easier and shorter sentences, compared to our main experiments. This may due to insufficient capacity of a small LM to produce a valid JSON-format response while simultaneously exploring diverse reasoning strategies.", + "bbox": [ + 169, + 852, + 823, + 907 + ], + "page_idx": 29 + }, + { + "type": "page_number", + "text": "30", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "Consider the rectangular region with the following points as vertices: $(5,4),(-5,4),(-5, - 4),(5, - 4)$ . How many points with integer coordinates will be strictly in the interior of this rectangular region?", + "bbox": [ + 187, + 99, + 805, + 119 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Output without high-level planning solves this question in a less optimal way, leading to a wrong answer:", + "text_level": 1, + "bbox": [ + 217, + 126, + 465, + 145 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "To determine how many points with integer coordinates will be strictly in the interior of the rectangular region with vertices at $(5,4)$ , $(-5,4)$ , $(-5, - 4)$ , and $(5, - 4)$ , we will follow these steps:", + "bbox": [ + 187, + 151, + 495, + 179 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "1. Identify the dimensions of the rectangle:", + "bbox": [ + 189, + 179, + 356, + 186 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "- The width of the rectangle can be calculated as the distance between the x-coordinates of the vertices. The x-coordinates are $-5$ and 5.", + "bbox": [ + 187, + 188, + 491, + 205 + ], + "page_idx": 30 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {W i d t h} = 5 - (- 5) = 1 0\n$$\n", + "text_format": "latex", + "bbox": [ + 290, + 212, + 393, + 223 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "- The height of the rectangle can be calculated as the distance between the y-coordinates of the vertices. The y-coordinates are 4 and -4.", + "bbox": [ + 187, + 229, + 491, + 247 + ], + "page_idx": 30 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {H e i g h t} = 4 - (- 4) = 8\n$$\n", + "text_format": "latex", + "bbox": [ + 292, + 253, + 392, + 263 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "2. Calculate the total number of integer points: - The total number of integer points in the rectangle (including the boundary) can be calculated by considering the range of x and y values: - The x-values range from $-5$ to 5, giving us 11 integer values $(-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)$ . - The y-values range from $-4$ to 4, giving us 9 integer values (", + "bbox": [ + 186, + 270, + 488, + 315 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "$-4, -3, -2, -1, 0, 1, 2, 3, 4)$ . The total number of points in the rectangle (including the boundary) is:", + "bbox": [ + 187, + 316, + 480, + 333 + ], + "page_idx": 30 + }, + { + "type": "equation", + "text": "\n$$\n\\text {T o t a l p o i n t s} = 1 1 \\times 9 = 9 9\n$$\n", + "text_format": "latex", + "bbox": [ + 284, + 340, + 401, + 349 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "3. Calculate the number of points on the boundary: - The boundary consists of the four sides of the rectangle. - The top and bottom sides (y = 4 and y = -4) each have 11 integer points (from -5 to 5). - The left and right sides (x = 5 and x = -5) each have 9 integer points (from -4 to 4). - Therefore, the total number of points on the boundary is:", + "bbox": [ + 186, + 356, + 496, + 402 + ], + "page_idx": 30 + }, + { + "type": "equation", + "text": "\n$$\n\\text {B o u n d a r y p o i n t s} = 2 \\times 1 1 + 2 \\times 9 = 2 2 + 1 8 = 4 0\n$$\n", + "text_format": "latex", + "bbox": [ + 235, + 407, + 449, + 417 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "4. Calculate the number of strictly interior points: - To find the number of points strictly in the interior, we subtract the points on the boundary from the total number of points:", + "bbox": [ + 186, + 424, + 486, + 452 + ], + "page_idx": 30 + }, + { + "type": "equation", + "text": "\n$$\nI n t e r i o r \\text {p o i n t s} = \\text {T o t a l p o i n t s - B o u n d a r y p o i n t s} = 9 9 - 4 0 = 5 9\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 458, + 482, + 469 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Thus, the number of points with integer coordinates that will be strictly in the interior of this rectangular region is 59.", + "bbox": [ + 187, + 474, + 488, + 494 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Answer with high-level planning identifies the optimal sub-tasks for the LLM to solve, increasing the chance of answering the question correctly", + "bbox": [ + 506, + 126, + 805, + 146 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "High-level policy planning: First, identify the boundaries of the rectangular region. Then, determine the integer coordinates that lie strictly within these boundaries. Finally, count the number of such points.", + "bbox": [ + 504, + 148, + 803, + 178 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Low-level policy reasoning following the high-policy plan: To solve the problem, we will follow the steps outlined in the instructions.", + "bbox": [ + 504, + 188, + 794, + 207 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Step 1: Identify the boundaries of the rectangular region. The vertices of the rectangular region are: $(-5,4)$ $(-5,4)$ $(-5, - 4)$ $(5, - 4)$ From these vertices, we can determine the boundaries:- The left boundary is $x = -5$ The right boundary is $x = 5$ .- The bottom boundary is $y = -4$ .- The top boundary is $y = 4$", + "bbox": [ + 503, + 214, + 800, + 261 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Step 2: Determine the integer coordinates that lie strictly within these boundaries. For a point $(x,y)$ to be strictly inside the rectangle, it must satisfy: $-5 < x < 5 - 4 < y < 4$", + "bbox": [ + 503, + 268, + 779, + 296 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Step 3: Count the integer coordinates that satisfy these conditions. Now, we will find the integer values for $x$ and $y$ that fall within these boundaries. For $x$ : The integer values that satisfy $-5 < x < 5$ are:", + "bbox": [ + 503, + 304, + 807, + 330 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "$-4, -3, -2, -1, 0, 1, 2, 3, 4$ This gives us 9 possible integer values. For $y$ The integer values that satisfy $-4 < y < 4$ are: $-3, -2, -1, 0, 1, 2, 3$ . This gives us 7 possible integer values.", + "bbox": [ + 503, + 330, + 800, + 358 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Step 4: Calculate the total number of points. Now, we multiply the number of possible integer values for $x$ by the number of possible integer values for $y$ .", + "bbox": [ + 503, + 366, + 805, + 385 + ], + "page_idx": 30 + }, + { + "type": "equation", + "text": "\n$$\n\\text {T o t a l p o i n t s} = 9 \\times 7 = 6 3\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 390, + 714, + 401 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Finally, the number of points with integer coordinates that lie strictly in the interior of the rectangular region is $\\boxed{63}$ .", + "bbox": [ + 503, + 407, + 795, + 426 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Figure 9: Case Study comparing with and without high-level metacognition results.", + "bbox": [ + 222, + 515, + 771, + 531 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "G Prompts", + "text_level": 1, + "bbox": [ + 171, + 574, + 282, + 593 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "G.1 Single-turn ReMA prompts", + "text_level": 1, + "bbox": [ + 171, + 618, + 410, + 633 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "G.1.1 Prompts for JSON data collection", + "text_level": 1, + "bbox": [ + 171, + 652, + 465, + 667 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Prompt for metacognition reasoning to rewrite:", + "bbox": [ + 171, + 685, + 483, + 700 + ], + "page_idx": 30 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "System prompt: \nYou are a math expert trying to solve mathematical problems. \nBefore answering a question, your task is to rewrite the original question to make it clearer. \nProvide your rewritten content in JSON format: \n{ \"action\": \"REWRITE\", \"output\": \"{clearer question content}\" \n} \nRespond only with valid JSON. Do not write an introduction or summary. \nUser prompt: \nHere is the question: [problem_text]", + "guess_lang": "txt", + "bbox": [ + 176, + 708, + 816, + 890 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Prompt for metacognition reasoning to decompose:", + "bbox": [ + 171, + 897, + 509, + 912 + ], + "page_idx": 30 + }, + { + "type": "page_number", + "text": "31", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 30 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Question: The equation $x^{10} + (13x - 1)^{10} = 0$ has 10 complex roots $r_1,\\overline{r}_1,r_2,\\overline{r}_2,r_3,\\overline{r}_3,r_4,\\overline{r}_4,r_5,\\overline{r}_5$ , where the bar denotes complex conjugation. Find the value of $\\frac{1}{r_1\\overline{r}_1} +\\frac{1}{r_2\\overline{r}_2} +\\frac{1}{r_3\\overline{r}_3} +\\frac{1}{r_4\\overline{r}_4} +\\frac{1}{r_5\\overline{r}_5}$", + "guess_lang": "txt", + "bbox": [ + 184, + 99, + 784, + 109 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "High-Level Agent's Output", + "text_level": 1, + "bbox": [ + 294, + 113, + 380, + 119 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "To solve this problem, let's break it down into steps that a low-level math-solving agent can follow:", + "bbox": [ + 186, + 122, + 431, + 128 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "1. Understand the given equation:", + "bbox": [ + 187, + 133, + 277, + 140 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "The equation is $x^{10} + (13x - 1)^{10} = 0$", + "bbox": [ + 187, + 141, + 290, + 146 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "2. Rewrite the equation:", + "bbox": [ + 187, + 147, + 250, + 152 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Notice that the equation can be rewritten as:", + "bbox": [ + 187, + 152, + 300, + 157 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {1 0} = - (1 3 x - 1) ^ {1 0}.\n$$\n", + "text_format": "latex", + "bbox": [ + 308, + 165, + 364, + 172 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "3. Consider the roots:", + "bbox": [ + 186, + 178, + 243, + 183 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "The roots of the equation are given as $r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5$ , where the bar denotes complex conjugation. 4. Use the property of complex conjugates:", + "For any complex number $z$ , the product of $z$ and its conjugate $\\overline{z}$ is the square of the modulus of $z$ i.e., $z\\overline{z} = |z|^2$ 5. Calculate the required sum:", + "3. Calculate the required sum $\\mathbf{W} = \\mathbf{w}_{1} + \\mathbf{w}_{2} + \\dots + \\mathbf{w}_{n}$" + ], + "bbox": [ + 186, + 184, + 478, + 208 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{r _ {1} \\overline {{F _ {1}}}} + \\frac {1}{r _ {2} \\overline {{F _ {2}}}} + \\frac {1}{r _ {3} \\overline {{F _ {3}}}} + \\frac {1}{r _ {4} \\overline {{F _ {4}}}} + \\frac {1}{r _ {5} \\overline {{F _ {5}}}}\n$$\n", + "text_format": "latex", + "bbox": [ + 285, + 220, + 388, + 234 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Using the property from step 4, this can be rewritten as:", + "bbox": [ + 189, + 237, + 328, + 243 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{| r _ {1} | ^ {2}} + \\frac {1}{| r _ {2} | ^ {2}} + \\frac {1}{| r _ {3} | ^ {2}} + \\frac {1}{| r _ {4} | ^ {2}} + \\frac {1}{| r _ {5} | ^ {2}},\n$$\n", + "text_format": "latex", + "bbox": [ + 285, + 252, + 390, + 266 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "6. Simplify the expression:", + "Since $r_1, r_2, r_3, r_4, r_5$ are roots of the equation $x^{10} = -(13x - 1)^{10}$ , the magnitudes $|r_i|$ are the same for each pair $r_i$ and $\\overline{r}_i$ . Let $|r_i| = |r_i|$ for all $i, j$ .", + "7. Find the common magnitude:", + "To find $|r_{1}|$ , consider the magnitudes of the terms on both sides of the equation $x^{10} = -(13x - 1)^{10}$ . The magnitude of the left side is $|x|^{10}$ and the magnitude of the right side is $|13x - 1|^{10}$ . Therefore:" + ], + "bbox": [ + 186, + 270, + 485, + 304 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\left| x \\right| ^ {1 0} = \\left| 1 3 x - 1 \\right| ^ {1 0}.\n$$\n", + "text_format": "latex", + "bbox": [ + 310, + 313, + 362, + 320 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Taking the 10th root of both sides, we get:", + "bbox": [ + 189, + 325, + 295, + 330 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n| x | = | 1 3 x - 1 |.\n$$\n", + "text_format": "latex", + "bbox": [ + 316, + 340, + 359, + 347 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "8. Solve for $|x|$ :", + "Let $|x| = a$ . Then:" + ], + "bbox": [ + 186, + 351, + 236, + 362 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "$\\therefore m - 1 \\neq 0$ ;", + "bbox": [ + 186, + 364, + 274, + 369 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\na = \\left| 1 3 a - 1 \\right|.\n$$\n", + "text_format": "latex", + "bbox": [ + 316, + 372, + 356, + 378 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "This gives us two cases:", + "- $a = 13$", + "- $a = -(13a - 1)$", + "Solving the first case:" + ], + "bbox": [ + 187, + 383, + 251, + 406 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\na = 1 3 a - 1 \\Longrightarrow 1 2 a = 1 \\Longrightarrow a = \\frac {1}{1 2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 281, + 415, + 393, + 428 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Solving the second case:", + "bbox": [ + 189, + 431, + 251, + 436 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\na = - 1 3 a + 1 \\Longrightarrow 1 4 a = 1 \\Longrightarrow a = \\frac {1}{1 4}.\n$$\n", + "text_format": "latex", + "bbox": [ + 279, + 445, + 395, + 458 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Since $a$ must be the same for all roots, we need to check which value is consistent. Given the nature of the problem, we can assume $a = \\frac{1}{2}$ as the correct magnitude.", + "9. Calculate the final sum:", + "Since $|r_i| = \\frac{1}{2}$ for all $i$ , we have" + ], + "bbox": [ + 186, + 460, + 485, + 483 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{| r _ {1} | ^ {2}} = \\frac {1}{(\\frac {1}{4}) ^ {2}} = 1 4 4.\n$$\n", + "text_format": "latex", + "bbox": [ + 305, + 493, + 367, + 508 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Therefore, the sum is:", + "bbox": [ + 189, + 513, + 245, + 518 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 = 5 \\times 1 4 4 = 7 2 0.\n$$\n", + "text_format": "latex", + "bbox": [ + 274, + 529, + 401, + 535 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "10. Final answer:", + "bbox": [ + 186, + 540, + 232, + 545 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{\\frac {1}{n} + \\frac {1}{n}} + \\frac {1}{\\frac {1}{n} + \\frac {1}{n}} + \\frac {1}{\\frac {1}{n} + \\frac {1}{n}} \\text {i s} 7 2 0.\n$$\n", + "text_format": "latex", + "bbox": [ + 243, + 545, + 326, + 551 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Low-Level Agent's Output", + "text_level": 1, + "bbox": [ + 611, + 113, + 696, + 119 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Let's go through the solution step by step to ensure clarity and correctness.", + "bbox": [ + 496, + 122, + 694, + 128 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Understand the given equation:", + "The equation is $x^{10} + (13x - 1)^{10} = 0$", + "2. Rewrite the equation:", + "Notice that the equation can be rewritten as:" + ], + "bbox": [ + 496, + 133, + 609, + 156 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {1 0} = - (1 3 x - 1) ^ {1 0}.\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 165, + 681, + 172 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "3. Consider the roots:", + "bbox": [ + 496, + 178, + 553, + 183 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "The roots of the equation are given as $r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5$ , where the bar denotes complex conjugation. 4. Use the property of complex conjugates:", + "For any complex number $z$ , the product of $z$ and its conjugate $\\overline{z}$ is the square of the modulus of $z$ , i.e., $z\\overline{z} = |z|^2$ . 5. Calculate the required sum:", + "We need to find the value of:" + ], + "bbox": [ + 496, + 184, + 787, + 210 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{r _ {1} F _ {1}} + \\frac {1}{r _ {2} F _ {2}} + \\frac {1}{r _ {3} F _ {3}} + \\frac {1}{r _ {4} F _ {4}} + \\frac {1}{r _ {5} F _ {5}}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 220, + 705, + 234 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Using the property from step 4, this can be rewritten as:", + "bbox": [ + 500, + 237, + 638, + 243 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{| r _ {1} | ^ {2}} + \\frac {1}{| r _ {2} | ^ {2}} + \\frac {1}{| r _ {3} | ^ {2}} + \\frac {1}{| r _ {4} | ^ {2}} + \\frac {1}{| r _ {5} | ^ {2}} + \\frac {1}{| r _ {6} | ^ {2}}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 251, + 705, + 265 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "6. Simplify the expression:", + "Since $r_1, r_2, r_3, r_4, r_5$ are roots of the equation $x^{10} = -(13x - 1)^{10}$ , the magnitudes $|r_i|$ are the same for each pair $r_1$ and $\\overline{r}_i$ . Let $|r_i| = |r_i|$ for all $i, j$ .", + "7. Find the common magnitude:", + "To find $|\\boldsymbol{r}_i|$ , consider the determinants of the terms on both sides of the equation $x^{10} = -(13x - 1)^{10}$ . The magnitude of the left side is $|z|^10$ and the magnitude of the right side is $|13z - 1|^{10}$ . Therefore:" + ], + "bbox": [ + 496, + 270, + 808, + 304 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n| x | ^ {1 0} = | 1 3 x - 1 | ^ {1 0}.\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 311, + 679, + 320 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Taking the 10th root of both sides, we get:", + "bbox": [ + 500, + 324, + 606, + 330 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\left| x \\right| = \\left| 1 3 x - 1 \\right|.\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 339, + 674, + 345 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "8. Solve for $|x|$ :", + "bbox": [ + 496, + 349, + 537, + 356 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Let $|x| = a$ . Then:", + "bbox": [ + 496, + 357, + 547, + 362 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\na = | 1 3 x - 1 |.\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 372, + 673, + 378 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "This gives us two cases:", + "-α=13a-1", + "- $a = -(13a - 1)$", + "Solving the first case:" + ], + "bbox": [ + 496, + 383, + 560, + 406 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\na = 1 3 a - 1 \\Longrightarrow 1 2 a = 1 \\Longrightarrow a = \\frac {1}{1 2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 415, + 709, + 428 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Solving the second case:", + "bbox": [ + 500, + 431, + 563, + 436 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\na = - 1 3 a + 1 \\Rightarrow 1 4 a = 1 \\Rightarrow a = \\frac {1}{1 4}.\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 445, + 710, + 458 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Since $a$ must be the same for all roots, we need to check which value is consistent. Given the nature of the problem, we can assume $a = \\frac{1}{2}$ as the correct magnitude.", + "9. Calculate the final sum:", + "Since $|r_i| = \\frac{1}{12}$ for all i, we have:" + ], + "bbox": [ + 496, + 460, + 805, + 484 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{| r _ {i} | ^ {2}} = \\frac {1}{(\\mathrm {古}) ^ {2}} = 1 4 4.\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 493, + 684, + 510 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Therefore, the sum is:", + "bbox": [ + 500, + 513, + 555, + 518 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 = 5 \\times 1 4 4 = 7 2 0.\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 527, + 717, + 535 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "10. Final answer:", + "bbox": [ + 496, + 540, + 542, + 545 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\text {The v a l u e o f} \\frac {1}{r _ {1} r _ {1}} + \\frac {1}{r _ {2} r _ {2}} + \\frac {1}{r _ {3} r _ {3}} + \\frac {1}{r _ {4} r _ {4}} + \\frac {1}{r _ {5} r _ {5}} \\text {i s} \\boxed {7 2 0}.\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 545, + 640, + 551 + ], + "page_idx": 31 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Question: The equation $x^{10} + (13x - 1)^{10} = 0$ has 10 complex roots $r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5$ , where the bar denotes complex conjugation. Find the value of $\\frac{1}{r_1r_4} + \\frac{1}{r_2r_2} + \\frac{1}{r_3r_3} + \\frac{1}{r_4r_4} + \\frac{1}{r_5r_5}$ .", + "guess_lang": "latex", + "bbox": [ + 184, + 604, + 782, + 616 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "High-Level Agent's Output", + "bbox": [ + 186, + 618, + 279, + 623 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Low-Level Agent's Output (part I)", + "bbox": [ + 354, + 618, + 462, + 625 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "To solve this problem, we need to follow these steps:", + "1. Understand the given equation: The equation is $x^{10} - (13x - 1)^{10} = 0$ .", + "2. Identify the roots: The roots of the", + "equation are given as", + "$\\overline{r_1},\\overline{r_2},\\overline{r_3},\\overline{r_4},\\overline{r_5},\\overline{r_6},\\overline{r_7},\\overline{r_8}$ where the bar denotes complex conjugation.", + "3. Use properties of complex conjugates:", + "For any complex number $z$ , the product $z \\cdot z$ is a complex function of the modulus of $z$ , i.e., $|z \\cdot \\overline{z}| = |z|^2$ .", + "4. Simplify the expression: We need to find", + "the value of 1", + "r1+ r2r3+ r4", + "#", + "Apply an property of complex conjugates. Since $\\pi_1 \\cdot \\overline{\\pi}_1 = |\\pi_1|^2$ , we have", + "1+", + "A", + "6.Sum the reciprocals: Sum the values", + "1+1 1 1", + "7. Use Vieta's formulas: To find the sum of the reciprocals of the moduli squared, we can use the fact that the sum of the roots of the polynomial and their properties.", + "8. Finalize the solution: Combine all the", + "steps to find the final value", + "Now, let's guide the low-level math solving", + "agent to implement these steps." + ], + "bbox": [ + 176, + 625, + 290, + 839 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "To solve the given problem, we start by analyzing the equation $x^{10} + (13x - 1)^{10} = 0$ .", + "bbox": [ + 297, + 625, + 516, + 628 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "This can be rewritten as:", + "bbox": [ + 297, + 630, + 357, + 635 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {1 0} = - (1 3 x - 1) ^ {1 0}.\n$$\n", + "text_format": "latex", + "bbox": [ + 382, + 640, + 437, + 645 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Taking the 10th root on both sides, we get:", + "bbox": [ + 297, + 650, + 403, + 656 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\nx = \\omega (1 3 x - 1),\n$$\n", + "text_format": "latex", + "bbox": [ + 359, + 661, + 431, + 666 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "where $\\omega$ is a 10th root of $-1$ . The 10th roots of $-1$ are given by $\\omega = e^{\\pi (2k + 1) / 10}$ for $k = 0, 1, 2, \\ldots, 9$ .", + "bbox": [ + 297, + 671, + 506, + 683 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Rewriting the equation, we have:", + "bbox": [ + 297, + 688, + 380, + 694 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "$x = \\omega (13x - 1)\\Rightarrow x - 13\\omega x = -\\omega \\Rightarrow x(1 - 13\\omega) = -\\omega \\Rightarrow x = \\frac{-\\omega}{1 - 13\\omega}$", + "bbox": [ + 299, + 698, + 517, + 710 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Thus, the roots of the equation are:", + "bbox": [ + 297, + 712, + 383, + 717 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\nr _ {k} = \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}}\n$$\n", + "text_format": "latex", + "bbox": [ + 299, + 724, + 431, + 734 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "where $\\omega_{k} = e^{i\\pi (2k + 1) / 10}$ for $k = 0,1,2$", + "bbox": [ + 297, + 738, + 393, + 743 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "The roots come in conjugate pairs, so the roots are $r_1, \\overline{r_1}, r_2, \\overline{r_2}, r_3, \\overline{r_3}, r_4, \\overline{r_4}, r_5, \\overline{r_5}$ . We need to find the value of:", + "bbox": [ + 297, + 750, + 514, + 761 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{r _ {1} \\overline {{r _ {1}}}} + \\frac {1}{r _ {2} \\overline {{r _ {2}}}} + \\frac {1}{r _ {3} \\overline {{r _ {3}}}} + \\frac {1}{r _ {4} \\overline {{r _ {4}}}} + \\frac {1}{r _ {5} \\overline {{r _ {5}}}}\n$$\n", + "text_format": "latex", + "bbox": [ + 357, + 763, + 460, + 777 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Since $r_k\\overline{r_k} = |r_k|^2$ we have:", + "bbox": [ + 297, + 780, + 370, + 786 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{r _ {k} r _ {k}} = \\frac {1}{| r _ {k} | ^ {2}}\n$$\n", + "text_format": "latex", + "bbox": [ + 390, + 790, + 429, + 804 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "We need to find $|r_k|^2$ . Note that:", + "bbox": [ + 297, + 808, + 377, + 813 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\nr _ {k} = \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}}\n$$\n", + "text_format": "latex", + "bbox": [ + 387, + 818, + 429, + 829 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Low-Level Agent's Output (part II)", + "bbox": [ + 616, + 619, + 728, + 625 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "The magnitude of $r_k$ is:", + "bbox": [ + 527, + 628, + 586, + 635 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n| r _ {k} | = \\left| \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}} \\right| = \\left| \\frac {| \\omega_ {k} |}{1 - 1 3 \\omega_ {k}} \\right| = \\frac {1}{1 - 1 3 \\omega_ {k}}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 638, + 733, + 652 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Thus,", + "bbox": [ + 527, + 656, + 542, + 661 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n| r _ {k} | ^ {2} = \\frac {1}{| 1 - 1 3 \\omega_ {k} | ^ {2}}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 665, + 699, + 678 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Therefore,", + "bbox": [ + 527, + 681, + 553, + 686 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{r _ {2} r _ {1}} = | 1 - 1 3 \\omega_ {k} | ^ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 691, + 700, + 704 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "We need to sum this over the 5 pairs of roots:", + "bbox": [ + 527, + 709, + 640, + 714 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {k = 0} ^ {4} | 1 - 1 3 \\omega_ {k} | ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 650, + 718, + 692, + 732 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Since $\\omega_{k} = e^{i\\pi (2k + 1) / 10}$ , we have", + "bbox": [ + 527, + 738, + 609, + 743 + ], + "page_idx": 31 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "$|1 - 13\\omega_{k}|^{2} = (1 - 13\\omega_{k})(1 - 13\\overline{\\omega_{k}}) = (1 - 13\\omega_{k})(1 - 13e^{-i\\pi (2k + 1) / 10}) = 1 - 13\\omega_{k} - 13e^{-i\\pi (2k + 1) / 10} + 169.$", + "Since $\\omega_{k}\\overline{\\omega_{k}} = 1$ we get:" + ], + "bbox": [ + 527, + 747, + 812, + 763 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\left| 1 - 1 3 \\omega_ {k} \\right| ^ {2} = 1 6 9 - 1 3 (\\omega_ {k} + e ^ {- i \\pi (2 k + 1) \\cdot 1 0}) + 1 = 1 7 0 - 1 3 \\cdot 2 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right) = 1 7 0 - 2 6 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 768, + 816, + 781 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Summing over $k = 0,1,2,3,4$ we get:", + "bbox": [ + 527, + 785, + 625, + 791 + ], + "page_idx": 31 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {k = 0} ^ {n - 1} \\left(1 7 0 - 2 6 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right)\\right) = 5 \\cdot 1 7 0 - 2 6 \\sum_ {k = 0} ^ {n - 1} \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right) = 8 5 0 - 2 6 \\cdot 0 = 8 5 0.\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 795, + 795, + 810 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Thus, the value is:", + "bbox": [ + 527, + 815, + 573, + 820 + ], + "page_idx": 31 + }, + { + "type": "image", + "img_path": "images/6cce98a8906c58ccf3aa6cedf13fe8485572fcdb57dd27e9b6cd696eb48335fd.jpg", + "image_caption": [ + "Figure 10: Case Study for consistency reward of high-level agent", + "Figure 11: Case Study for base correctness reward of high-level agent" + ], + "image_footnote": [], + "bbox": [ + 663, + 824, + 679, + 830 + ], + "page_idx": 31 + }, + { + "type": "page_number", + "text": "32", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 31 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [ + "Llama3.2-1B-Instruct training Output:" + ], + "code_body": "Question: The product of $3t^{2} + 5t + a$ and $4t^{2} + bt - 2$ is $12t^{4} + 26t^{3} - 8t^{2} - 16t + 6$ . What is $a + b$ ?", + "guess_lang": "txt", + "bbox": [ + 241, + 97, + 754, + 109 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [ + "Llama3.1-8B-Instruct training Output:" + ], + "code_body": "{\n \"action\": \"DECOMPOSE\",\n \"output\": \"Decompose the problem into finding the coefficients of the product of two polynomials and then solving for a and b.\"\n}", + "guess_lang": "json", + "bbox": [ + 176, + 133, + 496, + 181 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "{ \"action\": \"EMPTY\", \"output\".\"\" }", + "guess_lang": "txt", + "bbox": [ + 508, + 133, + 821, + 183 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 1: To find the product of the two polynomials $3t^{2} + 5t + a$ and $4t^{2} + bt - 2$ , we need to multiply each term of the first polynomial by each term of the second polynomial and then combine like terms. \nStep 2: The product of the two polynomials can be written as $(3t^{2} + 5t + a)(4t^{2} + bt - 2)$ . \nStep 3: Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial: $(3t^{2})(4t^{2}) + (3t^{2})(bt) + (3t^{2})(-2) + (5t)(4t^{2}) + (5t)(bt) + (5t)(-2) + (a)(4t^{2}) + (a)(bt) + (a)(-2)$ . \nStep 4: Simplifying the products, we get $12t^{4} + 3b^{3} - 6t^{2} + 20t^{3} + 5bt^{2} - 10t + 4at^{2} + abt - 2a$ . \nStep 5: Combining like terms, we have $12t^{4} + (3b + 20)t^{3} + (5b - 6 + 4a)t^{2} + (ab - 10)t - 2a$ . \nStep 6: We are given that the product of the two polynomials is $12t^{4} + 26t^{3} - 8t^{2} - 16t + 6$ . \nWe can equate the coefficients of the corresponding powers of $t$ in the two expressions. \nStep 7: Equating the coefficients of $t^3$ , we get $3b + 20 = 26$ . \nStep 8: Equating the coefficients of $t^2$ , we get $5b - 6 + 4a = -8$ . \nStep 9: Equating the constant terms, we get $-2a = 6$ . \nStep 10: Solving the equation $-2a = 6$ , we find that $a = -3$ . \nStep 11: Substituting $a = -3$ into the equation $5b - 6 + 4a = -8$ , we get $5b - 6 + 4(-3) = -8$ , which simplifies to $5b - 18 = -8$ . \nStep 12: Solving for $b$ , we find that $5b = 10$ , so $b = 2$ . \nStep 13: Now that we have found the values of $a$ and $b$ , we can calculate their sum: $a + b = -3 + 2 = -1$ . \nThe final answer is: $\\boxed{-1}$", + "guess_lang": "txt", + "bbox": [ + 176, + 189, + 480, + 465 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 1: The problem asks us to find the values of $a$ and $b$ in the quadratic expressions $3t^2 + 5t + a$ and $4t^2 + bt - 2$ , respectively, given that their product is $12t^4 + 26t^3 - 8t^2 - 16t + 6$ .", + "guess_lang": "txt", + "bbox": [ + 506, + 194, + 810, + 223 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 2: To solve this, we need to multiply the two quadratic expressions and equate the resulting expression to the given product $12t^4 + 26t^3 - 8t^2 - 16t + 6$ .", + "guess_lang": "txt", + "bbox": [ + 506, + 232, + 818, + 261 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 3: We start by multiplying the two quadratic expressions: $(3t^{2} + 5t + a)(4t^{2} + bt - 2)$ .", + "guess_lang": "txt", + "bbox": [ + 506, + 270, + 761, + 290 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 4: This gives us $12t^4 + (3b + 5)t^3 + (4a + 5b - 6)t^2 + (-2b + 10t + 2a)t - 2a.$", + "guess_lang": "txt", + "bbox": [ + 506, + 299, + 779, + 318 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 5: We know that the coefficients of the resulting expression must be equal to the coefficients of the given product $12t^4 + 26t^3 - 8t^2 - 16t + 6$ .", + "guess_lang": "txt", + "bbox": [ + 506, + 325, + 815, + 345 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 6: Equating the coefficients of $t^3$ gives us the equation $3b + 5 = 26$ , which simplifies to $3b = 21$ and thus $b = 7$ .", + "guess_lang": "txt", + "bbox": [ + 506, + 354, + 808, + 373 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 7: Equating the constant terms gives us $-2a = -6$ , which simplifies to $a = 3$ .", + "guess_lang": "txt", + "bbox": [ + 506, + 382, + 810, + 402 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 8: Now that we have the values of $b$ and $a$ , we can find the sum $a + b$ .", + "guess_lang": "txt", + "bbox": [ + 506, + 411, + 815, + 421 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Step 9: Adding $a = 3$ and $b = 7$ gives us $a + b = 10$ .", + "guess_lang": "txt", + "bbox": [ + 506, + 429, + 728, + 439 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "The final answer is: $\\boxed{10}$", + "guess_lang": "txt", + "bbox": [ + 506, + 448, + 609, + 459 + ], + "page_idx": 32 + }, + { + "type": "text", + "text": "Figure 12: Case Study for interpretability experiments in Section 4.2.2", + "bbox": [ + 264, + 476, + 730, + 491 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [ + "System prompt:" + ], + "code_body": "You are a math expert trying to solve mathematical problems. Before answering a question, your task is to decompose the original question to make it clearer. \nProvide your rewritten content in JSON format: \n{\"action\": \"DECOMPOSE\", \"output\": \"{decomposed question content}}\" \n}} \nRespond only with valid JSON. Do not write an introduction or summary. \nUser prompt: \nHere is the question: [problem.text]", + "guess_lang": "txt", + "bbox": [ + 176, + 534, + 777, + 713 + ], + "page_idx": 32 + }, + { + "type": "text", + "text": "Prompt for generating final answers using on the question and metacognition reasoning:", + "bbox": [ + 173, + 720, + 748, + 734 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [ + "System prompt:", + "User prompt:" + ], + "code_body": "You are a math expert tasked with solving problems step by step. Follow the provided instructions precisely, showing all reasoning and intermediate steps. Present the final answer within \\boxed{\\{\\}}\\}.", + "guess_lang": "txt", + "bbox": [ + 176, + 760, + 816, + 815 + ], + "page_idx": 32 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "Here is the question and instructions: \nQuestion \n[problem_text] \nProvided Instruction \n[instruction_text]", + "guess_lang": "txt", + "bbox": [ + 176, + 828, + 550, + 896 + ], + "page_idx": 32 + }, + { + "type": "page_number", + "text": "33", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 32 + }, + { + "type": "text", + "text": "G.1.2 Prompts for Math problems", + "text_level": 1, + "bbox": [ + 171, + 90, + 426, + 107 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "VRP prompt:", + "text_level": 1, + "bbox": [ + 173, + 114, + 272, + 130 + ], + "page_idx": 33 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "System prompt: \nYou are a math expert tasked with solving problems step by step. Present the final answer within \\boxed{}?. \nUser prompt: \nHere is the question: \n{Question}", + "guess_lang": "txt", + "bbox": [ + 173, + 131, + 805, + 218 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "MRP prompt:", + "text_level": 1, + "bbox": [ + 173, + 224, + 276, + 239 + ], + "page_idx": 33 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "System prompt: \nYou are a math expert tasked with solving problems. When solving a problem, your first task is to provide a high-level solution plan as an instruction. Then you need to follow the provided instructions precisely, showing all reasoning and intermediate steps. Finally, you must present the final answer within boxed}. \nUser prompt: \nHere is the question: {Question}", + "guess_lang": "txt", + "bbox": [ + 173, + 241, + 818, + 382 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "MAMRP prompt:", + "text_level": 1, + "bbox": [ + 173, + 388, + 303, + 404 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "high-level agent:", + "bbox": [ + 173, + 404, + 285, + 417 + ], + "page_idx": 33 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "System prompt: \nYou are a math expert specialized in solving mathematical problems, you need to teach a weaker agent with minimal capability in math how to solve a problem step-by-step. \nYour task is to provide a high-level solution plan for the given problem, in order to guide a low-level math solving agent to solve the problem. \nYou can not directly answer the question. You'll be punished if you include any answer in your response. \nYou need to first think deeply in mind and output your final instruction. \nUser prompt: \nHere is the question: \n{Question}", + "guess_lang": "txt", + "bbox": [ + 173, + 419, + 828, + 614 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "low-level agent:", + "bbox": [ + 173, + 617, + 279, + 631 + ], + "page_idx": 33 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "System prompt: \nYou are a math expert tasked with solving problems step by step. Follow the provided instructions precisely, showing all reasoning and intermediate steps. Present the final answer within \\boxed{}/. User prompt: Here is the question and instructions: [Question] {Question} [End of Question] [Provided Instruction] {instruction} [End of Instruction]", + "guess_lang": "txt", + "bbox": [ + 173, + 632, + 818, + 827 + ], + "page_idx": 33 + }, + { + "type": "page_number", + "text": "34", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "G.1.3 Prompts for LLM-as-a-Judge problems", + "text_level": 1, + "bbox": [ + 171, + 90, + 504, + 107 + ], + "page_idx": 34 + }, + { + "type": "text", + "text": "We adopt the prompts from Saha et al. [2025a].", + "bbox": [ + 171, + 114, + 485, + 128 + ], + "page_idx": 34 + }, + { + "type": "text", + "text": "VRP prompt:", + "text_level": 1, + "bbox": [ + 171, + 128, + 272, + 143 + ], + "page_idx": 34 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "System prompt: \nPlease act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses. Begin your evaluation by comparing the two responses and provide a short explanation. Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision.. \nDo not allow the length of the responses to influence your evaluation.. \nDo not favor certain names of the assistants. Be as objective as possible. After providing your explanation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better.. \nUser prompt: \n[User Question] {instruction} [End of User Question] [The Start of Assistant A's Answer] {response_A} [The End of Assistant A's Answer] [The Start of Assistant B's Answer] {response_B} [The End of Assistant B's Answer]", + "guess_lang": "txt", + "bbox": [ + 173, + 145, + 828, + 520 + ], + "page_idx": 34 + }, + { + "type": "page_number", + "text": "35", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 34 + }, + { + "type": "text", + "text": "MRP prompt:", + "text_level": 1, + "bbox": [ + 173, + 90, + 274, + 106 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "System prompt:", + "text_level": 1, + "bbox": [ + 176, + 108, + 285, + 122 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. First of your task is to build an evaluation plan that can then be executed to assess the response quality. Whenever appropriate, you can choose to also include a step-by-step reference answer as part of the evaluation plan. Enclose your evaluation plan between the tags \"[Start of Evaluation Plan]\" and \"[End of Evaluation Plan)\". After that, please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses. Begin your evaluation by comparing the two responses and provide a short explanation. Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision. Do not allow the length of the responses to influence your evaluation. Do not favor certain names of the assistants. Be as objective as possible. After providing your explanation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better. User prompt: [User Question] {instruction} [End of User Question] [The Start of Assistant A's Answer] {response_A} [The End of Assistant A's Answer] [The Start of Assistant B's Answer] {response_B} [The End of Assistant B's Answer]", + "bbox": [ + 176, + 123, + 825, + 633 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "MAMRP prompt: high-level agent:", + "text_level": 1, + "bbox": [ + 173, + 640, + 415, + 655 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "System prompt:", + "text_level": 1, + "bbox": [ + 176, + 657, + 285, + 672 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "We want to evaluate the quality of the responses provided by AI assistants to the user question displayed below. For that, your task is to help us build an evaluation plan that can then be executed to assess the response quality. Whenever appropriate, you can choose to also include a step-by-step reference answer as part of the evaluation plan.", + "bbox": [ + 176, + 672, + 797, + 755 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "User prompt:", + "text_level": 1, + "bbox": [ + 178, + 755, + 267, + 768 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "[User Question] \n{Question} \n[End of User Question]", + "bbox": [ + 179, + 768, + 393, + 809 + ], + "page_idx": 35 + }, + { + "type": "page_number", + "text": "36", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "low-level agent:", + "text_level": 1, + "bbox": [ + 173, + 92, + 279, + 104 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "System prompt:", + "text_level": 1, + "bbox": [ + 178, + 109, + 284, + 122 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. Your evaluation should be performed by following the provided evaluation plan step-by-step. Avoid copying the plan when doing the evaluation.", + "bbox": [ + 176, + 123, + 828, + 189 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "Please also only stick to the given plan and provide explanation of how the plan is executed to compare the two responses.", + "bbox": [ + 176, + 191, + 808, + 219 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision.", + "bbox": [ + 176, + 220, + 807, + 246 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "Do not allow the length of the responses to influence your evaluation. Do not favor certain names of the assistants. Be as objective as possible.", + "bbox": [ + 176, + 247, + 790, + 287 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "After providing your evaluation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better.", + "bbox": [ + 176, + 287, + 823, + 328 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "User prompt:", + "text_level": 1, + "bbox": [ + 179, + 330, + 267, + 343 + ], + "page_idx": 36 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "[User Question] \n{instruction} \n{End of User Question] \n{The Start of Assistant A's Answer} \n{response_A} \n{The End of Assistant A's Answer} \n{The Start of Assistant B's Answer} \n{response_B} \n{The End of Assistant B's Answer} \n{The Start of Evaluation Plan} \n{evaluation計劃} \n{The End of Evaluation Plan}", + "guess_lang": "txt", + "bbox": [ + 178, + 343, + 521, + 508 + ], + "page_idx": 36 + }, + { + "type": "page_number", + "text": "37", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "G.2 Multi-turn ReMA prompts", + "text_level": 1, + "bbox": [ + 171, + 90, + 408, + 107 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "G.2.1 SFT data collection of multi-turn MAMRP", + "text_level": 1, + "bbox": [ + 171, + 116, + 529, + 130 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "System prompt:", + "text_level": 1, + "bbox": [ + 176, + 141, + 285, + 155 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "You are classifying reasoning process data into two types of thinking. You will be given a question-answer pair from a reasoning dataset. Your task is to split all words into two parts. These words are crucial for analyzing reasoning patterns, so do not skip any details.", + "bbox": [ + 176, + 155, + 813, + 223 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "- **Meta-Thinking Agent (MTA):** Responsible for high-level thought processes. This includes planning, evaluating steps, expressing uncertainty, making observations, or setting goals. Avoid detailed calculations. The content should be enclosed in `` and ``.", + "bbox": [ + 176, + 224, + 797, + 292 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "- $\\star \\star$ Reasoning Agent (RA): $\\star \\star$ Responsible for detailed problem-solving steps, such as calculations, logical deductions, or breaking down a problem into subproblems. The content should be enclosed in `` and ``.", + "bbox": [ + 176, + 292, + 807, + 348 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "\\*\\*Rules to follow: \\*\\*", + "bbox": [ + 176, + 349, + 377, + 359 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "1. **Do not assign large chunks of text to a single type of thinking.** The reasoning process consists of small, nonlinear thinking steps, so alternate appropriately between Meta-Thinking and Reasoning steps.", + "bbox": [ + 176, + 362, + 805, + 416 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "2. **Keep the words from the original solution unmodified whenever possible.** Words like \"Wait,\" \"Hmm,\" \"But,\" etc., typically indicate Meta-Thinking and should be preserved.", + "bbox": [ + 176, + 417, + 754, + 458 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "3. $\\star \\star$ When finalizing the answer: $\\star \\star$", + "bbox": [ + 176, + 459, + 524, + 470 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "- The \\*\\*Meta-Thinking Agent (MTA) \\*\\* must explicitly confirm the answer before completion and output '[FINISH]'.", + "bbox": [ + 176, + 472, + 797, + 500 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "- The $\\star \\star$ Reasoning Agent (RA) $\\star \\star$ should then provide the final answer in the correct format.", + "bbox": [ + 176, + 500, + 767, + 525 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "4. **Do not skip any reasoning steps, even if they seem redundant, incorrect or irrelevant**", + "bbox": [ + 176, + 527, + 730, + 553 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "5. **Do not modify or remove any part of the original reasoning process**, even if it seems redundant or repetitive. The goal is to **preserve the exact flow of thought** as it naturally occurs.", + "bbox": [ + 176, + 554, + 816, + 595 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "6. **Retain all expressions such as \"Wait,\" \"Hmm,\" \"But wait,\" etc., exactly as they appear. These indicate important cognitive processes and should not be skipped or altered.**", + "bbox": [ + 176, + 595, + 816, + 637 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "Here are examples for you: [Examples] ...", + "bbox": [ + 176, + 638, + 433, + 664 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "User prompt:", + "text_level": 1, + "bbox": [ + 176, + 665, + 267, + 678 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "[Begin of Question] \n{question} \n[End of Question] \n[Begin of Solution] \n{solution} \n[End of Solution]", + "bbox": [ + 176, + 679, + 364, + 761 + ], + "page_idx": 37 + }, + { + "type": "page_number", + "text": "38", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 37 + }, + { + "type": "text", + "text": "G.2.2 Prompt for math problems", + "text_level": 1, + "bbox": [ + 171, + 90, + 416, + 107 + ], + "page_idx": 38 + }, + { + "type": "text", + "text": "Meta-Thinking Agent (MTA):", + "text_level": 1, + "bbox": [ + 173, + 114, + 383, + 128 + ], + "page_idx": 38 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "System prompt: \nYou are a meta-think agent that represents human high-level think process, when solving a question, you will have a discussion with human, each time you think about what to do next: e.g. \n- Exploring multiple angles and approaches \n- Breaking down the solution into clear steps \n- Continuously reflecting on intermediate results honestly and adapt your strategy as you progress \n- Backtracking when necessary \n- Requesting exploration of multiple solutions individually \n- Finally confirm the answer with the tag [FINISH] \nUser prompt: \n{question}", + "guess_lang": "txt", + "bbox": [ + 173, + 137, + 826, + 321 + ], + "page_idx": 38 + }, + { + "type": "text", + "text": "Reasoning Agent (RA):", + "text_level": 1, + "bbox": [ + 173, + 327, + 338, + 343 + ], + "page_idx": 38 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "System prompt: Please reason step by step follow the given instruction, when asked to finalize your answer, put your answer within \\boxed{} User prompt: {question} {instruction}", + "guess_lang": "txt", + "bbox": [ + 173, + 349, + 807, + 436 + ], + "page_idx": 38 + }, + { + "type": "page_number", + "text": "39", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 38 + } +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_model.json b/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2df6fbf6437128e6a96195d28904d158e87b31ae --- /dev/null +++ b/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_model.json @@ -0,0 +1,8363 @@ +[ + [ + { + "type": "aside_text", + "bbox": [ + 0.023, + 0.264, + 0.061, + 0.707 + ], + "angle": 270, + "content": "arXiv:2503.09501v3 [cs.AI] 27 May 2025" + }, + { + "type": "title", + "bbox": [ + 0.215, + 0.123, + 0.783, + 0.174 + ], + "angle": 0, + "content": "ReMA: Learning to Meta-think for LLMs with Multi-agent Reinforcement Learning" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.224, + 0.796, + 0.257 + ], + "angle": 0, + "content": "Ziyu Wan\\(^{1,2*}\\), Yunxiang Li\\(^{3*}\\), Xiaoyu Wen\\(^{1,2}\\), Yan Song\\(^{4}\\), Hanjing Wang\\(^{1}\\), Linyi Yang\\(^{4}\\), Mark Schmidt\\(^{3}\\), Jun Wang\\(^{4}\\), Weinan Zhang\\(^{1}\\), Shuyue Hu\\(^{2\\ddagger}\\), Ying Wen\\(^{1\\ddagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.394, + 0.269, + 0.607, + 0.285 + ], + "angle": 0, + "content": "1 Shanghai Jiao Tong University" + }, + { + "type": "text", + "bbox": [ + 0.352, + 0.284, + 0.645, + 0.299 + ], + "angle": 0, + "content": "\\(^{2}\\) Shanghai Artificial Intelligence Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.392, + 0.299, + 0.607, + 0.313 + ], + "angle": 0, + "content": "3 University of British Columbia" + }, + { + "type": "text", + "bbox": [ + 0.403, + 0.314, + 0.594, + 0.329 + ], + "angle": 0, + "content": "4 University College London" + }, + { + "type": "list", + "bbox": [ + 0.352, + 0.269, + 0.645, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.46, + 0.364, + 0.538, + 0.38 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.395, + 0.767, + 0.685 + ], + "angle": 0, + "content": "Recent research on Reasoning of Large Language Models (LLMs) has sought to further enhance their performance by integrating meta-thinking—enabling models to monitor, evaluate, and control their reasoning processes for more adaptive and effective problem-solving. However, current single-agent work lacks a specialized design for acquiring meta-thinking, resulting in low efficacy. To address this challenge, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages Multi-Agent Reinforcement Learning (MARL) to elicit meta-thinking behaviors, encouraging LLMs to think about thinking. ReMA decouples the reasoning process into two hierarchical agents: a high-level meta-thinking agent responsible for generating strategic oversight and plans, and a low-level reasoning agent for detailed executions. Through iterative reinforcement learning with aligned objectives, these agents explore and learn collaboration, leading to improved generalization and robustness. Empirical results from single-turn experiments demonstrate that ReMA outperforms single-agent RL baselines on complex reasoning tasks, including competitive-level mathematical benchmarks and LLM-as-a-Judge benchmarks. Additionally, we further extend ReMA to multi-turn interaction settings, leveraging turn-level ratio and parameter sharing to improve efficiency. Comprehensive ablation studies further illustrate the evolving dynamics of each distinct agent, providing valuable insights into how the meta-thinking reasoning process enhances the reasoning capabilities of LLMs. Our code can be found in https://github.com/ziyuwan/ReMA-public" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.71, + 0.314, + 0.726 + ], + "angle": 0, + "content": "1 Introduction" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.741, + 0.827, + 0.853 + ], + "angle": 0, + "content": "Large language models (LLMs) have demonstrated remarkable capabilities in knowledge understanding and complex reasoning tasks [Chowdhery et al., 2023, Achiam et al., 2023, Anil et al., 2023, Dubey et al., 2024]. The paradigm in developing LLM-based reasoning models is shifting from scaling training-time computation towards scaling test-time computation [Snell et al., 2024]. Recent advancements, such as OpenAI-o1 [OpenAI, 2024], Deepseek R1 [DeepSeek-AI et al., 2025], and Gemini 2.0 Flash Thinking [DeepMind, 2025], have demonstrated that allowing LLMs to think before generating answers can significantly enhance performance and lead to the emergence of human-like reasoning patterns. These patterns like \"Wait, hold on.\" or \"Let's break this down.\"" + }, + { + "type": "page_footnote", + "bbox": [ + 0.191, + 0.86, + 0.316, + 0.874 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.193, + 0.874, + 0.642, + 0.888 + ], + "angle": 0, + "content": "\\(^{\\dagger}\\)Work done during internship at Shanghai Artificial Intelligence Laboratory" + }, + { + "type": "page_footnote", + "bbox": [ + 0.194, + 0.888, + 0.336, + 0.902 + ], + "angle": 0, + "content": "Corresponding Author" + }, + { + "type": "footer", + "bbox": [ + 0.172, + 0.923, + 0.315, + 0.937 + ], + "angle": 0, + "content": "Preprint. Under review." + } + ], + [ + { + "type": "text", + "bbox": [ + 0.307, + 0.094, + 0.692, + 0.107 + ], + "angle": 0, + "content": "Question: \\( T = 9.5 \\). If \\( \\log_2 x^T - \\log_4 x = \\log_8 x^k \\) is an identity for all \\( x > 0 \\), compute the value of \\( k \\)." + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.109, + 0.824, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.307, + 0.825, + 0.364 + ], + "angle": 0, + "content": "Figure 1: Left: A construction-based method that fine-tunes LLMs using rejection sampling, searching among combinations of pre-defined templates. Middle: R1-like method learns to mix meta-thinking and detailed reasoning steps during training. Right: Our method ReMA separates the meta-thinking and reasoning steps in a multi-agent system and updated by reinforcement learning." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.381, + 0.825, + 0.424 + ], + "angle": 0, + "content": "indicate that LLMs can develop a form of meta-thinking abilities that can generalize well to out-of-distribution (OOD) tasks [Xiang et al., 2025]. Meta-thinking, also known as metacognitive skills [Flavell, 1979], is an ability traditionally considered uniquely human [Didolkar et al., 2024]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.43, + 0.827, + 0.651 + ], + "angle": 0, + "content": "To cultivate meta-thinking patterns from LLMs themselves, recent construction-based supervised approaches leverage supervised finetuning on structured reasoning trajectories. Specifically, these methods sampling reasoning trajectories from predefined meta-thinking templates and then use supervised finetuning (SFT) or direct preference optimization (DPO) [Rafailov et al., 2023] to teach LLMs imitate these patterns [Qi et al., 2024, Yue et al., Xi et al., 2024, Yang et al., 2025, Muenighoff et al., 2025, Ye et al., 2025c]. However, such methods lack sufficient flexibility for LLMs to explore suitable meta-thinking patterns. Thus, they often fail to generalize to out-of-distribution (OOD) problems, leading to unstable performance on unseen data [Kirk et al., Chu et al., 2025]. Besides construction-based methods, R1-like single-agent reinforcement learning (SARL) has also been adopted for meta-thinking in reasoning [DeepSeek-AI et al., 2025, Xie et al., 2025]. However, these SARL attempts typically rely on strong foundational models for easier exploration or extensive task-specific fine-tuning for stable training [Xu et al., 2025, Gandhi et al., 2025]. Furthermore, SARL needs to learn meta-thinking and reasoning within a single forward pass, seeking to capture complex reasoning structures purely in an autoregressive manner [Xie et al., 2025]. This can potentially lead to issues such as inefficient exploration as well as reduced readability and early convergence to local optima [DeepSeek-AI et al., 2025, Xiang et al., 2025]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.657, + 0.827, + 0.809 + ], + "angle": 0, + "content": "To address these limitations, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages multi-agent reinforcement learning (MARL) to encourage LLMs to think about thinking. Our approach employs a multi-agent system (MAS) composed of a high-level meta-thinking agent, responsible for strategic oversight and instruction generation, and a low-level reasoning agent tasked with detailed executing processes based on provided guidance. We compare the inference process among the construction-based method, R1-like method, and ReMA in Fig. 1. Since MAS distributes the exploration space of SARL into multiple agents, it enables each agent to explore more structurally and efficiently during training. Then we apply reinforcement learning on each agent with aligned reward functions. In this way, ReMA effectively balances the trade-off between generalization capability and exploration efficiency. As a result, they can learn to play the best of their role (either to meta-think or to follow instructions), at the present of the other agent." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.815, + 0.825, + 0.913 + ], + "angle": 0, + "content": "To our knowledge, we are the first to formally define and optimize a multi-agent meta-thinking reasoning process (MAMRP) through multi-agent reinforcement learning. Our extensive experiments span both math reasoning and LLM-as-a-Judge tasks, where ReMA consistently achieves the highest average performance across three backbone pretrained models. We further extend ReMA to multi-turn interaction settings on math reasoning tasks, implementing turn-level ratio to optimize trajectory returns and stabilize training. Through comprehensive ablation studies, we illustrate the evolving dynamics between agents, revealing unexpected interaction patterns such as role reversals" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.504, + 0.948 + ], + "angle": 0, + "content": "2" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.825, + 0.123 + ], + "angle": 0, + "content": "under different reward settings. These findings provide valuable insights into how meta-thinking processes enhance the reasoning capabilities of LLMs." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.141, + 0.321, + 0.158 + ], + "angle": 0, + "content": "2 Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.173, + 0.825, + 0.203 + ], + "angle": 0, + "content": "In this section, we outline the formulation of the vanilla reasoning process (Sec. 2.1) and the representative training methods (Sec. 2.2) along with the notation used throughout the paper." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.219, + 0.445, + 0.235 + ], + "angle": 0, + "content": "2.1 Vanilla Reasoning Process (VRP)" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.245, + 0.825, + 0.29 + ], + "angle": 0, + "content": "The probability of generating a response \\(\\mathbf{y}\\) equals the product of its stepwise probabilities. Given a model \\(\\pi_{\\theta}\\) and a prompt \\(\\mathbf{x} = (x_1, \\ldots, x_N)\\), the vanilla reasoning process (VRP) autoregressively produces a response \\(\\mathbf{y} = (y_1, \\ldots, y_L)\\) with" + }, + { + "type": "equation", + "bbox": [ + 0.264, + 0.297, + 0.732, + 0.34 + ], + "angle": 0, + "content": "\\[\n\\pi_ {\\theta} (\\mathbf {y} | \\mathbf {x}) = \\prod_ {l = 1} ^ {L} \\pi_ {\\theta} (y _ {l} | x _ {1}, x _ {2}, \\dots x _ {N}, y _ {1}, \\dots , y _ {l - 1}) = \\prod_ {l = 1} ^ {L} \\pi_ {\\theta} (\\mathbf {y} _ {l} | \\mathbf {x}, \\mathbf {y} _ {< l})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.347, + 0.825, + 0.378 + ], + "angle": 0, + "content": "The response usually contains intermediate reasoning steps before arriving at the final answer, this process is also known as chain-of-thought (CoT) [Wei et al., 2022], which can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.423, + 0.386, + 0.825, + 0.407 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} \\xrightarrow {\\text {r e a s o n i n g s t e p s}} \\mathbf {y} \\sim \\mathbf {a}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.414, + 0.647, + 0.43 + ], + "angle": 0, + "content": "where \\(\\mathbf{a}\\) is the extracted final answer, which is included in the answer \\(\\mathbf{y}\\)." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.446, + 0.513, + 0.463 + ], + "angle": 0, + "content": "2.2 Training VRP via Reinforcement Learning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.472, + 0.825, + 0.502 + ], + "angle": 0, + "content": "RL frames VRP decoding process as a deterministic, token-level Markov Decision process (MDP) [Wang et al., 2024a]. Its objective is" + }, + { + "type": "equation", + "bbox": [ + 0.374, + 0.509, + 0.622, + 0.528 + ], + "angle": 0, + "content": "\\[\n\\mathcal {J} (\\theta) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\mathbf {y} \\sim \\pi_ {\\theta}} \\left[ R (\\mathbf {y}, \\mathbf {y} ^ {*}) \\right].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.535, + 0.825, + 0.565 + ], + "angle": 0, + "content": "where \\( R(\\cdot, \\cdot) \\) represents a reward function comparing generated answer \\( \\mathbf{y} \\) with the golden answer \\( \\mathbf{y}^* \\) for any question \\( \\mathbf{x} \\) sampled from dataset \\( \\mathcal{D} \\)." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.568, + 0.825, + 0.622 + ], + "angle": 0, + "content": "To compute the gradient \\(\\nabla_{\\theta}\\mathcal{J}(\\theta)\\), computationally efficient algorithms GRPO [Shao et al., 2024] and REINFORCE++ [Hu, 2025] are widely adopted. Take GRPO as an example, given a question-answer pair \\(\\mathbf{x},\\mathbf{y}^*\\) and a group of \\(G\\) generated responses \\(\\mathbf{y}_i\\), denote \\(\\mathbf{y}_{i,j}\\) as the \\(j\\)-th token of the \\(i\\)-th response, it optimizes the following token-level objective:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.628, + 0.825, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {J} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\{\\mathbf {y} _ {i} \\} _ {i = 1} ^ {G} \\sim \\pi_ {\\boldsymbol {\\theta} _ {\\mathrm {o l d}}} (\\cdot | \\mathbf {x})} \\\\ \\left[ \\frac {1}{G} \\sum_ {i = 1} ^ {G} \\frac {1}{| \\mathbf {y} _ {i} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i} |} \\left(\\min \\left(r _ {i, j} (\\theta) \\hat {A} _ {i, j}, \\operatorname {c l i p} \\left(r _ {i, j} (\\theta), 1 - \\epsilon , 1 + \\epsilon\\right) \\hat {A} _ {i, j}\\right) - \\beta D _ {\\mathrm {K L}} \\left(\\pi_ {\\theta} \\| \\pi_ {\\text {r e f}}\\right)\\right) \\right], \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.698, + 0.777, + 0.716 + ], + "angle": 0, + "content": "where the token-level ratio \\( r_{i,j}(\\theta) \\) and the group-normalized advantage \\( \\hat{A}_{i,j} \\) are defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.286, + 0.723, + 0.71, + 0.761 + ], + "angle": 0, + "content": "\\[\nr _ {i, j} (\\theta) = \\frac {\\pi_ {\\theta} \\left(\\mathbf {y} _ {i , j} \\mid \\mathbf {x} , \\mathbf {y} _ {i , < j}\\right)}{\\pi_ {\\theta_ {\\mathrm {o l d}}} \\left(\\mathbf {y} _ {i , j} \\mid \\mathbf {x} , \\mathbf {y} _ {i , < j}\\right)}, \\hat {A} _ {i, j} = \\frac {R _ {i} - \\operatorname {m e a n} \\left(\\left\\{R _ {i} \\right\\} _ {i = 1} ^ {G}\\right)}{\\operatorname {s t d} \\left(\\left\\{R _ {i} \\right\\} _ {i = 1} ^ {G}\\right)}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.775, + 0.825, + 0.819 + ], + "angle": 0, + "content": "However, RL on base LLMs that haven't been well-aligned may suffer from issues like poor readability and language mixing, preventing researchers from verifying, understanding, and further developing their LLMs. And huge searching space makes efficient learning of meta-thinking daunting." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.838, + 0.273, + 0.854 + ], + "angle": 0, + "content": "3 Method" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.87, + 0.826, + 0.914 + ], + "angle": 0, + "content": "In this section, we present Reinforced Meta-thinking Agents (ReMA), a RL method integrating meta-thinking into the reasoning process of LLM under multi-agent settings (Sec. 3.1), then describe the learning process enabled by MARL of single- and multi-turn LLM setting (Secs. 3.2.1 and 3.2.2)." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.505, + 0.948 + ], + "angle": 0, + "content": "3" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.172, + 0.092, + 0.6, + 0.107 + ], + "angle": 0, + "content": "3.1 Deploying Meta-Thinking Reasoning Process for LLMs" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.117, + 0.825, + 0.201 + ], + "angle": 0, + "content": "Beyond VRP (Sec. 2.1), recent studies [Muennighoff et al., 2025, Ye et al., 2025c] have shown that integrating meta-thinking behaviors in reasoning process can largely improve the accuracy of the final answers. By integrating Meta-thinking, ReMA decomposes problem solving into two sequential phases: a meta-thinking phase that plans, monitors, or revises strategy, followed by a reasoning phase that produces the detailed solution. We analyse Meta-thinking Reasoning Process along two orthogonal axes—single- vs. multi-agent and single- vs. multi-turn." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.207, + 0.825, + 0.236 + ], + "angle": 0, + "content": "In a single-agent setting, such a process calls LLM once and generates meta-thinking and the following reasoning autoregressively. We formulate the meta-thinking reasoning process (MRP) below:" + }, + { + "type": "equation", + "bbox": [ + 0.397, + 0.243, + 0.825, + 0.259 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} \\sim \\pi_ {\\theta} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\cdot \\pi_ {\\theta} (\\mathbf {m} \\mid \\mathbf {x}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.265, + 0.825, + 0.291 + ], + "angle": 0, + "content": "where \\(\\mathbf{m}\\) and \\(\\mathbf{y}\\) are the output of meta-thinking and reasoning respectively. We present the procedure as shown below:" + }, + { + "type": "equation", + "bbox": [ + 0.377, + 0.292, + 0.824, + 0.311 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} \\xrightarrow {\\text {m e t a - t h i n k i n g}} \\mathbf {m} \\xrightarrow {\\text {r e a s o n i n g s t e p s}} \\mathbf {y} \\sim \\mathbf {a}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.314, + 0.825, + 0.398 + ], + "angle": 0, + "content": "Exploring MRP reasoning through a single-agent approach is often inefficient, as it requires the language model to simultaneously master both meta-thinking and detailed problem-solving within one call. Prior research has demonstrated that activating different model capabilities through specialized agents significantly improves MRP exploration efficiency. To leverage this insight, we decouple meta-thinking and reasoning into two separate LLM agents: a high-level agent dedicated to generating meta-thinking, and a low-level agent focused on executing reasoning steps." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.403, + 0.825, + 0.459 + ], + "angle": 0, + "content": "During a conversation, the high-level and low-level agents (i.e., \\(\\pi_h\\) and \\(\\pi_l\\)) act in an interleaving manner. The high-level agent generates and summarizes meta-thoughts from the prompt and interaction history, while the low-level agent executes detailed problem-solving under those instructions. We formulate the multi-agent meta-thinking reasoning process (MAMRP) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.401, + 0.467, + 0.824, + 0.482 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} \\sim \\pi_ {l} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\pi_ {h} (\\mathbf {m} \\mid \\mathbf {x}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.488, + 0.825, + 0.543 + ], + "angle": 0, + "content": "While the single-turn MAMRP offers a straightforward approach, it lacks the ability to perform immediate and fine-grained cognitive switching during the reasoning process, which limits its effectiveness on complex, long-horizon planning tasks. Therefore, we extend Eq. (5) and formulate the multi-turn MAMRP as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.306, + 0.55, + 0.825, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} _ {T} \\sim \\prod_ {t = 1} ^ {T} \\pi_ {l} \\left(\\mathbf {y} _ {t} \\mid \\mathbf {x}, \\{\\mathbf {m}, \\mathbf {y} \\} _ {< t}, \\mathbf {m} _ {t}\\right) \\pi_ {h} \\left(\\mathbf {m} _ {t} \\mid \\mathbf {x}, \\{\\mathbf {m}, \\mathbf {y} \\} _ {< t}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.597, + 0.75, + 0.612 + ], + "angle": 0, + "content": "where \\( T \\) is the number of turns. Similarly, we present the process with a directed graph:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.62, + 0.825, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\mathbf {m} _ {1} \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {1} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\mathbf {m} _ {2} \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {2} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\dots \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {T} \\sim \\mathbf {a}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.653, + 0.825, + 0.681 + ], + "angle": 0, + "content": "As a complex reasoning system, MAMRP provides various optimization opportunities in scaling inference-time computation. We leave further discussion of these aspects in Appendix C.1." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.697, + 0.54, + 0.712 + ], + "angle": 0, + "content": "3.2 Training MAMRP: A Multi-Agent RL Method" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.722, + 0.825, + 0.765 + ], + "angle": 0, + "content": "Multi-agent RL, unlike single-agent RL in a deterministic MDP, must contend with stochastic, nonstationary dynamics and rewards, making optimization more challenging. We start by considering an easier case, the optimization of single-turn MAMRP." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.779, + 0.457, + 0.794 + ], + "angle": 0, + "content": "3.2.1 Optimizing Single-turn MAMRP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.803, + 0.825, + 0.845 + ], + "angle": 0, + "content": "To train the system from Sec. 3.1, we embed it as a Markov Game between the two agents. Suppose the two LLM agents are parameterized by \\(\\theta_h\\) and \\(\\theta_l\\), respectively. Define a joint hierarchical policy over sequential decisions \\(\\mathbf{m}\\) and \\(\\mathbf{y}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.329, + 0.852, + 0.825, + 0.869 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} \\sim \\pi_ {\\left(\\theta_ {h}, \\theta_ {l}\\right)} (\\mathbf {y} \\mid \\mathbf {x}) := \\pi_ {\\theta_ {l}} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\cdot \\pi_ {\\theta_ {h}} (\\mathbf {m} \\mid \\mathbf {x}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.875, + 0.82, + 0.891 + ], + "angle": 0, + "content": "Let \\( R(\\mathbf{y}, \\mathbf{y}^*) \\) denote the final reward serves as the objective function \\( \\mathcal{J}(\\theta_h, \\theta_l) \\) for the joint policy:" + }, + { + "type": "equation", + "bbox": [ + 0.368, + 0.898, + 0.825, + 0.916 + ], + "angle": 0, + "content": "\\[\n\\mathcal {J} \\left(\\theta_ {h}, \\theta_ {l}\\right) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\mathbb {E} _ {\\mathbf {y} \\sim \\pi \\left(\\theta_ {h}, \\theta_ {l}\\right)} R (\\mathbf {y}, \\mathbf {y} ^ {*}). \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.505, + 0.947 + ], + "angle": 0, + "content": "4" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.194, + 0.089, + 0.329, + 0.101 + ], + "angle": 0, + "content": "RL for VRP & MRP" + }, + { + "type": "image", + "bbox": [ + 0.177, + 0.103, + 0.346, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.365, + 0.089, + 0.581, + 0.103 + ], + "angle": 0, + "content": "ReMA with Separate Parameters" + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.104, + 0.603, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.608, + 0.089, + 0.815, + 0.102 + ], + "angle": 0, + "content": "ReMA with Shared Parameters" + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.104, + 0.822, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.17, + 0.279, + 0.825, + 0.378 + ], + "angle": 0, + "content": "Figure 2: Comparison of training pipelines. Left: RL training of VRP and MRP, where a single LM agent is updated either with mixed (VRP) or explicit (MRP) meta-thinking. Middle: ReMA with separate parameters for the high-level (meta-thinking) and low-level (reasoning) agents; training alternates between freezing one agent and updating the other. Right: ReMA with shared parameters and multi-turn interactions: both agents share the same parameters and are distinguished by their system prompts. Training employs a turn-level ratio for stable multi-turn reinforcement learning and efficient updates, ensuring each turn's contribution is controlled to prevent instability." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.394, + 0.825, + 0.423 + ], + "angle": 0, + "content": "During optimization procedure, the high-level policy \\(\\pi_{\\theta_h}\\) and low-level policy \\(\\pi_{\\theta_l}\\) aim to maximize their respective rewards independently. The optimization goals for agents are:" + }, + { + "type": "equation", + "bbox": [ + 0.324, + 0.43, + 0.825, + 0.453 + ], + "angle": 0, + "content": "\\[\n\\theta_ {h} ^ {*} = \\arg \\max _ {\\theta_ {h}} \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\mathbf {m} \\sim \\pi_ {\\theta_ {h}}, \\mathbf {y} \\sim \\pi_ {\\theta_ {l} ^ {*}}} \\left[ R _ {h} (\\mathbf {m}, \\mathbf {y}, \\mathbf {y} ^ {*}) \\right], \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.298, + 0.455, + 0.825, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\theta_ {l} ^ {*} \\left(\\theta_ {h}\\right) = \\arg \\max _ {\\theta_ {l}} \\mathbb {E} _ {\\left(\\mathbf {x}, \\mathbf {y} ^ {*}\\right) \\sim \\mathcal {D}, \\mathbf {m} \\sim \\pi_ {\\theta_ {h}}, \\mathbf {y} \\sim \\pi_ {\\theta_ {l}}} \\left[ R _ {l} \\left(\\mathbf {m}, \\mathbf {y}, \\mathbf {y} ^ {*}\\right) \\right], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.487, + 0.825, + 0.545 + ], + "angle": 0, + "content": "where \\( R_{h} \\) and \\( R_{l} \\) are policies' individual reward functions, including \\( R \\) and regularization according to tasks and models, e.g., different format rewards (refer to Appendix C.2 for details). The detailed algorithm is in the Algorithm 1. We illustrate the MAMRP inference procedure and the proposed training method in Fig. 2. We also provide an analysis of different loss functions in Appendix C.5." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.56, + 0.466, + 0.575 + ], + "angle": 0, + "content": "3.2.2 Scaling up to Multi-turn MAMRP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.584, + 0.825, + 0.613 + ], + "angle": 0, + "content": "To scale up to multi-turn MAMRP, we can still adopt the iterative training strategy in Sec. 3.2.1. However, we make some changes to improve the efficiency of rollout and training." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.619, + 0.825, + 0.703 + ], + "angle": 0, + "content": "First, we implement a parameter-sharing strategy where both high-level and low-level agents utilize identical model weights \\(\\theta\\), distinguished only by role-specific system prompts \\(S_{h}\\) and \\(S_{l}\\). Formally, we define \\(\\pi_h = \\pi_\\theta (\\cdot |S_h,\\cdot)\\) and \\(\\pi_l = \\pi_\\theta (\\cdot |S_l,\\cdot)\\), sharing the same underlying parameters rather than maintaining separate model instances. This approach eliminates the need for frequent model swapping on GPU during rollout, avoiding inefficient wait times, while enabling larger batch sizes during training to simultaneously optimize policies for both meta-thinking and reasoning roles." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.707, + 0.825, + 0.748 + ], + "angle": 0, + "content": "Second, we propose a multi-turn GRPO with turn-level ratio to address the challenges of multi-turn MAMRP. The trajectory-level averaged objective with turn-level ratio of \\(\\pi_{l}\\) is defined as (The objective of \\(\\pi_h\\) is the similar but with different system prompt):" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.754, + 0.435, + 0.773 + ], + "angle": 0, + "content": "\\[\n\\mathcal {J} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\{(\\mathbf {m} _ {i}, \\mathbf {y} _ {i}) \\} _ {i = 1} ^ {G} \\sim \\pi_ {\\theta_ {\\mathrm {o l d}}} (\\cdot | \\mathbf {x})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.776, + 0.824, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\left. \\left[ \\frac {1}{G} \\sum_ {i = 1} ^ {G} \\frac {1}{T _ {i}} \\sum_ {t = 1} ^ {T _ {i}} \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} \\left(\\min \\left(r _ {i, t} (\\theta) \\hat {A} _ {i, t, j}, \\operatorname {c l i p} \\left(r _ {i, t} (\\theta), 1 - \\epsilon , 1 + \\epsilon\\right) \\hat {A} _ {i, t, j}\\right) - \\beta D _ {\\mathrm {K L}} \\left(\\pi_ {\\theta} \\| \\pi_ {\\text {r e f}}\\right)\\right) \\right] \\right. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.827, + 0.825, + 0.856 + ], + "angle": 0, + "content": "where \\(\\mathbf{y}_{i,t,j}\\) is the \\(j\\)-th token at turn \\(t\\) of the reasoning agent of the \\(i\\)-th trajectory. And the turn-level ratio for clipping is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.865, + 0.825, + 0.909 + ], + "angle": 0, + "content": "\\[\nr _ {i, t} (\\theta) = \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} r _ {i, t, j} (\\theta) = \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} \\frac {\\pi_ {\\theta} \\left(\\mathbf {y} _ {i , t , j} \\mid \\mathbf {x} , \\left\\{\\mathbf {m} _ {i , ,} , \\mathbf {y} _ {i ,} \\right\\} _ {< t} , \\mathbf {m} _ {i , t} , \\mathbf {y} _ {i , t , < j}\\right)}{\\pi_ {\\theta_ {\\mathrm {o l d}}} \\left(\\mathbf {y} _ {i , t , j} \\mid \\mathbf {x} , \\left\\{\\mathbf {m} _ {i , ,}, \\mathbf {y} _ {i ,} \\right\\} _ {< t} , \\mathbf {m} _ {i , t} , \\mathbf {y} _ {i , t , < j}\\right)}. \\tag {13}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.504, + 0.948 + ], + "angle": 0, + "content": "5" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.825, + 0.162 + ], + "angle": 0, + "content": "The introduction of the turn-level ratio serves two key purposes. First, using a token-level ratio (Eq. (2)) in the objective introduces bias for multi-turn training, as it averages over all tokens in a trajectory. This means that tokens within longer turns (those containing more tokens) can disproportionately influence the overall loss, and averaging at the token level may encourage excessively long single-turn responses. Second, clipping each token independently risks instability during training." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.168, + 0.827, + 0.239 + ], + "angle": 0, + "content": "In contrast, the turn-level ratio aligns more closely with the underlying MDP formulation by treating all tokens within a turn as a single action and applying clipping at the turn level. Intuitively, this approach stabilizes training by preventing the LLM from making unstable updates that could result in extreme outputs, such as overly long repetitions or incoherent text. We conduct experimental verification in subsequent empirical results (Sec. 4.3)." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.259, + 0.315, + 0.276 + ], + "angle": 0, + "content": "4 Experiments" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.292, + 0.825, + 0.348 + ], + "angle": 0, + "content": "To evaluate the effectiveness and efficiency of ReMA, we conduct experiments on challenging benchmarks for two types of tasks: mathematical reasoning and LLM-as-a-Judge with three different LLMs. Then, we investigate the models' performance in both single- & multi-turn settings. Finally, we provide ablation studies and qualitative analyses of our method." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.366, + 0.357, + 0.381 + ], + "angle": 0, + "content": "4.1 Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.392, + 0.825, + 0.449 + ], + "angle": 0, + "content": "We first analyze the single-turn case of ReMA, i.e., \\( T = 1 \\). The high-level agent generates a complete meta-thinking trace in one shot, and the low-level agent follows the instructions and outputs the final results. Single-turn ReMA reduces stochasticity and training cost while our experiments show that it still provides meaningful performance gains." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.465, + 0.825, + 0.548 + ], + "angle": 0, + "content": "Benchmarks We conduct experiments on two types of tasks: mathematical reasoning and LLM-as-a-Judge. For mathematical reasoning experiments, we train models on 7.5k training samples in MATH [Hendrycks et al., 2021] and use MATH500 [Lightman et al., 2023] as the in-distribution test dataset. Additionally, we test the optimized models on out-of-distribution datasets: GSM8K [Cobbe et al., 2021], AIME24\\(^{4}\\), AMC23\\(^{5}\\), GaoKao2023En [Zhang et al., 2023], Minerva Math [Lewkowycz et al., 2022], and Olympiad Bench [He et al., 2024]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.554, + 0.825, + 0.624 + ], + "angle": 0, + "content": "For LLM-as-a-Judge benchmarks, we train models on RewardBench [Lambert et al., 2024]. Specifically, we convert the original data into a pair-ranking format and split it into a training set of 5k items and a test set of 970 items, denoted as RewardBench970. The models are also tested on JudgeBench [Tan et al., 2024] to assess out-of-distribution performance. We refer to Appendix D.1.2 for detailed comparisons and results." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.641, + 0.825, + 0.698 + ], + "angle": 0, + "content": "Baselines, Models, Training Settings We compare pass@1 performance across the following methods: (1) VRP (CoT, step-by-step prompting, Sec. 3.1); (2) \\(\\mathbf{VRP}_{\\mathbf{RL}}\\) (RL under VRP); (3) \\(\\mathbf{MRP}_{\\mathbf{RL}}\\) (RL under MRP with high-level task analysis, Eq. (4)), and (4) ReMA (ours, RL under MAMRP, Eq. (7))." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.702, + 0.825, + 0.801 + ], + "angle": 0, + "content": "We train and test Llama-3-8B-Instruct, Llama-3.1-8B-Instruct [Dubey et al., 2024], and Qwen2.5-7B-Instruct [Team, 2024] on mathematical reasoning benchmarks. For LLM-as-a-judge benchmarks, we train and test Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct. We use instruct-tuned LLMs to prompt them to perform VRP, MRP, and MAMRP directly during training. Unless specified, we use two separate copies of the same model for high- and low-level agents in ReMA. We use the base reward setting in Appendix C.2 by default. And for the underlying RL algorithm, we use REINFORCE++ [Hu, 2025]. We refer to Appendix D for detailed training settings." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.818, + 0.416, + 0.833 + ], + "angle": 0, + "content": "4.2 Results of Single-turn ReMA" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.845, + 0.825, + 0.873 + ], + "angle": 0, + "content": "Question 1. Does single-turn ReMA outperforms baselines on both in-distribution and out-of-distribution test sets?" + }, + { + "type": "page_footnote", + "bbox": [ + 0.191, + 0.884, + 0.713, + 0.898 + ], + "angle": 0, + "content": "4https://huggingface.co/datasets/AI-MO/aimo-validation-aime" + }, + { + "type": "page_footnote", + "bbox": [ + 0.193, + 0.899, + 0.705, + 0.911 + ], + "angle": 0, + "content": "5https://huggingface.co/datasets/AI-MO/aimo-validation-amc" + }, + { + "type": "list", + "bbox": [ + 0.191, + 0.884, + 0.713, + 0.911 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.506, + 0.948 + ], + "angle": 0, + "content": "6" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.171, + 0.1, + 0.825, + 0.155 + ], + "angle": 0, + "content": "Table 1: Performance on in-distribution test sets and out-of-distribution test sets. We also report the improvement/degradation w.r.t. basic CoT performance(VRP). On average, ReMA outperforms all baselines. Particularly on out-of-distribution datasets, ReMA achieves the highest performance on most of the benchmarks." + }, + { + "type": "table_caption", + "bbox": [ + 0.386, + 0.159, + 0.611, + 0.17 + ], + "angle": 0, + "content": "(a) Performance on math benchmarks" + }, + { + "type": "table", + "bbox": [ + 0.207, + 0.173, + 0.794, + 0.54 + ], + "angle": 0, + "content": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3-8B-InstructMATH50030.8033.40 (+2.60)32.80 (+2.00)33.80 (+3.00)
GSM8K67.4881.80 (+14.32)79.68 (+12.20)79.38 (+11.90)
AIME240.000.00 (+0.00)3.33 (+3.33)0.00 (+0.00)
AMC232.5010.00 (+7.50)12.50 (+10.00)22.50 (+20.00)
Gaokao2023en22.3427.53 (+5.19)23.38 (+1.04)28.57 (+6.23)
Minerva Math8.8216.54 (+7.72)18.01 (+9.19)13.97 (+5.15)
Olympiad Bench8.448.89 (+0.45)9.33 (+0.89)8.89 (+0.45)
Average20.0525.45 (+5.40)25.58 (+5.53)26.73 (+6.68)
Llama3.1-8B-InstructMATH50050.8050.20 (-0.60)48.60 (-2.20)53.20 (+2.40)
GSM8K86.0584.53 (-1.52)85.37 (-0.68)87.26 (+1.21)
AIME2410.003.33 (-6.67)6.67 (-3.33)13.33 (+3.33)
AMC2327.5012.50 (-15.00)30.00 (+2.50)20.00 (-7.50)
Gaokao2023en38.9636.10 (-2.86)37.14 (-1.82)37.14 (-1.82)
Minerva Math22.7926.84 (+4.05)25.37 (+2.58)28.31 (+5.52)
Olympiad Bench15.1119.70 (+4.59)15.70 (+0.59)19.56 (+4.45)
Average35.8933.32 (-2.57)35.55 (-0.34)36.97 (+1.08)
Qwen2.5-7B-InstructMATH50075.0077.20 (+2.20)76.40 (+1.40)74.40 (-0.60)
GSM8K92.0491.36 (-0.68)91.81 (-0.23)90.60 (-1.44)
AIME246.676.67 (+0.00)10.00 (+3.33)20.00 (+13.33)
AMC2347.5050.00 (+2.50)52.50 (+5.00)57.50 (+10.00)
Gaokao2023en56.6254.81 (-1.81)55.06 (-1.56)57.92 (+1.30)
Minerva Math35.6634.93 (-0.73)32.35 (-3.31)34.93 (-0.73)
Olympiad Bench38.2238.37 (+0.15)37.78 (-0.44)36.30 (-1.92)
Average50.2450.48 (+0.24)50.84 (+0.60)53.09 (+2.85)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.352, + 0.548, + 0.646, + 0.561 + ], + "angle": 0, + "content": "(b) Performance on LLM-as-a-Judge benchmarks" + }, + { + "type": "table", + "bbox": [ + 0.204, + 0.562, + 0.795, + 0.699 + ], + "angle": 0, + "content": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3.1-8B-InstructRewardBench97069.4882.89 (+13.41)81.13 (+11.65)83.71 (+14.23)
JudgeBench51.2951.94 (+0.65)52.90 (+1.61)52.90 (+1.61)
Average60.3967.41 (+7.02)67.02 (+6.63)68.31 (+7.92)
Qwen2.5-7B-InstructRewardBench97078.5685.36 (+6.80)86.49 (+7.93)83.51 (+4.95)
JudgeBench58.3956.94 (-1.45)58.39 (+0.00)56.94 (-1.45)
Average68.4771.15 (+2.68)72.44 (+3.97)70.22 (+1.75)
" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.739, + 0.825, + 0.795 + ], + "angle": 0, + "content": "Table 1 compares the greedy decoding performance of ReMA against various RL baselines across mathematical benchmarks (Table 1a) and LLM-as-a-Judge benchmarks (Table 1b). Results across different LLMs indicate that, on average, ReMA outperforms all baselines, achieving a maximum improvement of \\(6.68\\%\\) on mathematical benchmarks and \\(8.49\\%\\) on LLM-as-a-Judge benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.801, + 0.825, + 0.912 + ], + "angle": 0, + "content": "Notably, ReMA achieves the highest performance on most benchmarks, particularly on out-of-distribution datasets, with a maximum improvement of \\(20\\%\\) on AMC23 for Llama3-8B-Instruct, \\(13.33\\%\\) on AIME24 for Qwen2.5-7B-Instruct, \\(14.23\\%\\) on RewardBench970 for Llama3.1-8B-Instruct. These results demonstrate the superior out-of-distribution generalization ability conferred by the meta-thinking mechanism in ReMA. However, we observe that the accuracy gains from RL training on instruction-tuned LMs are smaller than from base models (Sec. 4.2.1). This may be due to the higher initial performance and the relatively fixed output distribution of instruction-tuned models, which limits the improvement and peak performance in RL." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.504, + 0.947 + ], + "angle": 0, + "content": "7" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.187, + 0.083, + 0.81, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.267, + 0.825, + 0.296 + ], + "angle": 0, + "content": "Figure 3: An RL experiment with 3 training schemes. While RL from SFT excels on easier problems, RL under Meta-thinking shows superior generalization to harder problems like AIME24." + }, + { + "type": "image", + "bbox": [ + 0.174, + 0.302, + 0.486, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.302, + 0.819, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.423, + 0.825, + 0.454 + ], + "angle": 0, + "content": "Figure 4: Average problem difficulty by action type during training. Left: 1B LM collapses to the EMPTY action. Right: 8B LM adapts to a more complex meta-thinking strategy for harder problems." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.469, + 0.538, + 0.485 + ], + "angle": 0, + "content": "4.2.1 Meta-thoughts boost low-level generalization" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.494, + 0.547, + 0.51 + ], + "angle": 0, + "content": "Question 2. Can Reasoning benefit from Meta-thinking?" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.515, + 0.825, + 0.613 + ], + "angle": 0, + "content": "Here we provide a tiny but motivating example of how ReMA gives better learning dynamics. We use Qwen2.5-Math-7B [Yang et al., 2024] as the starting base model, MATH (level 3-5, about \\(5.5\\mathrm{K}\\) number of instances) as the training dataset, and we compare three reinforcement learning training schemes, in particular: (1) RL from Base: train the base model directly on MATH with binary outcome reward; (2) RL from SFT: SFT the base model with GPT-4o's CoT answers; then RL on train dataset with binary outcome reward; (3) RL under Meta-thinking: SFT the base model with GPT-4o's meta-thinking plans; then RL on train dataset with binary outcome reward." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.619, + 0.825, + 0.675 + ], + "angle": 0, + "content": "The models are evaluated on 3 benchmarks (Fig. 3). SFT brings the best initial accuracy on in-distribution and easier sets, but fails to improve on harder ones. RL from Base yields limited gains. In contrast, RL under Meta-thinking achieves the best learning dynamics and generalizes better to challenging problems (AIME24). See Appendix F.1 for case studies." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.693, + 0.551, + 0.709 + ], + "angle": 0, + "content": "4.2.2 Diverse meta-thinking characteristics of LLMs" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.718, + 0.531, + 0.733 + ], + "angle": 0, + "content": "Question 3. How well can LLMs learn to meta-think?" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.739, + 0.825, + 0.837 + ], + "angle": 0, + "content": "To further analyze meta-thinking behaviors, we train models with structured JSON-format actions inspired by Yue et al.. The meta-thinking agent generate two entries in one LM call, first selects from three actions: DECOMPOSE (breaking into subproblems), REWRITE (simplifying the problem), or EMPTY (direct solving), then generates the corresponding text. We compare Llama-3.1-8B-Instruct and Llama-3.2-1B-Instruct to study scale effects (two 1B models vs two 8B models) on meta-thinking agent's training. We use vLLM guided JSON decoding [Dong et al., 2024] for valid formatting and base reward (reasoning agent's solution accuracy with format constraints)." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.843, + 0.825, + 0.913 + ], + "angle": 0, + "content": "We observe that smaller LMs produce simpler outputs, likely due to limited capacity to maintain valid JSON formatting while exploring diverse reasoning strategies. As Fig. 4 shows, smaller LMs like Llama-3.2-1B-Instruct quickly converge to the simplest EMPTY action to avoid formatting penalties, while larger LMs like Llama-3.1-8B-Instruct can adapt meta-thinking strategies based on problem difficulty. See Appendix F.3 for detailed case studies." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.504, + 0.948 + ], + "angle": 0, + "content": "8" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.177, + 0.079, + 0.468, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.079, + 0.822, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.215, + 0.825, + 0.258 + ], + "angle": 0, + "content": "Figure 5: Training results of multi-turn Figure 6: Ablations of multi-turn ReMA on a tiny subReMA on MATH-Level3-5-8K under different set of MATH, we only show here the training curves of different training and rollout configurations." + }, + { + "type": "title", + "bbox": [ + 0.171, + 0.289, + 0.502, + 0.305 + ], + "angle": 0, + "content": "4.3 Extending ReMA to Multi-turn MAMRP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.322, + 0.825, + 0.352 + ], + "angle": 0, + "content": "We further extend ReMA to multi-turn MAMRP settings, enabling multiple rounds of interaction between the meta-thinking agent and the reasoning agent as defined in Eq. (7)." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.357, + 0.825, + 0.413 + ], + "angle": 0, + "content": "Unlike the inherent VRP capabilities of most LLMs, multi-turn ReMA requires initial bootstrapping. Thus, we constructed a supervised fine-tuning dataset (about 0.8K samples) from LIMO [Ye et al., 2025c] using GPT-4o to establish the starting point for multi-turn interaction capabilities. Then we finetune Qwen2.5-7B before RL training." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.419, + 0.825, + 0.476 + ], + "angle": 0, + "content": "As described in Sec.3.2.2, we deploy the proposed GRPO with turn-level ratio clipping and trajectory-level averaging loss during training. And we remove the KL-divergence term to allow more flexible exploration. By default, the agents share the same parameters and are simultaneously updated using their trajectories. We refer to details in Appendix D.2." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.508, + 0.379, + 0.523 + ], + "angle": 0, + "content": "4.3.1 Results and Ablations" + }, + { + "type": "title", + "bbox": [ + 0.171, + 0.539, + 0.547, + 0.555 + ], + "angle": 0, + "content": "Question 4. Can ReMA be scaled to multi-turn settings?" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.56, + 0.825, + 0.644 + ], + "angle": 0, + "content": "There are two key points revealed by our multi-turn ReMA experiments, as shown in Fig. 5. On one hand, the algorithm can demonstrate effective convergence on the training set, with accuracy steadily increasing from approximately \\(55\\%\\) to \\(70\\%\\) during training. It also achieves an average performance gain of about \\(5\\%\\) across all seven test benchmarks, indicating stable improvements on out-of-distribution data. (Experiment with the rollout config of turn30_token512, see Appendix D.2.2 and Fig. 8 for more details.)" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.649, + 0.826, + 0.775 + ], + "angle": 0, + "content": "On the other hand, we observe that the performance of multi-turn ReMA is highly sensitive to hyperparameters such as the maximum response length per turn and the maximum number of turns. For certain configurations, the model either collapses into producing massive repetitions within a single turn or generates empty responses after only a few turns. Similar phenomena have been reported in concurrent works such as RAGEN [Wang et al., 2025], where these issues are attributed to the lack of fine-grained, reasoning-aware guidance. As a result, multi-turn RL becomes susceptible to long-horizon credit assignment challenges and state drift, often leading to reduced exploration diversity—a phenomenon referred to as the \"Echo Trap\". To address this challenge, it is essential to comprehensively explore the training recipe w.r.t. model, data, and algorithm." + }, + { + "type": "title", + "bbox": [ + 0.171, + 0.78, + 0.747, + 0.796 + ], + "angle": 0, + "content": "Question 5. How does parameter sharing and turn-level ratio affect multi-turn ReMA?" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.801, + 0.826, + 0.913 + ], + "angle": 0, + "content": "As shown in Fig. 6, we compare different configurations on a smaller dataset consisting of 133 samples—19 from each of the 7 MATH problem types—to evaluate sample efficiency and convergence speed. First, all configurations eventually achieve nearly \\(100\\%\\) accuracy on the training dataset. Notably, the trajectory-level loss with turn-level ratio (Turn-Ratio, Eq. (13)) demonstrates substantially better sample efficiency than its token-level variants (Eq. (2)), reaching higher training rewards with fewer steps. We also present the training curve of separate weight setting, the empirical results show that shared parameters with simultaneous updates converge noticeably faster." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.505, + 0.948 + ], + "angle": 0, + "content": "9" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.176, + 0.091, + 0.3, + 0.106 + ], + "angle": 0, + "content": "5 Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.121, + 0.825, + 0.273 + ], + "angle": 0, + "content": "In this paper, we introduced ReMA, a novel framework that leverages multi-agent reinforcement learning to elicit meta-thinking in large language models. By explicitly separating meta-thinking and reasoning processes into distinct agents, our approach enhances both exploration during training and the interpretability of model outputs. We tailored RL algorithms and reward functions to ensure reliable performance. Through comprehensive experiments on mathematical reasoning and LLM-as-a-Judge benchmarks, ReMA consistently achieved superior results, particularly on out-of-distribution datasets. We further extend ReMA to multi-turn settings, enabling the framework to handle more complex reasoning scenarios that require more communication between agents. Our ablations demonstrate how effective coordination between agents evolves, highlighting the promise of reinforcement learning and structured agents' collaboration for advancing the capabilities of language models in complex reasoning tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.492, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "10" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.174, + 0.09, + 0.27, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.173, + 0.113, + 0.826, + 0.157 + ], + "angle": 0, + "content": "Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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Reasoning 20" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.18, + 0.825, + 0.194 + ], + "angle": 0, + "content": "-A.4RL in LLM 21" + }, + { + "type": "list", + "bbox": [ + 0.246, + 0.133, + 0.825, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.198, + 0.824, + 0.212 + ], + "angle": 0, + "content": "B Limitation and Future Work 21" + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.216, + 0.824, + 0.23 + ], + "angle": 0, + "content": "C Supplementary Materials for Method in Section 3 21" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.234, + 0.825, + 0.248 + ], + "angle": 0, + "content": "- C.1 Inference-time Scaling For ReMA 21" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.25, + 0.825, + 0.263 + ], + "angle": 0, + "content": "- C.2 Detailed reward design 22" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.265, + 0.825, + 0.278 + ], + "angle": 0, + "content": "- C.3 Pseudocode of ReMA 23" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.28, + 0.825, + 0.294 + ], + "angle": 0, + "content": "- C.4 Brief convergence analysis 23" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.296, + 0.825, + 0.31 + ], + "angle": 0, + "content": "- C.5 Learning to reason from the perspective of Leader Follower Game 24" + }, + { + "type": "list", + "bbox": [ + 0.246, + 0.234, + 0.825, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.314, + 0.824, + 0.328 + ], + "angle": 0, + "content": "D Training Details 26" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.332, + 0.825, + 0.346 + ], + "angle": 0, + "content": "- D.1 Single-turn ReMA 26" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.348, + 0.825, + 0.361 + ], + "angle": 0, + "content": "\\* D.1.1 Supervised fine-tuning data collection 27" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.362, + 0.825, + 0.375 + ], + "angle": 0, + "content": "\\* D.1.2 Dataset Curation of RewardBench970 27" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.377, + 0.825, + 0.39 + ], + "angle": 0, + "content": "\\*D.1.3 Training on MATH 28" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.391, + 0.825, + 0.405 + ], + "angle": 0, + "content": "\\* D.1.4 Training on Reward Bench 28" + }, + { + "type": "list", + "bbox": [ + 0.273, + 0.348, + 0.825, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.407, + 0.825, + 0.42 + ], + "angle": 0, + "content": "- D.2 Multi-turn ReMA 28" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.422, + 0.825, + 0.435 + ], + "angle": 0, + "content": "\\* D.2.1 SFT data collection of multi-turn MAMRP 29" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.437, + 0.825, + 0.451 + ], + "angle": 0, + "content": "\\* D.2.2 Training on MATH 29" + }, + { + "type": "list", + "bbox": [ + 0.273, + 0.422, + 0.825, + 0.451 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.454, + 0.824, + 0.468 + ], + "angle": 0, + "content": "E Other Experiments 29" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.472, + 0.825, + 0.486 + ], + "angle": 0, + "content": "-E.1 Reward functions shape cross-agent behaviors 29" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.488, + 0.825, + 0.502 + ], + "angle": 0, + "content": "- E.2 Detailed Training Curves on Different Datasets of Multi-turn ReMA 30" + }, + { + "type": "list", + "bbox": [ + 0.246, + 0.472, + 0.825, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.506, + 0.824, + 0.52 + ], + "angle": 0, + "content": "F Qualitative results 30" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.523, + 0.825, + 0.538 + ], + "angle": 0, + "content": "- F.1 High-level policy finds better plans 30" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.539, + 0.825, + 0.553 + ], + "angle": 0, + "content": "- F.2 Case study for Experiments of Different Reward Functions in Appendix E.1 .30" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.554, + 0.825, + 0.568 + ], + "angle": 0, + "content": "- F.3 Case study for Adaptive Meta-thinking in Single-Turn ReMA in Section 4.2.2 30" + }, + { + "type": "list", + "bbox": [ + 0.246, + 0.523, + 0.825, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.573, + 0.824, + 0.587 + ], + "angle": 0, + "content": "G Prompts 31" + }, + { + "type": "title", + "bbox": [ + 0.173, + 0.605, + 0.323, + 0.621 + ], + "angle": 0, + "content": "A Related work" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.635, + 0.827, + 0.734 + ], + "angle": 0, + "content": "Drawing from the bitter lesson [Sutton, 2019], two methods that appear to scale effectively are searching and learning, aligning with current trends in large language models [Xu et al., 2025]. At present, researchers are leveraging these methods to maximize the capabilities of individual transformers, while other efforts are exploring architectures that involve multiple interacting entities. In this paper, we examine this divergence within the context of LLM reasoning, a capability that allows large language models to solve problems through logical reasoning, step-by-step analysis, and inference [Wang et al., 2024a]." + }, + { + "type": "title", + "bbox": [ + 0.173, + 0.748, + 0.379, + 0.764 + ], + "angle": 0, + "content": "A.1 Single LLM Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.773, + 0.827, + 0.913 + ], + "angle": 0, + "content": "Main research works in reasoning involving a single LLM utilize search-based and post-training methods. The fundamental elements of searching methods are text generation and evaluation. Generation schemes include In-Context Learning [Brown et al., 2020], Beam Search [Graves, 2012], and various tree-based searching [Snell et al., 2024]; Evaluation approaches often use outcome accuracy, self-consistency [Wang et al., 2022], or process reward signal [Lightman et al., 2023] as the criteria to select high-quality responses from the generated texts. Post-training method is another research line in opposition to pre-training. Popular training pipelines often involve specific data construction followed by Supervised Fine-tuning [Qin et al., 2024, Ouyang et al., 2022, Hui et al., 2024, Liu et al., 2024], or reinforcement learning to interactively explore learning patterns [Wang et al., 2024a, Zhang et al., 2024a, DeepSeek-AI et al., 2025, Xu et al., 2025]." + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "19" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.176, + 0.093, + 0.394, + 0.106 + ], + "angle": 0, + "content": "A.2 Multiple LLM Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.121, + 0.825, + 0.563 + ], + "angle": 0, + "content": "Integrating multiple entities can potentially surpass the intelligence of the individual model [Chen et al., 2023]. With the rapid emergence of large language models showing a varying level of abilities, some studies have explored facilitating discussions among multiple off-the-shelf LLMs [Zhang et al., 2025a, Chen et al., 2024a, Wang et al., 2023, Du et al., 2023, Zhuge et al., 2023, Tang et al., 2023, Hao et al., 2025, Akata et al., 2023, Hong et al., 2023, Zhang et al., 2024b], taking the form of free discussion [Du et al., 2023, Liang et al., 2023] or structured role assignments [Hong et al., 2023, Zhang et al., 2024b]. Some have applied routing mechanisms to assign tasks to the most suitable expert models [Hu et al., 2024b, Stripelis et al., 2024, Ding et al., 2024, Yue et al., 2025a, Chen et al., 2024c] or merging mechanisms to develop more versatile models [Yadav et al., 2024, Yu et al., 2024, Zhang et al., 2025b]. Beyond aggregating static knowledge from multiple agents, multi-agent LLM training can also enhance reasoning capabilities. For example, multi-agent debates can generate diverse synthetic data, which can subsequently be used for supervised fine-tuning [Estornell et al., 2024, Li et al., 2024, Motwani et al., 2024, Dong and Ma, 2025, Perez et al., 2022, Ye et al., 2025a, Subramaniam et al., 2025]. Reinforcement learning (RL) methods have also been adopted to improve LLM reasoning in areas such as alignment [Perez et al., 2022, Ma et al., 2023] and legibility [Kirchner et al., 2024]. Motwani et al. [2024] utilize a three-agent system for generation and fine-tune the models using Direct Preference Optimization (DPO). Reinforcement Learning with Generative Reward Models (GenRM) [Mahan et al., 2024, Ye et al., 2025b, Jiao et al., 2024, Wang et al., 2024b] represents another common approach of multi-agent training, where the reward signal is derived from the token probabilities of another LLM, coupled with the reasoning process. While our work aligns with these efforts, it diverges by using an additional tunable LLM to provide metacognitive instructions, guiding the low-level LLM during learning, rather than relying on a static GenRM. The most closely related works to ours are MAPoRL [Park et al., 2025] and COPYR [Ma et al., 2024]. MAPoRL is a multi-agent debating framework that uses multi-agent reinforcement learning (MARL) with a learned verifier to fine-tune each LLM agent. COPYR duplicates an LLM into two agents, training them simultaneously in the roles of pioneer and observer using RL. Shen et al. [2025] trained with a novel Chain-of-Action-Thought (COAT) framework that embeds meta-action tokens for self-reflection and exploration into an autoregressive search process. However, unlike our approach, which explicitly separates metacognition from plan execution, these methods do not decompose the reasoning process but instead focus on improving direct chain-of-thought generation. Furthermore, our experiments are conducted on a larger scale and include more challenging problems." + }, + { + "type": "title", + "bbox": [ + 0.176, + 0.593, + 0.38, + 0.606 + ], + "angle": 0, + "content": "A.3 Hierarchical Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.621, + 0.825, + 0.911 + ], + "angle": 0, + "content": "Partitioning reasoning into hierarchical processes has been explored in prior research to make biological sense [Ye et al., 2018, Langley et al., 2004]. In the context of language models, a hierarchical structure has been used to facilitate diverse reasoning patterns, including planning [Puerta-Merino et al., 2025, Sun et al., 2024, Song et al., 2023, Rana et al., 2023, Chen et al., 2024d, Yan et al., 2023, Xiao et al., 2024], validation [Haji et al., 2024, Xi et al., 2024] and self-refinement [Madaan et al., 2023, Kumar et al., 2024, Welleck et al., 2022]. For instance, EvalPlanner [Saha et al., 2025b] is a framework that conducts reasoning through plan generation and execution. DOTS [Yue et al., 2024] extends decomposition by integrating a tree-based searching method with Analysis, Solution, and Verification layers. Marco-o1 [Zhao et al., 2024] focuses on open-ended problem-solving and abstract thinking, dynamically adjusting reasoning granularity and incorporating reflection mechanisms to enhance reasoning performance. Beyond these approaches, metacognition [Flavell, 1979] has been identified as another critical component of reasoning, referring to the intuitive understanding of one's own cognitive and reasoning processes [Gao et al., 2024, Wang and Zhao, 2023]. Wang and Zhao [2023] proposed a metacognitive prompting strategy to improve large language model (LLM) capabilities. Didolkar et al. [2024] further developed a prompt-guided method that enables models to label math problems with the required skills and subsequently use these labels to solve new problems. Gao et al. [2024] introduce meta-reasoner which use contextual multi-arm bandit to learn a high-level \"advisor\" over low-level reasoning process. Xiang et al. [2025] provides a Meta-CoT framework to think about its own thinking. They use construction-based methods as well as reinforcement learning to develop meta-cognitive skills. Qingsong et al. [2025] introduces a RL framework for dynamic instruction selection during fine-tuning. In our work, we also value reflect-" + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.937, + 0.508, + 0.947 + ], + "angle": 0, + "content": "20" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.825, + 0.123 + ], + "angle": 0, + "content": "ing on reasoning processes, and we enhance metacognitive abilities through two-agent interaction and reinforcement learning at both end." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.138, + 0.303, + 0.153 + ], + "angle": 0, + "content": "A.4 RL in LLM" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.164, + 0.827, + 0.399 + ], + "angle": 0, + "content": "Recent advancements in applying RL to LLMs have enhanced their reasoning and decision-making capabilities. Liu et al. [2025] examines token-level optimization biases by introducing Dr. GRPO to stabilize policy gradients. VAPO [Yue et al., 2025b] enhances PPO with value-aware perturbations and adaptive reward shaping to improve robustness in sparse-reward reasoning tasks. DAPO [Yu et al., 2025] provides a scalable, modular RL framework that integrates distributed rollout collection and dynamic replay buffers for reproducible training at scale. SimpleRL-Zoo [Zeng et al., 2025] conducts zero-shot RL experiments across open-base LLMs to uncover emergent cognitive behaviors under minimal reward signals. Echo Chamber [Zhao et al., 2025] investigates how RL fine-tuning algorithms can amplify pretrained model biases and proposes regularization to mitigate over-amplification. Wen et al. [2024] decomposes high-level language actions into token-level operations to achieve finer-grained credit assignment. Some works push RL training for single-turn to multi-turn. Search-R1 [Jin et al., 2025] trains LLMs to orchestrate multi-turn search strategies with RL-optimized decision policies to improve question-answering accuracy. ArCHer [Zhou et al., 2024] employs a hierarchical, multi-turn RL architecture with manager and worker policies to efficiently handle long-horizon dialogue tasks. RAGEN [Wang et al., 2025] introduces trajectory filtering and critic modules within a multi-turn RL framework to stabilize learning and reduce shallow policy behaviors." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.42, + 0.453, + 0.436 + ], + "angle": 0, + "content": "B Limitation and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.451, + 0.825, + 0.548 + ], + "angle": 0, + "content": "In this work, we only test ReMA on math and LLM-as-a-Judge benchmarks. Though the results show the effectiveness of ReMA, adopting ReMA to tasks where naturally needs multi-turn interaction between several interleaved agents has great potential. Moreover, a comprehensive understanding of the learning dynamics of multi-turn RL and multi-turn MARL for LLMs is needed. Finally, there's still sufficient space to further improve the procedure of multi-turn multi-agent rollout through modern LLM speed up techniques, e.g. prefetch-decode disaggregation and asynchronous rollout." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.569, + 0.627, + 0.587 + ], + "angle": 0, + "content": "C Supplementary Materials for Method in Section 3" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.601, + 0.444, + 0.617 + ], + "angle": 0, + "content": "C.1 Inference-time Scaling of ReMA" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.627, + 0.825, + 0.683 + ], + "angle": 0, + "content": "In this section, we discuss how to enhance the inference-time computation of our hierarchical system, specifically focusing on the interaction between the high-level and low-level agents. The total number of model samples required for inference is determined by the product of the sampling budget allocated to each agent." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.689, + 0.825, + 0.731 + ], + "angle": 0, + "content": "For instance, in a simple single-turn setting, if the high-level agent samples \\( k_{1} \\) responses and each of these responses leads to \\( k_{2} \\) samples from the low-level agent, the total number of model calls required is:" + }, + { + "type": "equation", + "bbox": [ + 0.412, + 0.732, + 0.584, + 0.747 + ], + "angle": 0, + "content": "\\[\n\\text {T o t a l s a m p l e s} = k _ {1} \\times k _ {2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.753, + 0.825, + 0.822 + ], + "angle": 0, + "content": "Given a fixed computational budget, an important question arises: how should the sampling budget be distributed between the high-level and low-level agents to maximize performance? Allocating more samples to the high-level agent may increase diversity in reasoning strategies while allocating more to the low-level agent may yield more refined solutions for a given metacognitive plan." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.829, + 0.825, + 0.857 + ], + "angle": 0, + "content": "Another crucial consideration is how to perform reranking on the final outputs. Two potential strategies include:" + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.87, + 0.825, + 0.913 + ], + "angle": 0, + "content": "- Hierarchical reranking: First, for each high-level response, rank and aggregate the low-level responses under it. Then, rank the aggregated results across different high-level responses." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "21" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.217, + 0.092, + 0.825, + 0.121 + ], + "angle": 0, + "content": "- Flat reranking: Directly rank all sampled responses together, regardless of the hierarchy of high-level reasoning steps." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.132, + 0.826, + 0.175 + ], + "angle": 0, + "content": "Balancing sampling allocation and designing an effective reranking strategy are key challenges in efficiently scaling our multi-agent reasoning system. In the next section, we explore empirical results comparing different allocation strategies and ranking methods." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.19, + 0.379, + 0.206 + ], + "angle": 0, + "content": "C.2 Detailed reward design" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.215, + 0.825, + 0.245 + ], + "angle": 0, + "content": "As described in Sec. 3.2, we update both high-level and low-level agents by assigning rewards based on the low-level policy output. Below, we outline several potential reward designs:" + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.254, + 0.825, + 0.284 + ], + "angle": 0, + "content": "- Correctness reward: For tasks with explicit ground truth, we assign rewards based on the correctness of the low-level agent's output." + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.286, + 0.825, + 0.315 + ], + "angle": 0, + "content": "- Format reward: For tasks that require a specific output format, we enforce adherence to the prescribed structure by providing a format reward." + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.318, + 0.825, + 0.362 + ], + "angle": 0, + "content": "- To encourage the high-level agent to generate informative and unambiguous meta-thinking, and to stabilize the low-level outputs, we reward the high-level agent when the low-level agent produces consistent responses. Specifically, the consistency reward is defined as" + }, + { + "type": "list", + "bbox": [ + 0.217, + 0.254, + 0.825, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.404, + 0.367, + 0.652, + 0.399 + ], + "angle": 0, + "content": "\\[\nR _ {h} = \\frac {\\text {m a x o c c u r r e n c e o f a n a n s w e r}}{\\text {t o t a l n u m b e r o f r e s p o n s e s}}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.407, + 0.825, + 0.451 + ], + "angle": 0, + "content": "To examine multi-agent metacognition-integrated reasoning with different reward designs, we experiment with different reward function designs to encourage effective collaboration and structured reasoning. Below, we introduce and justify several reward schemes." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.463, + 0.826, + 0.52 + ], + "angle": 0, + "content": "1. Correctness and Format-Aware Reward (Base Setting) In our primary reward setting, the system's overall correctness is used as the primary reward signal, supplemented by format-based rewards for both the high-level and low-level agents. Using mathematical problem-solving as an example:" + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.531, + 0.825, + 0.561 + ], + "angle": 0, + "content": "- Low-level agent \\((\\pi_{\\theta_l})\\): Receives a reward of \\(+1.0\\) for a correct answer. If the answer is incorrect, the agent is further penalized based on format compliance. Specifically:" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.563, + 0.825, + 0.59 + ], + "angle": 0, + "content": "- If the output contains the designated answer-indicating format (e.g., boxed in Latex), it receives \\(-0.5\\)." + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.593, + 0.825, + 0.621 + ], + "angle": 0, + "content": "- Otherwise, it receives \\(-1.0\\), as a missing format often suggests an incomplete or unstructured response." + }, + { + "type": "list", + "bbox": [ + 0.245, + 0.563, + 0.825, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.625, + 0.826, + 0.682 + ], + "angle": 0, + "content": "- High-level agent \\((\\pi_{\\theta_h})\\): Receives the average correctness of the low-level agent's sampled responses as its reward. Additionally, to prevent the high-level agent from directly generating explicit answers instead of guiding reasoning, a strong penalty of \\(-1.0\\) is applied if it includes an explicit answer format (e.g., boxed)." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.695, + 0.826, + 0.753 + ], + "angle": 0, + "content": "2. Consistency-Based Reward Instead of using correctness as the high-level reward signal, this approach rewards the high-level agent for promoting consistent responses from the low-level agent, regardless of actual correctness. The consistency reward is defined as the proportion of the most frequently occurring answer among all sampled responses:" + }, + { + "type": "equation", + "bbox": [ + 0.377, + 0.768, + 0.825, + 0.8 + ], + "angle": 0, + "content": "\\[\nR _ {h} = \\frac {\\text {m a x o c c u r r e n c e o f a n a n s w e r}}{\\text {t o t a l n u m b e r o f r e s p o n s e s}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.808, + 0.825, + 0.866 + ], + "angle": 0, + "content": "If the majority of responses do not contain a definitive answer, the reward is set to zero. We also add the format penalty to the high-level agent if its output contains the designated answer-indicating format. This incentivizes the high-level agent to guide the low-level agent toward more stable, detailed, reproducible outputs rather than erratic reasoning paths." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.87, + 0.825, + 0.913 + ], + "angle": 0, + "content": "These different reward formulations allow us to investigate various dimensions of metacognitive reasoning: correctness, consistency, etc. We empirically compare their effects on learned metacognitive reasoning patterns in Sec. E.1." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "22" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.202, + 0.096, + 0.764, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.319, + 0.825, + 0.39 + ], + "angle": 0, + "content": "Figure 7: Our method can be viewed as a combination of practical TRPO and block coordinate ascent, with the high and low-level models treated as distinct components within a larger neural network. Note that the figure does not represent the exact gradient back-propagation flow but rather highlights the key idea that we separate the high- and low-level models. This separation allows for the independent computation of gradients and the independent training of each model." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.423, + 0.367, + 0.436 + ], + "angle": 0, + "content": "C.3 Pseudocode of ReMA" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.452, + 0.449, + 0.467 + ], + "angle": 0, + "content": "The pseudocode is shown in Algorithm 1." + }, + { + "type": "code_caption", + "bbox": [ + 0.174, + 0.489, + 0.404, + 0.504 + ], + "angle": 0, + "content": "Algorithm 1 Single turn MAMRP" + }, + { + "type": "algorithm", + "bbox": [ + 0.174, + 0.508, + 0.825, + 0.744 + ], + "angle": 0, + "content": "Require: High-level policy \\(\\pi_h\\), Low-level policy \\(\\pi_l\\), Dataset \\(\\mathcal{D}\\), Optimizers for \\(\\pi_h\\) and \\(\\pi_l\\). \\(\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}\\) to filter training dataset \n1: Initialize \\(\\pi_h\\) and \\(\\pi_l\\) \n2: while not converged do \n3: build training dataset \\(\\mathcal{D}_l\\) with \\(\\pi_h, \\pi_l, \\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}\\) \n4: for Sample \\((\\mathbf{x}, \\mathbf{m}, \\mathbf{y}^*) \\sim \\mathcal{D}_l\\) do \n5: Generate \\(\\mathbf{y} \\sim \\pi_l(\\mathbf{x}, \\mathbf{m})\\) \n6: Compute low-level reward \\(R_l(\\mathbf{y}, \\mathbf{y}^*)\\) \n7: Update \\(\\pi_l\\) using \\(\\nabla_{\\theta_l} \\mathbb{E}[R_l]\\) \n8: end for \n9: build training dataset \\(\\mathcal{D}_h\\) with \\(\\pi_h, \\pi_l, \\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}\\) \n10: for Sample \\((\\mathbf{x}, \\mathbf{y}^*) \\sim \\mathcal{D}_h\\) do \n11: Generate \\(\\mathbf{m} \\sim \\pi_h(\\mathbf{x})\\) and \\(\\mathbf{y} \\sim \\pi_l(\\mathbf{x}, \\mathbf{m})\\) \n12: Compute high-level reward \\(R_h(\\mathbf{m}, \\mathbf{y}, \\mathbf{y}^*)\\) \n13: Update \\(\\pi_h\\) using \\(\\nabla_{\\theta_h} \\mathbb{E}[R_h]\\) \n14: end for \n15: end while" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.793, + 0.402, + 0.808 + ], + "angle": 0, + "content": "C.4 Brief convergence analysis" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.822, + 0.825, + 0.879 + ], + "angle": 0, + "content": "We reuse the notations from Sec. 3.2, where \\(\\mathbf{x}\\) is task prompt, \\(\\mathbf{y}\\) is generated answer, \\(\\mathbf{y}^*\\) is groundtruth, \\(\\mathbf{m}\\) is metacognition on task solving, \\(\\pi_{\\theta_h}\\) and \\(\\pi_{\\theta_l}\\) are high- and low-level agents with parameters \\(\\theta_h\\) and \\(\\theta_l\\). We consider the joint hierarchical policy defined in Eq. (8) and update the objective as in Eq. (9)." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.884, + 0.825, + 0.913 + ], + "angle": 0, + "content": "To leverage existing RL and optimization convergence analysis methods, we treat the two models as components of a larger model, as illustrated in Fig. 7. When updating one model, we treat the other" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "23" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.172, + 0.092, + 0.741, + 0.107 + ], + "angle": 0, + "content": "model as part of a stationary environment. The gradients with respect to \\(\\theta_h\\) and \\(\\theta_l\\) are:" + }, + { + "type": "equation", + "bbox": [ + 0.227, + 0.113, + 0.768, + 0.147 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\theta_ {h}} J (\\theta_ {h}, \\theta_ {l}) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\sum_ {\\mathbf {m} \\sim \\pi_ {h} (\\mathbf {m} | \\mathbf {x}; \\theta_ {h})} \\nabla_ {\\theta_ {h}} \\pi_ {h} (\\mathbf {m} | \\mathbf {x}; \\theta_ {h}) \\left[ \\mathbb {E} _ {\\mathbf {y} \\sim \\pi_ {l} (\\mathbf {y} | \\mathbf {x}, \\mathbf {m})} R (\\mathbf {y}, \\mathbf {y} ^ {*}) \\right],\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.23, + 0.149, + 0.672, + 0.184 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\theta_ {l}} J (\\theta_ {h}, \\theta_ {l}) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\sum_ {\\mathbf {y} \\sim \\pi (\\theta_ {h}, \\theta_ {l})} \\nabla_ {\\theta_ {l}} \\pi_ {l} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}; \\theta_ {h}); \\theta_ {l}) R (\\mathbf {y}, \\mathbf {y} ^ {*}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.189, + 0.825, + 0.217 + ], + "angle": 0, + "content": "We can compute the gradients with log trick and estimate \\(\\mathbb{E}_{\\mathbf{y}\\sim \\pi_l(\\mathbf{y}|\\mathbf{x},\\mathbf{m})}R(\\mathbf{y},\\mathbf{y}^*)\\) with Monte Carlo method." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.224, + 0.825, + 0.253 + ], + "angle": 0, + "content": "Equipped with the objective function and gradient computation, we update the models iteratively. Without loss of generality, we analyze the case where the high-level policy is updated first:" + }, + { + "type": "equation", + "bbox": [ + 0.39, + 0.257, + 0.594, + 0.284 + ], + "angle": 0, + "content": "\\[\n\\theta_ {h} ^ {(t + 1)} = \\arg \\max _ {\\theta_ {h}} J (\\theta_ {h}, \\theta_ {l} ^ {(t)}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.393, + 0.286, + 0.605, + 0.311 + ], + "angle": 0, + "content": "\\[\n\\theta_ {l} ^ {(t + 1)} = \\arg \\max _ {\\theta_ {l}} J \\left(\\theta_ {h} ^ {(t + 1)}, \\theta_ {l}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.317, + 0.825, + 0.373 + ], + "angle": 0, + "content": "Regarding the different regularizations \\( R_{h} \\) and \\( R_{l} \\) in Eqs. (10) and (11) for the different policies, instead of directly integrating them into the loss function, we treat them as constraints, as done in Trust Region Policy Optimization (TRPO) [Schulman et al., 2015]. Note that when one policy is fixed, the other policy operates in a stationary decision process." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.38, + 0.825, + 0.436 + ], + "angle": 0, + "content": "Based on the defined objective and update method, we apply TRPO and block coordinate ascent. First, recall that when updating a single policy, TRPO guarantees monotonic improvement by optimizing a lower bound. Specifically, let \\(\\pi_{\\mathrm{old}}\\) and \\(\\pi\\) represent the old and current policies, respectively. We define a surrogate objective as:" + }, + { + "type": "equation", + "bbox": [ + 0.336, + 0.441, + 0.662, + 0.475 + ], + "angle": 0, + "content": "\\[\nL _ {\\pi_ {\\mathrm {o l d}}} (\\pi) = \\mathbb {E} _ {s \\sim \\pi_ {\\mathrm {o l d}}, a \\sim \\pi_ {\\mathrm {o l d}}} \\left[ \\frac {\\pi (a | s)}{\\pi_ {\\mathrm {o l d}} (a | s)} A ^ {\\pi_ {\\mathrm {o l d}}} (s, a) \\right],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.478, + 0.708, + 0.493 + ], + "angle": 0, + "content": "As shown by Schulman et al. [2015], the true objective of \\(\\pi\\) is lower-bounded by:" + }, + { + "type": "equation", + "bbox": [ + 0.325, + 0.497, + 0.673, + 0.519 + ], + "angle": 0, + "content": "\\[\nJ (\\pi) \\geq L _ {\\pi_ {\\mathrm {o l d}}} (\\pi) - C \\cdot \\max _ {s} \\mathrm {K L} [ \\pi_ {\\mathrm {o l d}} (\\cdot | s), \\pi (\\cdot | s) ],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.524, + 0.825, + 0.566 + ], + "angle": 0, + "content": "for some constant \\( C \\). By optimizing the right-hand side of the above inequality, we are guaranteed to improve the performance of \\( \\pi \\). Therefore, for policies \\( \\pi^t \\) and \\( \\pi^{t + 1} \\) obtained from iterations \\( t \\) and \\( t + 1 \\) using the TRPO method, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.436, + 0.57, + 0.56, + 0.589 + ], + "angle": 0, + "content": "\\[\nJ (\\pi^ {t + 1}) \\geq J (\\pi^ {t}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.599, + 0.825, + 0.667 + ], + "angle": 0, + "content": "Now, returning to our updating method, we treat the high- and low-level policies as two blocks of a single agent. The iterative update process can thus be viewed as a cyclic block coordinate ascent, where the two policies are updated in a fixed order. By updating each block using the TRPO method, and improving the surrogate objective within the KL constraint, each block update does not decrease \\( J \\):" + }, + { + "type": "equation", + "bbox": [ + 0.4, + 0.673, + 0.567, + 0.69 + ], + "angle": 0, + "content": "\\[\nJ \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t}\\right) \\geq J \\left(\\theta_ {h} ^ {t}, \\theta_ {l} ^ {t}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.402, + 0.693, + 0.597, + 0.712 + ], + "angle": 0, + "content": "\\[\nJ \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t + 1}\\right) \\geq J \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.723, + 0.825, + 0.754 + ], + "angle": 0, + "content": "Thus \\( J(\\theta_h^{t + 1},\\theta_l^{t + 1})\\geq J(\\theta_h^t,\\theta_l^t) \\). This repeated coordinate maximization converges to a fixed point, where no single coordinate update can further improve \\( J(\\theta_h,\\theta_l) \\)." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.759, + 0.825, + 0.802 + ], + "angle": 0, + "content": "Given the theoretical monotonic improvement with TRPO and block coordinate ascent, we adopt a practical version of TRPO in our experiments, specifically Proximal Policy Optimization (PPO) [Schulman et al., 2017] or GRPO [Shao et al., 2024]." + }, + { + "type": "title", + "bbox": [ + 0.171, + 0.817, + 0.679, + 0.832 + ], + "angle": 0, + "content": "C.5 Learning to reason from the perspective of Leader Follower Game" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.843, + 0.826, + 0.913 + ], + "angle": 0, + "content": "Besides the loss function in the main part, we also propose to frame the problem as a leader-follower game. By analyzing the equilibria of the leader-follower game, we demonstrate that our framework inherently identifies the optimal sub-tasks aligned with the capabilities of the low-level model. This ensures that the high-level decisions are guided by the low-level model's strengths, leading to more efficient and targeted task decomposition." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "24" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.173, + 0.092, + 0.383, + 0.108 + ], + "angle": 0, + "content": "C.5.1 Leader-follower game" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.115, + 0.825, + 0.214 + ], + "angle": 0, + "content": "The leader-follower game, also known as the Stackelberg game, models interaction between two agents with parametrized strategies \\(\\pmb{\\theta} = (\\pmb{\\theta}_1, \\pmb{\\theta}_2)\\) and differentiable objective functions \\((\\mathcal{L}_1, \\mathcal{L}_2): \\mathbb{R}^d \\to \\mathbb{R}\\). In this framework, the leader announces its strategy first, and the follower observes this decision to respond optimally. This sequential structure enables the leader to anticipate the follower's reaction and adjust its strategy accordingly. A Stackelberg equilibrium occurs when neither agent can unilaterally improve its objective. Denoting \\(\\pmb{\\theta}_1\\) as the leader's strategy and \\(\\pmb{\\theta}_2\\) as the follower's, the loss functions \\(\\mathcal{L}_1\\) and \\(\\mathcal{L}_2\\) are optimized with the following bi-level structure:" + }, + { + "type": "equation", + "bbox": [ + 0.282, + 0.219, + 0.713, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\theta} _ {1} ^ {*} = \\operatorname {a r g m i n} _ {\\boldsymbol {\\theta} _ {1}} \\mathcal {L} _ {1} (\\boldsymbol {\\theta}, \\boldsymbol {\\theta} _ {2} ^ {*} (\\boldsymbol {\\theta} _ {1})), \\quad \\boldsymbol {w} _ {2} ^ {*} (\\boldsymbol {\\theta} _ {1}) = \\operatorname {a r g m i n} _ {\\boldsymbol {\\theta} _ {2}} \\mathcal {L} _ {2} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.247, + 0.825, + 0.345 + ], + "angle": 0, + "content": "Anil et al. [2021] apply the leader-follower game to ensure checkable answers in a prover-verifier game (PVG). The objective is a verifier that is both complete (accepts all correct proofs from a verifier) and sound (rejects all incorrect proofs from a verifier). They analyze different scenarios where the verifier acts as the leader, the prover as the follower, and both announce strategies simultaneously, forming a Nash equilibrium. The study concludes that in verifier-led SVG, a Stackelberg equilibrium is both necessary and sufficient for achieving a sound and complete verifier, whereas in other configurations, a Stackelberg equilibrium is not necessary or sufficient for this outcome." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.359, + 0.345, + 0.373 + ], + "angle": 0, + "content": "C.5.2 Efficacy of LLM" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.382, + 0.825, + 0.519 + ], + "angle": 0, + "content": "Because the high-level policy possesses strong generalization capabilities, it is impractical for it to exhaustively explore every potential sub-task for each question. Instead, it naturally focuses on tasks within a feasible range of difficulty, leveraging only a limited set of coarse planning actions. Rather than pinpointing perfectly tailored sub-tasks, the policy searches for general tasks of particular computational complexity, i.e., difficulty, that it can handle reliably. Motivated by this perspective, we incorporate the concept of a reasoning boundary for large language models (LLMs) [Chen et al., 2024b]. Intuitively, the reasoning boundary circumscribes the maximum difficulty of problems a model can solve at a desired accuracy level. Formally, for a model \\(\\theta\\), a task \\(t\\), and a predefined threshold \\(A\\), the reasoning boundary of \\(\\theta\\) represents the maximum problem difficulty \\(d\\) that satisfies:" + }, + { + "type": "equation", + "bbox": [ + 0.36, + 0.525, + 0.637, + 0.549 + ], + "angle": 0, + "content": "\\[\n\\mathcal {B} _ {A c c = A} (t | \\theta) = \\sup _ {d} \\{d | A c c (t | d, \\theta) = A \\}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.555, + 0.825, + 0.611 + ], + "angle": 0, + "content": "where \\(d\\) denotes the problem difficulty. By quantifying the difficulty level a model can reliably handle, the reasoning boundary provides a systematic way to align the high-level policy's focus with the model's actual capabilities, gauge the efficacy of the low-level policy, and determine the optimal strategy for solving the question." + }, + { + "type": "title", + "bbox": [ + 0.171, + 0.625, + 0.53, + 0.641 + ], + "angle": 0, + "content": "C.5.3 Leader-follower Game for LLM Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.649, + 0.825, + 0.678 + ], + "angle": 0, + "content": "Our goal is to find the high-level policy that searches for the sub-task sequence based on the efficacy of the low-level policy to solve the question. We design the loss functions as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.315, + 0.684, + 0.671, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {h} = \\mathbb {E} _ {(x, y) \\sim p _ {D}, t _ {1: K}} \\left[ - \\log \\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}, y _ {1: K - 1}\\right) \\right],\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.315, + 0.703, + 0.684, + 0.718 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {l} = \\mathbb {E} _ {x \\sim p _ {D}, t _ {1: k} \\sim \\pi_ {h}, \\hat {y} _ {k} \\sim \\pi_ {l}} \\left[ - r \\left(y _ {k}, \\hat {y} _ {k} \\mid x, t _ {1: k}, y _ {1: k - 1}\\right) \\right],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.723, + 0.825, + 0.793 + ], + "angle": 0, + "content": "where \\( r(y_k, \\hat{y}_k \\mid x, t_{1:k}, y_{1:k-1}) \\) represents the step reward for the correctness of \\( \\hat{y}_k \\) derived from the question \\( x \\), the sub-task sequence \\( t_{1:k} \\) from the high policy and prior intermediate answer \\( y_{1:k-1} \\). The loss functions can be interpreted as follows: the high-level policy is incentivized to find subtasks that lead to the correct answer based on the capabilities of the low-level policy, while the low-level policy is incentivized to enhance its instruction-following ability." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.799, + 0.825, + 0.87 + ], + "angle": 0, + "content": "How to minimize the loss functions and whether such minimization leads to the desired results remain questions. To explore this, we consider a simplified case of our method, where the high-level policy plans the complete sub-task sequence at the beginning and the low-level executes the instruction in a single interaction. The corresponding parameterized policies are defined as \\(\\pi_h((t_1,\\ldots ,t_K)\\mid x)\\) and \\(\\pi_l((\\hat{y}_1,\\dots ,\\hat{y}_K)\\mid x,(t_1,\\dots ,t_K))\\) . The corresponding loss functions are:" + }, + { + "type": "equation", + "bbox": [ + 0.314, + 0.875, + 0.823, + 0.89 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {h} = \\mathbb {E} _ {(x, y) \\sim p _ {D}, t _ {1: K}} \\left[ - \\log \\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}\\right) \\right], \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.315, + 0.894, + 0.823, + 0.909 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {l} = \\mathbb {E} _ {x \\sim p _ {D}, t _ {1: k} \\sim \\pi_ {h}, \\hat {y} _ {k} \\sim \\pi_ {l}} \\left[ - r \\left(y _ {k}, \\hat {y} _ {k} \\mid x, t _ {1: k}, y _ {1: k - 1}\\right) \\right]. \\tag {16}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "25" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.825, + 0.135 + ], + "angle": 0, + "content": "In this step, the high-level policy generates the entire sub-task sequence without relying on intermediate answers, while the low-level policy follows the sequence to produce answers for the sub-tasks. The low-level policy can still leverage prior intermediate answers to sequentially refine its responses." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.14, + 0.825, + 0.239 + ], + "angle": 0, + "content": "To analyze the result agents by minimizing the loss functions, we adopt the completeness and soundness properties from the PVG framework for LLM reasoning. Specifically, if the high-level policy generates a sub-task sequence that is executable within the low-level policy's capabilities, the problem must be solved (completeness). Conversely, if the sub-task sequence is incorrect or beyond the low-level policy's capacity, the problem cannot be solved (soundness). To achieve this, we utilize the conclusion from Anil et al. [2021], which positions the low-level policy as the leader and the high-level policy as the follower, equilibria guarantee the complete and sound low-level policy." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.243, + 0.827, + 0.382 + ], + "angle": 0, + "content": "When the high-level policy takes the lead, the low-level policy is forced to adapt to the specific strategy defined by the high-level policy, which can result in neither complete nor sound low-level policy. For example, if the high-level policy dictates that it will only generate sub-tasks involving addition and subtraction, the low-level policy is constrained to optimize only for these tasks. While they may reach an equilibrium, the low-level policy remains incomplete, and this limitation impacts both policies. In the case of the simultaneous PVG game, convergence to a Nash equilibrium is possible, but it is not sufficient for completeness and soundness. For instance, the low-level policy might disregard the high-level policy entirely (e.g., if the high-level provides incorrect instructions, but the low-level still performs correctly). This approach, however, is challenging to implement due to the significantly larger search space involved." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.388, + 0.825, + 0.472 + ], + "angle": 0, + "content": "Furthermore, the loss functions we design ensure that, at a Stackelberg equilibrium, the high-level policy identifies sub-task sequences that the low-level policy can execute to solve the problem with the highest probability. With the low-level policy acting as the leader, it establishes its reasoning boundary for tasks. Based on the reasoning boundary, let \\(\\theta_h\\) and \\(\\theta_l\\) represent the policy parameters for the high-level and low-level policies, respectively. The probability that the low-level policy correctly solves the question is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.368, + 0.477, + 0.629, + 0.518 + ], + "angle": 0, + "content": "\\[\n\\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}\\right) = \\prod_ {k = 1} ^ {K} \\operatorname {A c c} \\left(t _ {k} \\mid x, \\theta_ {l}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.524, + 0.825, + 0.58 + ], + "angle": 0, + "content": "where we can compute the difficulty \\( d_{k} \\) from \\( t_k \\) and \\( x \\). where the difficulty \\( d_{k} \\) can be derived from \\( t_k \\) and \\( x \\). The loss function in Eq. (15) ensures that the selected sub-tasks are optimal for the low-level policy. Here we provide a theoretical condition under which the most efficient solution strategy can be identified, according to the efficacy of the LLM." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.586, + 0.825, + 0.67 + ], + "angle": 0, + "content": "This approach can be viewed as a game between a high-level \"prover\" and a low-level \"verifier\". The verifier, representing the low-level policy, adheres the high-level policy's instructions to validate its reasoning. Unlike the classic PVG setting, where the prover has ground-truth labels, the label of our high-level policy depends on the tunable low-level policy. This distinction, where the low-level policy (leader) is inherently more complex, contrasts with traditional PVG setups and adds complexity due to the interdependence between the high- and low-level policies." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.675, + 0.825, + 0.718 + ], + "angle": 0, + "content": "By framing the problem-solving process as a leader-follower game, with the low-level policy designated as the leader, we can construct a bi-level optimization problem to identify an equilibrium. Following the formulation in Sec. C.5.1, the problem is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.299, + 0.722, + 0.697, + 0.748 + ], + "angle": 0, + "content": "\\[\n\\theta_ {l} ^ {*} = \\underset {\\theta_ {l}} {\\arg \\min } \\mathcal {L} _ {l} (\\theta_ {h} ^ {*} (\\theta_ {l}), \\theta_ {l}) \\quad \\theta_ {h} ^ {*} (\\theta_ {l}) = \\underset {\\theta_ {l}} {\\arg \\min } \\mathcal {L} _ {h} (\\theta_ {h}, \\theta_ {l}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.753, + 0.518, + 0.768 + ], + "angle": 0, + "content": "Then we can apply bi-level optimization techniques." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.787, + 0.347, + 0.804 + ], + "angle": 0, + "content": "D Training Details" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.817, + 0.347, + 0.832 + ], + "angle": 0, + "content": "D.1 Single-turn ReMA" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.842, + 0.825, + 0.913 + ], + "angle": 0, + "content": "We refer to Appendix G for prompts we use during training. We implement the training pipeline with OpenRLHF [Hu et al., 2024a] which is a highly efficient codebase and is easy to scale up. We select REINFORCE++ to save resources and for efficient training. All experiments are conducted in a node of 8 NVIDIA A100 GPUs. We use bf16, Zero2, Flash-Attention and gradient checkpointing to run our experiments." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.51, + 0.948 + ], + "angle": 0, + "content": "26" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.17, + 0.092, + 0.825, + 0.189 + ], + "angle": 0, + "content": "During rollout, we set temperature \\(= 1.0\\), top_p \\(= 1.0\\), top_k \\(= -1\\), and use vLLM for inference acceleration. We set the max generation length to be 2048 and, the rollout batch size to be 1000. The number of samples per prompt is 4. During training, we use Adam Optimizer with a learning rate of 5e-7. We set the mini-batch size to be 500, and the clip ratio to be 0.2. Other hyperparameters, such as KL coefficients and the number of training episodes, were carefully tuned based on validation set performance to ensure robust and reliable results. To align with the hyperparameter in OpenRLHF, we use #Training Episode as the number of reinforcement learning epoch on the entire dataset." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.195, + 0.827, + 0.295 + ], + "angle": 0, + "content": "In ReMA, during prompt filtering of the high-level model, the high-level agent first samples 10 candidates for each question with \\( t = 1.0 \\), and for each output the low-level agents sample 1 solution with \\( t = 0.0 \\), then we select questions of success rate between \\( [\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}] \\). And for the low-level agent's prompt filtering, the high-level agent first samples 1 candidate for each question with \\( t = 0.0 \\) and for each output the low-level agents sample 10 solutions with \\( t = 1.0 \\), then we select questions of success rate between \\( [\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}] \\) and use the high-level agent to sample 4 meta-thoughts with \\( t = 1.0 \\) as the input." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.307, + 0.492, + 0.323 + ], + "angle": 0, + "content": "D.1.1 Supervised fine-tuning data collection" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.33, + 0.827, + 0.483 + ], + "angle": 0, + "content": "For experiments in Sec. 4.2.1, we collect expert data to enhance the reasoning pattern, i.e. \\( RL \\) from SFT. Specifically, we collect demonstration data from GPT-4o Mini on MATH training dataset (7.5k problems) Hendrycks et al. [2021] and use it to fine-tune the LLMs. The data generation follows these steps: First, we prompt GPT-4o Mini to produce metacognitive reasoning for high-level model training. Specifically, we use different prompts to instruct it to rewrite and decompose a given question without providing a final answer. We collect metacognitive reasoning using two predefined actions, \"rewrite\" and \"decompose\", which align with human approaches to complex problem-solving while preserving answer diversity. Next, we use the generated instructions to prompt GPT-4o Mini to follow the metacognitive steps and solve the question, obtaining SFT data for low-level policy training. Below, we present the prompts used for both high-level and low-level models. Prompts can be found in Appendix G.1.1." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.497, + 0.495, + 0.511 + ], + "angle": 0, + "content": "D.1.2 Dataset Curation of RewardBench970" + }, + { + "type": "table_caption", + "bbox": [ + 0.172, + 0.533, + 0.825, + 0.561 + ], + "angle": 0, + "content": "Table 2: Performance on LLM-as-a-Judge benchmarks, trained on dataset under the loose setting. The two-agent workflow in ReMA" + }, + { + "type": "table", + "bbox": [ + 0.18, + 0.562, + 0.819, + 0.703 + ], + "angle": 0, + "content": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3.1-8B-InstructRewardBench97071.2481.86 (+10.62)80.41 (+9.17)86.29 (+15.05)
JudgeBench51.7751.45 (-0.32)50.65 (-1.12)53.71 (+1.94)
Average61.5166.65 (+5.14)65.53 (+4.02)70.00 (+8.49)
Qwen2.5-7B-InstructRewardBench97086.4987.22 (+0.73)80.31 (-6.18)90.72 (+4.23)
JudgeBench58.3954.84 (-3.55)55.81 (-2.58)58.71 (+0.32)
Average72.4471.03 (-1.41)68.06 (-4.38)74.72 (+2.28)
" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.718, + 0.825, + 0.748 + ], + "angle": 0, + "content": "We process the original dataset in RewardBench by splitting it into a training set containing 5,000 tuples of (instruction, response A, response B) and a test set with the remaining 970 tuples." + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.753, + 0.664, + 0.768 + ], + "angle": 0, + "content": "To ensure a meaningful dataset split, we validate two separation strategies:" + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.778, + 0.825, + 0.806 + ], + "angle": 0, + "content": "- Loose setting: We only ensure that there is no direct overlap of tuples between the training and test sets." + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.81, + 0.825, + 0.839 + ], + "angle": 0, + "content": "- Strict setting: We further enforce that no instruction appears in both the training and test sets. The results for this setting are presented in the main results (Table 1b)." + }, + { + "type": "list", + "bbox": [ + 0.217, + 0.778, + 0.825, + 0.839 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.849, + 0.825, + 0.878 + ], + "angle": 0, + "content": "Additionally, since the original RewardBench data originates from different subsets, we ensure that all original subsets are evenly represented in both the training and test sets." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.884, + 0.825, + 0.913 + ], + "angle": 0, + "content": "Table 2 reports the learning performance of various methods under the loose dataset split setting. Compared to the results in Table 1b, ReMA significantly outperforms other RL tuning baselines" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "27" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.825, + 0.135 + ], + "angle": 0, + "content": "across all models, particularly on out-of-distribution (OOD) benchmarks. The consistent improvements on OOD datasets of these two settings suggest that ReMA enhances meta-thinking ability, resulting in better generalization across diverse task distributions." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.149, + 0.367, + 0.164 + ], + "angle": 0, + "content": "D.1.3 Training on MATH" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.173, + 0.825, + 0.215 + ], + "angle": 0, + "content": "VRP For Llama3-8B-Instruct, Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 12,6,6 for these 3 models respectively. For Llama3-8B-Instruct, we set the learning rate of 2e-7 for stable training." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.23, + 0.825, + 0.26 + ], + "angle": 0, + "content": "MRP For Llama3-8B-Instruct, Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 10,6,6 for these 3 models respectively." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.273, + 0.825, + 0.329 + ], + "angle": 0, + "content": "MAMRP We use \\(\\varepsilon_{\\mathrm{min}} = 0.2, \\varepsilon_{\\mathrm{max}} = 0.8\\) for prompt filtering. We use the same #Training Episode=4 for all models, and for #Update Iteration, we use 3 for Llama3-8B-Instruct and Llama3.1-8B-Instruct, 10 for Qwen2.5-7B-Instruct. And we set the KL coefficient to be 1e-2 for all the 3 models." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.344, + 0.418, + 0.359 + ], + "angle": 0, + "content": "D.1.4 Training on Reward Bench" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.368, + 0.825, + 0.398 + ], + "angle": 0, + "content": "VRP For Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 4,6 for these 2 models respectively." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.411, + 0.825, + 0.44 + ], + "angle": 0, + "content": "MRP For Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 4,6 for these 2 models respectively." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.455, + 0.825, + 0.526 + ], + "angle": 0, + "content": "MAMRP We set #Update Iteration=1 for all models. We set the KL coefficient to be 1e-2 for Llama3.1-8B-Instruct and 1e-2 for Qwen2.5-7B-Instruct all models. For Llama3.1-8B-Instruct, we use \\(\\varepsilon_{\\mathrm{min}} = 0.2\\), \\(\\varepsilon_{\\mathrm{max}} = 0.8\\) for prompt filtering and we use #Training Episode of 2 during training. For Llama3.1-8B-Instruct, we use \\(\\varepsilon_{\\mathrm{min}} = 0.1\\), \\(\\varepsilon_{\\mathrm{max}} = 0.9\\) for prompt filtering and we use #Training Episode of 1 during training." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.542, + 0.343, + 0.556 + ], + "angle": 0, + "content": "D.2 Multi-turn ReMA" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.567, + 0.825, + 0.623 + ], + "angle": 0, + "content": "We refer to Appendix G for prompts we use during training. We implement a multi-turn ReMA training pipeline with VeRL [Sheng et al., 2024] since it's easier to implement complex training pipeline with a single centralized controller. Similar to OpenRLHF, VeRL is also a highly efficient and scalable codebase for further development." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.629, + 0.825, + 0.727 + ], + "angle": 0, + "content": "For the multi-turn ReMA rollout, we use parameter sharing and simultaneous update by default. In details, we maintain two message lists with the system prompt of meta-thinking agent and reasoning agent respectively. During rollout, each agent acts as 'assistant' in its own message list and the other agent acts as 'user'. We use three hyperparameters to control the rollout length: (1) 'max_num_turns': the maximum number of turns for each trajectory. (2) 'max_response_length': the maximum number of tokens for each turn's response. (3) 'max_prompt_length': the maximum number of tokens for each trajectory." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.732, + 0.825, + 0.762 + ], + "angle": 0, + "content": "During training, we apply the collected message list to Qwen2.5-7B's chat template and build loss masks in order to compute the loss for all turns of one trajectory (message list)." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.767, + 0.825, + 0.837 + ], + "angle": 0, + "content": "Moreover, for multi-turn ReMA rollout, unlike single agent single turn rollout, we need to carefully design the termination logic. Basically, we let the meta-thinking agent automatically decide when to finish the solving procedure, we use a special tag '[FINISH]' to indicate the end of the solving procedure. After we detect this tag, we will terminate trajectory after the reasoning agent generates its output." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.843, + 0.826, + 0.912 + ], + "angle": 0, + "content": "We also design other termination conditions to ensure the quality of the generated trajectories. If the last agent's response is too long, we will terminate the whole trajectory and setting the reward to 0. We also introduce a different version of format reward: we give a reward of 1.0 only if the reasoning agent's last turn response is correct and the meta-thinking agent's last turn response include '[FINISH]'. We use math_check as the default verifier." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "28" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.172, + 0.092, + 0.529, + 0.106 + ], + "angle": 0, + "content": "D.2.1 SFT data collection of multi-turn MAMRP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.118, + 0.825, + 0.203 + ], + "angle": 0, + "content": "We use GPT-4o to translate 817 samples in LIMO [Ye et al., 2025c] by prompting it to wrap each sentence with meta-thinking and reasoning tags. We use a temperature of 0. After filtering, we get 800 conversations for training. The prompt can be found in Appendix G.2.1. For supervised finetuning, we use LlamaFactory as the codebase and train the model for 3 epochs with a learning rate of 1e-5, consine learning rate scheduler, and batch size of 8. Use DeepSpeed Zero2 for distributed training." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.223, + 0.367, + 0.238 + ], + "angle": 0, + "content": "D.2.2 Training on MATH" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.249, + 0.825, + 0.334 + ], + "angle": 0, + "content": "For training of multi-turn ReMA on MATH, we use GRPO [Shao et al., 2024] as the default learning algorithm. We refer to Appendix G.2.2 for prompts. For experiment in Sec 4.3, we use sample 128 prompts, each with 16 trajectories. During training, we drop the KL loss term to improve the numerical stability. We use a learning rate of 1e-6, bfloat16 precision, FSDP backend for distributed training. We split the rollout data into 4 mini-batches for update. For the sake of numerical stability, we do pre-clip before computing the exponential of log-prob for a upperbound of 3.0." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.339, + 0.825, + 0.381 + ], + "angle": 0, + "content": "For the main result in Fig 5, we test different rollout configurations with a max_prompt_length of 4096, training for 500 steps. We use 32 NVIDIA A800 GPUs, the longest training cost about 40 hours due to large scale validation per 10 steps." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.387, + 0.825, + 0.43 + ], + "angle": 0, + "content": "For the ablation results in Fig 6, we use a tiny subset of MATH Level 3-5, training for 300 steps. Specifically, we sample 19 questions for every single type (133 instances in total). We use 8 NVIDIA A800 GPUs, the training cost about 30 hours" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.436, + 0.434, + 0.449 + ], + "angle": 0, + "content": "We test different rollout configurations:" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.45, + 0.825, + 0.478 + ], + "angle": 0, + "content": "(1) max_num_turns=30, max_response_length=256, max_prompt_length=4096 (2) \nmax_num_turns=30, max_response_length=1024, max_prompt_length=3072" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.484, + 0.825, + 0.527 + ], + "angle": 0, + "content": "And for the experiment of separate parameter in multi-turn ReMA, we iteratively train each agent with the same configuration as above, but with a switch interval of 10 steps, starting from the metathinking agent." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.552, + 0.373, + 0.569 + ], + "angle": 0, + "content": "E Other Experiments" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.587, + 0.54, + 0.602 + ], + "angle": 0, + "content": "E.1 Reward functions shape cross-agent behaviors" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.615, + 0.825, + 0.727 + ], + "angle": 0, + "content": "We also investigate the impact of different reward function designs on ReMA's behavior. In addition to the base reward setting described in Appendix C.2, we evaluate a consistency-based reward function using Qwen2.5-7B-Instruct. This reward function is designed to encourage the high-level agent to generate more detailed guidance. Indeed, we observe that the high-level agent trained in this manner produces more detailed solution steps compared to the one trained with the basic correctness format reward. However, we also find that this approach often leads to jailbreak behavior, where the high-level agent tends to include the final answer within its output, compromising the intended hierarchical reasoning process." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.732, + 0.827, + 0.913 + ], + "angle": 0, + "content": "Furthermore, we discover an interesting evolution of a pattern during training: although our experimental setup is designed for the high-level agent to provide a solution plan while the lower-level agent executes it, we find that under the consistency-based reward, the lower-level agent significantly increases its attempt of verification rather than straightforward execution. We observed a certain sentence commonly appearing in the low-level agent's responses: \"Let's go through the solution step by step to ensure clarity and correctness.\" To quantify this effect, we track the frequency of it. We analyze this pattern across all mathematical test sets, sampling eight completions per question at a temperature of 0.7. Our empirical results have identified a \\(30\\mathrm{x}\\) increase of such self-verifying patterns in the model trained with the consistency-based reward compared to the one trained with the base reward. Moreover, we also observe additional variations of this pattern, e.g. \"Let's carefully re-evaluate the problem and solution to ensure accuracy and clarity.\" These phrases indicate that the low-level agent is actively exploring to verify the detailed response provided by the high-level agent." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "29" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.825, + 0.162 + ], + "angle": 0, + "content": "This suggests that (1) meta-thinking can not only emerge and be reinforced in the high-level agent but also in the low-level agent. During reinforcement learning (RL) training, the two agents develop a novel problem-solving pattern characterized by a role reversal. (2) Consistency-based rewards promote a more self-corrective approach at the lower level, potentially disrupting the intended separation of roles between planning and execution. For a detailed case study, refer to Appendix F.2." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.178, + 0.691, + 0.193 + ], + "angle": 0, + "content": "E.2 Detailed Training Curves on Different Datasets of Multi-turn ReMA" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.203, + 0.774, + 0.218 + ], + "angle": 0, + "content": "We show the detailed training curves of the multi-turn ReMA on different datasets in Fig. 8." + }, + { + "type": "image", + "bbox": [ + 0.177, + 0.233, + 0.825, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.24, + 0.489, + 0.757, + 0.505 + ], + "angle": 0, + "content": "Figure 8: Detailed Training Curves on Different Datasets of Multi-turn ReMA" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.54, + 0.37, + 0.557 + ], + "angle": 0, + "content": "F Qualitative Results" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.57, + 0.456, + 0.586 + ], + "angle": 0, + "content": "F.1 High-level policy finds better plans" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.596, + 0.825, + 0.667 + ], + "angle": 0, + "content": "Here is an example of how a high-level policy alters the solving method of an LLM, increasing the likelihood of providing correct answers. As we can see from the following example, without the high-level policy, the LLM counts all integer coordinates, including those on the boundary, and then subtracts the boundary coordinates. In contrast, the high-level policy identifies a better approach, directly instructing the LLM to count only the coordinates strictly inside the boundary." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.682, + 0.506, + 0.697 + ], + "angle": 0, + "content": "F.2 Case study for Experiments in Section E.1" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.708, + 0.61, + 0.723 + ], + "angle": 0, + "content": "Fig. 10 and Fig. 11 show an case study of experiments in Sec. E.1." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.728, + 0.825, + 0.812 + ], + "angle": 0, + "content": "Although both agents are prompted with the same instructions as in our main results, the consistency reward of the high-level agent significantly alters the learning dynamics. As illustrated in Fig. 10, the high-level agent generates detailed solution attempts rather than a strategic plan. Consequently, the low-level agent evolves to verify the high-level agent's solutions. This suggests that, during reinforcement learning (RL) training, the two agents develop a novel problem-solving pattern characterized by a role reversal, where one agent generates an answer while the other verifies it." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.828, + 0.517, + 0.843 + ], + "angle": 0, + "content": "F.3 Case study for Experiments in Section 4.2.2" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.853, + 0.825, + 0.909 + ], + "angle": 0, + "content": "Fig. 12 shows the detailed outputs of the two groups of LLMs trained in JSON action. The outputs finally converge to relative easier and shorter sentences, compared to our main experiments. This may due to insufficient capacity of a small LM to produce a valid JSON-format response while simultaneously exploring diverse reasoning strategies." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "30" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.188, + 0.1, + 0.806, + 0.121 + ], + "angle": 0, + "content": "Consider the rectangular region with the following points as vertices: \\((5,4),(-5,4),(-5, - 4),(5, - 4)\\) . How many points with integer coordinates will be strictly in the interior of this rectangular region?" + }, + { + "type": "title", + "bbox": [ + 0.218, + 0.127, + 0.466, + 0.146 + ], + "angle": 0, + "content": "Output without high-level planning solves this question in a less optimal way, leading to a wrong answer:" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.152, + 0.496, + 0.18 + ], + "angle": 0, + "content": "To determine how many points with integer coordinates will be strictly in the interior of the rectangular region with vertices at \\((5,4)\\), \\((-5,4)\\), \\((-5, - 4)\\), and \\((5, - 4)\\), we will follow these steps:" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.18, + 0.357, + 0.188 + ], + "angle": 0, + "content": "1. Identify the dimensions of the rectangle:" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.189, + 0.493, + 0.206 + ], + "angle": 0, + "content": "- The width of the rectangle can be calculated as the distance between the x-coordinates of the vertices. The x-coordinates are \\(-5\\) and 5." + }, + { + "type": "equation", + "bbox": [ + 0.291, + 0.213, + 0.395, + 0.224 + ], + "angle": 0, + "content": "\\[\n\\mathrm {W i d t h} = 5 - (- 5) = 1 0\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.23, + 0.493, + 0.248 + ], + "angle": 0, + "content": "- The height of the rectangle can be calculated as the distance between the y-coordinates of the vertices. The y-coordinates are 4 and -4." + }, + { + "type": "equation", + "bbox": [ + 0.293, + 0.255, + 0.393, + 0.265 + ], + "angle": 0, + "content": "\\[\n\\mathrm {H e i g h t} = 4 - (- 4) = 8\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.271, + 0.49, + 0.316 + ], + "angle": 0, + "content": "2. Calculate the total number of integer points: - The total number of integer points in the rectangle (including the boundary) can be calculated by considering the range of x and y values: - The x-values range from \\(-5\\) to 5, giving us 11 integer values \\((-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)\\). - The y-values range from \\(-4\\) to 4, giving us 9 integer values (" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.317, + 0.482, + 0.334 + ], + "angle": 0, + "content": "\\(-4, -3, -2, -1, 0, 1, 2, 3, 4)\\). The total number of points in the rectangle (including the boundary) is:" + }, + { + "type": "equation", + "bbox": [ + 0.285, + 0.341, + 0.402, + 0.351 + ], + "angle": 0, + "content": "\\[\n\\text {T o t a l p o i n t s} = 1 1 \\times 9 = 9 9\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.357, + 0.497, + 0.403 + ], + "angle": 0, + "content": "3. Calculate the number of points on the boundary: - The boundary consists of the four sides of the rectangle. - The top and bottom sides (y = 4 and y = -4) each have 11 integer points (from -5 to 5). - The left and right sides (x = 5 and x = -5) each have 9 integer points (from -4 to 4). - Therefore, the total number of points on the boundary is:" + }, + { + "type": "equation", + "bbox": [ + 0.236, + 0.409, + 0.45, + 0.419 + ], + "angle": 0, + "content": "\\[\n\\text {B o u n d a r y p o i n t s} = 2 \\times 1 1 + 2 \\times 9 = 2 2 + 1 8 = 4 0\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.425, + 0.488, + 0.453 + ], + "angle": 0, + "content": "4. Calculate the number of strictly interior points: - To find the number of points strictly in the interior, we subtract the points on the boundary from the total number of points:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.459, + 0.483, + 0.47 + ], + "angle": 0, + "content": "\\[\nI n t e r i o r \\text {p o i n t s} = \\text {T o t a l p o i n t s - B o u n d a r y p o i n t s} = 9 9 - 4 0 = 5 9\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.476, + 0.49, + 0.495 + ], + "angle": 0, + "content": "Thus, the number of points with integer coordinates that will be strictly in the interior of this rectangular region is 59." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.127, + 0.806, + 0.147 + ], + "angle": 0, + "content": "Answer with high-level planning identifies the optimal sub-tasks for the LLM to solve, increasing the chance of answering the question correctly" + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.15, + 0.804, + 0.179 + ], + "angle": 0, + "content": "High-level policy planning: First, identify the boundaries of the rectangular region. Then, determine the integer coordinates that lie strictly within these boundaries. Finally, count the number of such points." + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.189, + 0.795, + 0.208 + ], + "angle": 0, + "content": "Low-level policy reasoning following the high-policy plan: To solve the problem, we will follow the steps outlined in the instructions." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.215, + 0.801, + 0.262 + ], + "angle": 0, + "content": "Step 1: Identify the boundaries of the rectangular region. The vertices of the rectangular region are: \\((-5,4)\\) \\((-5,4)\\) \\((-5, - 4)\\) \\((5, - 4)\\) From these vertices, we can determine the boundaries:- The left boundary is \\(x = -5\\) The right boundary is \\(x = 5\\) .- The bottom boundary is \\(y = -4\\) .- The top boundary is \\(y = 4\\)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.269, + 0.781, + 0.297 + ], + "angle": 0, + "content": "Step 2: Determine the integer coordinates that lie strictly within these boundaries. For a point \\((x,y)\\) to be strictly inside the rectangle, it must satisfy: \\(-5 < x < 5 - 4 < y < 4\\)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.305, + 0.808, + 0.332 + ], + "angle": 0, + "content": "Step 3: Count the integer coordinates that satisfy these conditions. Now, we will find the integer values for \\( x \\) and \\( y \\) that fall within these boundaries. For \\( x \\) : The integer values that satisfy \\( -5 < x < 5 \\) are:" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.332, + 0.802, + 0.359 + ], + "angle": 0, + "content": "\\(-4, -3, -2, -1, 0, 1, 2, 3, 4\\) This gives us 9 possible integer values. For \\( y \\) The integer values that satisfy \\(-4 < y < 4\\) are: \\(-3, -2, -1, 0, 1, 2, 3\\). This gives us 7 possible integer values." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.367, + 0.807, + 0.386 + ], + "angle": 0, + "content": "Step 4: Calculate the total number of points. Now, we multiply the number of possible integer values for \\( x \\) by the number of possible integer values for \\( y \\)." + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.391, + 0.715, + 0.402 + ], + "angle": 0, + "content": "\\[\n\\text {T o t a l p o i n t s} = 9 \\times 7 = 6 3\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.408, + 0.797, + 0.428 + ], + "angle": 0, + "content": "Finally, the number of points with integer coordinates that lie strictly in the interior of the rectangular region is \\(\\boxed{63}\\)." + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.516, + 0.772, + 0.532 + ], + "angle": 0, + "content": "Figure 9: Case Study comparing with and without high-level metacognition results." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.575, + 0.284, + 0.594 + ], + "angle": 0, + "content": "G Prompts" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.619, + 0.411, + 0.635 + ], + "angle": 0, + "content": "G.1 Single-turn ReMA prompts" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.653, + 0.466, + 0.669 + ], + "angle": 0, + "content": "G.1.1 Prompts for JSON data collection" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.686, + 0.485, + 0.701 + ], + "angle": 0, + "content": "Prompt for metacognition reasoning to rewrite:" + }, + { + "type": "code", + "bbox": [ + 0.177, + 0.709, + 0.818, + 0.891 + ], + "angle": 0, + "content": "System prompt: \nYou are a math expert trying to solve mathematical problems. \nBefore answering a question, your task is to rewrite the original question to make it clearer. \nProvide your rewritten content in JSON format: \n{ \"action\": \"REWRITE\", \"output\": \"{clearer question content}\" \n} \nRespond only with valid JSON. Do not write an introduction or summary. \nUser prompt: \nHere is the question: [problem_text]" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.898, + 0.51, + 0.913 + ], + "angle": 0, + "content": "Prompt for metacognition reasoning to decompose:" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.507, + 0.948 + ], + "angle": 0, + "content": "31" + } + ], + [ + { + "type": "code", + "bbox": [ + 0.186, + 0.1, + 0.785, + 0.111 + ], + "angle": 0, + "content": "Question: The equation \\(x^{10} + (13x - 1)^{10} = 0\\) has 10 complex roots \\(r_1,\\overline{r}_1,r_2,\\overline{r}_2,r_3,\\overline{r}_3,r_4,\\overline{r}_4,r_5,\\overline{r}_5\\) , where the bar denotes complex conjugation. Find the value of \\(\\frac{1}{r_1\\overline{r}_1} +\\frac{1}{r_2\\overline{r}_2} +\\frac{1}{r_3\\overline{r}_3} +\\frac{1}{r_4\\overline{r}_4} +\\frac{1}{r_5\\overline{r}_5}\\)" + }, + { + "type": "title", + "bbox": [ + 0.295, + 0.114, + 0.381, + 0.121 + ], + "angle": 0, + "content": "High-Level Agent's Output" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.123, + 0.432, + 0.129 + ], + "angle": 0, + "content": "To solve this problem, let's break it down into steps that a low-level math-solving agent can follow:" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.135, + 0.278, + 0.141 + ], + "angle": 0, + "content": "1. Understand the given equation:" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.142, + 0.291, + 0.147 + ], + "angle": 0, + "content": "The equation is \\(x^{10} + (13x - 1)^{10} = 0\\)" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.148, + 0.25, + 0.153 + ], + "angle": 0, + "content": "2. Rewrite the equation:" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.153, + 0.301, + 0.158 + ], + "angle": 0, + "content": "Notice that the equation can be rewritten as:" + }, + { + "type": "equation", + "bbox": [ + 0.31, + 0.166, + 0.366, + 0.174 + ], + "angle": 0, + "content": "\\[\nx ^ {1 0} = - (1 3 x - 1) ^ {1 0}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.179, + 0.245, + 0.184 + ], + "angle": 0, + "content": "3. Consider the roots:" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.185, + 0.48, + 0.195 + ], + "angle": 0, + "content": "The roots of the equation are given as \\(r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5\\), where the bar denotes complex conjugation. 4. Use the property of complex conjugates:" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.196, + 0.468, + 0.204 + ], + "angle": 0, + "content": "For any complex number \\(z\\) , the product of \\(z\\) and its conjugate \\(\\overline{z}\\) is the square of the modulus of \\(z\\) i.e., \\(z\\overline{z} = |z|^2\\) 5. Calculate the required sum:" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.204, + 0.266, + 0.209 + ], + "angle": 0, + "content": "3. Calculate the required sum \\( \\mathbf{W} = \\mathbf{w}_{1} + \\mathbf{w}_{2} + \\dots + \\mathbf{w}_{n} \\)" + }, + { + "type": "list", + "bbox": [ + 0.187, + 0.185, + 0.48, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.286, + 0.221, + 0.389, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{r _ {1} \\overline {{F _ {1}}}} + \\frac {1}{r _ {2} \\overline {{F _ {2}}}} + \\frac {1}{r _ {3} \\overline {{F _ {3}}}} + \\frac {1}{r _ {4} \\overline {{F _ {4}}}} + \\frac {1}{r _ {5} \\overline {{F _ {5}}}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.238, + 0.329, + 0.244 + ], + "angle": 0, + "content": "Using the property from step 4, this can be rewritten as:" + }, + { + "type": "equation", + "bbox": [ + 0.286, + 0.253, + 0.391, + 0.267 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{| r _ {1} | ^ {2}} + \\frac {1}{| r _ {2} | ^ {2}} + \\frac {1}{| r _ {3} | ^ {2}} + \\frac {1}{| r _ {4} | ^ {2}} + \\frac {1}{| r _ {5} | ^ {2}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.271, + 0.257, + 0.276 + ], + "angle": 0, + "content": "6. Simplify the expression:" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.277, + 0.483, + 0.286 + ], + "angle": 0, + "content": "Since \\( r_1, r_2, r_3, r_4, r_5 \\) are roots of the equation \\( x^{10} = -(13x - 1)^{10} \\), the magnitudes \\( |r_i| \\) are the same for each pair \\( r_i \\) and \\( \\overline{r}_i \\). Let \\( |r_i| = |r_i| \\) for all \\( i, j \\)." + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.287, + 0.272, + 0.292 + ], + "angle": 0, + "content": "7. Find the common magnitude:" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.293, + 0.486, + 0.305 + ], + "angle": 0, + "content": "To find \\( |r_{1}| \\), consider the magnitudes of the terms on both sides of the equation \\( x^{10} = -(13x - 1)^{10} \\). The magnitude of the left side is \\( |x|^{10} \\) and the magnitude of the right side is \\( |13x - 1|^{10} \\). Therefore:" + }, + { + "type": "list", + "bbox": [ + 0.187, + 0.271, + 0.486, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.312, + 0.314, + 0.364, + 0.321 + ], + "angle": 0, + "content": "\\[\n\\left| x \\right| ^ {1 0} = \\left| 1 3 x - 1 \\right| ^ {1 0}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.326, + 0.296, + 0.332 + ], + "angle": 0, + "content": "Taking the 10th root of both sides, we get:" + }, + { + "type": "equation", + "bbox": [ + 0.318, + 0.341, + 0.36, + 0.348 + ], + "angle": 0, + "content": "\\[\n| x | = | 1 3 x - 1 |.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.352, + 0.228, + 0.357 + ], + "angle": 0, + "content": "8. Solve for \\( |x| \\):" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.358, + 0.238, + 0.363 + ], + "angle": 0, + "content": "Let \\( |x| = a \\). Then:" + }, + { + "type": "list", + "bbox": [ + 0.187, + 0.352, + 0.238, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.365, + 0.276, + 0.37 + ], + "angle": 0, + "content": "\\( \\therefore m - 1 \\neq 0 \\) ;" + }, + { + "type": "equation", + "bbox": [ + 0.318, + 0.373, + 0.357, + 0.38 + ], + "angle": 0, + "content": "\\[\na = \\left| 1 3 a - 1 \\right|.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.385, + 0.252, + 0.39 + ], + "angle": 0, + "content": "This gives us two cases:" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.391, + 0.214, + 0.396 + ], + "angle": 0, + "content": "- \\(a = 13\\)" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.397, + 0.237, + 0.402 + ], + "angle": 0, + "content": "- \\(a = -(13a - 1)\\)" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.403, + 0.246, + 0.407 + ], + "angle": 0, + "content": "Solving the first case:" + }, + { + "type": "list", + "bbox": [ + 0.188, + 0.385, + 0.252, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.282, + 0.416, + 0.394, + 0.429 + ], + "angle": 0, + "content": "\\[\na = 1 3 a - 1 \\Longrightarrow 1 2 a = 1 \\Longrightarrow a = \\frac {1}{1 2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.432, + 0.253, + 0.438 + ], + "angle": 0, + "content": "Solving the second case:" + }, + { + "type": "equation", + "bbox": [ + 0.28, + 0.446, + 0.396, + 0.459 + ], + "angle": 0, + "content": "\\[\na = - 1 3 a + 1 \\Longrightarrow 1 4 a = 1 \\Longrightarrow a = \\frac {1}{1 4}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.462, + 0.486, + 0.472 + ], + "angle": 0, + "content": "Since \\(a\\) must be the same for all roots, we need to check which value is consistent. Given the nature of the problem, we can assume \\(a = \\frac{1}{2}\\) as the correct magnitude." + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.473, + 0.256, + 0.478 + ], + "angle": 0, + "content": "9. Calculate the final sum:" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.479, + 0.276, + 0.484 + ], + "angle": 0, + "content": "Since \\(|r_i| = \\frac{1}{2}\\) for all \\(i\\), we have" + }, + { + "type": "list", + "bbox": [ + 0.187, + 0.462, + 0.486, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.307, + 0.494, + 0.369, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{| r _ {1} | ^ {2}} = \\frac {1}{(\\frac {1}{4}) ^ {2}} = 1 4 4.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.514, + 0.246, + 0.52 + ], + "angle": 0, + "content": "Therefore, the sum is:" + }, + { + "type": "equation", + "bbox": [ + 0.275, + 0.53, + 0.402, + 0.536 + ], + "angle": 0, + "content": "\\[\n1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 = 5 \\times 1 4 4 = 7 2 0.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.541, + 0.233, + 0.546 + ], + "angle": 0, + "content": "10. Final answer:" + }, + { + "type": "equation", + "bbox": [ + 0.245, + 0.546, + 0.328, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{\\frac {1}{n} + \\frac {1}{n}} + \\frac {1}{\\frac {1}{n} + \\frac {1}{n}} + \\frac {1}{\\frac {1}{n} + \\frac {1}{n}} \\text {i s} 7 2 0.\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.612, + 0.114, + 0.697, + 0.121 + ], + "angle": 0, + "content": "Low-Level Agent's Output" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.123, + 0.695, + 0.129 + ], + "angle": 0, + "content": "Let's go through the solution step by step to ensure clarity and correctness." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.134, + 0.588, + 0.139 + ], + "angle": 0, + "content": "1. Understand the given equation:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.14, + 0.601, + 0.145 + ], + "angle": 0, + "content": "The equation is \\(x^{10} + (13x - 1)^{10} = 0\\)" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.145, + 0.561, + 0.151 + ], + "angle": 0, + "content": "2. Rewrite the equation:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.152, + 0.611, + 0.157 + ], + "angle": 0, + "content": "Notice that the equation can be rewritten as:" + }, + { + "type": "list", + "bbox": [ + 0.497, + 0.134, + 0.611, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.626, + 0.166, + 0.682, + 0.174 + ], + "angle": 0, + "content": "\\[\nx ^ {1 0} = - (1 3 x - 1) ^ {1 0}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.179, + 0.555, + 0.184 + ], + "angle": 0, + "content": "3. Consider the roots:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.185, + 0.789, + 0.195 + ], + "angle": 0, + "content": "The roots of the equation are given as \\(r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5\\), where the bar denotes complex conjugation. 4. Use the property of complex conjugates:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.196, + 0.779, + 0.205 + ], + "angle": 0, + "content": "For any complex number \\(z\\), the product of \\(z\\) and its conjugate \\(\\overline{z}\\) is the square of the modulus of \\(z\\), i.e., \\(z\\overline{z} = |z|^2\\). 5. Calculate the required sum:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.206, + 0.575, + 0.212 + ], + "angle": 0, + "content": "We need to find the value of:" + }, + { + "type": "list", + "bbox": [ + 0.497, + 0.185, + 0.789, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.221, + 0.706, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{r _ {1} F _ {1}} + \\frac {1}{r _ {2} F _ {2}} + \\frac {1}{r _ {3} F _ {3}} + \\frac {1}{r _ {4} F _ {4}} + \\frac {1}{r _ {5} F _ {5}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.238, + 0.639, + 0.244 + ], + "angle": 0, + "content": "Using the property from step 4, this can be rewritten as:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.252, + 0.706, + 0.266 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{| r _ {1} | ^ {2}} + \\frac {1}{| r _ {2} | ^ {2}} + \\frac {1}{| r _ {3} | ^ {2}} + \\frac {1}{| r _ {4} | ^ {2}} + \\frac {1}{| r _ {5} | ^ {2}} + \\frac {1}{| r _ {6} | ^ {2}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.271, + 0.567, + 0.276 + ], + "angle": 0, + "content": "6. Simplify the expression:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.276, + 0.81, + 0.286 + ], + "angle": 0, + "content": "Since \\( r_1, r_2, r_3, r_4, r_5 \\) are roots of the equation \\( x^{10} = -(13x - 1)^{10} \\), the magnitudes \\( |r_i| \\) are the same for each pair \\( r_1 \\) and \\( \\overline{r}_i \\). Let \\( |r_i| = |r_i| \\) for all \\( i, j \\)." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.287, + 0.583, + 0.292 + ], + "angle": 0, + "content": "7. Find the common magnitude:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.293, + 0.806, + 0.305 + ], + "angle": 0, + "content": "To find \\( |\\boldsymbol{r}_i| \\), consider the determinants of the terms on both sides of the equation \\( x^{10} = -(13x - 1)^{10} \\). The magnitude of the left side is \\( |z|^10 \\) and the magnitude of the right side is \\( |13z - 1|^{10} \\). Therefore:" + }, + { + "type": "list", + "bbox": [ + 0.497, + 0.271, + 0.81, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.313, + 0.681, + 0.321 + ], + "angle": 0, + "content": "\\[\n| x | ^ {1 0} = | 1 3 x - 1 | ^ {1 0}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.325, + 0.607, + 0.331 + ], + "angle": 0, + "content": "Taking the 10th root of both sides, we get:" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.34, + 0.676, + 0.347 + ], + "angle": 0, + "content": "\\[\n\\left| x \\right| = \\left| 1 3 x - 1 \\right|.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.351, + 0.539, + 0.357 + ], + "angle": 0, + "content": "8. Solve for \\( |x| \\):" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.358, + 0.548, + 0.363 + ], + "angle": 0, + "content": "Let \\( |x| = a \\). Then:" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.373, + 0.674, + 0.38 + ], + "angle": 0, + "content": "\\[\na = | 1 3 x - 1 |.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.385, + 0.562, + 0.39 + ], + "angle": 0, + "content": "This gives us two cases:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.391, + 0.548, + 0.397 + ], + "angle": 0, + "content": "-α=13a-1" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.397, + 0.548, + 0.402 + ], + "angle": 0, + "content": "- \\(a = -(13a - 1)\\)" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.403, + 0.556, + 0.407 + ], + "angle": 0, + "content": "Solving the first case:" + }, + { + "type": "list", + "bbox": [ + 0.497, + 0.385, + 0.562, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.416, + 0.71, + 0.429 + ], + "angle": 0, + "content": "\\[\na = 1 3 a - 1 \\Longrightarrow 1 2 a = 1 \\Longrightarrow a = \\frac {1}{1 2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.432, + 0.564, + 0.437 + ], + "angle": 0, + "content": "Solving the second case:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.446, + 0.712, + 0.459 + ], + "angle": 0, + "content": "\\[\na = - 1 3 a + 1 \\Rightarrow 1 4 a = 1 \\Rightarrow a = \\frac {1}{1 4}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.462, + 0.806, + 0.472 + ], + "angle": 0, + "content": "Since \\( a \\) must be the same for all roots, we need to check which value is consistent. Given the nature of the problem, we can assume \\( a = \\frac{1}{2} \\) as the correct magnitude." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.473, + 0.567, + 0.479 + ], + "angle": 0, + "content": "9. Calculate the final sum:" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.479, + 0.587, + 0.485 + ], + "angle": 0, + "content": "Since \\(|r_i| = \\frac{1}{12}\\) for all i, we have:" + }, + { + "type": "list", + "bbox": [ + 0.497, + 0.462, + 0.806, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.494, + 0.685, + 0.511 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{| r _ {i} | ^ {2}} = \\frac {1}{(\\mathrm {古}) ^ {2}} = 1 4 4.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.514, + 0.557, + 0.519 + ], + "angle": 0, + "content": "Therefore, the sum is:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.529, + 0.718, + 0.536 + ], + "angle": 0, + "content": "\\[\n1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 = 5 \\times 1 4 4 = 7 2 0.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.541, + 0.544, + 0.546 + ], + "angle": 0, + "content": "10. Final answer:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.546, + 0.642, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\text {The v a l u e o f} \\frac {1}{r _ {1} r _ {1}} + \\frac {1}{r _ {2} r _ {2}} + \\frac {1}{r _ {3} r _ {3}} + \\frac {1}{r _ {4} r _ {4}} + \\frac {1}{r _ {5} r _ {5}} \\text {i s} \\boxed {7 2 0}.\n\\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.57, + 0.713, + 0.585 + ], + "angle": 0, + "content": "Figure 10: Case Study for consistency reward of high-level agent" + }, + { + "type": "code", + "bbox": [ + 0.186, + 0.606, + 0.784, + 0.617 + ], + "angle": 0, + "content": "Question: The equation \\(x^{10} + (13x - 1)^{10} = 0\\) has 10 complex roots \\(r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5\\), where the bar denotes complex conjugation. Find the value of \\(\\frac{1}{r_1r_4} + \\frac{1}{r_2r_2} + \\frac{1}{r_3r_3} + \\frac{1}{r_4r_4} + \\frac{1}{r_5r_5}\\)." + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.619, + 0.28, + 0.624 + ], + "angle": 0, + "content": "High-Level Agent's Output" + }, + { + "type": "text", + "bbox": [ + 0.355, + 0.619, + 0.464, + 0.625 + ], + "angle": 0, + "content": "Low-Level Agent's Output (part I)" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.626, + 0.28, + 0.639 + ], + "angle": 0, + "content": "To solve this problem, we need to follow these steps:" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.643, + 0.28, + 0.655 + ], + "angle": 0, + "content": "1. Understand the given equation: The equation is \\( x^{10} - (13x - 1)^{10} = 0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.659, + 0.272, + 0.665 + ], + "angle": 0, + "content": "2. Identify the roots: The roots of the" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.665, + 0.233, + 0.67 + ], + "angle": 0, + "content": "equation are given as" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.671, + 0.289, + 0.684 + ], + "angle": 0, + "content": "\\(\\overline{r_1},\\overline{r_2},\\overline{r_3},\\overline{r_4},\\overline{r_5},\\overline{r_6},\\overline{r_7},\\overline{r_8}\\) where the bar denotes complex conjugation." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.689, + 0.289, + 0.695 + ], + "angle": 0, + "content": "3. Use properties of complex conjugates:" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.696, + 0.29, + 0.712 + ], + "angle": 0, + "content": "For any complex number \\(z\\), the product \\(z \\cdot z\\) is a complex function of the modulus of \\(z\\), i.e., \\(|z \\cdot \\overline{z}| = |z|^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.718, + 0.29, + 0.724 + ], + "angle": 0, + "content": "4. Simplify the expression: We need to find" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.725, + 0.265, + 0.73 + ], + "angle": 0, + "content": "the value of 1" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.731, + 0.265, + 0.736 + ], + "angle": 0, + "content": "r1+ r2r3+ r4" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.738, + 0.265, + 0.743 + ], + "angle": 0, + "content": "#" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.745, + 0.284, + 0.75 + ], + "angle": 0, + "content": "Apply an property of complex conjugates. Since \\( \\pi_1 \\cdot \\overline{\\pi}_1 = |\\pi_1|^2 \\), we have" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.751, + 0.207, + 0.756 + ], + "angle": 0, + "content": "1+" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.758, + 0.207, + 0.763 + ], + "angle": 0, + "content": "A" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.765, + 0.28, + 0.77 + ], + "angle": 0, + "content": "6.Sum the reciprocals: Sum the values" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.771, + 0.266, + 0.777 + ], + "angle": 0, + "content": "1+1 1 1" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.783, + 0.291, + 0.807 + ], + "angle": 0, + "content": "7. Use Vieta's formulas: To find the sum of the reciprocals of the moduli squared, we can use the fact that the sum of the roots of the polynomial and their properties." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.812, + 0.282, + 0.817 + ], + "angle": 0, + "content": "8. Finalize the solution: Combine all the" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.818, + 0.247, + 0.823 + ], + "angle": 0, + "content": "steps to find the final value" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.828, + 0.287, + 0.833 + ], + "angle": 0, + "content": "Now, let's guide the low-level math solving" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.834, + 0.258, + 0.84 + ], + "angle": 0, + "content": "agent to implement these steps." + }, + { + "type": "list", + "bbox": [ + 0.178, + 0.626, + 0.291, + 0.84 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.625, + 0.517, + 0.63 + ], + "angle": 0, + "content": "To solve the given problem, we start by analyzing the equation \\( x^{10} + (13x - 1)^{10} = 0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.631, + 0.359, + 0.636 + ], + "angle": 0, + "content": "This can be rewritten as:" + }, + { + "type": "equation", + "bbox": [ + 0.383, + 0.641, + 0.438, + 0.646 + ], + "angle": 0, + "content": "\\[\nx ^ {1 0} = - (1 3 x - 1) ^ {1 0}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.651, + 0.404, + 0.657 + ], + "angle": 0, + "content": "Taking the 10th root on both sides, we get:" + }, + { + "type": "equation", + "bbox": [ + 0.361, + 0.662, + 0.433, + 0.667 + ], + "angle": 0, + "content": "\\[\nx = \\omega (1 3 x - 1),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.672, + 0.507, + 0.684 + ], + "angle": 0, + "content": "where \\(\\omega\\) is a 10th root of \\(-1\\). The 10th roots of \\(-1\\) are given by \\(\\omega = e^{\\pi (2k + 1) / 10}\\) for \\(k = 0, 1, 2, \\ldots, 9\\)." + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.689, + 0.381, + 0.695 + ], + "angle": 0, + "content": "Rewriting the equation, we have:" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.699, + 0.519, + 0.711 + ], + "angle": 0, + "content": "\\(x = \\omega (13x - 1)\\Rightarrow x - 13\\omega x = -\\omega \\Rightarrow x(1 - 13\\omega) = -\\omega \\Rightarrow x = \\frac{-\\omega}{1 - 13\\omega}\\)" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.713, + 0.384, + 0.718 + ], + "angle": 0, + "content": "Thus, the roots of the equation are:" + }, + { + "type": "equation", + "bbox": [ + 0.3, + 0.725, + 0.432, + 0.736 + ], + "angle": 0, + "content": "\\[\nr _ {k} = \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.739, + 0.394, + 0.744 + ], + "angle": 0, + "content": "where \\(\\omega_{k} = e^{i\\pi (2k + 1) / 10}\\) for \\(k = 0,1,2\\)" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.75, + 0.516, + 0.762 + ], + "angle": 0, + "content": "The roots come in conjugate pairs, so the roots are \\( r_1, \\overline{r_1}, r_2, \\overline{r_2}, r_3, \\overline{r_3}, r_4, \\overline{r_4}, r_5, \\overline{r_5} \\). We need to find the value of:" + }, + { + "type": "equation", + "bbox": [ + 0.359, + 0.765, + 0.462, + 0.779 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{r _ {1} \\overline {{r _ {1}}}} + \\frac {1}{r _ {2} \\overline {{r _ {2}}}} + \\frac {1}{r _ {3} \\overline {{r _ {3}}}} + \\frac {1}{r _ {4} \\overline {{r _ {4}}}} + \\frac {1}{r _ {5} \\overline {{r _ {5}}}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.781, + 0.371, + 0.787 + ], + "angle": 0, + "content": "Since \\(r_k\\overline{r_k} = |r_k|^2\\) we have:" + }, + { + "type": "equation", + "bbox": [ + 0.392, + 0.791, + 0.43, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{r _ {k} r _ {k}} = \\frac {1}{| r _ {k} | ^ {2}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.298, + 0.809, + 0.378, + 0.814 + ], + "angle": 0, + "content": "We need to find \\( |r_k|^2 \\). Note that:" + }, + { + "type": "equation", + "bbox": [ + 0.388, + 0.819, + 0.431, + 0.83 + ], + "angle": 0, + "content": "\\[\nr _ {k} = \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.617, + 0.62, + 0.73, + 0.626 + ], + "angle": 0, + "content": "Low-Level Agent's Output (part II)" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.63, + 0.587, + 0.636 + ], + "angle": 0, + "content": "The magnitude of \\(r_k\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.639, + 0.735, + 0.653 + ], + "angle": 0, + "content": "\\[\n| r _ {k} | = \\left| \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}} \\right| = \\left| \\frac {| \\omega_ {k} |}{1 - 1 3 \\omega_ {k}} \\right| = \\frac {1}{1 - 1 3 \\omega_ {k}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.657, + 0.543, + 0.662 + ], + "angle": 0, + "content": "Thus," + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.666, + 0.7, + 0.679 + ], + "angle": 0, + "content": "\\[\n| r _ {k} | ^ {2} = \\frac {1}{| 1 - 1 3 \\omega_ {k} | ^ {2}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.683, + 0.555, + 0.688 + ], + "angle": 0, + "content": "Therefore," + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.693, + 0.701, + 0.705 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{r _ {2} r _ {1}} = | 1 - 1 3 \\omega_ {k} | ^ {2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.71, + 0.641, + 0.715 + ], + "angle": 0, + "content": "We need to sum this over the 5 pairs of roots:" + }, + { + "type": "equation", + "bbox": [ + 0.651, + 0.719, + 0.694, + 0.733 + ], + "angle": 0, + "content": "\\[\n\\sum_ {k = 0} ^ {4} | 1 - 1 3 \\omega_ {k} | ^ {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.739, + 0.611, + 0.744 + ], + "angle": 0, + "content": "Since \\(\\omega_{k} = e^{i\\pi (2k + 1) / 10}\\), we have" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.748, + 0.813, + 0.754 + ], + "angle": 0, + "content": "\\(|1 - 13\\omega_{k}|^{2} = (1 - 13\\omega_{k})(1 - 13\\overline{\\omega_{k}}) = (1 - 13\\omega_{k})(1 - 13e^{-i\\pi (2k + 1) / 10}) = 1 - 13\\omega_{k} - 13e^{-i\\pi (2k + 1) / 10} + 169.\\)" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.758, + 0.59, + 0.764 + ], + "angle": 0, + "content": "Since \\(\\omega_{k}\\overline{\\omega_{k}} = 1\\) we get:" + }, + { + "type": "list", + "bbox": [ + 0.528, + 0.748, + 0.813, + 0.764 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.769, + 0.817, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\left| 1 - 1 3 \\omega_ {k} \\right| ^ {2} = 1 6 9 - 1 3 (\\omega_ {k} + e ^ {- i \\pi (2 k + 1) \\cdot 1 0}) + 1 = 1 7 0 - 1 3 \\cdot 2 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right) = 1 7 0 - 2 6 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.786, + 0.626, + 0.792 + ], + "angle": 0, + "content": "Summing over \\(k = 0,1,2,3,4\\) we get:" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.796, + 0.797, + 0.811 + ], + "angle": 0, + "content": "\\[\n\\sum_ {k = 0} ^ {n - 1} \\left(1 7 0 - 2 6 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right)\\right) = 5 \\cdot 1 7 0 - 2 6 \\sum_ {k = 0} ^ {n - 1} \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right) = 8 5 0 - 2 6 \\cdot 0 = 8 5 0.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.528, + 0.816, + 0.574, + 0.821 + ], + "angle": 0, + "content": "Thus, the value is:" + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.825, + 0.68, + 0.832 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.269, + 0.852, + 0.729, + 0.867 + ], + "angle": 0, + "content": "Figure 11: Case Study for base correctness reward of high-level agent" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "32" + } + ], + [ + { + "type": "code", + "bbox": [ + 0.242, + 0.098, + 0.756, + 0.111 + ], + "angle": 0, + "content": "Question: The product of \\(3t^{2} + 5t + a\\) and \\(4t^{2} + bt - 2\\) is \\(12t^{4} + 26t^{3} - 8t^{2} - 16t + 6\\). What is \\(a + b\\)?" + }, + { + "type": "code_caption", + "bbox": [ + 0.177, + 0.118, + 0.359, + 0.13 + ], + "angle": 0, + "content": "Llama3.1-8B-Instruct training Output:" + }, + { + "type": "code", + "bbox": [ + 0.178, + 0.135, + 0.498, + 0.183 + ], + "angle": 0, + "content": "{\n \"action\": \"DECOMPOSE\",\n \"output\": \"Decompose the problem into finding the coefficients of the product of two polynomials and then solving for a and b.\"\n}" + }, + { + "type": "code_caption", + "bbox": [ + 0.506, + 0.118, + 0.689, + 0.13 + ], + "angle": 0, + "content": "Llama3.2-1B-Instruct training Output:" + }, + { + "type": "code", + "bbox": [ + 0.509, + 0.135, + 0.822, + 0.184 + ], + "angle": 0, + "content": "{ \"action\": \"EMPTY\", \"output\".\"\" }" + }, + { + "type": "code", + "bbox": [ + 0.178, + 0.19, + 0.482, + 0.467 + ], + "angle": 0, + "content": "Step 1: To find the product of the two polynomials \\(3t^{2} + 5t + a\\) and \\(4t^{2} + bt - 2\\), we need to multiply each term of the first polynomial by each term of the second polynomial and then combine like terms. \nStep 2: The product of the two polynomials can be written as \\((3t^{2} + 5t + a)(4t^{2} + bt - 2)\\). \nStep 3: Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial: \\((3t^{2})(4t^{2}) + (3t^{2})(bt) + (3t^{2})(-2) + (5t)(4t^{2}) + (5t)(bt) + (5t)(-2) + (a)(4t^{2}) + (a)(bt) + (a)(-2)\\). \nStep 4: Simplifying the products, we get \\(12t^{4} + 3b^{3} - 6t^{2} + 20t^{3} + 5bt^{2} - 10t + 4at^{2} + abt - 2a\\). \nStep 5: Combining like terms, we have \\(12t^{4} + (3b + 20)t^{3} + (5b - 6 + 4a)t^{2} + (ab - 10)t - 2a\\). \nStep 6: We are given that the product of the two polynomials is \\(12t^{4} + 26t^{3} - 8t^{2} - 16t + 6\\). \nWe can equate the coefficients of the corresponding powers of \\(t\\) in the two expressions. \nStep 7: Equating the coefficients of \\(t^3\\), we get \\(3b + 20 = 26\\). \nStep 8: Equating the coefficients of \\(t^2\\), we get \\(5b - 6 + 4a = -8\\). \nStep 9: Equating the constant terms, we get \\(-2a = 6\\). \nStep 10: Solving the equation \\(-2a = 6\\), we find that \\(a = -3\\). \nStep 11: Substituting \\(a = -3\\) into the equation \\(5b - 6 + 4a = -8\\), we get \\(5b - 6 + 4(-3) = -8\\), which simplifies to \\(5b - 18 = -8\\). \nStep 12: Solving for \\(b\\), we find that \\(5b = 10\\), so \\(b = 2\\). \nStep 13: Now that we have found the values of \\(a\\) and \\(b\\), we can calculate their sum: \\(a + b = -3 + 2 = -1\\). \nThe final answer is: \\(\\boxed{-1}\\)" + }, + { + "type": "code", + "bbox": [ + 0.507, + 0.195, + 0.811, + 0.224 + ], + "angle": 0, + "content": "Step 1: The problem asks us to find the values of \\( a \\) and \\( b \\) in the quadratic expressions \\( 3t^2 + 5t + a \\) and \\( 4t^2 + bt - 2 \\), respectively, given that their product is \\( 12t^4 + 26t^3 - 8t^2 - 16t + 6 \\)." + }, + { + "type": "code", + "bbox": [ + 0.508, + 0.233, + 0.819, + 0.262 + ], + "angle": 0, + "content": "Step 2: To solve this, we need to multiply the two quadratic expressions and equate the resulting expression to the given product \\(12t^4 + 26t^3 - 8t^2 - 16t + 6\\)." + }, + { + "type": "code", + "bbox": [ + 0.508, + 0.271, + 0.763, + 0.291 + ], + "angle": 0, + "content": "Step 3: We start by multiplying the two quadratic expressions: \\((3t^{2} + 5t + a)(4t^{2} + bt - 2)\\)." + }, + { + "type": "code", + "bbox": [ + 0.508, + 0.3, + 0.78, + 0.319 + ], + "angle": 0, + "content": "Step 4: This gives us \\(12t^4 + (3b + 5)t^3 + (4a + 5b - 6)t^2 + (-2b + 10t + 2a)t - 2a.\\)" + }, + { + "type": "code", + "bbox": [ + 0.507, + 0.327, + 0.816, + 0.347 + ], + "angle": 0, + "content": "Step 5: We know that the coefficients of the resulting expression must be equal to the coefficients of the given product \\(12t^4 + 26t^3 - 8t^2 - 16t + 6\\)." + }, + { + "type": "code", + "bbox": [ + 0.507, + 0.356, + 0.81, + 0.374 + ], + "angle": 0, + "content": "Step 6: Equating the coefficients of \\( t^3 \\) gives us the equation \\( 3b + 5 = 26 \\), which simplifies to \\( 3b = 21 \\) and thus \\( b = 7 \\)." + }, + { + "type": "code", + "bbox": [ + 0.507, + 0.383, + 0.811, + 0.403 + ], + "angle": 0, + "content": "Step 7: Equating the constant terms gives us \\(-2a = -6\\), which simplifies to \\(a = 3\\)." + }, + { + "type": "code", + "bbox": [ + 0.507, + 0.412, + 0.816, + 0.422 + ], + "angle": 0, + "content": "Step 8: Now that we have the values of \\( b \\) and \\( a \\), we can find the sum \\( a + b \\)." + }, + { + "type": "code", + "bbox": [ + 0.508, + 0.43, + 0.729, + 0.44 + ], + "angle": 0, + "content": "Step 9: Adding \\( a = 3 \\) and \\( b = 7 \\) gives us \\( a + b = 10 \\)." + }, + { + "type": "code", + "bbox": [ + 0.508, + 0.449, + 0.61, + 0.46 + ], + "angle": 0, + "content": "The final answer is: \\(\\boxed{10}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.477, + 0.731, + 0.492 + ], + "angle": 0, + "content": "Figure 12: Case Study for interpretability experiments in Section 4.2.2" + }, + { + "type": "code_caption", + "bbox": [ + 0.178, + 0.52, + 0.286, + 0.534 + ], + "angle": 0, + "content": "System prompt:" + }, + { + "type": "code", + "bbox": [ + 0.178, + 0.535, + 0.779, + 0.714 + ], + "angle": 0, + "content": "You are a math expert trying to solve mathematical problems. Before answering a question, your task is to decompose the original question to make it clearer. \nProvide your rewritten content in JSON format: \n{\"action\": \"DECOMPOSE\", \"output\": \"{decomposed question content}}\" \n}} \nRespond only with valid JSON. Do not write an introduction or summary. \nUser prompt: \nHere is the question: [problem.text]" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.722, + 0.749, + 0.736 + ], + "angle": 0, + "content": "Prompt for generating final answers using on the question and metacognition reasoning:" + }, + { + "type": "code_caption", + "bbox": [ + 0.178, + 0.745, + 0.285, + 0.759 + ], + "angle": 0, + "content": "System prompt:" + }, + { + "type": "code", + "bbox": [ + 0.178, + 0.761, + 0.817, + 0.816 + ], + "angle": 0, + "content": "You are a math expert tasked with solving problems step by step. Follow the provided instructions precisely, showing all reasoning and intermediate steps. Present the final answer within \\boxed{\\{\\}}\\}." + }, + { + "type": "code_caption", + "bbox": [ + 0.179, + 0.816, + 0.268, + 0.828 + ], + "angle": 0, + "content": "User prompt:" + }, + { + "type": "code", + "bbox": [ + 0.178, + 0.829, + 0.551, + 0.897 + ], + "angle": 0, + "content": "Here is the question and instructions: \nQuestion \n[problem_text] \nProvided Instruction \n[instruction_text]" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "33" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.173, + 0.092, + 0.427, + 0.108 + ], + "angle": 0, + "content": "G.1.2 Prompts for Math problems" + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.115, + 0.273, + 0.131 + ], + "angle": 0, + "content": "VRP prompt:" + }, + { + "type": "code", + "bbox": [ + 0.174, + 0.132, + 0.806, + 0.219 + ], + "angle": 0, + "content": "System prompt: \nYou are a math expert tasked with solving problems step by step. Present the final answer within \\boxed{}?. \nUser prompt: \nHere is the question: \n{Question}" + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.225, + 0.277, + 0.24 + ], + "angle": 0, + "content": "MRP prompt:" + }, + { + "type": "code", + "bbox": [ + 0.174, + 0.242, + 0.82, + 0.383 + ], + "angle": 0, + "content": "System prompt: \nYou are a math expert tasked with solving problems. When solving a problem, your first task is to provide a high-level solution plan as an instruction. Then you need to follow the provided instructions precisely, showing all reasoning and intermediate steps. Finally, you must present the final answer within boxed}. \nUser prompt: \nHere is the question: {Question}" + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.39, + 0.304, + 0.405 + ], + "angle": 0, + "content": "MAMRP prompt:" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.405, + 0.286, + 0.419 + ], + "angle": 0, + "content": "high-level agent:" + }, + { + "type": "code", + "bbox": [ + 0.174, + 0.42, + 0.83, + 0.616 + ], + "angle": 0, + "content": "System prompt: \nYou are a math expert specialized in solving mathematical problems, you need to teach a weaker agent with minimal capability in math how to solve a problem step-by-step. \nYour task is to provide a high-level solution plan for the given problem, in order to guide a low-level math solving agent to solve the problem. \nYou can not directly answer the question. You'll be punished if you include any answer in your response. \nYou need to first think deeply in mind and output your final instruction. \nUser prompt: \nHere is the question: \n{Question}" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.618, + 0.281, + 0.632 + ], + "angle": 0, + "content": "low-level agent:" + }, + { + "type": "code", + "bbox": [ + 0.174, + 0.633, + 0.82, + 0.828 + ], + "angle": 0, + "content": "System prompt: \nYou are a math expert tasked with solving problems step by step. Follow the provided instructions precisely, showing all reasoning and intermediate steps. Present the final answer within \\boxed{}/. User prompt: Here is the question and instructions: [Question] {Question} [End of Question] [Provided Instruction] {instruction} [End of Instruction]" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "34" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.172, + 0.092, + 0.506, + 0.108 + ], + "angle": 0, + "content": "G.1.3 Prompts for LLM-as-a-Judge problems" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.115, + 0.486, + 0.13 + ], + "angle": 0, + "content": "We adopt the prompts from Saha et al. [2025a]." + }, + { + "type": "title", + "bbox": [ + 0.173, + 0.13, + 0.273, + 0.144 + ], + "angle": 0, + "content": "VRP prompt:" + }, + { + "type": "code", + "bbox": [ + 0.174, + 0.146, + 0.83, + 0.521 + ], + "angle": 0, + "content": "System prompt: \nPlease act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses. Begin your evaluation by comparing the two responses and provide a short explanation. Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision.. \nDo not allow the length of the responses to influence your evaluation.. \nDo not favor certain names of the assistants. Be as objective as possible. After providing your explanation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better.. \nUser prompt: \n[User Question] {instruction} [End of User Question] [The Start of Assistant A's Answer] {response_A} [The End of Assistant A's Answer] [The Start of Assistant B's Answer] {response_B} [The End of Assistant B's Answer]" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "35" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.174, + 0.092, + 0.276, + 0.107 + ], + "angle": 0, + "content": "MRP prompt:" + }, + { + "type": "title", + "bbox": [ + 0.178, + 0.109, + 0.286, + 0.123 + ], + "angle": 0, + "content": "System prompt:" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.124, + 0.826, + 0.634 + ], + "angle": 0, + "content": "Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. First of your task is to build an evaluation plan that can then be executed to assess the response quality. Whenever appropriate, you can choose to also include a step-by-step reference answer as part of the evaluation plan. Enclose your evaluation plan between the tags \"[Start of Evaluation Plan]\" and \"[End of Evaluation Plan)\". After that, please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses. Begin your evaluation by comparing the two responses and provide a short explanation. Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision. Do not allow the length of the responses to influence your evaluation. Do not favor certain names of the assistants. Be as objective as possible. After providing your explanation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better. User prompt: [User Question] {instruction} [End of User Question] [The Start of Assistant A's Answer] {response_A} [The End of Assistant A's Answer] [The Start of Assistant B's Answer] {response_B} [The End of Assistant B's Answer]" + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.641, + 0.416, + 0.656 + ], + "angle": 0, + "content": "MAMRP prompt: high-level agent:" + }, + { + "type": "title", + "bbox": [ + 0.178, + 0.658, + 0.286, + 0.673 + ], + "angle": 0, + "content": "System prompt:" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.673, + 0.798, + 0.756 + ], + "angle": 0, + "content": "We want to evaluate the quality of the responses provided by AI assistants to the user question displayed below. For that, your task is to help us build an evaluation plan that can then be executed to assess the response quality. Whenever appropriate, you can choose to also include a step-by-step reference answer as part of the evaluation plan." + }, + { + "type": "title", + "bbox": [ + 0.179, + 0.756, + 0.269, + 0.769 + ], + "angle": 0, + "content": "User prompt:" + }, + { + "type": "text", + "bbox": [ + 0.18, + 0.77, + 0.395, + 0.81 + ], + "angle": 0, + "content": "[User Question] \n{Question} \n[End of User Question]" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "36" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.174, + 0.093, + 0.281, + 0.106 + ], + "angle": 0, + "content": "low-level agent:" + }, + { + "type": "title", + "bbox": [ + 0.179, + 0.11, + 0.285, + 0.123 + ], + "angle": 0, + "content": "System prompt:" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.124, + 0.829, + 0.19 + ], + "angle": 0, + "content": "Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. Your evaluation should be performed by following the provided evaluation plan step-by-step. Avoid copying the plan when doing the evaluation." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.192, + 0.81, + 0.22 + ], + "angle": 0, + "content": "Please also only stick to the given plan and provide explanation of how the plan is executed to compare the two responses." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.221, + 0.808, + 0.247 + ], + "angle": 0, + "content": "Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.248, + 0.792, + 0.288 + ], + "angle": 0, + "content": "Do not allow the length of the responses to influence your evaluation. Do not favor certain names of the assistants. Be as objective as possible." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.289, + 0.825, + 0.329 + ], + "angle": 0, + "content": "After providing your evaluation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better." + }, + { + "type": "title", + "bbox": [ + 0.18, + 0.331, + 0.269, + 0.344 + ], + "angle": 0, + "content": "User prompt:" + }, + { + "type": "code", + "bbox": [ + 0.179, + 0.344, + 0.522, + 0.51 + ], + "angle": 0, + "content": "[User Question] \n{instruction} \n{End of User Question] \n{The Start of Assistant A's Answer} \n{response_A} \n{The End of Assistant A's Answer} \n{The Start of Assistant B's Answer} \n{response_B} \n{The End of Assistant B's Answer} \n{The Start of Evaluation Plan} \n{evaluation計劃} \n{The End of Evaluation Plan}" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "37" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.172, + 0.092, + 0.409, + 0.108 + ], + "angle": 0, + "content": "G.2 Multi-turn ReMA prompts" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.117, + 0.53, + 0.131 + ], + "angle": 0, + "content": "G.2.1 SFT data collection of multi-turn MAMRP" + }, + { + "type": "title", + "bbox": [ + 0.178, + 0.142, + 0.286, + 0.156 + ], + "angle": 0, + "content": "System prompt:" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.156, + 0.814, + 0.224 + ], + "angle": 0, + "content": "You are classifying reasoning process data into two types of thinking. You will be given a question-answer pair from a reasoning dataset. Your task is to split all words into two parts. These words are crucial for analyzing reasoning patterns, so do not skip any details." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.225, + 0.798, + 0.293 + ], + "angle": 0, + "content": "- **Meta-Thinking Agent (MTA):** Responsible for high-level thought processes. This includes planning, evaluating steps, expressing uncertainty, making observations, or setting goals. Avoid detailed calculations. The content should be enclosed in `` and ``." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.293, + 0.808, + 0.349 + ], + "angle": 0, + "content": "- \\(\\star \\star\\) Reasoning Agent (RA): \\(\\star \\star\\) Responsible for detailed problem-solving steps, such as calculations, logical deductions, or breaking down a problem into subproblems. The content should be enclosed in `` and ``." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.35, + 0.378, + 0.361 + ], + "angle": 0, + "content": "\\*\\*Rules to follow: \\*\\*" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.363, + 0.807, + 0.417 + ], + "angle": 0, + "content": "1. **Do not assign large chunks of text to a single type of thinking.** The reasoning process consists of small, nonlinear thinking steps, so alternate appropriately between Meta-Thinking and Reasoning steps." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.418, + 0.756, + 0.459 + ], + "angle": 0, + "content": "2. **Keep the words from the original solution unmodified whenever possible.** Words like \"Wait,\" \"Hmm,\" \"But,\" etc., typically indicate Meta-Thinking and should be preserved." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.46, + 0.525, + 0.472 + ], + "angle": 0, + "content": "3. \\(\\star \\star\\) When finalizing the answer: \\(\\star \\star\\)" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.473, + 0.798, + 0.5 + ], + "angle": 0, + "content": "- The \\*\\*Meta-Thinking Agent (MTA) \\*\\* must explicitly confirm the answer before completion and output '[FINISH]'." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.501, + 0.768, + 0.526 + ], + "angle": 0, + "content": "- The \\(\\star \\star\\) Reasoning Agent (RA) \\(\\star \\star\\) should then provide the final answer in the correct format." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.528, + 0.731, + 0.554 + ], + "angle": 0, + "content": "4. **Do not skip any reasoning steps, even if they seem redundant, incorrect or irrelevant**" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.555, + 0.817, + 0.596 + ], + "angle": 0, + "content": "5. **Do not modify or remove any part of the original reasoning process**, even if it seems redundant or repetitive. The goal is to **preserve the exact flow of thought** as it naturally occurs." + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.597, + 0.817, + 0.638 + ], + "angle": 0, + "content": "6. **Retain all expressions such as \"Wait,\" \"Hmm,\" \"But wait,\" etc., exactly as they appear. These indicate important cognitive processes and should not be skipped or altered.**" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.639, + 0.434, + 0.665 + ], + "angle": 0, + "content": "Here are examples for you: [Examples] ..." + }, + { + "type": "title", + "bbox": [ + 0.178, + 0.666, + 0.268, + 0.679 + ], + "angle": 0, + "content": "User prompt:" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.68, + 0.365, + 0.762 + ], + "angle": 0, + "content": "[Begin of Question] \n{question} \n[End of Question] \n[Begin of Solution] \n{solution} \n[End of Solution]" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "38" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.173, + 0.092, + 0.417, + 0.108 + ], + "angle": 0, + "content": "G.2.2 Prompt for math problems" + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.115, + 0.385, + 0.13 + ], + "angle": 0, + "content": "Meta-Thinking Agent (MTA):" + }, + { + "type": "code", + "bbox": [ + 0.174, + 0.138, + 0.827, + 0.322 + ], + "angle": 0, + "content": "System prompt: \nYou are a meta-think agent that represents human high-level think process, when solving a question, you will have a discussion with human, each time you think about what to do next: e.g. \n- Exploring multiple angles and approaches \n- Breaking down the solution into clear steps \n- Continuously reflecting on intermediate results honestly and adapt your strategy as you progress \n- Backtracking when necessary \n- Requesting exploration of multiple solutions individually \n- Finally confirm the answer with the tag [FINISH] \nUser prompt: \n{question}" + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.328, + 0.339, + 0.344 + ], + "angle": 0, + "content": "Reasoning Agent (RA):" + }, + { + "type": "code", + "bbox": [ + 0.174, + 0.351, + 0.808, + 0.438 + ], + "angle": 0, + "content": "System prompt: Please reason step by step follow the given instruction, when asked to finalize your answer, put your answer within \\boxed{} User prompt: {question} {instruction}" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "39" + } + ] +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_origin.pdf b/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f945eb03ea30030c63d54d502929627d6ee64d7e --- /dev/null +++ b/data/2025/2503_09xxx/2503.09501/7c196e4e-1362-4974-a470-65c83d863927_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0d97124752934b219f49f7d517e9e61a977326fdc765a9f6512c2949e106e159 +size 6136590 diff --git a/data/2025/2503_09xxx/2503.09501/full.md b/data/2025/2503_09xxx/2503.09501/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8ee45810363ff40c7c7e47061203309e6b9f69d8 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09501/full.md @@ -0,0 +1,1466 @@ +# ReMA: Learning to Meta-think for LLMs with Multi-agent Reinforcement Learning + +Ziyu Wan $^{1,2*}$ , Yunxiang Li $^{3*}$ , Xiaoyu Wen $^{1,2}$ , Yan Song $^{4}$ , Hanjing Wang $^{1}$ , Linyi Yang $^{4}$ , Mark Schmidt $^{3}$ , Jun Wang $^{4}$ , Weinan Zhang $^{1}$ , Shuyue Hu $^{2\ddagger}$ , Ying Wen $^{1\ddagger}$ + +1 Shanghai Jiao Tong University +$^{2}$ Shanghai Artificial Intelligence Laboratory +3 University of British Columbia +4 University College London + +# Abstract + +Recent research on Reasoning of Large Language Models (LLMs) has sought to further enhance their performance by integrating meta-thinking—enabling models to monitor, evaluate, and control their reasoning processes for more adaptive and effective problem-solving. However, current single-agent work lacks a specialized design for acquiring meta-thinking, resulting in low efficacy. To address this challenge, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages Multi-Agent Reinforcement Learning (MARL) to elicit meta-thinking behaviors, encouraging LLMs to think about thinking. ReMA decouples the reasoning process into two hierarchical agents: a high-level meta-thinking agent responsible for generating strategic oversight and plans, and a low-level reasoning agent for detailed executions. Through iterative reinforcement learning with aligned objectives, these agents explore and learn collaboration, leading to improved generalization and robustness. Empirical results from single-turn experiments demonstrate that ReMA outperforms single-agent RL baselines on complex reasoning tasks, including competitive-level mathematical benchmarks and LLM-as-a-Judge benchmarks. Additionally, we further extend ReMA to multi-turn interaction settings, leveraging turn-level ratio and parameter sharing to improve efficiency. Comprehensive ablation studies further illustrate the evolving dynamics of each distinct agent, providing valuable insights into how the meta-thinking reasoning process enhances the reasoning capabilities of LLMs. Our code can be found in https://github.com/ziyuwan/ReMA-public + +# 1 Introduction + +Large language models (LLMs) have demonstrated remarkable capabilities in knowledge understanding and complex reasoning tasks [Chowdhery et al., 2023, Achiam et al., 2023, Anil et al., 2023, Dubey et al., 2024]. The paradigm in developing LLM-based reasoning models is shifting from scaling training-time computation towards scaling test-time computation [Snell et al., 2024]. Recent advancements, such as OpenAI-o1 [OpenAI, 2024], Deepseek R1 [DeepSeek-AI et al., 2025], and Gemini 2.0 Flash Thinking [DeepMind, 2025], have demonstrated that allowing LLMs to think before generating answers can significantly enhance performance and lead to the emergence of human-like reasoning patterns. These patterns like "Wait, hold on." or "Let's break this down." + +Question: $T = 9.5$ . If $\log_2 x^T - \log_4 x = \log_8 x^k$ is an identity for all $x > 0$ , compute the value of $k$ . + +![](images/fd5b40d644792636991a20db79d8c4202f072f2e023bbd6106c186898b906286.jpg) +Figure 1: Left: A construction-based method that fine-tunes LLMs using rejection sampling, searching among combinations of pre-defined templates. Middle: R1-like method learns to mix meta-thinking and detailed reasoning steps during training. Right: Our method ReMA separates the meta-thinking and reasoning steps in a multi-agent system and updated by reinforcement learning. + +indicate that LLMs can develop a form of meta-thinking abilities that can generalize well to out-of-distribution (OOD) tasks [Xiang et al., 2025]. Meta-thinking, also known as metacognitive skills [Flavell, 1979], is an ability traditionally considered uniquely human [Didolkar et al., 2024]. + +To cultivate meta-thinking patterns from LLMs themselves, recent construction-based supervised approaches leverage supervised finetuning on structured reasoning trajectories. Specifically, these methods sampling reasoning trajectories from predefined meta-thinking templates and then use supervised finetuning (SFT) or direct preference optimization (DPO) [Rafailov et al., 2023] to teach LLMs imitate these patterns [Qi et al., 2024, Yue et al., Xi et al., 2024, Yang et al., 2025, Muenighoff et al., 2025, Ye et al., 2025c]. However, such methods lack sufficient flexibility for LLMs to explore suitable meta-thinking patterns. Thus, they often fail to generalize to out-of-distribution (OOD) problems, leading to unstable performance on unseen data [Kirk et al., Chu et al., 2025]. Besides construction-based methods, R1-like single-agent reinforcement learning (SARL) has also been adopted for meta-thinking in reasoning [DeepSeek-AI et al., 2025, Xie et al., 2025]. However, these SARL attempts typically rely on strong foundational models for easier exploration or extensive task-specific fine-tuning for stable training [Xu et al., 2025, Gandhi et al., 2025]. Furthermore, SARL needs to learn meta-thinking and reasoning within a single forward pass, seeking to capture complex reasoning structures purely in an autoregressive manner [Xie et al., 2025]. This can potentially lead to issues such as inefficient exploration as well as reduced readability and early convergence to local optima [DeepSeek-AI et al., 2025, Xiang et al., 2025]. + +To address these limitations, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages multi-agent reinforcement learning (MARL) to encourage LLMs to think about thinking. Our approach employs a multi-agent system (MAS) composed of a high-level meta-thinking agent, responsible for strategic oversight and instruction generation, and a low-level reasoning agent tasked with detailed executing processes based on provided guidance. We compare the inference process among the construction-based method, R1-like method, and ReMA in Fig. 1. Since MAS distributes the exploration space of SARL into multiple agents, it enables each agent to explore more structurally and efficiently during training. Then we apply reinforcement learning on each agent with aligned reward functions. In this way, ReMA effectively balances the trade-off between generalization capability and exploration efficiency. As a result, they can learn to play the best of their role (either to meta-think or to follow instructions), at the present of the other agent. + +To our knowledge, we are the first to formally define and optimize a multi-agent meta-thinking reasoning process (MAMRP) through multi-agent reinforcement learning. Our extensive experiments span both math reasoning and LLM-as-a-Judge tasks, where ReMA consistently achieves the highest average performance across three backbone pretrained models. We further extend ReMA to multi-turn interaction settings on math reasoning tasks, implementing turn-level ratio to optimize trajectory returns and stabilize training. Through comprehensive ablation studies, we illustrate the evolving dynamics between agents, revealing unexpected interaction patterns such as role reversals + +under different reward settings. These findings provide valuable insights into how meta-thinking processes enhance the reasoning capabilities of LLMs. + +# 2 Preliminaries + +In this section, we outline the formulation of the vanilla reasoning process (Sec. 2.1) and the representative training methods (Sec. 2.2) along with the notation used throughout the paper. + +# 2.1 Vanilla Reasoning Process (VRP) + +The probability of generating a response $\mathbf{y}$ equals the product of its stepwise probabilities. Given a model $\pi_{\theta}$ and a prompt $\mathbf{x} = (x_1, \ldots, x_N)$ , the vanilla reasoning process (VRP) autoregressively produces a response $\mathbf{y} = (y_1, \ldots, y_L)$ with + +$$ +\pi_ {\theta} (\mathbf {y} | \mathbf {x}) = \prod_ {l = 1} ^ {L} \pi_ {\theta} (y _ {l} | x _ {1}, x _ {2}, \dots x _ {N}, y _ {1}, \dots , y _ {l - 1}) = \prod_ {l = 1} ^ {L} \pi_ {\theta} (\mathbf {y} _ {l} | \mathbf {x}, \mathbf {y} _ {< l}) +$$ + +The response usually contains intermediate reasoning steps before arriving at the final answer, this process is also known as chain-of-thought (CoT) [Wei et al., 2022], which can be represented as: + +$$ +\mathbf {x} \xrightarrow {\text {r e a s o n i n g s t e p s}} \mathbf {y} \sim \mathbf {a}, \tag {1} +$$ + +where $\mathbf{a}$ is the extracted final answer, which is included in the answer $\mathbf{y}$ . + +# 2.2 Training VRP via Reinforcement Learning + +RL frames VRP decoding process as a deterministic, token-level Markov Decision process (MDP) [Wang et al., 2024a]. Its objective is + +$$ +\mathcal {J} (\theta) = \mathbb {E} _ {(\mathbf {x}, \mathbf {y} ^ {*}) \sim \mathcal {D}, \mathbf {y} \sim \pi_ {\theta}} \left[ R (\mathbf {y}, \mathbf {y} ^ {*}) \right]. +$$ + +where $R(\cdot, \cdot)$ represents a reward function comparing generated answer $\mathbf{y}$ with the golden answer $\mathbf{y}^*$ for any question $\mathbf{x}$ sampled from dataset $\mathcal{D}$ . + +To compute the gradient $\nabla_{\theta}\mathcal{J}(\theta)$ , computationally efficient algorithms GRPO [Shao et al., 2024] and REINFORCE++ [Hu, 2025] are widely adopted. Take GRPO as an example, given a question-answer pair $\mathbf{x},\mathbf{y}^*$ and a group of $G$ generated responses $\mathbf{y}_i$ , denote $\mathbf{y}_{i,j}$ as the $j$ -th token of the $i$ -th response, it optimizes the following token-level objective: + +$$ +\begin{array}{l} \mathcal {J} (\boldsymbol {\theta}) = \mathbb {E} _ {(\mathbf {x}, \mathbf {y} ^ {*}) \sim \mathcal {D}, \{\mathbf {y} _ {i} \} _ {i = 1} ^ {G} \sim \pi_ {\boldsymbol {\theta} _ {\mathrm {o l d}}} (\cdot | \mathbf {x})} \\ \left[ \frac {1}{G} \sum_ {i = 1} ^ {G} \frac {1}{| \mathbf {y} _ {i} |} \sum_ {j = 1} ^ {| \mathbf {y} _ {i} |} \left(\min \left(r _ {i, j} (\theta) \hat {A} _ {i, j}, \operatorname {c l i p} \left(r _ {i, j} (\theta), 1 - \epsilon , 1 + \epsilon\right) \hat {A} _ {i, j}\right) - \beta D _ {\mathrm {K L}} \left(\pi_ {\theta} \| \pi_ {\text {r e f}}\right)\right) \right], \tag {2} \\ \end{array} +$$ + +where the token-level ratio $r_{i,j}(\theta)$ and the group-normalized advantage $\hat{A}_{i,j}$ are defined as: + +$$ +r _ {i, j} (\theta) = \frac {\pi_ {\theta} \left(\mathbf {y} _ {i , j} \mid \mathbf {x} , \mathbf {y} _ {i , < j}\right)}{\pi_ {\theta_ {\mathrm {o l d}}} \left(\mathbf {y} _ {i , j} \mid \mathbf {x} , \mathbf {y} _ {i , < j}\right)}, \hat {A} _ {i, j} = \frac {R _ {i} - \operatorname {m e a n} \left(\left\{R _ {i} \right\} _ {i = 1} ^ {G}\right)}{\operatorname {s t d} \left(\left\{R _ {i} \right\} _ {i = 1} ^ {G}\right)}. +$$ + +However, RL on base LLMs that haven't been well-aligned may suffer from issues like poor readability and language mixing, preventing researchers from verifying, understanding, and further developing their LLMs. And huge searching space makes efficient learning of meta-thinking daunting. + +# 3 Method + +In this section, we present Reinforced Meta-thinking Agents (ReMA), a RL method integrating meta-thinking into the reasoning process of LLM under multi-agent settings (Sec. 3.1), then describe the learning process enabled by MARL of single- and multi-turn LLM setting (Secs. 3.2.1 and 3.2.2). + +# 3.1 Deploying Meta-Thinking Reasoning Process for LLMs + +Beyond VRP (Sec. 2.1), recent studies [Muennighoff et al., 2025, Ye et al., 2025c] have shown that integrating meta-thinking behaviors in reasoning process can largely improve the accuracy of the final answers. By integrating Meta-thinking, ReMA decomposes problem solving into two sequential phases: a meta-thinking phase that plans, monitors, or revises strategy, followed by a reasoning phase that produces the detailed solution. We analyse Meta-thinking Reasoning Process along two orthogonal axes—single- vs. multi-agent and single- vs. multi-turn. + +In a single-agent setting, such a process calls LLM once and generates meta-thinking and the following reasoning autoregressively. We formulate the meta-thinking reasoning process (MRP) below: + +$$ +\mathbf {y} \sim \pi_ {\theta} (\mathbf {y} \mid \mathbf {x}, \mathbf {m}) \cdot \pi_ {\theta} (\mathbf {m} \mid \mathbf {x}), \tag {3} +$$ + +where $\mathbf{m}$ and $\mathbf{y}$ are the output of meta-thinking and reasoning respectively. We present the procedure as shown below: + +$$ +\mathbf {x} \xrightarrow {\text {m e t a - t h i n k i n g}} \mathbf {m} \xrightarrow {\text {r e a s o n i n g s t e p s}} \mathbf {y} \sim \mathbf {a}. \tag {4} +$$ + +Exploring MRP reasoning through a single-agent approach is often inefficient, as it requires the language model to simultaneously master both meta-thinking and detailed problem-solving within one call. Prior research has demonstrated that activating different model capabilities through specialized agents significantly improves MRP exploration efficiency. To leverage this insight, we decouple meta-thinking and reasoning into two separate LLM agents: a high-level agent dedicated to generating meta-thinking, and a low-level agent focused on executing reasoning steps. + +During a conversation, the high-level and low-level agents (i.e., $\pi_h$ and $\pi_l$ ) act in an interleaving manner. The high-level agent generates and summarizes meta-thoughts from the prompt and interaction history, while the low-level agent executes detailed problem-solving under those instructions. We formulate the multi-agent meta-thinking reasoning process (MAMRP) as follows: + +$$ +\mathbf {y} \sim \pi_ {l} (\mathbf {y} \mid \mathbf {x}, \mathbf {m}) \pi_ {h} (\mathbf {m} \mid \mathbf {x}). \tag {5} +$$ + +While the single-turn MAMRP offers a straightforward approach, it lacks the ability to perform immediate and fine-grained cognitive switching during the reasoning process, which limits its effectiveness on complex, long-horizon planning tasks. Therefore, we extend Eq. (5) and formulate the multi-turn MAMRP as follows: + +$$ +\mathbf {y} _ {T} \sim \prod_ {t = 1} ^ {T} \pi_ {l} \left(\mathbf {y} _ {t} \mid \mathbf {x}, \{\mathbf {m}, \mathbf {y} \} _ {< t}, \mathbf {m} _ {t}\right) \pi_ {h} \left(\mathbf {m} _ {t} \mid \mathbf {x}, \{\mathbf {m}, \mathbf {y} \} _ {< t}\right) \tag {6} +$$ + +where $T$ is the number of turns. Similarly, we present the process with a directed graph: + +$$ +\mathbf {x} \xrightarrow [ \pi_ {h} ]{\text {m e t a - t h i n k i n g}} \mathbf {m} _ {1} \xrightarrow [ \pi_ {l} ]{\text {r e a s o n i n g}} \mathbf {y} _ {1} \xrightarrow [ \pi_ {h} ]{\text {m e t a - t h i n k i n g}} \mathbf {m} _ {2} \xrightarrow [ \pi_ {l} ]{\text {r e a s o n i n g}} \mathbf {y} _ {2} \xrightarrow [ \pi_ {h} ]{\text {m e t a - t h i n k i n g}} \dots \xrightarrow [ \pi_ {l} ]{\text {r e a s o n i n g}} \mathbf {y} _ {T} \sim \mathbf {a}. \tag {7} +$$ + +As a complex reasoning system, MAMRP provides various optimization opportunities in scaling inference-time computation. We leave further discussion of these aspects in Appendix C.1. + +# 3.2 Training MAMRP: A Multi-Agent RL Method + +Multi-agent RL, unlike single-agent RL in a deterministic MDP, must contend with stochastic, nonstationary dynamics and rewards, making optimization more challenging. We start by considering an easier case, the optimization of single-turn MAMRP. + +# 3.2.1 Optimizing Single-turn MAMRP + +To train the system from Sec. 3.1, we embed it as a Markov Game between the two agents. Suppose the two LLM agents are parameterized by $\theta_h$ and $\theta_l$ , respectively. Define a joint hierarchical policy over sequential decisions $\mathbf{m}$ and $\mathbf{y}$ : + +$$ +\mathbf {y} \sim \pi_ {\left(\theta_ {h}, \theta_ {l}\right)} (\mathbf {y} \mid \mathbf {x}) := \pi_ {\theta_ {l}} (\mathbf {y} \mid \mathbf {x}, \mathbf {m}) \cdot \pi_ {\theta_ {h}} (\mathbf {m} \mid \mathbf {x}), \tag {8} +$$ + +Let $R(\mathbf{y}, \mathbf{y}^*)$ denote the final reward serves as the objective function $\mathcal{J}(\theta_h, \theta_l)$ for the joint policy: + +$$ +\mathcal {J} \left(\theta_ {h}, \theta_ {l}\right) = \mathbb {E} _ {\mathbf {x}, \mathbf {y} ^ {*}} \mathbb {E} _ {\mathbf {y} \sim \pi \left(\theta_ {h}, \theta_ {l}\right)} R (\mathbf {y}, \mathbf {y} ^ {*}). \tag {9} +$$ + +![](images/f246502d1a54bf77abbf1b84a3d339ae985d445d9515b42b122262754119fa92.jpg) +RL for VRP & MRP + +![](images/7f3231499e748935cfc4e1cfa6d56049cf9d1cab539e1879a81522875ddbfa66.jpg) +ReMA with Separate Parameters + +![](images/c1b6f6aaf161ccb2d707eb51858e4b49250221c289f22f7d7fd725b003912a00.jpg) +ReMA with Shared Parameters +Figure 2: Comparison of training pipelines. Left: RL training of VRP and MRP, where a single LM agent is updated either with mixed (VRP) or explicit (MRP) meta-thinking. Middle: ReMA with separate parameters for the high-level (meta-thinking) and low-level (reasoning) agents; training alternates between freezing one agent and updating the other. Right: ReMA with shared parameters and multi-turn interactions: both agents share the same parameters and are distinguished by their system prompts. Training employs a turn-level ratio for stable multi-turn reinforcement learning and efficient updates, ensuring each turn's contribution is controlled to prevent instability. + +During optimization procedure, the high-level policy $\pi_{\theta_h}$ and low-level policy $\pi_{\theta_l}$ aim to maximize their respective rewards independently. The optimization goals for agents are: + +$$ +\theta_ {h} ^ {*} = \arg \max _ {\theta_ {h}} \mathbb {E} _ {(\mathbf {x}, \mathbf {y} ^ {*}) \sim \mathcal {D}, \mathbf {m} \sim \pi_ {\theta_ {h}}, \mathbf {y} \sim \pi_ {\theta_ {l} ^ {*}}} \left[ R _ {h} (\mathbf {m}, \mathbf {y}, \mathbf {y} ^ {*}) \right], \tag {10} +$$ + +$$ +\theta_ {l} ^ {*} \left(\theta_ {h}\right) = \arg \max _ {\theta_ {l}} \mathbb {E} _ {\left(\mathbf {x}, \mathbf {y} ^ {*}\right) \sim \mathcal {D}, \mathbf {m} \sim \pi_ {\theta_ {h}}, \mathbf {y} \sim \pi_ {\theta_ {l}}} \left[ R _ {l} \left(\mathbf {m}, \mathbf {y}, \mathbf {y} ^ {*}\right) \right], \tag {11} +$$ + +where $R_{h}$ and $R_{l}$ are policies' individual reward functions, including $R$ and regularization according to tasks and models, e.g., different format rewards (refer to Appendix C.2 for details). The detailed algorithm is in the Algorithm 1. We illustrate the MAMRP inference procedure and the proposed training method in Fig. 2. We also provide an analysis of different loss functions in Appendix C.5. + +# 3.2.2 Scaling up to Multi-turn MAMRP + +To scale up to multi-turn MAMRP, we can still adopt the iterative training strategy in Sec. 3.2.1. However, we make some changes to improve the efficiency of rollout and training. + +First, we implement a parameter-sharing strategy where both high-level and low-level agents utilize identical model weights $\theta$ , distinguished only by role-specific system prompts $S_{h}$ and $S_{l}$ . Formally, we define $\pi_h = \pi_\theta (\cdot |S_h,\cdot)$ and $\pi_l = \pi_\theta (\cdot |S_l,\cdot)$ , sharing the same underlying parameters rather than maintaining separate model instances. This approach eliminates the need for frequent model swapping on GPU during rollout, avoiding inefficient wait times, while enabling larger batch sizes during training to simultaneously optimize policies for both meta-thinking and reasoning roles. + +Second, we propose a multi-turn GRPO with turn-level ratio to address the challenges of multi-turn MAMRP. The trajectory-level averaged objective with turn-level ratio of $\pi_{l}$ is defined as (The objective of $\pi_h$ is the similar but with different system prompt): + +$$ +\mathcal {J} (\boldsymbol {\theta}) = \mathbb {E} _ {(\mathbf {x}, \mathbf {y} ^ {*}) \sim \mathcal {D}, \{(\mathbf {m} _ {i}, \mathbf {y} _ {i}) \} _ {i = 1} ^ {G} \sim \pi_ {\theta_ {\mathrm {o l d}}} (\cdot | \mathbf {x}) +$$ + +$$ +\left. \left[ \frac {1}{G} \sum_ {i = 1} ^ {G} \frac {1}{T _ {i}} \sum_ {t = 1} ^ {T _ {i}} \frac {1}{| \mathbf {y} _ {i , t} |} \sum_ {j = 1} ^ {| \mathbf {y} _ {i, t} |} \left(\min \left(r _ {i, t} (\theta) \hat {A} _ {i, t, j}, \operatorname {c l i p} \left(r _ {i, t} (\theta), 1 - \epsilon , 1 + \epsilon\right) \hat {A} _ {i, t, j}\right) - \beta D _ {\mathrm {K L}} \left(\pi_ {\theta} \| \pi_ {\text {r e f}}\right)\right) \right] \right. \tag {12} +$$ + +where $\mathbf{y}_{i,t,j}$ is the $j$ -th token at turn $t$ of the reasoning agent of the $i$ -th trajectory. And the turn-level ratio for clipping is defined as: + +$$ +r _ {i, t} (\theta) = \frac {1}{| \mathbf {y} _ {i , t} |} \sum_ {j = 1} ^ {| \mathbf {y} _ {i, t} |} r _ {i, t, j} (\theta) = \frac {1}{| \mathbf {y} _ {i , t} |} \sum_ {j = 1} ^ {| \mathbf {y} _ {i, t} |} \frac {\pi_ {\theta} \left(\mathbf {y} _ {i , t , j} \mid \mathbf {x} , \left\{\mathbf {m} _ {i , ,} , \mathbf {y} _ {i ,} \right\} _ {< t} , \mathbf {m} _ {i , t} , \mathbf {y} _ {i , t , < j}\right)}{\pi_ {\theta_ {\mathrm {o l d}}} \left(\mathbf {y} _ {i , t , j} \mid \mathbf {x} , \left\{\mathbf {m} _ {i , ,}, \mathbf {y} _ {i ,} \right\} _ {< t} , \mathbf {m} _ {i , t} , \mathbf {y} _ {i , t , < j}\right)}. \tag {13} +$$ + +The introduction of the turn-level ratio serves two key purposes. First, using a token-level ratio (Eq. (2)) in the objective introduces bias for multi-turn training, as it averages over all tokens in a trajectory. This means that tokens within longer turns (those containing more tokens) can disproportionately influence the overall loss, and averaging at the token level may encourage excessively long single-turn responses. Second, clipping each token independently risks instability during training. + +In contrast, the turn-level ratio aligns more closely with the underlying MDP formulation by treating all tokens within a turn as a single action and applying clipping at the turn level. Intuitively, this approach stabilizes training by preventing the LLM from making unstable updates that could result in extreme outputs, such as overly long repetitions or incoherent text. We conduct experimental verification in subsequent empirical results (Sec. 4.3). + +# 4 Experiments + +To evaluate the effectiveness and efficiency of ReMA, we conduct experiments on challenging benchmarks for two types of tasks: mathematical reasoning and LLM-as-a-Judge with three different LLMs. Then, we investigate the models' performance in both single- & multi-turn settings. Finally, we provide ablation studies and qualitative analyses of our method. + +# 4.1 Experiment Settings + +We first analyze the single-turn case of ReMA, i.e., $T = 1$ . The high-level agent generates a complete meta-thinking trace in one shot, and the low-level agent follows the instructions and outputs the final results. Single-turn ReMA reduces stochasticity and training cost while our experiments show that it still provides meaningful performance gains. + +Benchmarks We conduct experiments on two types of tasks: mathematical reasoning and LLM-as-a-Judge. For mathematical reasoning experiments, we train models on 7.5k training samples in MATH [Hendrycks et al., 2021] and use MATH500 [Lightman et al., 2023] as the in-distribution test dataset. Additionally, we test the optimized models on out-of-distribution datasets: GSM8K [Cobbe et al., 2021], AIME24 $^{4}$ , AMC23 $^{5}$ , GaoKao2023En [Zhang et al., 2023], Minerva Math [Lewkowycz et al., 2022], and Olympiad Bench [He et al., 2024]. + +For LLM-as-a-Judge benchmarks, we train models on RewardBench [Lambert et al., 2024]. Specifically, we convert the original data into a pair-ranking format and split it into a training set of 5k items and a test set of 970 items, denoted as RewardBench970. The models are also tested on JudgeBench [Tan et al., 2024] to assess out-of-distribution performance. We refer to Appendix D.1.2 for detailed comparisons and results. + +Baselines, Models, Training Settings We compare pass@1 performance across the following methods: (1) VRP (CoT, step-by-step prompting, Sec. 3.1); (2) $\mathbf{VRP}_{\mathbf{RL}}$ (RL under VRP); (3) $\mathbf{MRP}_{\mathbf{RL}}$ (RL under MRP with high-level task analysis, Eq. (4)), and (4) ReMA (ours, RL under MAMRP, Eq. (7)). + +We train and test Llama-3-8B-Instruct, Llama-3.1-8B-Instruct [Dubey et al., 2024], and Qwen2.5-7B-Instruct [Team, 2024] on mathematical reasoning benchmarks. For LLM-as-a-judge benchmarks, we train and test Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct. We use instruct-tuned LLMs to prompt them to perform VRP, MRP, and MAMRP directly during training. Unless specified, we use two separate copies of the same model for high- and low-level agents in ReMA. We use the base reward setting in Appendix C.2 by default. And for the underlying RL algorithm, we use REINFORCE++ [Hu, 2025]. We refer to Appendix D for detailed training settings. + +# 4.2 Results of Single-turn ReMA + +Question 1. Does single-turn ReMA outperforms baselines on both in-distribution and out-of-distribution test sets? + +Table 1: Performance on in-distribution test sets and out-of-distribution test sets. We also report the improvement/degradation w.r.t. basic CoT performance(VRP). On average, ReMA outperforms all baselines. Particularly on out-of-distribution datasets, ReMA achieves the highest performance on most of the benchmarks. + +(a) Performance on math benchmarks + +
ModelBenchmarkVRP(CoT)\( \mathbf{V R P_{R L}} \)\( \mathbf{M R P_{R L}} \)ReMA(Ours)
Llama3-8B-InstructMATH50030.8033.40 (+2.60)32.80 (+2.00)33.80 (+3.00)
GSM8K67.4881.80 (+14.32)79.68 (+12.20)79.38 (+11.90)
AIME240.000.00 (+0.00)3.33 (+3.33)0.00 (+0.00)
AMC232.5010.00 (+7.50)12.50 (+10.00)22.50 (+20.00)
Gaokao2023en22.3427.53 (+5.19)23.38 (+1.04)28.57 (+6.23)
Minerva Math8.8216.54 (+7.72)18.01 (+9.19)13.97 (+5.15)
Olympiad Bench8.448.89 (+0.45)9.33 (+0.89)8.89 (+0.45)
Average20.0525.45 (+5.40)25.58 (+5.53)26.73 (+6.68)
Llama3.1-8B-InstructMATH50050.8050.20 (-0.60)48.60 (-2.20)53.20 (+2.40)
GSM8K86.0584.53 (-1.52)85.37 (-0.68)87.26 (+1.21)
AIME2410.003.33 (-6.67)6.67 (-3.33)13.33 (+3.33)
AMC2327.5012.50 (-15.00)30.00 (+2.50)20.00 (-7.50)
Gaokao2023en38.9636.10 (-2.86)37.14 (-1.82)37.14 (-1.82)
Minerva Math22.7926.84 (+4.05)25.37 (+2.58)28.31 (+5.52)
Olympiad Bench15.1119.70 (+4.59)15.70 (+0.59)19.56 (+4.45)
Average35.8933.32 (-2.57)35.55 (-0.34)36.97 (+1.08)
Qwen2.5-7B-InstructMATH50075.0077.20 (+2.20)76.40 (+1.40)74.40 (-0.60)
GSM8K92.0491.36 (-0.68)91.81 (-0.23)90.60 (-1.44)
AIME246.676.67 (+0.00)10.00 (+3.33)20.00 (+13.33)
AMC2347.5050.00 (+2.50)52.50 (+5.00)57.50 (+10.00)
Gaokao2023en56.6254.81 (-1.81)55.06 (-1.56)57.92 (+1.30)
Minerva Math35.6634.93 (-0.73)32.35 (-3.31)34.93 (-0.73)
Olympiad Bench38.2238.37 (+0.15)37.78 (-0.44)36.30 (-1.92)
Average50.2450.48 (+0.24)50.84 (+0.60)53.09 (+2.85)
+ +(b) Performance on LLM-as-a-Judge benchmarks + +
ModelBenchmarkVRP(CoT)\( \mathbf{V R P_{R L}} \)\( \mathbf{M R P_{R L}} \)ReMA(Ours)
Llama3.1-8B-InstructRewardBench97069.4882.89 (+13.41)81.13 (+11.65)83.71 (+14.23)
JudgeBench51.2951.94 (+0.65)52.90 (+1.61)52.90 (+1.61)
Average60.3967.41 (+7.02)67.02 (+6.63)68.31 (+7.92)
Qwen2.5-7B-InstructRewardBench97078.5685.36 (+6.80)86.49 (+7.93)83.51 (+4.95)
JudgeBench58.3956.94 (-1.45)58.39 (+0.00)56.94 (-1.45)
Average68.4771.15 (+2.68)72.44 (+3.97)70.22 (+1.75)
+ +Table 1 compares the greedy decoding performance of ReMA against various RL baselines across mathematical benchmarks (Table 1a) and LLM-as-a-Judge benchmarks (Table 1b). Results across different LLMs indicate that, on average, ReMA outperforms all baselines, achieving a maximum improvement of $6.68\%$ on mathematical benchmarks and $8.49\%$ on LLM-as-a-Judge benchmarks. + +Notably, ReMA achieves the highest performance on most benchmarks, particularly on out-of-distribution datasets, with a maximum improvement of $20\%$ on AMC23 for Llama3-8B-Instruct, $13.33\%$ on AIME24 for Qwen2.5-7B-Instruct, $14.23\%$ on RewardBench970 for Llama3.1-8B-Instruct. These results demonstrate the superior out-of-distribution generalization ability conferred by the meta-thinking mechanism in ReMA. However, we observe that the accuracy gains from RL training on instruction-tuned LMs are smaller than from base models (Sec. 4.2.1). This may be due to the higher initial performance and the relatively fixed output distribution of instruction-tuned models, which limits the improvement and peak performance in RL. + +![](images/37ed86a4d76064b8e7dc589771be62484945d0a0fbaf36c2bdeedac73830355d.jpg) +Figure 3: An RL experiment with 3 training schemes. While RL from SFT excels on easier problems, RL under Meta-thinking shows superior generalization to harder problems like AIME24. + +![](images/7cef31214b1e22f8feceb774c7c2fda0d8822a64668c93c676a445aa329e03c2.jpg) +Figure 4: Average problem difficulty by action type during training. Left: 1B LM collapses to the EMPTY action. Right: 8B LM adapts to a more complex meta-thinking strategy for harder problems. + +![](images/8067de4a34648160295745db52239f10161f855ef4f748f78627686ff344515e.jpg) + +# 4.2.1 Meta-thoughts boost low-level generalization + +# Question 2. Can Reasoning benefit from Meta-thinking? + +Here we provide a tiny but motivating example of how ReMA gives better learning dynamics. We use Qwen2.5-Math-7B [Yang et al., 2024] as the starting base model, MATH (level 3-5, about $5.5\mathrm{K}$ number of instances) as the training dataset, and we compare three reinforcement learning training schemes, in particular: (1) RL from Base: train the base model directly on MATH with binary outcome reward; (2) RL from SFT: SFT the base model with GPT-4o's CoT answers; then RL on train dataset with binary outcome reward; (3) RL under Meta-thinking: SFT the base model with GPT-4o's meta-thinking plans; then RL on train dataset with binary outcome reward. + +The models are evaluated on 3 benchmarks (Fig. 3). SFT brings the best initial accuracy on in-distribution and easier sets, but fails to improve on harder ones. RL from Base yields limited gains. In contrast, RL under Meta-thinking achieves the best learning dynamics and generalizes better to challenging problems (AIME24). See Appendix F.1 for case studies. + +# 4.2.2 Diverse meta-thinking characteristics of LLMs + +# Question 3. How well can LLMs learn to meta-think? + +To further analyze meta-thinking behaviors, we train models with structured JSON-format actions inspired by Yue et al.. The meta-thinking agent generate two entries in one LM call, first selects from three actions: DECOMPOSE (breaking into subproblems), REWRITE (simplifying the problem), or EMPTY (direct solving), then generates the corresponding text. We compare Llama-3.1-8B-Instruct and Llama-3.2-1B-Instruct to study scale effects (two 1B models vs two 8B models) on meta-thinking agent's training. We use vLLM guided JSON decoding [Dong et al., 2024] for valid formatting and base reward (reasoning agent's solution accuracy with format constraints). + +We observe that smaller LMs produce simpler outputs, likely due to limited capacity to maintain valid JSON formatting while exploring diverse reasoning strategies. As Fig. 4 shows, smaller LMs like Llama-3.2-1B-Instruct quickly converge to the simplest EMPTY action to avoid formatting penalties, while larger LMs like Llama-3.1-8B-Instruct can adapt meta-thinking strategies based on problem difficulty. See Appendix F.3 for detailed case studies. + +![](images/7be77f52a452cae631a3999a5c1a37f14186bd400761aa6b2200170fc2818d62.jpg) +Figure 5: Training results of multi-turn Figure 6: Ablations of multi-turn ReMA on a tiny subReMA on MATH-Level3-5-8K under different set of MATH, we only show here the training curves of different training and rollout configurations. + +![](images/0a12a930e142fe2cdce1144a9d1bcf93a65808b7f66fd19e01bc8a6c088ffc04.jpg) + +# 4.3 Extending ReMA to Multi-turn MAMRP + +We further extend ReMA to multi-turn MAMRP settings, enabling multiple rounds of interaction between the meta-thinking agent and the reasoning agent as defined in Eq. (7). + +Unlike the inherent VRP capabilities of most LLMs, multi-turn ReMA requires initial bootstrapping. Thus, we constructed a supervised fine-tuning dataset (about 0.8K samples) from LIMO [Ye et al., 2025c] using GPT-4o to establish the starting point for multi-turn interaction capabilities. Then we finetune Qwen2.5-7B before RL training. + +As described in Sec.3.2.2, we deploy the proposed GRPO with turn-level ratio clipping and trajectory-level averaging loss during training. And we remove the KL-divergence term to allow more flexible exploration. By default, the agents share the same parameters and are simultaneously updated using their trajectories. We refer to details in Appendix D.2. + +# 4.3.1 Results and Ablations + +# Question 4. Can ReMA be scaled to multi-turn settings? + +There are two key points revealed by our multi-turn ReMA experiments, as shown in Fig. 5. On one hand, the algorithm can demonstrate effective convergence on the training set, with accuracy steadily increasing from approximately $55\%$ to $70\%$ during training. It also achieves an average performance gain of about $5\%$ across all seven test benchmarks, indicating stable improvements on out-of-distribution data. (Experiment with the rollout config of turn30_token512, see Appendix D.2.2 and Fig. 8 for more details.) + +On the other hand, we observe that the performance of multi-turn ReMA is highly sensitive to hyperparameters such as the maximum response length per turn and the maximum number of turns. For certain configurations, the model either collapses into producing massive repetitions within a single turn or generates empty responses after only a few turns. Similar phenomena have been reported in concurrent works such as RAGEN [Wang et al., 2025], where these issues are attributed to the lack of fine-grained, reasoning-aware guidance. As a result, multi-turn RL becomes susceptible to long-horizon credit assignment challenges and state drift, often leading to reduced exploration diversity—a phenomenon referred to as the "Echo Trap". To address this challenge, it is essential to comprehensively explore the training recipe w.r.t. model, data, and algorithm. + +# Question 5. How does parameter sharing and turn-level ratio affect multi-turn ReMA? + +As shown in Fig. 6, we compare different configurations on a smaller dataset consisting of 133 samples—19 from each of the 7 MATH problem types—to evaluate sample efficiency and convergence speed. First, all configurations eventually achieve nearly $100\%$ accuracy on the training dataset. Notably, the trajectory-level loss with turn-level ratio (Turn-Ratio, Eq. (13)) demonstrates substantially better sample efficiency than its token-level variants (Eq. (2)), reaching higher training rewards with fewer steps. We also present the training curve of separate weight setting, the empirical results show that shared parameters with simultaneous updates converge noticeably faster. + +# 5 Conclusion + +In this paper, we introduced ReMA, a novel framework that leverages multi-agent reinforcement learning to elicit meta-thinking in large language models. By explicitly separating meta-thinking and reasoning processes into distinct agents, our approach enhances both exploration during training and the interpretability of model outputs. We tailored RL algorithms and reward functions to ensure reliable performance. Through comprehensive experiments on mathematical reasoning and LLM-as-a-Judge benchmarks, ReMA consistently achieved superior results, particularly on out-of-distribution datasets. We further extend ReMA to multi-turn settings, enabling the framework to handle more complex reasoning scenarios that require more communication between agents. 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Mindstorms in natural language-based societies of mind. arXiv preprint arXiv:2305.17066, 2023. + +# Appendix Table of Contents + +- A Related work 19 + +-A.1 Single LLM Reasoning 19 +-A.2MultipleLLMReasoning 20 +-A.3 Hierarchical Reasoning 20 +-A.4RL in LLM 21 + +B Limitation and Future Work 21 + +C Supplementary Materials for Method in Section 3 21 + +- C.1 Inference-time Scaling For ReMA 21 +- C.2 Detailed reward design 22 +- C.3 Pseudocode of ReMA 23 +- C.4 Brief convergence analysis 23 +- C.5 Learning to reason from the perspective of Leader Follower Game 24 + +D Training Details 26 + +- D.1 Single-turn ReMA 26 + +\* D.1.1 Supervised fine-tuning data collection 27 +\* D.1.2 Dataset Curation of RewardBench970 27 +\*D.1.3 Training on MATH 28 +\* D.1.4 Training on Reward Bench 28 + +- D.2 Multi-turn ReMA 28 + +\* D.2.1 SFT data collection of multi-turn MAMRP 29 +\* D.2.2 Training on MATH 29 + +E Other Experiments 29 + +-E.1 Reward functions shape cross-agent behaviors 29 +- E.2 Detailed Training Curves on Different Datasets of Multi-turn ReMA 30 + +F Qualitative results 30 + +- F.1 High-level policy finds better plans 30 +- F.2 Case study for Experiments of Different Reward Functions in Appendix E.1 .30 +- F.3 Case study for Adaptive Meta-thinking in Single-Turn ReMA in Section 4.2.2 30 + +G Prompts 31 + +# A Related work + +Drawing from the bitter lesson [Sutton, 2019], two methods that appear to scale effectively are searching and learning, aligning with current trends in large language models [Xu et al., 2025]. At present, researchers are leveraging these methods to maximize the capabilities of individual transformers, while other efforts are exploring architectures that involve multiple interacting entities. In this paper, we examine this divergence within the context of LLM reasoning, a capability that allows large language models to solve problems through logical reasoning, step-by-step analysis, and inference [Wang et al., 2024a]. + +# A.1 Single LLM Reasoning + +Main research works in reasoning involving a single LLM utilize search-based and post-training methods. The fundamental elements of searching methods are text generation and evaluation. Generation schemes include In-Context Learning [Brown et al., 2020], Beam Search [Graves, 2012], and various tree-based searching [Snell et al., 2024]; Evaluation approaches often use outcome accuracy, self-consistency [Wang et al., 2022], or process reward signal [Lightman et al., 2023] as the criteria to select high-quality responses from the generated texts. Post-training method is another research line in opposition to pre-training. Popular training pipelines often involve specific data construction followed by Supervised Fine-tuning [Qin et al., 2024, Ouyang et al., 2022, Hui et al., 2024, Liu et al., 2024], or reinforcement learning to interactively explore learning patterns [Wang et al., 2024a, Zhang et al., 2024a, DeepSeek-AI et al., 2025, Xu et al., 2025]. + +# A.2 Multiple LLM Reasoning + +Integrating multiple entities can potentially surpass the intelligence of the individual model [Chen et al., 2023]. With the rapid emergence of large language models showing a varying level of abilities, some studies have explored facilitating discussions among multiple off-the-shelf LLMs [Zhang et al., 2025a, Chen et al., 2024a, Wang et al., 2023, Du et al., 2023, Zhuge et al., 2023, Tang et al., 2023, Hao et al., 2025, Akata et al., 2023, Hong et al., 2023, Zhang et al., 2024b], taking the form of free discussion [Du et al., 2023, Liang et al., 2023] or structured role assignments [Hong et al., 2023, Zhang et al., 2024b]. Some have applied routing mechanisms to assign tasks to the most suitable expert models [Hu et al., 2024b, Stripelis et al., 2024, Ding et al., 2024, Yue et al., 2025a, Chen et al., 2024c] or merging mechanisms to develop more versatile models [Yadav et al., 2024, Yu et al., 2024, Zhang et al., 2025b]. Beyond aggregating static knowledge from multiple agents, multi-agent LLM training can also enhance reasoning capabilities. For example, multi-agent debates can generate diverse synthetic data, which can subsequently be used for supervised fine-tuning [Estornell et al., 2024, Li et al., 2024, Motwani et al., 2024, Dong and Ma, 2025, Perez et al., 2022, Ye et al., 2025a, Subramaniam et al., 2025]. Reinforcement learning (RL) methods have also been adopted to improve LLM reasoning in areas such as alignment [Perez et al., 2022, Ma et al., 2023] and legibility [Kirchner et al., 2024]. Motwani et al. [2024] utilize a three-agent system for generation and fine-tune the models using Direct Preference Optimization (DPO). Reinforcement Learning with Generative Reward Models (GenRM) [Mahan et al., 2024, Ye et al., 2025b, Jiao et al., 2024, Wang et al., 2024b] represents another common approach of multi-agent training, where the reward signal is derived from the token probabilities of another LLM, coupled with the reasoning process. While our work aligns with these efforts, it diverges by using an additional tunable LLM to provide metacognitive instructions, guiding the low-level LLM during learning, rather than relying on a static GenRM. The most closely related works to ours are MAPoRL [Park et al., 2025] and COPYR [Ma et al., 2024]. MAPoRL is a multi-agent debating framework that uses multi-agent reinforcement learning (MARL) with a learned verifier to fine-tune each LLM agent. COPYR duplicates an LLM into two agents, training them simultaneously in the roles of pioneer and observer using RL. Shen et al. [2025] trained with a novel Chain-of-Action-Thought (COAT) framework that embeds meta-action tokens for self-reflection and exploration into an autoregressive search process. However, unlike our approach, which explicitly separates metacognition from plan execution, these methods do not decompose the reasoning process but instead focus on improving direct chain-of-thought generation. Furthermore, our experiments are conducted on a larger scale and include more challenging problems. + +# A.3 Hierarchical Reasoning + +Partitioning reasoning into hierarchical processes has been explored in prior research to make biological sense [Ye et al., 2018, Langley et al., 2004]. In the context of language models, a hierarchical structure has been used to facilitate diverse reasoning patterns, including planning [Puerta-Merino et al., 2025, Sun et al., 2024, Song et al., 2023, Rana et al., 2023, Chen et al., 2024d, Yan et al., 2023, Xiao et al., 2024], validation [Haji et al., 2024, Xi et al., 2024] and self-refinement [Madaan et al., 2023, Kumar et al., 2024, Welleck et al., 2022]. For instance, EvalPlanner [Saha et al., 2025b] is a framework that conducts reasoning through plan generation and execution. DOTS [Yue et al., 2024] extends decomposition by integrating a tree-based searching method with Analysis, Solution, and Verification layers. Marco-o1 [Zhao et al., 2024] focuses on open-ended problem-solving and abstract thinking, dynamically adjusting reasoning granularity and incorporating reflection mechanisms to enhance reasoning performance. Beyond these approaches, metacognition [Flavell, 1979] has been identified as another critical component of reasoning, referring to the intuitive understanding of one's own cognitive and reasoning processes [Gao et al., 2024, Wang and Zhao, 2023]. Wang and Zhao [2023] proposed a metacognitive prompting strategy to improve large language model (LLM) capabilities. Didolkar et al. [2024] further developed a prompt-guided method that enables models to label math problems with the required skills and subsequently use these labels to solve new problems. Gao et al. [2024] introduce meta-reasoner which use contextual multi-arm bandit to learn a high-level "advisor" over low-level reasoning process. Xiang et al. [2025] provides a Meta-CoT framework to think about its own thinking. They use construction-based methods as well as reinforcement learning to develop meta-cognitive skills. Qingsong et al. [2025] introduces a RL framework for dynamic instruction selection during fine-tuning. In our work, we also value reflect- + +ing on reasoning processes, and we enhance metacognitive abilities through two-agent interaction and reinforcement learning at both end. + +# A.4 RL in LLM + +Recent advancements in applying RL to LLMs have enhanced their reasoning and decision-making capabilities. Liu et al. [2025] examines token-level optimization biases by introducing Dr. GRPO to stabilize policy gradients. VAPO [Yue et al., 2025b] enhances PPO with value-aware perturbations and adaptive reward shaping to improve robustness in sparse-reward reasoning tasks. DAPO [Yu et al., 2025] provides a scalable, modular RL framework that integrates distributed rollout collection and dynamic replay buffers for reproducible training at scale. SimpleRL-Zoo [Zeng et al., 2025] conducts zero-shot RL experiments across open-base LLMs to uncover emergent cognitive behaviors under minimal reward signals. Echo Chamber [Zhao et al., 2025] investigates how RL fine-tuning algorithms can amplify pretrained model biases and proposes regularization to mitigate over-amplification. Wen et al. [2024] decomposes high-level language actions into token-level operations to achieve finer-grained credit assignment. Some works push RL training for single-turn to multi-turn. Search-R1 [Jin et al., 2025] trains LLMs to orchestrate multi-turn search strategies with RL-optimized decision policies to improve question-answering accuracy. ArCHer [Zhou et al., 2024] employs a hierarchical, multi-turn RL architecture with manager and worker policies to efficiently handle long-horizon dialogue tasks. RAGEN [Wang et al., 2025] introduces trajectory filtering and critic modules within a multi-turn RL framework to stabilize learning and reduce shallow policy behaviors. + +# B Limitation and Future Work + +In this work, we only test ReMA on math and LLM-as-a-Judge benchmarks. Though the results show the effectiveness of ReMA, adopting ReMA to tasks where naturally needs multi-turn interaction between several interleaved agents has great potential. Moreover, a comprehensive understanding of the learning dynamics of multi-turn RL and multi-turn MARL for LLMs is needed. Finally, there's still sufficient space to further improve the procedure of multi-turn multi-agent rollout through modern LLM speed up techniques, e.g. prefetch-decode disaggregation and asynchronous rollout. + +# C Supplementary Materials for Method in Section 3 + +# C.1 Inference-time Scaling of ReMA + +In this section, we discuss how to enhance the inference-time computation of our hierarchical system, specifically focusing on the interaction between the high-level and low-level agents. The total number of model samples required for inference is determined by the product of the sampling budget allocated to each agent. + +For instance, in a simple single-turn setting, if the high-level agent samples $k_{1}$ responses and each of these responses leads to $k_{2}$ samples from the low-level agent, the total number of model calls required is: + +$$ +\text {T o t a l s a m p l e s} = k _ {1} \times k _ {2}. +$$ + +Given a fixed computational budget, an important question arises: how should the sampling budget be distributed between the high-level and low-level agents to maximize performance? Allocating more samples to the high-level agent may increase diversity in reasoning strategies while allocating more to the low-level agent may yield more refined solutions for a given metacognitive plan. + +Another crucial consideration is how to perform reranking on the final outputs. Two potential strategies include: + +- Hierarchical reranking: First, for each high-level response, rank and aggregate the low-level responses under it. Then, rank the aggregated results across different high-level responses. + +- Flat reranking: Directly rank all sampled responses together, regardless of the hierarchy of high-level reasoning steps. + +Balancing sampling allocation and designing an effective reranking strategy are key challenges in efficiently scaling our multi-agent reasoning system. In the next section, we explore empirical results comparing different allocation strategies and ranking methods. + +# C.2 Detailed reward design + +As described in Sec. 3.2, we update both high-level and low-level agents by assigning rewards based on the low-level policy output. Below, we outline several potential reward designs: + +- Correctness reward: For tasks with explicit ground truth, we assign rewards based on the correctness of the low-level agent's output. +- Format reward: For tasks that require a specific output format, we enforce adherence to the prescribed structure by providing a format reward. +- To encourage the high-level agent to generate informative and unambiguous meta-thinking, and to stabilize the low-level outputs, we reward the high-level agent when the low-level agent produces consistent responses. Specifically, the consistency reward is defined as + +$$ +R _ {h} = \frac {\text {m a x o c c u r r e n c e o f a n a n s w e r}}{\text {t o t a l n u m b e r o f r e s p o n s e s}}. +$$ + +To examine multi-agent metacognition-integrated reasoning with different reward designs, we experiment with different reward function designs to encourage effective collaboration and structured reasoning. Below, we introduce and justify several reward schemes. + +1. Correctness and Format-Aware Reward (Base Setting) In our primary reward setting, the system's overall correctness is used as the primary reward signal, supplemented by format-based rewards for both the high-level and low-level agents. Using mathematical problem-solving as an example: + +- Low-level agent $(\pi_{\theta_l})$ : Receives a reward of $+1.0$ for a correct answer. If the answer is incorrect, the agent is further penalized based on format compliance. Specifically: + +- If the output contains the designated answer-indicating format (e.g., boxed in Latex), it receives $-0.5$ . +- Otherwise, it receives $-1.0$ , as a missing format often suggests an incomplete or unstructured response. + +- High-level agent $(\pi_{\theta_h})$ : Receives the average correctness of the low-level agent's sampled responses as its reward. Additionally, to prevent the high-level agent from directly generating explicit answers instead of guiding reasoning, a strong penalty of $-1.0$ is applied if it includes an explicit answer format (e.g., boxed). + +2. Consistency-Based Reward Instead of using correctness as the high-level reward signal, this approach rewards the high-level agent for promoting consistent responses from the low-level agent, regardless of actual correctness. The consistency reward is defined as the proportion of the most frequently occurring answer among all sampled responses: + +$$ +R _ {h} = \frac {\text {m a x o c c u r r e n c e o f a n a n s w e r}}{\text {t o t a l n u m b e r o f r e s p o n s e s}} \tag {14} +$$ + +If the majority of responses do not contain a definitive answer, the reward is set to zero. We also add the format penalty to the high-level agent if its output contains the designated answer-indicating format. This incentivizes the high-level agent to guide the low-level agent toward more stable, detailed, reproducible outputs rather than erratic reasoning paths. + +These different reward formulations allow us to investigate various dimensions of metacognitive reasoning: correctness, consistency, etc. We empirically compare their effects on learned metacognitive reasoning patterns in Sec. E.1. + +![](images/315cafbb1d2055dded17eaabf88749be03cfea772911a86fa7b194d2357e1c64.jpg) +Figure 7: Our method can be viewed as a combination of practical TRPO and block coordinate ascent, with the high and low-level models treated as distinct components within a larger neural network. Note that the figure does not represent the exact gradient back-propagation flow but rather highlights the key idea that we separate the high- and low-level models. This separation allows for the independent computation of gradients and the independent training of each model. + +# C.3 Pseudocode of ReMA + +The pseudocode is shown in Algorithm 1. + +Algorithm 1 Single turn MAMRP +Require: High-level policy $\pi_h$ , Low-level policy $\pi_l$ , Dataset $\mathcal{D}$ , Optimizers for $\pi_h$ and $\pi_l$ . $\varepsilon_{\mathrm{min}}, \varepsilon_{\mathrm{max}}$ to filter training dataset +1: Initialize $\pi_h$ and $\pi_l$ +2: while not converged do +3: build training dataset $\mathcal{D}_l$ with $\pi_h, \pi_l, \varepsilon_{\mathrm{min}}, \varepsilon_{\mathrm{max}}$ +4: for Sample $(\mathbf{x}, \mathbf{m}, \mathbf{y}^*) \sim \mathcal{D}_l$ do +5: Generate $\mathbf{y} \sim \pi_l(\mathbf{x}, \mathbf{m})$ +6: Compute low-level reward $R_l(\mathbf{y}, \mathbf{y}^*)$ +7: Update $\pi_l$ using $\nabla_{\theta_l} \mathbb{E}[R_l]$ +8: end for +9: build training dataset $\mathcal{D}_h$ with $\pi_h, \pi_l, \varepsilon_{\mathrm{min}}, \varepsilon_{\mathrm{max}}$ +10: for Sample $(\mathbf{x}, \mathbf{y}^*) \sim \mathcal{D}_h$ do +11: Generate $\mathbf{m} \sim \pi_h(\mathbf{x})$ and $\mathbf{y} \sim \pi_l(\mathbf{x}, \mathbf{m})$ +12: Compute high-level reward $R_h(\mathbf{m}, \mathbf{y}, \mathbf{y}^*)$ +13: Update $\pi_h$ using $\nabla_{\theta_h} \mathbb{E}[R_h]$ +14: end for +15: end while + +# C.4 Brief convergence analysis + +We reuse the notations from Sec. 3.2, where $\mathbf{x}$ is task prompt, $\mathbf{y}$ is generated answer, $\mathbf{y}^*$ is groundtruth, $\mathbf{m}$ is metacognition on task solving, $\pi_{\theta_h}$ and $\pi_{\theta_l}$ are high- and low-level agents with parameters $\theta_h$ and $\theta_l$ . We consider the joint hierarchical policy defined in Eq. (8) and update the objective as in Eq. (9). + +To leverage existing RL and optimization convergence analysis methods, we treat the two models as components of a larger model, as illustrated in Fig. 7. When updating one model, we treat the other + +model as part of a stationary environment. The gradients with respect to $\theta_h$ and $\theta_l$ are: + +$$ +\nabla_ {\theta_ {h}} J (\theta_ {h}, \theta_ {l}) = \mathbb {E} _ {\mathbf {x}, \mathbf {y} ^ {*}} \sum_ {\mathbf {m} \sim \pi_ {h} (\mathbf {m} | \mathbf {x}; \theta_ {h})} \nabla_ {\theta_ {h}} \pi_ {h} (\mathbf {m} | \mathbf {x}; \theta_ {h}) \left[ \mathbb {E} _ {\mathbf {y} \sim \pi_ {l} (\mathbf {y} | \mathbf {x}, \mathbf {m})} R (\mathbf {y}, \mathbf {y} ^ {*}) \right], +$$ + +$$ +\nabla_ {\theta_ {l}} J (\theta_ {h}, \theta_ {l}) = \mathbb {E} _ {\mathbf {x}, \mathbf {y} ^ {*}} \sum_ {\mathbf {y} \sim \pi (\theta_ {h}, \theta_ {l})} \nabla_ {\theta_ {l}} \pi_ {l} (\mathbf {y} \mid \mathbf {x}, \mathbf {m}; \theta_ {h}); \theta_ {l}) R (\mathbf {y}, \mathbf {y} ^ {*}). +$$ + +We can compute the gradients with log trick and estimate $\mathbb{E}_{\mathbf{y}\sim \pi_l(\mathbf{y}|\mathbf{x},\mathbf{m})}R(\mathbf{y},\mathbf{y}^*)$ with Monte Carlo method. + +Equipped with the objective function and gradient computation, we update the models iteratively. Without loss of generality, we analyze the case where the high-level policy is updated first: + +$$ +\theta_ {h} ^ {(t + 1)} = \arg \max _ {\theta_ {h}} J (\theta_ {h}, \theta_ {l} ^ {(t)}), +$$ + +$$ +\theta_ {l} ^ {(t + 1)} = \arg \max _ {\theta_ {l}} J \left(\theta_ {h} ^ {(t + 1)}, \theta_ {l}\right). +$$ + +Regarding the different regularizations $R_{h}$ and $R_{l}$ in Eqs. (10) and (11) for the different policies, instead of directly integrating them into the loss function, we treat them as constraints, as done in Trust Region Policy Optimization (TRPO) [Schulman et al., 2015]. Note that when one policy is fixed, the other policy operates in a stationary decision process. + +Based on the defined objective and update method, we apply TRPO and block coordinate ascent. First, recall that when updating a single policy, TRPO guarantees monotonic improvement by optimizing a lower bound. Specifically, let $\pi_{\mathrm{old}}$ and $\pi$ represent the old and current policies, respectively. We define a surrogate objective as: + +$$ +L _ {\pi_ {\mathrm {o l d}}} (\pi) = \mathbb {E} _ {s \sim \pi_ {\mathrm {o l d}}, a \sim \pi_ {\mathrm {o l d}}} \left[ \frac {\pi (a | s)}{\pi_ {\mathrm {o l d}} (a | s)} A ^ {\pi_ {\mathrm {o l d}}} (s, a) \right], +$$ + +As shown by Schulman et al. [2015], the true objective of $\pi$ is lower-bounded by: + +$$ +J (\pi) \geq L _ {\pi_ {\mathrm {o l d}}} (\pi) - C \cdot \max _ {s} \mathrm {K L} [ \pi_ {\mathrm {o l d}} (\cdot | s), \pi (\cdot | s) ], +$$ + +for some constant $C$ . By optimizing the right-hand side of the above inequality, we are guaranteed to improve the performance of $\pi$ . Therefore, for policies $\pi^t$ and $\pi^{t + 1}$ obtained from iterations $t$ and $t + 1$ using the TRPO method, we have: + +$$ +J (\pi^ {t + 1}) \geq J (\pi^ {t}). +$$ + +Now, returning to our updating method, we treat the high- and low-level policies as two blocks of a single agent. The iterative update process can thus be viewed as a cyclic block coordinate ascent, where the two policies are updated in a fixed order. By updating each block using the TRPO method, and improving the surrogate objective within the KL constraint, each block update does not decrease $J$ : + +$$ +J \left(\theta_ {h} ^ {t + 1}, \theta_ {l} ^ {t}\right) \geq J \left(\theta_ {h} ^ {t}, \theta_ {l} ^ {t}\right), +$$ + +$$ +J \left(\theta_ {h} ^ {t + 1}, \theta_ {l} ^ {t + 1}\right) \geq J \left(\theta_ {h} ^ {t + 1}, \theta_ {l} ^ {t}\right). +$$ + +Thus $J(\theta_h^{t + 1},\theta_l^{t + 1})\geq J(\theta_h^t,\theta_l^t)$ . This repeated coordinate maximization converges to a fixed point, where no single coordinate update can further improve $J(\theta_h,\theta_l)$ . + +Given the theoretical monotonic improvement with TRPO and block coordinate ascent, we adopt a practical version of TRPO in our experiments, specifically Proximal Policy Optimization (PPO) [Schulman et al., 2017] or GRPO [Shao et al., 2024]. + +# C.5 Learning to reason from the perspective of Leader Follower Game + +Besides the loss function in the main part, we also propose to frame the problem as a leader-follower game. By analyzing the equilibria of the leader-follower game, we demonstrate that our framework inherently identifies the optimal sub-tasks aligned with the capabilities of the low-level model. This ensures that the high-level decisions are guided by the low-level model's strengths, leading to more efficient and targeted task decomposition. + +# C.5.1 Leader-follower game + +The leader-follower game, also known as the Stackelberg game, models interaction between two agents with parametrized strategies $\pmb{\theta} = (\pmb{\theta}_1, \pmb{\theta}_2)$ and differentiable objective functions $(\mathcal{L}_1, \mathcal{L}_2): \mathbb{R}^d \to \mathbb{R}$ . In this framework, the leader announces its strategy first, and the follower observes this decision to respond optimally. This sequential structure enables the leader to anticipate the follower's reaction and adjust its strategy accordingly. A Stackelberg equilibrium occurs when neither agent can unilaterally improve its objective. Denoting $\pmb{\theta}_1$ as the leader's strategy and $\pmb{\theta}_2$ as the follower's, the loss functions $\mathcal{L}_1$ and $\mathcal{L}_2$ are optimized with the following bi-level structure: + +$$ +\boldsymbol {\theta} _ {1} ^ {*} = \operatorname {a r g m i n} _ {\boldsymbol {\theta} _ {1}} \mathcal {L} _ {1} (\boldsymbol {\theta}, \boldsymbol {\theta} _ {2} ^ {*} (\boldsymbol {\theta} _ {1})), \quad \boldsymbol {w} _ {2} ^ {*} (\boldsymbol {\theta} _ {1}) = \operatorname {a r g m i n} _ {\boldsymbol {\theta} _ {2}} \mathcal {L} _ {2} (\boldsymbol {\theta} _ {1}, \boldsymbol {\theta} _ {2}). +$$ + +Anil et al. [2021] apply the leader-follower game to ensure checkable answers in a prover-verifier game (PVG). The objective is a verifier that is both complete (accepts all correct proofs from a verifier) and sound (rejects all incorrect proofs from a verifier). They analyze different scenarios where the verifier acts as the leader, the prover as the follower, and both announce strategies simultaneously, forming a Nash equilibrium. The study concludes that in verifier-led SVG, a Stackelberg equilibrium is both necessary and sufficient for achieving a sound and complete verifier, whereas in other configurations, a Stackelberg equilibrium is not necessary or sufficient for this outcome. + +# C.5.2 Efficacy of LLM + +Because the high-level policy possesses strong generalization capabilities, it is impractical for it to exhaustively explore every potential sub-task for each question. Instead, it naturally focuses on tasks within a feasible range of difficulty, leveraging only a limited set of coarse planning actions. Rather than pinpointing perfectly tailored sub-tasks, the policy searches for general tasks of particular computational complexity, i.e., difficulty, that it can handle reliably. Motivated by this perspective, we incorporate the concept of a reasoning boundary for large language models (LLMs) [Chen et al., 2024b]. Intuitively, the reasoning boundary circumscribes the maximum difficulty of problems a model can solve at a desired accuracy level. Formally, for a model $\theta$ , a task $t$ , and a predefined threshold $A$ , the reasoning boundary of $\theta$ represents the maximum problem difficulty $d$ that satisfies: + +$$ +\mathcal {B} _ {A c c = A} (t | \theta) = \sup _ {d} \{d | A c c (t | d, \theta) = A \}. +$$ + +where $d$ denotes the problem difficulty. By quantifying the difficulty level a model can reliably handle, the reasoning boundary provides a systematic way to align the high-level policy's focus with the model's actual capabilities, gauge the efficacy of the low-level policy, and determine the optimal strategy for solving the question. + +# C.5.3 Leader-follower Game for LLM Reasoning + +Our goal is to find the high-level policy that searches for the sub-task sequence based on the efficacy of the low-level policy to solve the question. We design the loss functions as follows: + +$$ +\mathcal {L} _ {h} = \mathbb {E} _ {(x, y) \sim p _ {D}, t _ {1: K}} \left[ - \log \pi_ {l} \left(y _ {K} \mid x, t _ {1: K}, y _ {1: K - 1}\right) \right], +$$ + +$$ +\mathcal {L} _ {l} = \mathbb {E} _ {x \sim p _ {D}, t _ {1: k} \sim \pi_ {h}, \hat {y} _ {k} \sim \pi_ {l}} \left[ - r \left(y _ {k}, \hat {y} _ {k} \mid x, t _ {1: k}, y _ {1: k - 1}\right) \right], +$$ + +where $r(y_k, \hat{y}_k \mid x, t_{1:k}, y_{1:k-1})$ represents the step reward for the correctness of $\hat{y}_k$ derived from the question $x$ , the sub-task sequence $t_{1:k}$ from the high policy and prior intermediate answer $y_{1:k-1}$ . The loss functions can be interpreted as follows: the high-level policy is incentivized to find subtasks that lead to the correct answer based on the capabilities of the low-level policy, while the low-level policy is incentivized to enhance its instruction-following ability. + +How to minimize the loss functions and whether such minimization leads to the desired results remain questions. To explore this, we consider a simplified case of our method, where the high-level policy plans the complete sub-task sequence at the beginning and the low-level executes the instruction in a single interaction. The corresponding parameterized policies are defined as $\pi_h((t_1,\ldots ,t_K)\mid x)$ and $\pi_l((\hat{y}_1,\dots ,\hat{y}_K)\mid x,(t_1,\dots ,t_K))$ . The corresponding loss functions are: + +$$ +\mathcal {L} _ {h} = \mathbb {E} _ {(x, y) \sim p _ {D}, t _ {1: K}} \left[ - \log \pi_ {l} \left(y _ {K} \mid x, t _ {1: K}\right) \right], \tag {15} +$$ + +$$ +\mathcal {L} _ {l} = \mathbb {E} _ {x \sim p _ {D}, t _ {1: k} \sim \pi_ {h}, \hat {y} _ {k} \sim \pi_ {l}} \left[ - r \left(y _ {k}, \hat {y} _ {k} \mid x, t _ {1: k}, y _ {1: k - 1}\right) \right]. \tag {16} +$$ + +In this step, the high-level policy generates the entire sub-task sequence without relying on intermediate answers, while the low-level policy follows the sequence to produce answers for the sub-tasks. The low-level policy can still leverage prior intermediate answers to sequentially refine its responses. + +To analyze the result agents by minimizing the loss functions, we adopt the completeness and soundness properties from the PVG framework for LLM reasoning. Specifically, if the high-level policy generates a sub-task sequence that is executable within the low-level policy's capabilities, the problem must be solved (completeness). Conversely, if the sub-task sequence is incorrect or beyond the low-level policy's capacity, the problem cannot be solved (soundness). To achieve this, we utilize the conclusion from Anil et al. [2021], which positions the low-level policy as the leader and the high-level policy as the follower, equilibria guarantee the complete and sound low-level policy. + +When the high-level policy takes the lead, the low-level policy is forced to adapt to the specific strategy defined by the high-level policy, which can result in neither complete nor sound low-level policy. For example, if the high-level policy dictates that it will only generate sub-tasks involving addition and subtraction, the low-level policy is constrained to optimize only for these tasks. While they may reach an equilibrium, the low-level policy remains incomplete, and this limitation impacts both policies. In the case of the simultaneous PVG game, convergence to a Nash equilibrium is possible, but it is not sufficient for completeness and soundness. For instance, the low-level policy might disregard the high-level policy entirely (e.g., if the high-level provides incorrect instructions, but the low-level still performs correctly). This approach, however, is challenging to implement due to the significantly larger search space involved. + +Furthermore, the loss functions we design ensure that, at a Stackelberg equilibrium, the high-level policy identifies sub-task sequences that the low-level policy can execute to solve the problem with the highest probability. With the low-level policy acting as the leader, it establishes its reasoning boundary for tasks. Based on the reasoning boundary, let $\theta_h$ and $\theta_l$ represent the policy parameters for the high-level and low-level policies, respectively. The probability that the low-level policy correctly solves the question is defined as: + +$$ +\pi_ {l} \left(y _ {K} \mid x, t _ {1: K}\right) = \prod_ {k = 1} ^ {K} \operatorname {A c c} \left(t _ {k} \mid x, \theta_ {l}\right), +$$ + +where we can compute the difficulty $d_{k}$ from $t_k$ and $x$ . where the difficulty $d_{k}$ can be derived from $t_k$ and $x$ . The loss function in Eq. (15) ensures that the selected sub-tasks are optimal for the low-level policy. Here we provide a theoretical condition under which the most efficient solution strategy can be identified, according to the efficacy of the LLM. + +This approach can be viewed as a game between a high-level "prover" and a low-level "verifier". The verifier, representing the low-level policy, adheres the high-level policy's instructions to validate its reasoning. Unlike the classic PVG setting, where the prover has ground-truth labels, the label of our high-level policy depends on the tunable low-level policy. This distinction, where the low-level policy (leader) is inherently more complex, contrasts with traditional PVG setups and adds complexity due to the interdependence between the high- and low-level policies. + +By framing the problem-solving process as a leader-follower game, with the low-level policy designated as the leader, we can construct a bi-level optimization problem to identify an equilibrium. Following the formulation in Sec. C.5.1, the problem is expressed as: + +$$ +\theta_ {l} ^ {*} = \underset {\theta_ {l}} {\arg \min } \mathcal {L} _ {l} (\theta_ {h} ^ {*} (\theta_ {l}), \theta_ {l}) \quad \theta_ {h} ^ {*} (\theta_ {l}) = \underset {\theta_ {l}} {\arg \min } \mathcal {L} _ {h} (\theta_ {h}, \theta_ {l}). +$$ + +Then we can apply bi-level optimization techniques. + +# D Training Details + +# D.1 Single-turn ReMA + +We refer to Appendix G for prompts we use during training. We implement the training pipeline with OpenRLHF [Hu et al., 2024a] which is a highly efficient codebase and is easy to scale up. We select REINFORCE++ to save resources and for efficient training. All experiments are conducted in a node of 8 NVIDIA A100 GPUs. We use bf16, Zero2, Flash-Attention and gradient checkpointing to run our experiments. + +During rollout, we set temperature $= 1.0$ , top_p $= 1.0$ , top_k $= -1$ , and use vLLM for inference acceleration. We set the max generation length to be 2048 and, the rollout batch size to be 1000. The number of samples per prompt is 4. During training, we use Adam Optimizer with a learning rate of 5e-7. We set the mini-batch size to be 500, and the clip ratio to be 0.2. Other hyperparameters, such as KL coefficients and the number of training episodes, were carefully tuned based on validation set performance to ensure robust and reliable results. To align with the hyperparameter in OpenRLHF, we use #Training Episode as the number of reinforcement learning epoch on the entire dataset. + +In ReMA, during prompt filtering of the high-level model, the high-level agent first samples 10 candidates for each question with $t = 1.0$ , and for each output the low-level agents sample 1 solution with $t = 0.0$ , then we select questions of success rate between $[\varepsilon_{\mathrm{min}}, \varepsilon_{\mathrm{max}}]$ . And for the low-level agent's prompt filtering, the high-level agent first samples 1 candidate for each question with $t = 0.0$ and for each output the low-level agents sample 10 solutions with $t = 1.0$ , then we select questions of success rate between $[\varepsilon_{\mathrm{min}}, \varepsilon_{\mathrm{max}}]$ and use the high-level agent to sample 4 meta-thoughts with $t = 1.0$ as the input. + +# D.1.1 Supervised fine-tuning data collection + +For experiments in Sec. 4.2.1, we collect expert data to enhance the reasoning pattern, i.e. $RL$ from SFT. Specifically, we collect demonstration data from GPT-4o Mini on MATH training dataset (7.5k problems) Hendrycks et al. [2021] and use it to fine-tune the LLMs. The data generation follows these steps: First, we prompt GPT-4o Mini to produce metacognitive reasoning for high-level model training. Specifically, we use different prompts to instruct it to rewrite and decompose a given question without providing a final answer. We collect metacognitive reasoning using two predefined actions, "rewrite" and "decompose", which align with human approaches to complex problem-solving while preserving answer diversity. Next, we use the generated instructions to prompt GPT-4o Mini to follow the metacognitive steps and solve the question, obtaining SFT data for low-level policy training. Below, we present the prompts used for both high-level and low-level models. Prompts can be found in Appendix G.1.1. + +# D.1.2 Dataset Curation of RewardBench970 + +Table 2: Performance on LLM-as-a-Judge benchmarks, trained on dataset under the loose setting. The two-agent workflow in ReMA + +
ModelBenchmarkVRP(CoT)\( \mathbf{V R P_{R L}} \)\( \mathbf{M R P_{R L}} \)ReMA(Ours)
Llama3.1-8B-InstructRewardBench97071.2481.86 (+10.62)80.41 (+9.17)86.29 (+15.05)
JudgeBench51.7751.45 (-0.32)50.65 (-1.12)53.71 (+1.94)
Average61.5166.65 (+5.14)65.53 (+4.02)70.00 (+8.49)
Qwen2.5-7B-InstructRewardBench97086.4987.22 (+0.73)80.31 (-6.18)90.72 (+4.23)
JudgeBench58.3954.84 (-3.55)55.81 (-2.58)58.71 (+0.32)
Average72.4471.03 (-1.41)68.06 (-4.38)74.72 (+2.28)
+ +We process the original dataset in RewardBench by splitting it into a training set containing 5,000 tuples of (instruction, response A, response B) and a test set with the remaining 970 tuples. + +To ensure a meaningful dataset split, we validate two separation strategies: + +- Loose setting: We only ensure that there is no direct overlap of tuples between the training and test sets. +- Strict setting: We further enforce that no instruction appears in both the training and test sets. The results for this setting are presented in the main results (Table 1b). + +Additionally, since the original RewardBench data originates from different subsets, we ensure that all original subsets are evenly represented in both the training and test sets. + +Table 2 reports the learning performance of various methods under the loose dataset split setting. Compared to the results in Table 1b, ReMA significantly outperforms other RL tuning baselines + +across all models, particularly on out-of-distribution (OOD) benchmarks. The consistent improvements on OOD datasets of these two settings suggest that ReMA enhances meta-thinking ability, resulting in better generalization across diverse task distributions. + +# D.1.3 Training on MATH + +VRP For Llama3-8B-Instruct, Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 12,6,6 for these 3 models respectively. For Llama3-8B-Instruct, we set the learning rate of 2e-7 for stable training. + +MRP For Llama3-8B-Instruct, Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 10,6,6 for these 3 models respectively. + +MAMRP We use $\varepsilon_{\mathrm{min}} = 0.2, \varepsilon_{\mathrm{max}} = 0.8$ for prompt filtering. We use the same #Training Episode=4 for all models, and for #Update Iteration, we use 3 for Llama3-8B-Instruct and Llama3.1-8B-Instruct, 10 for Qwen2.5-7B-Instruct. And we set the KL coefficient to be 1e-2 for all the 3 models. + +# D.1.4 Training on Reward Bench + +VRP For Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 4,6 for these 2 models respectively. + +MRP For Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 4,6 for these 2 models respectively. + +MAMRP We set #Update Iteration=1 for all models. We set the KL coefficient to be 1e-2 for Llama3.1-8B-Instruct and 1e-2 for Qwen2.5-7B-Instruct all models. For Llama3.1-8B-Instruct, we use $\varepsilon_{\mathrm{min}} = 0.2$ , $\varepsilon_{\mathrm{max}} = 0.8$ for prompt filtering and we use #Training Episode of 2 during training. For Llama3.1-8B-Instruct, we use $\varepsilon_{\mathrm{min}} = 0.1$ , $\varepsilon_{\mathrm{max}} = 0.9$ for prompt filtering and we use #Training Episode of 1 during training. + +# D.2 Multi-turn ReMA + +We refer to Appendix G for prompts we use during training. We implement a multi-turn ReMA training pipeline with VeRL [Sheng et al., 2024] since it's easier to implement complex training pipeline with a single centralized controller. Similar to OpenRLHF, VeRL is also a highly efficient and scalable codebase for further development. + +For the multi-turn ReMA rollout, we use parameter sharing and simultaneous update by default. In details, we maintain two message lists with the system prompt of meta-thinking agent and reasoning agent respectively. During rollout, each agent acts as 'assistant' in its own message list and the other agent acts as 'user'. We use three hyperparameters to control the rollout length: (1) 'max_num_turns': the maximum number of turns for each trajectory. (2) 'max_response_length': the maximum number of tokens for each turn's response. (3) 'max_prompt_length': the maximum number of tokens for each trajectory. + +During training, we apply the collected message list to Qwen2.5-7B's chat template and build loss masks in order to compute the loss for all turns of one trajectory (message list). + +Moreover, for multi-turn ReMA rollout, unlike single agent single turn rollout, we need to carefully design the termination logic. Basically, we let the meta-thinking agent automatically decide when to finish the solving procedure, we use a special tag '[FINISH]' to indicate the end of the solving procedure. After we detect this tag, we will terminate trajectory after the reasoning agent generates its output. + +We also design other termination conditions to ensure the quality of the generated trajectories. If the last agent's response is too long, we will terminate the whole trajectory and setting the reward to 0. We also introduce a different version of format reward: we give a reward of 1.0 only if the reasoning agent's last turn response is correct and the meta-thinking agent's last turn response include '[FINISH]'. We use math_check as the default verifier. + +# D.2.1 SFT data collection of multi-turn MAMRP + +We use GPT-4o to translate 817 samples in LIMO [Ye et al., 2025c] by prompting it to wrap each sentence with meta-thinking and reasoning tags. We use a temperature of 0. After filtering, we get 800 conversations for training. The prompt can be found in Appendix G.2.1. For supervised finetuning, we use LlamaFactory as the codebase and train the model for 3 epochs with a learning rate of 1e-5, consine learning rate scheduler, and batch size of 8. Use DeepSpeed Zero2 for distributed training. + +# D.2.2 Training on MATH + +For training of multi-turn ReMA on MATH, we use GRPO [Shao et al., 2024] as the default learning algorithm. We refer to Appendix G.2.2 for prompts. For experiment in Sec 4.3, we use sample 128 prompts, each with 16 trajectories. During training, we drop the KL loss term to improve the numerical stability. We use a learning rate of 1e-6, bfloat16 precision, FSDP backend for distributed training. We split the rollout data into 4 mini-batches for update. For the sake of numerical stability, we do pre-clip before computing the exponential of log-prob for a upperbound of 3.0. + +For the main result in Fig 5, we test different rollout configurations with a max_prompt_length of 4096, training for 500 steps. We use 32 NVIDIA A800 GPUs, the longest training cost about 40 hours due to large scale validation per 10 steps. + +For the ablation results in Fig 6, we use a tiny subset of MATH Level 3-5, training for 300 steps. Specifically, we sample 19 questions for every single type (133 instances in total). We use 8 NVIDIA A800 GPUs, the training cost about 30 hours + +We test different rollout configurations: + +(1) max_num_turns=30, max_response_length=256, max_prompt_length=4096 (2) +max_num_turns=30, max_response_length=1024, max_prompt_length=3072 + +And for the experiment of separate parameter in multi-turn ReMA, we iteratively train each agent with the same configuration as above, but with a switch interval of 10 steps, starting from the metathinking agent. + +# E Other Experiments + +# E.1 Reward functions shape cross-agent behaviors + +We also investigate the impact of different reward function designs on ReMA's behavior. In addition to the base reward setting described in Appendix C.2, we evaluate a consistency-based reward function using Qwen2.5-7B-Instruct. This reward function is designed to encourage the high-level agent to generate more detailed guidance. Indeed, we observe that the high-level agent trained in this manner produces more detailed solution steps compared to the one trained with the basic correctness format reward. However, we also find that this approach often leads to jailbreak behavior, where the high-level agent tends to include the final answer within its output, compromising the intended hierarchical reasoning process. + +Furthermore, we discover an interesting evolution of a pattern during training: although our experimental setup is designed for the high-level agent to provide a solution plan while the lower-level agent executes it, we find that under the consistency-based reward, the lower-level agent significantly increases its attempt of verification rather than straightforward execution. We observed a certain sentence commonly appearing in the low-level agent's responses: "Let's go through the solution step by step to ensure clarity and correctness." To quantify this effect, we track the frequency of it. We analyze this pattern across all mathematical test sets, sampling eight completions per question at a temperature of 0.7. Our empirical results have identified a $30\mathrm{x}$ increase of such self-verifying patterns in the model trained with the consistency-based reward compared to the one trained with the base reward. Moreover, we also observe additional variations of this pattern, e.g. "Let's carefully re-evaluate the problem and solution to ensure accuracy and clarity." These phrases indicate that the low-level agent is actively exploring to verify the detailed response provided by the high-level agent. + +This suggests that (1) meta-thinking can not only emerge and be reinforced in the high-level agent but also in the low-level agent. During reinforcement learning (RL) training, the two agents develop a novel problem-solving pattern characterized by a role reversal. (2) Consistency-based rewards promote a more self-corrective approach at the lower level, potentially disrupting the intended separation of roles between planning and execution. For a detailed case study, refer to Appendix F.2. + +# E.2 Detailed Training Curves on Different Datasets of Multi-turn ReMA + +We show the detailed training curves of the multi-turn ReMA on different datasets in Fig. 8. + +![](images/3a07830c095bd1b0e7d492fba662d270532fb4263b681ea523bd6daaeb0902da.jpg) +Figure 8: Detailed Training Curves on Different Datasets of Multi-turn ReMA + +# F Qualitative Results + +# F.1 High-level policy finds better plans + +Here is an example of how a high-level policy alters the solving method of an LLM, increasing the likelihood of providing correct answers. As we can see from the following example, without the high-level policy, the LLM counts all integer coordinates, including those on the boundary, and then subtracts the boundary coordinates. In contrast, the high-level policy identifies a better approach, directly instructing the LLM to count only the coordinates strictly inside the boundary. + +# F.2 Case study for Experiments in Section E.1 + +Fig. 10 and Fig. 11 show an case study of experiments in Sec. E.1. + +Although both agents are prompted with the same instructions as in our main results, the consistency reward of the high-level agent significantly alters the learning dynamics. As illustrated in Fig. 10, the high-level agent generates detailed solution attempts rather than a strategic plan. Consequently, the low-level agent evolves to verify the high-level agent's solutions. This suggests that, during reinforcement learning (RL) training, the two agents develop a novel problem-solving pattern characterized by a role reversal, where one agent generates an answer while the other verifies it. + +# F.3 Case study for Experiments in Section 4.2.2 + +Fig. 12 shows the detailed outputs of the two groups of LLMs trained in JSON action. The outputs finally converge to relative easier and shorter sentences, compared to our main experiments. This may due to insufficient capacity of a small LM to produce a valid JSON-format response while simultaneously exploring diverse reasoning strategies. + +Consider the rectangular region with the following points as vertices: $(5,4),(-5,4),(-5, - 4),(5, - 4)$ . How many points with integer coordinates will be strictly in the interior of this rectangular region? + +# Output without high-level planning solves this question in a less optimal way, leading to a wrong answer: + +To determine how many points with integer coordinates will be strictly in the interior of the rectangular region with vertices at $(5,4)$ , $(-5,4)$ , $(-5, - 4)$ , and $(5, - 4)$ , we will follow these steps: + +1. Identify the dimensions of the rectangle: + +- The width of the rectangle can be calculated as the distance between the x-coordinates of the vertices. The x-coordinates are $-5$ and 5. + +$$ +\mathrm {W i d t h} = 5 - (- 5) = 1 0 +$$ + +- The height of the rectangle can be calculated as the distance between the y-coordinates of the vertices. The y-coordinates are 4 and -4. + +$$ +\mathrm {H e i g h t} = 4 - (- 4) = 8 +$$ + +2. Calculate the total number of integer points: - The total number of integer points in the rectangle (including the boundary) can be calculated by considering the range of x and y values: - The x-values range from $-5$ to 5, giving us 11 integer values $(-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)$ . - The y-values range from $-4$ to 4, giving us 9 integer values ( + +$-4, -3, -2, -1, 0, 1, 2, 3, 4)$ . The total number of points in the rectangle (including the boundary) is: + +$$ +\text {T o t a l p o i n t s} = 1 1 \times 9 = 9 9 +$$ + +3. Calculate the number of points on the boundary: - The boundary consists of the four sides of the rectangle. - The top and bottom sides (y = 4 and y = -4) each have 11 integer points (from -5 to 5). - The left and right sides (x = 5 and x = -5) each have 9 integer points (from -4 to 4). - Therefore, the total number of points on the boundary is: + +$$ +\text {B o u n d a r y p o i n t s} = 2 \times 1 1 + 2 \times 9 = 2 2 + 1 8 = 4 0 +$$ + +4. Calculate the number of strictly interior points: - To find the number of points strictly in the interior, we subtract the points on the boundary from the total number of points: + +$$ +I n t e r i o r \text {p o i n t s} = \text {T o t a l p o i n t s - B o u n d a r y p o i n t s} = 9 9 - 4 0 = 5 9 +$$ + +Thus, the number of points with integer coordinates that will be strictly in the interior of this rectangular region is 59. + +Answer with high-level planning identifies the optimal sub-tasks for the LLM to solve, increasing the chance of answering the question correctly + +High-level policy planning: First, identify the boundaries of the rectangular region. Then, determine the integer coordinates that lie strictly within these boundaries. Finally, count the number of such points. + +Low-level policy reasoning following the high-policy plan: To solve the problem, we will follow the steps outlined in the instructions. + +Step 1: Identify the boundaries of the rectangular region. The vertices of the rectangular region are: $(-5,4)$ $(-5,4)$ $(-5, - 4)$ $(5, - 4)$ From these vertices, we can determine the boundaries:- The left boundary is $x = -5$ The right boundary is $x = 5$ .- The bottom boundary is $y = -4$ .- The top boundary is $y = 4$ + +Step 2: Determine the integer coordinates that lie strictly within these boundaries. For a point $(x,y)$ to be strictly inside the rectangle, it must satisfy: $-5 < x < 5 - 4 < y < 4$ + +Step 3: Count the integer coordinates that satisfy these conditions. Now, we will find the integer values for $x$ and $y$ that fall within these boundaries. For $x$ : The integer values that satisfy $-5 < x < 5$ are: + +$-4, -3, -2, -1, 0, 1, 2, 3, 4$ This gives us 9 possible integer values. For $y$ The integer values that satisfy $-4 < y < 4$ are: $-3, -2, -1, 0, 1, 2, 3$ . This gives us 7 possible integer values. + +Step 4: Calculate the total number of points. Now, we multiply the number of possible integer values for $x$ by the number of possible integer values for $y$ . + +$$ +\text {T o t a l p o i n t s} = 9 \times 7 = 6 3 +$$ + +Finally, the number of points with integer coordinates that lie strictly in the interior of the rectangular region is $\boxed{63}$ . + +Figure 9: Case Study comparing with and without high-level metacognition results. + +# G Prompts + +# G.1 Single-turn ReMA prompts + +# G.1.1 Prompts for JSON data collection + +Prompt for metacognition reasoning to rewrite: + +```txt +System prompt: +You are a math expert trying to solve mathematical problems. +Before answering a question, your task is to rewrite the original question to make it clearer. +Provide your rewritten content in JSON format: +{ "action": "REWRITE", "output": "{clearer question content}" +} +Respond only with valid JSON. Do not write an introduction or summary. +User prompt: +Here is the question: [problem_text] +``` + +Prompt for metacognition reasoning to decompose: + +```txt +Question: The equation $x^{10} + (13x - 1)^{10} = 0$ has 10 complex roots $r_1,\overline{r}_1,r_2,\overline{r}_2,r_3,\overline{r}_3,r_4,\overline{r}_4,r_5,\overline{r}_5$ , where the bar denotes complex conjugation. Find the value of $\frac{1}{r_1\overline{r}_1} +\frac{1}{r_2\overline{r}_2} +\frac{1}{r_3\overline{r}_3} +\frac{1}{r_4\overline{r}_4} +\frac{1}{r_5\overline{r}_5}$ +``` + +# High-Level Agent's Output + +To solve this problem, let's break it down into steps that a low-level math-solving agent can follow: + +1. Understand the given equation: + +The equation is $x^{10} + (13x - 1)^{10} = 0$ + +2. Rewrite the equation: + +Notice that the equation can be rewritten as: + +$$ +x ^ {1 0} = - (1 3 x - 1) ^ {1 0}. +$$ + +3. Consider the roots: + +The roots of the equation are given as $r_1, \overline{r}_1, r_2, \overline{r}_2, r_3, \overline{r}_3, r_4, \overline{r}_4, r_5, \overline{r}_5$ , where the bar denotes complex conjugation. 4. Use the property of complex conjugates: +For any complex number $z$ , the product of $z$ and its conjugate $\overline{z}$ is the square of the modulus of $z$ i.e., $z\overline{z} = |z|^2$ 5. Calculate the required sum: +3. Calculate the required sum $\mathbf{W} = \mathbf{w}_{1} + \mathbf{w}_{2} + \dots + \mathbf{w}_{n}$ + +$$ +\frac {1}{r _ {1} \overline {{F _ {1}}}} + \frac {1}{r _ {2} \overline {{F _ {2}}}} + \frac {1}{r _ {3} \overline {{F _ {3}}}} + \frac {1}{r _ {4} \overline {{F _ {4}}}} + \frac {1}{r _ {5} \overline {{F _ {5}}}} +$$ + +Using the property from step 4, this can be rewritten as: + +$$ +\frac {1}{| r _ {1} | ^ {2}} + \frac {1}{| r _ {2} | ^ {2}} + \frac {1}{| r _ {3} | ^ {2}} + \frac {1}{| r _ {4} | ^ {2}} + \frac {1}{| r _ {5} | ^ {2}}, +$$ + +6. Simplify the expression: +Since $r_1, r_2, r_3, r_4, r_5$ are roots of the equation $x^{10} = -(13x - 1)^{10}$ , the magnitudes $|r_i|$ are the same for each pair $r_i$ and $\overline{r}_i$ . Let $|r_i| = |r_i|$ for all $i, j$ . +7. Find the common magnitude: +To find $|r_{1}|$ , consider the magnitudes of the terms on both sides of the equation $x^{10} = -(13x - 1)^{10}$ . The magnitude of the left side is $|x|^{10}$ and the magnitude of the right side is $|13x - 1|^{10}$ . Therefore: + +$$ +\left| x \right| ^ {1 0} = \left| 1 3 x - 1 \right| ^ {1 0}. +$$ + +Taking the 10th root of both sides, we get: + +$$ +| x | = | 1 3 x - 1 |. +$$ + +8. Solve for $|x|$ : +Let $|x| = a$ . Then: + +$\therefore m - 1 \neq 0$ ; + +$$ +a = \left| 1 3 a - 1 \right|. +$$ + +This gives us two cases: +- $a = 13$ +- $a = -(13a - 1)$ +Solving the first case: + +$$ +a = 1 3 a - 1 \Longrightarrow 1 2 a = 1 \Longrightarrow a = \frac {1}{1 2}. +$$ + +Solving the second case: + +$$ +a = - 1 3 a + 1 \Longrightarrow 1 4 a = 1 \Longrightarrow a = \frac {1}{1 4}. +$$ + +Since $a$ must be the same for all roots, we need to check which value is consistent. Given the nature of the problem, we can assume $a = \frac{1}{2}$ as the correct magnitude. +9. Calculate the final sum: +Since $|r_i| = \frac{1}{2}$ for all $i$ , we have + +$$ +\frac {1}{| r _ {1} | ^ {2}} = \frac {1}{(\frac {1}{4}) ^ {2}} = 1 4 4. +$$ + +Therefore, the sum is: + +$$ +1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 = 5 \times 1 4 4 = 7 2 0. +$$ + +10. Final answer: + +$$ +\frac {1}{\frac {1}{n} + \frac {1}{n}} + \frac {1}{\frac {1}{n} + \frac {1}{n}} + \frac {1}{\frac {1}{n} + \frac {1}{n}} \text {i s} 7 2 0. +$$ + +# Low-Level Agent's Output + +Let's go through the solution step by step to ensure clarity and correctness. + +1. Understand the given equation: +The equation is $x^{10} + (13x - 1)^{10} = 0$ +2. Rewrite the equation: +Notice that the equation can be rewritten as: + +$$ +x ^ {1 0} = - (1 3 x - 1) ^ {1 0}. +$$ + +3. Consider the roots: + +The roots of the equation are given as $r_1, \overline{r}_1, r_2, \overline{r}_2, r_3, \overline{r}_3, r_4, \overline{r}_4, r_5, \overline{r}_5$ , where the bar denotes complex conjugation. 4. Use the property of complex conjugates: +For any complex number $z$ , the product of $z$ and its conjugate $\overline{z}$ is the square of the modulus of $z$ , i.e., $z\overline{z} = |z|^2$ . 5. Calculate the required sum: +We need to find the value of: + +$$ +\frac {1}{r _ {1} F _ {1}} + \frac {1}{r _ {2} F _ {2}} + \frac {1}{r _ {3} F _ {3}} + \frac {1}{r _ {4} F _ {4}} + \frac {1}{r _ {5} F _ {5}} +$$ + +Using the property from step 4, this can be rewritten as: + +$$ +\frac {1}{| r _ {1} | ^ {2}} + \frac {1}{| r _ {2} | ^ {2}} + \frac {1}{| r _ {3} | ^ {2}} + \frac {1}{| r _ {4} | ^ {2}} + \frac {1}{| r _ {5} | ^ {2}} + \frac {1}{| r _ {6} | ^ {2}} +$$ + +6. Simplify the expression: +Since $r_1, r_2, r_3, r_4, r_5$ are roots of the equation $x^{10} = -(13x - 1)^{10}$ , the magnitudes $|r_i|$ are the same for each pair $r_1$ and $\overline{r}_i$ . Let $|r_i| = |r_i|$ for all $i, j$ . +7. Find the common magnitude: +To find $|\boldsymbol{r}_i|$ , consider the determinants of the terms on both sides of the equation $x^{10} = -(13x - 1)^{10}$ . The magnitude of the left side is $|z|^10$ and the magnitude of the right side is $|13z - 1|^{10}$ . Therefore: + +$$ +| x | ^ {1 0} = | 1 3 x - 1 | ^ {1 0}. +$$ + +Taking the 10th root of both sides, we get: + +$$ +\left| x \right| = \left| 1 3 x - 1 \right|. +$$ + +8. Solve for $|x|$ : + +Let $|x| = a$ . Then: + +$$ +a = | 1 3 x - 1 |. +$$ + +This gives us two cases: +-α=13a-1 +- $a = -(13a - 1)$ +Solving the first case: + +$$ +a = 1 3 a - 1 \Longrightarrow 1 2 a = 1 \Longrightarrow a = \frac {1}{1 2}. +$$ + +Solving the second case: + +$$ +a = - 1 3 a + 1 \Rightarrow 1 4 a = 1 \Rightarrow a = \frac {1}{1 4}. +$$ + +Since $a$ must be the same for all roots, we need to check which value is consistent. Given the nature of the problem, we can assume $a = \frac{1}{2}$ as the correct magnitude. +9. Calculate the final sum: +Since $|r_i| = \frac{1}{12}$ for all i, we have: + +$$ +\frac {1}{| r _ {i} | ^ {2}} = \frac {1}{(\mathrm {古}) ^ {2}} = 1 4 4. +$$ + +Therefore, the sum is: + +$$ +1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 = 5 \times 1 4 4 = 7 2 0. +$$ + +10. Final answer: + +$$ +\text {The v a l u e o f} \frac {1}{r _ {1} r _ {1}} + \frac {1}{r _ {2} r _ {2}} + \frac {1}{r _ {3} r _ {3}} + \frac {1}{r _ {4} r _ {4}} + \frac {1}{r _ {5} r _ {5}} \text {i s} \boxed {7 2 0}. +$$ + +```latex +Question: The equation $x^{10} + (13x - 1)^{10} = 0$ has 10 complex roots $r_1, \overline{r}_1, r_2, \overline{r}_2, r_3, \overline{r}_3, r_4, \overline{r}_4, r_5, \overline{r}_5$ , where the bar denotes complex conjugation. Find the value of $\frac{1}{r_1r_4} + \frac{1}{r_2r_2} + \frac{1}{r_3r_3} + \frac{1}{r_4r_4} + \frac{1}{r_5r_5}$ . +``` + +High-Level Agent's Output + +Low-Level Agent's Output (part I) + +To solve this problem, we need to follow these steps: +1. Understand the given equation: The equation is $x^{10} - (13x - 1)^{10} = 0$ . +2. Identify the roots: The roots of the +equation are given as +$\overline{r_1},\overline{r_2},\overline{r_3},\overline{r_4},\overline{r_5},\overline{r_6},\overline{r_7},\overline{r_8}$ where the bar denotes complex conjugation. +3. Use properties of complex conjugates: +For any complex number $z$ , the product $z \cdot z$ is a complex function of the modulus of $z$ , i.e., $|z \cdot \overline{z}| = |z|^2$ . +4. Simplify the expression: We need to find +the value of 1 +r1+ r2r3+ r4 +# +Apply an property of complex conjugates. Since $\pi_1 \cdot \overline{\pi}_1 = |\pi_1|^2$ , we have +1+ +A +6.Sum the reciprocals: Sum the values +1+1 1 1 +7. Use Vieta's formulas: To find the sum of the reciprocals of the moduli squared, we can use the fact that the sum of the roots of the polynomial and their properties. +8. Finalize the solution: Combine all the +steps to find the final value +Now, let's guide the low-level math solving +agent to implement these steps. + +To solve the given problem, we start by analyzing the equation $x^{10} + (13x - 1)^{10} = 0$ . + +This can be rewritten as: + +$$ +x ^ {1 0} = - (1 3 x - 1) ^ {1 0}. +$$ + +Taking the 10th root on both sides, we get: + +$$ +x = \omega (1 3 x - 1), +$$ + +where $\omega$ is a 10th root of $-1$ . The 10th roots of $-1$ are given by $\omega = e^{\pi (2k + 1) / 10}$ for $k = 0, 1, 2, \ldots, 9$ . + +Rewriting the equation, we have: + +$x = \omega (13x - 1)\Rightarrow x - 13\omega x = -\omega \Rightarrow x(1 - 13\omega) = -\omega \Rightarrow x = \frac{-\omega}{1 - 13\omega}$ + +Thus, the roots of the equation are: + +$$ +r _ {k} = \frac {- \omega_ {k}}{1 - 1 3 \omega_ {k}} +$$ + +where $\omega_{k} = e^{i\pi (2k + 1) / 10}$ for $k = 0,1,2$ + +The roots come in conjugate pairs, so the roots are $r_1, \overline{r_1}, r_2, \overline{r_2}, r_3, \overline{r_3}, r_4, \overline{r_4}, r_5, \overline{r_5}$ . We need to find the value of: + +$$ +\frac {1}{r _ {1} \overline {{r _ {1}}}} + \frac {1}{r _ {2} \overline {{r _ {2}}}} + \frac {1}{r _ {3} \overline {{r _ {3}}}} + \frac {1}{r _ {4} \overline {{r _ {4}}}} + \frac {1}{r _ {5} \overline {{r _ {5}}}} +$$ + +Since $r_k\overline{r_k} = |r_k|^2$ we have: + +$$ +\frac {1}{r _ {k} r _ {k}} = \frac {1}{| r _ {k} | ^ {2}} +$$ + +We need to find $|r_k|^2$ . Note that: + +$$ +r _ {k} = \frac {- \omega_ {k}}{1 - 1 3 \omega_ {k}} +$$ + +Low-Level Agent's Output (part II) + +The magnitude of $r_k$ is: + +$$ +| r _ {k} | = \left| \frac {- \omega_ {k}}{1 - 1 3 \omega_ {k}} \right| = \left| \frac {| \omega_ {k} |}{1 - 1 3 \omega_ {k}} \right| = \frac {1}{1 - 1 3 \omega_ {k}} +$$ + +Thus, + +$$ +| r _ {k} | ^ {2} = \frac {1}{| 1 - 1 3 \omega_ {k} | ^ {2}} +$$ + +Therefore, + +$$ +\frac {1}{r _ {2} r _ {1}} = | 1 - 1 3 \omega_ {k} | ^ {2}. +$$ + +We need to sum this over the 5 pairs of roots: + +$$ +\sum_ {k = 0} ^ {4} | 1 - 1 3 \omega_ {k} | ^ {2} +$$ + +Since $\omega_{k} = e^{i\pi (2k + 1) / 10}$ , we have + +$|1 - 13\omega_{k}|^{2} = (1 - 13\omega_{k})(1 - 13\overline{\omega_{k}}) = (1 - 13\omega_{k})(1 - 13e^{-i\pi (2k + 1) / 10}) = 1 - 13\omega_{k} - 13e^{-i\pi (2k + 1) / 10} + 169.$ +Since $\omega_{k}\overline{\omega_{k}} = 1$ we get: + +$$ +\left| 1 - 1 3 \omega_ {k} \right| ^ {2} = 1 6 9 - 1 3 (\omega_ {k} + e ^ {- i \pi (2 k + 1) \cdot 1 0}) + 1 = 1 7 0 - 1 3 \cdot 2 \cos \left(\frac {\pi (2 k + 1)}{1 0}\right) = 1 7 0 - 2 6 \cos \left(\frac {\pi (2 k + 1)}{1 0}\right) +$$ + +Summing over $k = 0,1,2,3,4$ we get: + +$$ +\sum_ {k = 0} ^ {n - 1} \left(1 7 0 - 2 6 \cos \left(\frac {\pi (2 k + 1)}{1 0}\right)\right) = 5 \cdot 1 7 0 - 2 6 \sum_ {k = 0} ^ {n - 1} \cos \left(\frac {\pi (2 k + 1)}{1 0}\right) = 8 5 0 - 2 6 \cdot 0 = 8 5 0. +$$ + +Thus, the value is: + +![](images/6cce98a8906c58ccf3aa6cedf13fe8485572fcdb57dd27e9b6cd696eb48335fd.jpg) +Figure 10: Case Study for consistency reward of high-level agent +Figure 11: Case Study for base correctness reward of high-level agent + +Llama3.2-1B-Instruct training Output: +```txt +Question: The product of $3t^{2} + 5t + a$ and $4t^{2} + bt - 2$ is $12t^{4} + 26t^{3} - 8t^{2} - 16t + 6$ . What is $a + b$ ? +``` + +Llama3.1-8B-Instruct training Output: +```json +{ + "action": "DECOMPOSE", + "output": "Decompose the problem into finding the coefficients of the product of two polynomials and then solving for a and b." +} +``` + +```txt +{ "action": "EMPTY", "output"."" } +``` + +```txt +Step 1: To find the product of the two polynomials $3t^{2} + 5t + a$ and $4t^{2} + bt - 2$ , we need to multiply each term of the first polynomial by each term of the second polynomial and then combine like terms. +Step 2: The product of the two polynomials can be written as $(3t^{2} + 5t + a)(4t^{2} + bt - 2)$ . +Step 3: Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial: $(3t^{2})(4t^{2}) + (3t^{2})(bt) + (3t^{2})(-2) + (5t)(4t^{2}) + (5t)(bt) + (5t)(-2) + (a)(4t^{2}) + (a)(bt) + (a)(-2)$ . +Step 4: Simplifying the products, we get $12t^{4} + 3b^{3} - 6t^{2} + 20t^{3} + 5bt^{2} - 10t + 4at^{2} + abt - 2a$ . +Step 5: Combining like terms, we have $12t^{4} + (3b + 20)t^{3} + (5b - 6 + 4a)t^{2} + (ab - 10)t - 2a$ . +Step 6: We are given that the product of the two polynomials is $12t^{4} + 26t^{3} - 8t^{2} - 16t + 6$ . +We can equate the coefficients of the corresponding powers of $t$ in the two expressions. +Step 7: Equating the coefficients of $t^3$ , we get $3b + 20 = 26$ . +Step 8: Equating the coefficients of $t^2$ , we get $5b - 6 + 4a = -8$ . +Step 9: Equating the constant terms, we get $-2a = 6$ . +Step 10: Solving the equation $-2a = 6$ , we find that $a = -3$ . +Step 11: Substituting $a = -3$ into the equation $5b - 6 + 4a = -8$ , we get $5b - 6 + 4(-3) = -8$ , which simplifies to $5b - 18 = -8$ . +Step 12: Solving for $b$ , we find that $5b = 10$ , so $b = 2$ . +Step 13: Now that we have found the values of $a$ and $b$ , we can calculate their sum: $a + b = -3 + 2 = -1$ . +The final answer is: $\boxed{-1}$ +``` + +```txt +Step 1: The problem asks us to find the values of $a$ and $b$ in the quadratic expressions $3t^2 + 5t + a$ and $4t^2 + bt - 2$ , respectively, given that their product is $12t^4 + 26t^3 - 8t^2 - 16t + 6$ . +``` + +```txt +Step 2: To solve this, we need to multiply the two quadratic expressions and equate the resulting expression to the given product $12t^4 + 26t^3 - 8t^2 - 16t + 6$ . +``` + +```txt +Step 3: We start by multiplying the two quadratic expressions: $(3t^{2} + 5t + a)(4t^{2} + bt - 2)$ . +``` + +```txt +Step 4: This gives us $12t^4 + (3b + 5)t^3 + (4a + 5b - 6)t^2 + (-2b + 10t + 2a)t - 2a.$ +``` + +```txt +Step 5: We know that the coefficients of the resulting expression must be equal to the coefficients of the given product $12t^4 + 26t^3 - 8t^2 - 16t + 6$ . +``` + +```txt +Step 6: Equating the coefficients of $t^3$ gives us the equation $3b + 5 = 26$ , which simplifies to $3b = 21$ and thus $b = 7$ . +``` + +```txt +Step 7: Equating the constant terms gives us $-2a = -6$ , which simplifies to $a = 3$ . +``` + +```txt +Step 8: Now that we have the values of $b$ and $a$ , we can find the sum $a + b$ . +``` + +```txt +Step 9: Adding $a = 3$ and $b = 7$ gives us $a + b = 10$ . +``` + +```txt +The final answer is: $\boxed{10}$ +``` + +Figure 12: Case Study for interpretability experiments in Section 4.2.2 + +System prompt: +```txt +You are a math expert trying to solve mathematical problems. Before answering a question, your task is to decompose the original question to make it clearer. +Provide your rewritten content in JSON format: +{"action": "DECOMPOSE", "output": "{decomposed question content}}" +}} +Respond only with valid JSON. Do not write an introduction or summary. +User prompt: +Here is the question: [problem.text] +``` + +Prompt for generating final answers using on the question and metacognition reasoning: + +System prompt: +User prompt: +```txt +You are a math expert tasked with solving problems step by step. Follow the provided instructions precisely, showing all reasoning and intermediate steps. Present the final answer within \boxed{\{\}}\}. +``` + +```txt +Here is the question and instructions: +Question +[problem_text] +Provided Instruction +[instruction_text] +``` + +# G.1.2 Prompts for Math problems + +# VRP prompt: + +```txt +System prompt: +You are a math expert tasked with solving problems step by step. Present the final answer within \boxed{}?. +User prompt: +Here is the question: +{Question} +``` + +# MRP prompt: + +```txt +System prompt: +You are a math expert tasked with solving problems. When solving a problem, your first task is to provide a high-level solution plan as an instruction. Then you need to follow the provided instructions precisely, showing all reasoning and intermediate steps. Finally, you must present the final answer within boxed}. +User prompt: +Here is the question: {Question} +``` + +# MAMRP prompt: + +high-level agent: + +```txt +System prompt: +You are a math expert specialized in solving mathematical problems, you need to teach a weaker agent with minimal capability in math how to solve a problem step-by-step. +Your task is to provide a high-level solution plan for the given problem, in order to guide a low-level math solving agent to solve the problem. +You can not directly answer the question. You'll be punished if you include any answer in your response. +You need to first think deeply in mind and output your final instruction. +User prompt: +Here is the question: +{Question} +``` + +low-level agent: + +```txt +System prompt: +You are a math expert tasked with solving problems step by step. Follow the provided instructions precisely, showing all reasoning and intermediate steps. Present the final answer within \boxed{}/. User prompt: Here is the question and instructions: [Question] {Question} [End of Question] [Provided Instruction] {instruction} [End of Instruction] +``` + +# G.1.3 Prompts for LLM-as-a-Judge problems + +We adopt the prompts from Saha et al. [2025a]. + +# VRP prompt: + +```txt +System prompt: +Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses. Begin your evaluation by comparing the two responses and provide a short explanation. Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision.. +Do not allow the length of the responses to influence your evaluation.. +Do not favor certain names of the assistants. Be as objective as possible. After providing your explanation, output your final verdict by strictly following this format: "[A]" if assistant A is better, "[B]" if assistant B is better.. +User prompt: +[User Question] {instruction} [End of User Question] [The Start of Assistant A's Answer] {response_A} [The End of Assistant A's Answer] [The Start of Assistant B's Answer] {response_B} [The End of Assistant B's Answer] +``` + +# MRP prompt: + +# System prompt: + +Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. First of your task is to build an evaluation plan that can then be executed to assess the response quality. Whenever appropriate, you can choose to also include a step-by-step reference answer as part of the evaluation plan. Enclose your evaluation plan between the tags "[Start of Evaluation Plan]" and "[End of Evaluation Plan)". After that, please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses. Begin your evaluation by comparing the two responses and provide a short explanation. Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision. Do not allow the length of the responses to influence your evaluation. Do not favor certain names of the assistants. Be as objective as possible. After providing your explanation, output your final verdict by strictly following this format: "[A]" if assistant A is better, "[B]" if assistant B is better. User prompt: [User Question] {instruction} [End of User Question] [The Start of Assistant A's Answer] {response_A} [The End of Assistant A's Answer] [The Start of Assistant B's Answer] {response_B} [The End of Assistant B's Answer] + +# MAMRP prompt: high-level agent: + +# System prompt: + +We want to evaluate the quality of the responses provided by AI assistants to the user question displayed below. For that, your task is to help us build an evaluation plan that can then be executed to assess the response quality. Whenever appropriate, you can choose to also include a step-by-step reference answer as part of the evaluation plan. + +# User prompt: + +[User Question] +{Question} +[End of User Question] + +# low-level agent: + +# System prompt: + +Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. Your evaluation should be performed by following the provided evaluation plan step-by-step. Avoid copying the plan when doing the evaluation. + +Please also only stick to the given plan and provide explanation of how the plan is executed to compare the two responses. + +Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision. + +Do not allow the length of the responses to influence your evaluation. Do not favor certain names of the assistants. Be as objective as possible. + +After providing your evaluation, output your final verdict by strictly following this format: "[A]" if assistant A is better, "[B]" if assistant B is better. + +# User prompt: + +```txt +[User Question] +{instruction} +{End of User Question] +{The Start of Assistant A's Answer} +{response_A} +{The End of Assistant A's Answer} +{The Start of Assistant B's Answer} +{response_B} +{The End of Assistant B's Answer} +{The Start of Evaluation Plan} +{evaluation計劃} +{The End of Evaluation Plan} +``` + +# G.2 Multi-turn ReMA prompts + +# G.2.1 SFT data collection of multi-turn MAMRP + +# System prompt: + +You are classifying reasoning process data into two types of thinking. You will be given a question-answer pair from a reasoning dataset. Your task is to split all words into two parts. These words are crucial for analyzing reasoning patterns, so do not skip any details. + +- **Meta-Thinking Agent (MTA):** Responsible for high-level thought processes. This includes planning, evaluating steps, expressing uncertainty, making observations, or setting goals. Avoid detailed calculations. The content should be enclosed in `` and ``. + +- $\star \star$ Reasoning Agent (RA): $\star \star$ Responsible for detailed problem-solving steps, such as calculations, logical deductions, or breaking down a problem into subproblems. The content should be enclosed in `` and ``. + +\*\*Rules to follow: \*\* + +1. **Do not assign large chunks of text to a single type of thinking.** The reasoning process consists of small, nonlinear thinking steps, so alternate appropriately between Meta-Thinking and Reasoning steps. + +2. **Keep the words from the original solution unmodified whenever possible.** Words like "Wait," "Hmm," "But," etc., typically indicate Meta-Thinking and should be preserved. + +3. $\star \star$ When finalizing the answer: $\star \star$ + +- The \*\*Meta-Thinking Agent (MTA) \*\* must explicitly confirm the answer before completion and output '[FINISH]'. + +- The $\star \star$ Reasoning Agent (RA) $\star \star$ should then provide the final answer in the correct format. + +4. **Do not skip any reasoning steps, even if they seem redundant, incorrect or irrelevant** + +5. **Do not modify or remove any part of the original reasoning process**, even if it seems redundant or repetitive. The goal is to **preserve the exact flow of thought** as it naturally occurs. + +6. **Retain all expressions such as "Wait," "Hmm," "But wait," etc., exactly as they appear. These indicate important cognitive processes and should not be skipped or altered.** + +Here are examples for you: [Examples] ... + +# User prompt: + +[Begin of Question] +{question} +[End of Question] +[Begin of Solution] +{solution} +[End of Solution] + +# G.2.2 Prompt for math problems + +# Meta-Thinking Agent (MTA): + +```txt +System prompt: +You are a meta-think agent that represents human high-level think process, when solving a question, you will have a discussion with human, each time you think about what to do next: e.g. +- Exploring multiple angles and approaches +- Breaking down the solution into clear steps +- Continuously reflecting on intermediate results honestly and adapt your strategy as you progress +- Backtracking when necessary +- Requesting exploration of multiple solutions individually +- Finally confirm the answer with the tag [FINISH] +User prompt: +{question} +``` + +# Reasoning Agent (RA): + +```txt +System prompt: Please reason step by step follow the given 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+ "bbox": [ + 246, + 248, + 363, + 260 + ], + "type": "text", + "content": "4 University College London" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 281, + 288, + 329, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 288, + 329, + 300 + ], + "spans": [ + { + "bbox": [ + 281, + 288, + 329, + 300 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 140, + 312, + 469, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 312, + 469, + 542 + ], + "spans": [ + { + "bbox": [ + 140, + 312, + 469, + 542 + ], + "type": "text", + "content": "Recent research on Reasoning of Large Language Models (LLMs) has sought to further enhance their performance by integrating meta-thinking—enabling models to monitor, evaluate, and control their reasoning processes for more adaptive and effective problem-solving. However, current single-agent work lacks a specialized design for acquiring meta-thinking, resulting in low efficacy. To address this challenge, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages Multi-Agent Reinforcement Learning (MARL) to elicit meta-thinking behaviors, encouraging LLMs to think about thinking. ReMA decouples the reasoning process into two hierarchical agents: a high-level meta-thinking agent responsible for generating strategic oversight and plans, and a low-level reasoning agent for detailed executions. Through iterative reinforcement learning with aligned objectives, these agents explore and learn collaboration, leading to improved generalization and robustness. Empirical results from single-turn experiments demonstrate that ReMA outperforms single-agent RL baselines on complex reasoning tasks, including competitive-level mathematical benchmarks and LLM-as-a-Judge benchmarks. Additionally, we further extend ReMA to multi-turn interaction settings, leveraging turn-level ratio and parameter sharing to improve efficiency. Comprehensive ablation studies further illustrate the evolving dynamics of each distinct agent, providing valuable insights into how the meta-thinking reasoning process enhances the reasoning capabilities of LLMs. Our code can be found in https://github.com/ziyuwan/ReMA-public" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 562, + 192, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 562, + 192, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 562, + 192, + 574 + ], + "type": "text", + "content": "1 Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 586, + 506, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 586, + 506, + 675 + ], + "spans": [ + { + "bbox": [ + 104, + 586, + 506, + 675 + ], + "type": "text", + "content": "Large language models (LLMs) have demonstrated remarkable capabilities in knowledge understanding and complex reasoning tasks [Chowdhery et al., 2023, Achiam et al., 2023, Anil et al., 2023, Dubey et al., 2024]. The paradigm in developing LLM-based reasoning models is shifting from scaling training-time computation towards scaling test-time computation [Snell et al., 2024]. Recent advancements, such as OpenAI-o1 [OpenAI, 2024], Deepseek R1 [DeepSeek-AI et al., 2025], and Gemini 2.0 Flash Thinking [DeepMind, 2025], have demonstrated that allowing LLMs to think before generating answers can significantly enhance performance and lead to the emergence of human-like reasoning patterns. These patterns like \"Wait, hold on.\" or \"Let's break this down.\"" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 14, + 209, + 37, + 559 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 14, + 209, + 37, + 559 + ], + "spans": [ + { + "bbox": [ + 14, + 209, + 37, + 559 + ], + "type": "text", + "content": "arXiv:2503.09501v3 [cs.AI] 27 May 2025" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 116, + 681, + 193, + 692 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 681, + 193, + 692 + ], + "spans": [ + { + "bbox": [ + 116, + 681, + 193, + 692 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 118, + 692, + 392, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 692, + 392, + 703 + ], + "spans": [ + { + "bbox": [ + 118, + 692, + 392, + 703 + ], + "type": "inline_equation", + "content": "^{\\dagger}" + }, + { + "bbox": [ + 118, + 692, + 392, + 703 + ], + "type": "text", + "content": "Work done during internship at Shanghai Artificial Intelligence Laboratory" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 118, + 703, + 205, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 703, + 205, + 714 + ], + "spans": [ + { + "bbox": [ + 118, + 703, + 205, + 714 + ], + "type": "text", + "content": "Corresponding Author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 731, + 192, + 742 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 731, + 192, + 742 + ], + "spans": [ + { + "bbox": [ + 105, + 731, + 192, + 742 + ], + "type": "text", + "content": "Preprint. Under review." + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "spans": [ + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "text", + "content": "Question: " + }, + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "inline_equation", + "content": "T = 9.5" + }, + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "inline_equation", + "content": "\\log_2 x^T - \\log_4 x = \\log_8 x^k" + }, + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "text", + "content": " is an identity for all " + }, + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "inline_equation", + "content": "x > 0" + }, + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "text", + "content": ", compute the value of " + }, + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 187, + 74, + 423, + 84 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 109, + 86, + 504, + 235 + ], + "blocks": [ + { + "bbox": [ + 109, + 86, + 504, + 235 + ], + "lines": [ + { + "bbox": [ + 109, + 86, + 504, + 235 + ], + "spans": [ + { + "bbox": [ + 109, + 86, + 504, + 235 + ], + "type": "image", + "image_path": "fd5b40d644792636991a20db79d8c4202f072f2e023bbd6106c186898b906286.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 243, + 504, + 288 + ], + "lines": [ + { + "bbox": [ + 104, + 243, + 504, + 288 + ], + "spans": [ + { + "bbox": [ + 104, + 243, + 504, + 288 + ], + "type": "text", + "content": "Figure 1: Left: A construction-based method that fine-tunes LLMs using rejection sampling, searching among combinations of pre-defined templates. Middle: R1-like method learns to mix meta-thinking and detailed reasoning steps during training. Right: Our method ReMA separates the meta-thinking and reasoning steps in a multi-agent system and updated by reinforcement learning." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 301, + 504, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 301, + 504, + 335 + ], + "spans": [ + { + "bbox": [ + 104, + 301, + 504, + 335 + ], + "type": "text", + "content": "indicate that LLMs can develop a form of meta-thinking abilities that can generalize well to out-of-distribution (OOD) tasks [Xiang et al., 2025]. Meta-thinking, also known as metacognitive skills [Flavell, 1979], is an ability traditionally considered uniquely human [Didolkar et al., 2024]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 340, + 506, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 340, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 104, + 340, + 506, + 515 + ], + "type": "text", + "content": "To cultivate meta-thinking patterns from LLMs themselves, recent construction-based supervised approaches leverage supervised finetuning on structured reasoning trajectories. Specifically, these methods sampling reasoning trajectories from predefined meta-thinking templates and then use supervised finetuning (SFT) or direct preference optimization (DPO) [Rafailov et al., 2023] to teach LLMs imitate these patterns [Qi et al., 2024, Yue et al., Xi et al., 2024, Yang et al., 2025, Muenighoff et al., 2025, Ye et al., 2025c]. However, such methods lack sufficient flexibility for LLMs to explore suitable meta-thinking patterns. Thus, they often fail to generalize to out-of-distribution (OOD) problems, leading to unstable performance on unseen data [Kirk et al., Chu et al., 2025]. Besides construction-based methods, R1-like single-agent reinforcement learning (SARL) has also been adopted for meta-thinking in reasoning [DeepSeek-AI et al., 2025, Xie et al., 2025]. However, these SARL attempts typically rely on strong foundational models for easier exploration or extensive task-specific fine-tuning for stable training [Xu et al., 2025, Gandhi et al., 2025]. Furthermore, SARL needs to learn meta-thinking and reasoning within a single forward pass, seeking to capture complex reasoning structures purely in an autoregressive manner [Xie et al., 2025]. This can potentially lead to issues such as inefficient exploration as well as reduced readability and early convergence to local optima [DeepSeek-AI et al., 2025, Xiang et al., 2025]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 520, + 506, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 520, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 520, + 506, + 640 + ], + "type": "text", + "content": "To address these limitations, we introduce Reinforced Meta-thinking Agents (ReMA), a novel framework that leverages multi-agent reinforcement learning (MARL) to encourage LLMs to think about thinking. Our approach employs a multi-agent system (MAS) composed of a high-level meta-thinking agent, responsible for strategic oversight and instruction generation, and a low-level reasoning agent tasked with detailed executing processes based on provided guidance. We compare the inference process among the construction-based method, R1-like method, and ReMA in Fig. 1. Since MAS distributes the exploration space of SARL into multiple agents, it enables each agent to explore more structurally and efficiently during training. Then we apply reinforcement learning on each agent with aligned reward functions. In this way, ReMA effectively balances the trade-off between generalization capability and exploration efficiency. As a result, they can learn to play the best of their role (either to meta-think or to follow instructions), at the present of the other agent." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 645, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 645, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 645, + 504, + 723 + ], + "type": "text", + "content": "To our knowledge, we are the first to formally define and optimize a multi-agent meta-thinking reasoning process (MAMRP) through multi-agent reinforcement learning. Our extensive experiments span both math reasoning and LLM-as-a-Judge tasks, where ReMA consistently achieves the highest average performance across three backbone pretrained models. We further extend ReMA to multi-turn interaction settings on math reasoning tasks, implementing turn-level ratio to optimize trajectory returns and stabilize training. Through comprehensive ablation studies, we illustrate the evolving dynamics between agents, revealing unexpected interaction patterns such as role reversals" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "text", + "content": "2" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 97 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 97 + ], + "type": "text", + "content": "under different reward settings. These findings provide valuable insights into how meta-thinking processes enhance the reasoning capabilities of LLMs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 111, + 196, + 125 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 111, + 196, + 125 + ], + "spans": [ + { + "bbox": [ + 105, + 111, + 196, + 125 + ], + "type": "text", + "content": "2 Preliminaries" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 137, + 504, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 137, + 504, + 160 + ], + "spans": [ + { + "bbox": [ + 104, + 137, + 504, + 160 + ], + "type": "text", + "content": "In this section, we outline the formulation of the vanilla reasoning process (Sec. 2.1) and the representative training methods (Sec. 2.2) along with the notation used throughout the paper." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 173, + 272, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 173, + 272, + 186 + ], + "spans": [ + { + "bbox": [ + 105, + 173, + 272, + 186 + ], + "type": "text", + "content": "2.1 Vanilla Reasoning Process (VRP)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "spans": [ + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "text", + "content": "The probability of generating a response " + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "text", + "content": " equals the product of its stepwise probabilities. Given a model " + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "text", + "content": " and a prompt " + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = (x_1, \\ldots, x_N)" + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "text", + "content": ", the vanilla reasoning process (VRP) autoregressively produces a response " + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{y} = (y_1, \\ldots, y_L)" + }, + { + "bbox": [ + 104, + 194, + 504, + 229 + ], + "type": "text", + "content": " with" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 161, + 235, + 447, + 269 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 161, + 235, + 447, + 269 + ], + "spans": [ + { + "bbox": [ + 161, + 235, + 447, + 269 + ], + "type": "interline_equation", + "content": "\\pi_ {\\theta} (\\mathbf {y} | \\mathbf {x}) = \\prod_ {l = 1} ^ {L} \\pi_ {\\theta} (y _ {l} | x _ {1}, x _ {2}, \\dots x _ {N}, y _ {1}, \\dots , y _ {l - 1}) = \\prod_ {l = 1} ^ {L} \\pi_ {\\theta} (\\mathbf {y} _ {l} | \\mathbf {x}, \\mathbf {y} _ {< l})", + "image_path": "bb67bfe8bbe98dfdf746dc7ea8f055c99defa53d3bfef0dab1ba7eb652abfa26.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 274, + 504, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 274, + 504, + 299 + ], + "spans": [ + { + "bbox": [ + 104, + 274, + 504, + 299 + ], + "type": "text", + "content": "The response usually contains intermediate reasoning steps before arriving at the final answer, this process is also known as chain-of-thought (CoT) [Wei et al., 2022], which can be represented as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 258, + 305, + 504, + 322 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 258, + 305, + 504, + 322 + ], + "spans": [ + { + "bbox": [ + 258, + 305, + 504, + 322 + ], + "type": "interline_equation", + "content": "\\mathbf {x} \\xrightarrow {\\text {r e a s o n i n g s t e p s}} \\mathbf {y} \\sim \\mathbf {a}, \\tag {1}", + "image_path": "a63ca3479e328fb21c46992199228dda29325fd84852c51c35f55e058a3aa453.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 327, + 395, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 327, + 395, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 395, + 340 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 105, + 327, + 395, + 340 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 105, + 327, + 395, + 340 + ], + "type": "text", + "content": " is the extracted final answer, which is included in the answer " + }, + { + "bbox": [ + 105, + 327, + 395, + 340 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 105, + 327, + 395, + 340 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 353, + 313, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 353, + 313, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 313, + 366 + ], + "type": "text", + "content": "2.2 Training VRP via Reinforcement Learning" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 373, + 504, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 373, + 504, + 397 + ], + "spans": [ + { + "bbox": [ + 104, + 373, + 504, + 397 + ], + "type": "text", + "content": "RL frames VRP decoding process as a deterministic, token-level Markov Decision process (MDP) [Wang et al., 2024a]. Its objective is" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 228, + 403, + 380, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 228, + 403, + 380, + 418 + ], + "spans": [ + { + "bbox": [ + 228, + 403, + 380, + 418 + ], + "type": "interline_equation", + "content": "\\mathcal {J} (\\theta) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\mathbf {y} \\sim \\pi_ {\\theta}} \\left[ R (\\mathbf {y}, \\mathbf {y} ^ {*}) \\right].", + "image_path": "91f9b8b3200cd1fa5635daeedf1c6ecf50a917b18a2af5197eda5580d3dc874a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "spans": [ + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "inline_equation", + "content": "R(\\cdot, \\cdot)" + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "text", + "content": " represents a reward function comparing generated answer " + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "text", + "content": " with the golden answer " + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^*" + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "text", + "content": " for any question " + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "text", + "content": " sampled from dataset " + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 104, + 423, + 504, + 447 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "spans": [ + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "content": "To compute the gradient " + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "inline_equation", + "content": "\\nabla_{\\theta}\\mathcal{J}(\\theta)" + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "content": ", computationally efficient algorithms GRPO [Shao et al., 2024] and REINFORCE++ [Hu, 2025] are widely adopted. Take GRPO as an example, given a question-answer pair " + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "inline_equation", + "content": "\\mathbf{x},\\mathbf{y}^*" + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "content": " and a group of " + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "content": " generated responses " + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "content": ", denote " + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{i,j}" + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "content": " as the " + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "content": "-th token of the " + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 104, + 449, + 504, + 492 + ], + "type": "text", + "content": "-th response, it optimizes the following token-level objective:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 116, + 497, + 504, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 497, + 504, + 545 + ], + "spans": [ + { + "bbox": [ + 116, + 497, + 504, + 545 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {J} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\{\\mathbf {y} _ {i} \\} _ {i = 1} ^ {G} \\sim \\pi_ {\\boldsymbol {\\theta} _ {\\mathrm {o l d}}} (\\cdot | \\mathbf {x})} \\\\ \\left[ \\frac {1}{G} \\sum_ {i = 1} ^ {G} \\frac {1}{| \\mathbf {y} _ {i} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i} |} \\left(\\min \\left(r _ {i, j} (\\theta) \\hat {A} _ {i, j}, \\operatorname {c l i p} \\left(r _ {i, j} (\\theta), 1 - \\epsilon , 1 + \\epsilon\\right) \\hat {A} _ {i, j}\\right) - \\beta D _ {\\mathrm {K L}} \\left(\\pi_ {\\theta} \\| \\pi_ {\\text {r e f}}\\right)\\right) \\right], \\tag {2} \\\\ \\end{array}", + "image_path": "ee55be31f7c6103fd057348679e639180187cf989e289196bbf5b13e1e17c731.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 552, + 475, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 552, + 475, + 567 + ], + "spans": [ + { + "bbox": [ + 107, + 552, + 475, + 567 + ], + "type": "text", + "content": "where the token-level ratio " + }, + { + "bbox": [ + 107, + 552, + 475, + 567 + ], + "type": "inline_equation", + "content": "r_{i,j}(\\theta)" + }, + { + "bbox": [ + 107, + 552, + 475, + 567 + ], + "type": "text", + "content": " and the group-normalized advantage " + }, + { + "bbox": [ + 107, + 552, + 475, + 567 + ], + "type": "inline_equation", + "content": "\\hat{A}_{i,j}" + }, + { + "bbox": [ + 107, + 552, + 475, + 567 + ], + "type": "text", + "content": " are defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 175, + 572, + 434, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 572, + 434, + 602 + ], + "spans": [ + { + "bbox": [ + 175, + 572, + 434, + 602 + ], + "type": "interline_equation", + "content": "r _ {i, j} (\\theta) = \\frac {\\pi_ {\\theta} \\left(\\mathbf {y} _ {i , j} \\mid \\mathbf {x} , \\mathbf {y} _ {i , < j}\\right)}{\\pi_ {\\theta_ {\\mathrm {o l d}}} \\left(\\mathbf {y} _ {i , j} \\mid \\mathbf {x} , \\mathbf {y} _ {i , < j}\\right)}, \\hat {A} _ {i, j} = \\frac {R _ {i} - \\operatorname {m e a n} \\left(\\left\\{R _ {i} \\right\\} _ {i = 1} ^ {G}\\right)}{\\operatorname {s t d} \\left(\\left\\{R _ {i} \\right\\} _ {i = 1} ^ {G}\\right)}.", + "image_path": "1d56081a4c756eb34fc910f55c821d9ab5537407188b813453634d13845d2f6a.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 613, + 504, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 613, + 504, + 648 + ], + "spans": [ + { + "bbox": [ + 104, + 613, + 504, + 648 + ], + "type": "text", + "content": "However, RL on base LLMs that haven't been well-aligned may suffer from issues like poor readability and language mixing, preventing researchers from verifying, understanding, and further developing their LLMs. And huge searching space makes efficient learning of meta-thinking daunting." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 663, + 167, + 676 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 663, + 167, + 676 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 167, + 676 + ], + "type": "text", + "content": "3 Method" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "type": "text", + "content": "In this section, we present Reinforced Meta-thinking Agents (ReMA), a RL method integrating meta-thinking into the reasoning process of LLM under multi-agent settings (Sec. 3.1), then describe the learning process enabled by MARL of single- and multi-turn LLM setting (Secs. 3.2.1 and 3.2.2)." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "text", + "content": "3" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 367, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 367, + 84 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 367, + 84 + ], + "type": "text", + "content": "3.1 Deploying Meta-Thinking Reasoning Process for LLMs" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 92, + 504, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 92, + 504, + 159 + ], + "spans": [ + { + "bbox": [ + 104, + 92, + 504, + 159 + ], + "type": "text", + "content": "Beyond VRP (Sec. 2.1), recent studies [Muennighoff et al., 2025, Ye et al., 2025c] have shown that integrating meta-thinking behaviors in reasoning process can largely improve the accuracy of the final answers. By integrating Meta-thinking, ReMA decomposes problem solving into two sequential phases: a meta-thinking phase that plans, monitors, or revises strategy, followed by a reasoning phase that produces the detailed solution. We analyse Meta-thinking Reasoning Process along two orthogonal axes—single- vs. multi-agent and single- vs. multi-turn." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 163, + 504, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 163, + 504, + 186 + ], + "spans": [ + { + "bbox": [ + 104, + 163, + 504, + 186 + ], + "type": "text", + "content": "In a single-agent setting, such a process calls LLM once and generates meta-thinking and the following reasoning autoregressively. We formulate the meta-thinking reasoning process (MRP) below:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 242, + 192, + 504, + 205 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 242, + 192, + 504, + 205 + ], + "spans": [ + { + "bbox": [ + 242, + 192, + 504, + 205 + ], + "type": "interline_equation", + "content": "\\mathbf {y} \\sim \\pi_ {\\theta} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\cdot \\pi_ {\\theta} (\\mathbf {m} \\mid \\mathbf {x}), \\tag {3}", + "image_path": "75d16e4f13aaf643e0a515b5d8370809cade1a3c547cd2b914de320bdf6d4aa3.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 209, + 504, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 209, + 504, + 230 + ], + "spans": [ + { + "bbox": [ + 104, + 209, + 504, + 230 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 209, + 504, + 230 + ], + "type": "inline_equation", + "content": "\\mathbf{m}" + }, + { + "bbox": [ + 104, + 209, + 504, + 230 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 209, + 504, + 230 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 104, + 209, + 504, + 230 + ], + "type": "text", + "content": " are the output of meta-thinking and reasoning respectively. We present the procedure as shown below:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 230, + 231, + 504, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 230, + 231, + 504, + 246 + ], + "spans": [ + { + "bbox": [ + 230, + 231, + 504, + 246 + ], + "type": "interline_equation", + "content": "\\mathbf {x} \\xrightarrow {\\text {m e t a - t h i n k i n g}} \\mathbf {m} \\xrightarrow {\\text {r e a s o n i n g s t e p s}} \\mathbf {y} \\sim \\mathbf {a}. \\tag {4}", + "image_path": "2a12f2772fbb774a2c76affff4a8b8ba81eda3fe2d809a080d5e4968463bed50.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 248, + 504, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 248, + 504, + 315 + ], + "spans": [ + { + "bbox": [ + 104, + 248, + 504, + 315 + ], + "type": "text", + "content": "Exploring MRP reasoning through a single-agent approach is often inefficient, as it requires the language model to simultaneously master both meta-thinking and detailed problem-solving within one call. Prior research has demonstrated that activating different model capabilities through specialized agents significantly improves MRP exploration efficiency. To leverage this insight, we decouple meta-thinking and reasoning into two separate LLM agents: a high-level agent dedicated to generating meta-thinking, and a low-level agent focused on executing reasoning steps." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 319, + 504, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 319, + 504, + 363 + ], + "spans": [ + { + "bbox": [ + 104, + 319, + 504, + 363 + ], + "type": "text", + "content": "During a conversation, the high-level and low-level agents (i.e., " + }, + { + "bbox": [ + 104, + 319, + 504, + 363 + ], + "type": "inline_equation", + "content": "\\pi_h" + }, + { + "bbox": [ + 104, + 319, + 504, + 363 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 319, + 504, + 363 + ], + "type": "inline_equation", + "content": "\\pi_l" + }, + { + "bbox": [ + 104, + 319, + 504, + 363 + ], + "type": "text", + "content": ") act in an interleaving manner. The high-level agent generates and summarizes meta-thoughts from the prompt and interaction history, while the low-level agent executes detailed problem-solving under those instructions. We formulate the multi-agent meta-thinking reasoning process (MAMRP) as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 245, + 369, + 504, + 381 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 245, + 369, + 504, + 381 + ], + "spans": [ + { + "bbox": [ + 245, + 369, + 504, + 381 + ], + "type": "interline_equation", + "content": "\\mathbf {y} \\sim \\pi_ {l} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\pi_ {h} (\\mathbf {m} \\mid \\mathbf {x}). \\tag {5}", + "image_path": "569e05528f28d9bea18f232e9a85e68383a72aa9deef4c12e625df47568f6c0d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 386, + 504, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 386, + 504, + 430 + ], + "spans": [ + { + "bbox": [ + 104, + 386, + 504, + 430 + ], + "type": "text", + "content": "While the single-turn MAMRP offers a straightforward approach, it lacks the ability to perform immediate and fine-grained cognitive switching during the reasoning process, which limits its effectiveness on complex, long-horizon planning tasks. Therefore, we extend Eq. (5) and formulate the multi-turn MAMRP as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 187, + 435, + 504, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 187, + 435, + 504, + 467 + ], + "spans": [ + { + "bbox": [ + 187, + 435, + 504, + 467 + ], + "type": "interline_equation", + "content": "\\mathbf {y} _ {T} \\sim \\prod_ {t = 1} ^ {T} \\pi_ {l} \\left(\\mathbf {y} _ {t} \\mid \\mathbf {x}, \\{\\mathbf {m}, \\mathbf {y} \\} _ {< t}, \\mathbf {m} _ {t}\\right) \\pi_ {h} \\left(\\mathbf {m} _ {t} \\mid \\mathbf {x}, \\{\\mathbf {m}, \\mathbf {y} \\} _ {< t}\\right) \\tag {6}", + "image_path": "84b1ab344c27fac96d5118e071408306d75ee69bcc10b08024cab4b8d264d754.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 472, + 459, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 472, + 459, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 459, + 484 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 105, + 472, + 459, + 484 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 105, + 472, + 459, + 484 + ], + "type": "text", + "content": " is the number of turns. Similarly, we present the process with a directed graph:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 115, + 491, + 504, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 491, + 504, + 512 + ], + "spans": [ + { + "bbox": [ + 115, + 491, + 504, + 512 + ], + "type": "interline_equation", + "content": "\\mathbf {x} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\mathbf {m} _ {1} \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {1} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\mathbf {m} _ {2} \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {2} \\xrightarrow [ \\pi_ {h} ]{\\text {m e t a - t h i n k i n g}} \\dots \\xrightarrow [ \\pi_ {l} ]{\\text {r e a s o n i n g}} \\mathbf {y} _ {T} \\sim \\mathbf {a}. \\tag {7}", + "image_path": "bb5a0da380958a3094a2173fe72a961587f3d1da6dbe550666ba873b3b27827c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 517, + 504, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 517, + 504, + 539 + ], + "spans": [ + { + "bbox": [ + 104, + 517, + 504, + 539 + ], + "type": "text", + "content": "As a complex reasoning system, MAMRP provides various optimization opportunities in scaling inference-time computation. We leave further discussion of these aspects in Appendix C.1." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 552, + 330, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 552, + 330, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 330, + 563 + ], + "type": "text", + "content": "3.2 Training MAMRP: A Multi-Agent RL Method" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 571, + 504, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 571, + 504, + 605 + ], + "spans": [ + { + "bbox": [ + 104, + 571, + 504, + 605 + ], + "type": "text", + "content": "Multi-agent RL, unlike single-agent RL in a deterministic MDP, must contend with stochastic, nonstationary dynamics and rewards, making optimization more challenging. We start by considering an easier case, the optimization of single-turn MAMRP." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 616, + 279, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 616, + 279, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 279, + 628 + ], + "type": "text", + "content": "3.2.1 Optimizing Single-turn MAMRP" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "spans": [ + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "text", + "content": "To train the system from Sec. 3.1, we embed it as a Markov Game between the two agents. Suppose the two LLM agents are parameterized by " + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "inline_equation", + "content": "\\theta_l" + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "text", + "content": ", respectively. Define a joint hierarchical policy over sequential decisions " + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "inline_equation", + "content": "\\mathbf{m}" + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 104, + 635, + 504, + 669 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 201, + 674, + 504, + 688 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 201, + 674, + 504, + 688 + ], + "spans": [ + { + "bbox": [ + 201, + 674, + 504, + 688 + ], + "type": "interline_equation", + "content": "\\mathbf {y} \\sim \\pi_ {\\left(\\theta_ {h}, \\theta_ {l}\\right)} (\\mathbf {y} \\mid \\mathbf {x}) := \\pi_ {\\theta_ {l}} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}) \\cdot \\pi_ {\\theta_ {h}} (\\mathbf {m} \\mid \\mathbf {x}), \\tag {8}", + "image_path": "5117513c75d33b0d0f28a22b36d95dc4e9851d988c82b7161379bad840154e56.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 693, + 501, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 693, + 501, + 705 + ], + "spans": [ + { + "bbox": [ + 104, + 693, + 501, + 705 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 104, + 693, + 501, + 705 + ], + "type": "inline_equation", + "content": "R(\\mathbf{y}, \\mathbf{y}^*)" + }, + { + "bbox": [ + 104, + 693, + 501, + 705 + ], + "type": "text", + "content": " denote the final reward serves as the objective function " + }, + { + "bbox": [ + 104, + 693, + 501, + 705 + ], + "type": "inline_equation", + "content": "\\mathcal{J}(\\theta_h, \\theta_l)" + }, + { + "bbox": [ + 104, + 693, + 501, + 705 + ], + "type": "text", + "content": " for the joint policy:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 225, + 711, + 504, + 725 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 225, + 711, + 504, + 725 + ], + "spans": [ + { + "bbox": [ + 225, + 711, + 504, + 725 + ], + "type": "interline_equation", + "content": "\\mathcal {J} \\left(\\theta_ {h}, \\theta_ {l}\\right) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\mathbb {E} _ {\\mathbf {y} \\sim \\pi \\left(\\theta_ {h}, \\theta_ {l}\\right)} R (\\mathbf {y}, \\mathbf {y} ^ {*}). \\tag {9}", + "image_path": "05dc13f8590fd0e48920b97ac09cc7f97085627fc9eb5b18c41f8b40a2814e97.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "text", + "content": "4" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 108, 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Parameters" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 211, + 82, + 369, + 213 + ], + "lines": [ + { + "bbox": [ + 211, + 82, + 369, + 213 + ], + "spans": [ + { + "bbox": [ + 211, + 82, + 369, + 213 + ], + "type": "image", + "image_path": "7f3231499e748935cfc4e1cfa6d56049cf9d1cab539e1879a81522875ddbfa66.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 369, + 82, + 503, + 213 + ], + "blocks": [ + { + "bbox": [ + 372, + 70, + 498, + 80 + ], + "lines": [ + { + "bbox": [ + 372, + 70, + 498, + 80 + ], + "spans": [ + { + "bbox": [ + 372, + 70, + 498, + 80 + ], + "type": "text", + "content": "ReMA with Shared Parameters" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 369, + 82, + 503, + 213 + ], + "lines": [ + { + "bbox": [ + 369, + 82, + 503, + 213 + ], + "spans": [ + { + "bbox": [ + 369, + 82, + 503, + 213 + ], + "type": "image", + "image_path": "c1b6f6aaf161ccb2d707eb51858e4b49250221c289f22f7d7fd725b003912a00.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 220, + 504, + 299 + ], + "lines": [ + { + "bbox": [ + 104, + 220, + 504, + 299 + ], + "spans": [ + { + "bbox": [ + 104, + 220, + 504, + 299 + ], + "type": "text", + "content": "Figure 2: Comparison of training pipelines. Left: RL training of VRP and MRP, where a single LM agent is updated either with mixed (VRP) or explicit (MRP) meta-thinking. Middle: ReMA with separate parameters for the high-level (meta-thinking) and low-level (reasoning) agents; training alternates between freezing one agent and updating the other. Right: ReMA with shared parameters and multi-turn interactions: both agents share the same parameters and are distinguished by their system prompts. Training employs a turn-level ratio for stable multi-turn reinforcement learning and efficient updates, ensuring each turn's contribution is controlled to prevent instability." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 312, + 504, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 312, + 504, + 335 + ], + "spans": [ + { + "bbox": [ + 104, + 312, + 504, + 335 + ], + "type": "text", + "content": "During optimization procedure, the high-level policy " + }, + { + "bbox": [ + 104, + 312, + 504, + 335 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta_h}" + }, + { + "bbox": [ + 104, + 312, + 504, + 335 + ], + "type": "text", + "content": " and low-level policy " + }, + { + "bbox": [ + 104, + 312, + 504, + 335 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta_l}" + }, + { + "bbox": [ + 104, + 312, + 504, + 335 + ], + "type": "text", + "content": " aim to maximize their respective rewards independently. The optimization goals for agents are:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 198, + 340, + 504, + 358 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 340, + 504, + 358 + ], + "spans": [ + { + "bbox": [ + 198, + 340, + 504, + 358 + ], + "type": "interline_equation", + "content": "\\theta_ {h} ^ {*} = \\arg \\max _ {\\theta_ {h}} \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\mathbf {m} \\sim \\pi_ {\\theta_ {h}}, \\mathbf {y} \\sim \\pi_ {\\theta_ {l} ^ {*}}} \\left[ R _ {h} (\\mathbf {m}, \\mathbf {y}, \\mathbf {y} ^ {*}) \\right], \\tag {10}", + "image_path": "8113cac550a4f08accd48762ff47f3d3be5dc7819212ee3344ef23f9e79fceb8.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 182, + 360, + 504, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 360, + 504, + 379 + ], + "spans": [ + { + "bbox": [ + 182, + 360, + 504, + 379 + ], + "type": "interline_equation", + "content": "\\theta_ {l} ^ {*} \\left(\\theta_ {h}\\right) = \\arg \\max _ {\\theta_ {l}} \\mathbb {E} _ {\\left(\\mathbf {x}, \\mathbf {y} ^ {*}\\right) \\sim \\mathcal {D}, \\mathbf {m} \\sim \\pi_ {\\theta_ {h}}, \\mathbf {y} \\sim \\pi_ {\\theta_ {l}}} \\left[ R _ {l} \\left(\\mathbf {m}, \\mathbf {y}, \\mathbf {y} ^ {*}\\right) \\right], \\tag {11}", + "image_path": "f891e947f79753d2849f10bbf5382550512e2e05f5f7ecbdcdde601d0bbb9a59.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "spans": [ + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "type": "inline_equation", + "content": "R_{h}" + }, + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "type": "inline_equation", + "content": "R_{l}" + }, + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "type": "text", + "content": " are policies' individual reward functions, including " + }, + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 104, + 385, + 504, + 431 + ], + "type": "text", + "content": " and regularization according to tasks and models, e.g., different format rewards (refer to Appendix C.2 for details). The detailed algorithm is in the Algorithm 1. We illustrate the MAMRP inference procedure and the proposed training method in Fig. 2. We also provide an analysis of different loss functions in Appendix C.5." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 443, + 285, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 443, + 285, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 285, + 455 + ], + "type": "text", + "content": "3.2.2 Scaling up to Multi-turn MAMRP" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 462, + 504, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 462, + 504, + 485 + ], + "spans": [ + { + "bbox": [ + 104, + 462, + 504, + 485 + ], + "type": "text", + "content": "To scale up to multi-turn MAMRP, we can still adopt the iterative training strategy in Sec. 3.2.1. However, we make some changes to improve the efficiency of rollout and training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "spans": [ + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "text", + "content": "First, we implement a parameter-sharing strategy where both high-level and low-level agents utilize identical model weights " + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "text", + "content": ", distinguished only by role-specific system prompts " + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "inline_equation", + "content": "S_{h}" + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "inline_equation", + "content": "S_{l}" + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "text", + "content": ". Formally, we define " + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "inline_equation", + "content": "\\pi_h = \\pi_\\theta (\\cdot |S_h,\\cdot)" + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "inline_equation", + "content": "\\pi_l = \\pi_\\theta (\\cdot |S_l,\\cdot)" + }, + { + "bbox": [ + 104, + 490, + 504, + 556 + ], + "type": "text", + "content": ", sharing the same underlying parameters rather than maintaining separate model instances. This approach eliminates the need for frequent model swapping on GPU during rollout, avoiding inefficient wait times, while enabling larger batch sizes during training to simultaneously optimize policies for both meta-thinking and reasoning roles." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 559, + 504, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 559, + 504, + 592 + ], + "spans": [ + { + "bbox": [ + 104, + 559, + 504, + 592 + ], + "type": "text", + "content": "Second, we propose a multi-turn GRPO with turn-level ratio to address the challenges of multi-turn MAMRP. The trajectory-level averaged objective with turn-level ratio of " + }, + { + "bbox": [ + 104, + 559, + 504, + 592 + ], + "type": "inline_equation", + "content": "\\pi_{l}" + }, + { + "bbox": [ + 104, + 559, + 504, + 592 + ], + "type": "text", + "content": " is defined as (The objective of " + }, + { + "bbox": [ + 104, + 559, + 504, + 592 + ], + "type": "inline_equation", + "content": "\\pi_h" + }, + { + "bbox": [ + 104, + 559, + 504, + 592 + ], + "type": "text", + "content": " is the similar but with different system prompt):" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 597, + 266, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 597, + 266, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 597, + 266, + 612 + ], + "type": "interline_equation", + "content": "\\mathcal {J} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {(\\mathbf {x}, \\mathbf {y} ^ {*}) \\sim \\mathcal {D}, \\{(\\mathbf {m} _ {i}, \\mathbf {y} _ {i}) \\} _ {i = 1} ^ {G} \\sim \\pi_ {\\theta_ {\\mathrm {o l d}}} (\\cdot | \\mathbf {x})", + "image_path": "c2c45f6b75a3ecd7f886ca7735670f089d1dde49eae53b3ba52d5a768506d3ab.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 126, + 614, + 504, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 614, + 504, + 654 + ], + "spans": [ + { + "bbox": [ + 126, + 614, + 504, + 654 + ], + "type": "interline_equation", + "content": "\\left. \\left[ \\frac {1}{G} \\sum_ {i = 1} ^ {G} \\frac {1}{T _ {i}} \\sum_ {t = 1} ^ {T _ {i}} \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} \\left(\\min \\left(r _ {i, t} (\\theta) \\hat {A} _ {i, t, j}, \\operatorname {c l i p} \\left(r _ {i, t} (\\theta), 1 - \\epsilon , 1 + \\epsilon\\right) \\hat {A} _ {i, t, j}\\right) - \\beta D _ {\\mathrm {K L}} \\left(\\pi_ {\\theta} \\| \\pi_ {\\text {r e f}}\\right)\\right) \\right] \\right. \\tag {12}", + "image_path": "1bc2c9d3ff1fdd6b7268585f52555fec4647ff246738072f074f516e6a129d24.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{i,t,j}" + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "text", + "content": "-th token at turn " + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "text", + "content": " of the reasoning agent of the " + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 105, + 654, + 504, + 677 + ], + "type": "text", + "content": "-th trajectory. And the turn-level ratio for clipping is defined as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 116, + 685, + 504, + 719 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 685, + 504, + 719 + ], + "spans": [ + { + "bbox": [ + 116, + 685, + 504, + 719 + ], + "type": "interline_equation", + "content": "r _ {i, t} (\\theta) = \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} r _ {i, t, j} (\\theta) = \\frac {1}{| \\mathbf {y} _ {i , t} |} \\sum_ {j = 1} ^ {| \\mathbf {y} _ {i, t} |} \\frac {\\pi_ {\\theta} \\left(\\mathbf {y} _ {i , t , j} \\mid \\mathbf {x} , \\left\\{\\mathbf {m} _ {i , ,} , \\mathbf {y} _ {i ,} \\right\\} _ {< t} , \\mathbf {m} _ {i , t} , \\mathbf {y} _ {i , t , < j}\\right)}{\\pi_ {\\theta_ {\\mathrm {o l d}}} \\left(\\mathbf {y} _ {i , t , j} \\mid \\mathbf {x} , \\left\\{\\mathbf {m} _ {i , ,}, \\mathbf {y} _ {i ,} \\right\\} _ {< t} , \\mathbf {m} _ {i , t} , \\mathbf {y} _ {i , t , < j}\\right)}. \\tag {13}", + "image_path": "fdfa8f8cf4f66137f42c7aba7c2e2ef31d21edf331150f3efd0c1f3325151c96.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "text", + "content": "5" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 128 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 128 + ], + "type": "text", + "content": "The introduction of the turn-level ratio serves two key purposes. First, using a token-level ratio (Eq. (2)) in the objective introduces bias for multi-turn training, as it averages over all tokens in a trajectory. This means that tokens within longer turns (those containing more tokens) can disproportionately influence the overall loss, and averaging at the token level may encourage excessively long single-turn responses. Second, clipping each token independently risks instability during training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 133, + 506, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 133, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 104, + 133, + 506, + 189 + ], + "type": "text", + "content": "In contrast, the turn-level ratio aligns more closely with the underlying MDP formulation by treating all tokens within a turn as a single action and applying clipping at the turn level. Intuitively, this approach stabilizes training by preventing the LLM from making unstable updates that could result in extreme outputs, such as overly long repetitions or incoherent text. We conduct experimental verification in subsequent empirical results (Sec. 4.3)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 205, + 192, + 218 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 205, + 192, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 192, + 218 + ], + "type": "text", + "content": "4 Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 231, + 504, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 231, + 504, + 275 + ], + "spans": [ + { + "bbox": [ + 104, + 231, + 504, + 275 + ], + "type": "text", + "content": "To evaluate the effectiveness and efficiency of ReMA, we conduct experiments on challenging benchmarks for two types of tasks: mathematical reasoning and LLM-as-a-Judge with three different LLMs. Then, we investigate the models' performance in both single- & multi-turn settings. Finally, we provide ablation studies and qualitative analyses of our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 289, + 218, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 289, + 218, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 218, + 301 + ], + "type": "text", + "content": "4.1 Experiment Settings" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 310, + 504, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 310, + 504, + 355 + ], + "spans": [ + { + "bbox": [ + 104, + 310, + 504, + 355 + ], + "type": "text", + "content": "We first analyze the single-turn case of ReMA, i.e., " + }, + { + "bbox": [ + 104, + 310, + 504, + 355 + ], + "type": "inline_equation", + "content": "T = 1" + }, + { + "bbox": [ + 104, + 310, + 504, + 355 + ], + "type": "text", + "content": ". The high-level agent generates a complete meta-thinking trace in one shot, and the low-level agent follows the instructions and outputs the final results. Single-turn ReMA reduces stochasticity and training cost while our experiments show that it still provides meaningful performance gains." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 368, + 504, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 368, + 504, + 434 + ], + "spans": [ + { + "bbox": [ + 104, + 368, + 504, + 434 + ], + "type": "text", + "content": "Benchmarks We conduct experiments on two types of tasks: mathematical reasoning and LLM-as-a-Judge. For mathematical reasoning experiments, we train models on 7.5k training samples in MATH [Hendrycks et al., 2021] and use MATH500 [Lightman et al., 2023] as the in-distribution test dataset. Additionally, we test the optimized models on out-of-distribution datasets: GSM8K [Cobbe et al., 2021], AIME24" + }, + { + "bbox": [ + 104, + 368, + 504, + 434 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 104, + 368, + 504, + 434 + ], + "type": "text", + "content": ", AMC23" + }, + { + "bbox": [ + 104, + 368, + 504, + 434 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 104, + 368, + 504, + 434 + ], + "type": "text", + "content": ", GaoKao2023En [Zhang et al., 2023], Minerva Math [Lewkowycz et al., 2022], and Olympiad Bench [He et al., 2024]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 438, + 504, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 438, + 504, + 494 + ], + "spans": [ + { + "bbox": [ + 104, + 438, + 504, + 494 + ], + "type": "text", + "content": "For LLM-as-a-Judge benchmarks, we train models on RewardBench [Lambert et al., 2024]. Specifically, we convert the original data into a pair-ranking format and split it into a training set of 5k items and a test set of 970 items, denoted as RewardBench970. The models are also tested on JudgeBench [Tan et al., 2024] to assess out-of-distribution performance. We refer to Appendix D.1.2 for detailed comparisons and results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 507, + 504, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 507, + 504, + 552 + ], + "spans": [ + { + "bbox": [ + 104, + 507, + 504, + 552 + ], + "type": "text", + "content": "Baselines, Models, Training Settings We compare pass@1 performance across the following methods: (1) VRP (CoT, step-by-step prompting, Sec. 3.1); (2) " + }, + { + "bbox": [ + 104, + 507, + 504, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{VRP}_{\\mathbf{RL}}" + }, + { + "bbox": [ + 104, + 507, + 504, + 552 + ], + "type": "text", + "content": " (RL under VRP); (3) " + }, + { + "bbox": [ + 104, + 507, + 504, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{MRP}_{\\mathbf{RL}}" + }, + { + "bbox": [ + 104, + 507, + 504, + 552 + ], + "type": "text", + "content": " (RL under MRP with high-level task analysis, Eq. (4)), and (4) ReMA (ours, RL under MAMRP, Eq. (7))." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 555, + 504, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 555, + 504, + 634 + ], + "spans": [ + { + "bbox": [ + 104, + 555, + 504, + 634 + ], + "type": "text", + "content": "We train and test Llama-3-8B-Instruct, Llama-3.1-8B-Instruct [Dubey et al., 2024], and Qwen2.5-7B-Instruct [Team, 2024] on mathematical reasoning benchmarks. For LLM-as-a-judge benchmarks, we train and test Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct. We use instruct-tuned LLMs to prompt them to perform VRP, MRP, and MAMRP directly during training. Unless specified, we use two separate copies of the same model for high- and low-level agents in ReMA. We use the base reward setting in Appendix C.2 by default. And for the underlying RL algorithm, we use REINFORCE++ [Hu, 2025]. We refer to Appendix D for detailed training settings." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 647, + 254, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 647, + 254, + 659 + ], + "spans": [ + { + "bbox": [ + 105, + 647, + 254, + 659 + ], + "type": "text", + "content": "4.2 Results of Single-turn ReMA" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 669, + 504, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 669, + 504, + 691 + ], + "spans": [ + { + "bbox": [ + 104, + 669, + 504, + 691 + ], + "type": "text", + "content": "Question 1. Does single-turn ReMA outperforms baselines on both in-distribution and out-of-distribution test sets?" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 116, + 700, + 436, + 711 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 700, + 436, + 711 + ], + "spans": [ + { + "bbox": [ + 116, + 700, + 436, + 711 + ], + "type": "text", + "content": "4https://huggingface.co/datasets/AI-MO/aimo-validation-aime" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 118, + 712, + 431, + 721 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 712, + 431, + 721 + ], + "spans": [ + { + "bbox": [ + 118, + 712, + 431, + 721 + ], + "type": "text", + "content": "5https://huggingface.co/datasets/AI-MO/aimo-validation-amc" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "text", + "content": "6" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 79, + 504, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 79, + 504, + 122 + ], + "spans": [ + { + "bbox": [ + 104, + 79, + 504, + 122 + ], + "type": "text", + "content": "Table 1: Performance on in-distribution test sets and out-of-distribution test sets. We also report the improvement/degradation w.r.t. basic CoT performance(VRP). On average, ReMA outperforms all baselines. Particularly on out-of-distribution datasets, ReMA achieves the highest performance on most of the benchmarks." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 126, + 137, + 485, + 427 + ], + "blocks": [ + { + "bbox": [ + 236, + 125, + 373, + 134 + ], + "lines": [ + { + "bbox": [ + 236, + 125, + 373, + 134 + ], + "spans": [ + { + "bbox": [ + 236, + 125, + 373, + 134 + ], + "type": "text", + "content": "(a) Performance on math benchmarks" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 126, + 137, + 485, + 427 + ], + "lines": [ + { + "bbox": [ + 126, + 137, + 485, + 427 + ], + "spans": [ + { + "bbox": [ + 126, + 137, + 485, + 427 + ], + "type": "table", + "html": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3-8B-InstructMATH50030.8033.40 (+2.60)32.80 (+2.00)33.80 (+3.00)
GSM8K67.4881.80 (+14.32)79.68 (+12.20)79.38 (+11.90)
AIME240.000.00 (+0.00)3.33 (+3.33)0.00 (+0.00)
AMC232.5010.00 (+7.50)12.50 (+10.00)22.50 (+20.00)
Gaokao2023en22.3427.53 (+5.19)23.38 (+1.04)28.57 (+6.23)
Minerva Math8.8216.54 (+7.72)18.01 (+9.19)13.97 (+5.15)
Olympiad Bench8.448.89 (+0.45)9.33 (+0.89)8.89 (+0.45)
Average20.0525.45 (+5.40)25.58 (+5.53)26.73 (+6.68)
Llama3.1-8B-InstructMATH50050.8050.20 (-0.60)48.60 (-2.20)53.20 (+2.40)
GSM8K86.0584.53 (-1.52)85.37 (-0.68)87.26 (+1.21)
AIME2410.003.33 (-6.67)6.67 (-3.33)13.33 (+3.33)
AMC2327.5012.50 (-15.00)30.00 (+2.50)20.00 (-7.50)
Gaokao2023en38.9636.10 (-2.86)37.14 (-1.82)37.14 (-1.82)
Minerva Math22.7926.84 (+4.05)25.37 (+2.58)28.31 (+5.52)
Olympiad Bench15.1119.70 (+4.59)15.70 (+0.59)19.56 (+4.45)
Average35.8933.32 (-2.57)35.55 (-0.34)36.97 (+1.08)
Qwen2.5-7B-InstructMATH50075.0077.20 (+2.20)76.40 (+1.40)74.40 (-0.60)
GSM8K92.0491.36 (-0.68)91.81 (-0.23)90.60 (-1.44)
AIME246.676.67 (+0.00)10.00 (+3.33)20.00 (+13.33)
AMC2347.5050.00 (+2.50)52.50 (+5.00)57.50 (+10.00)
Gaokao2023en56.6254.81 (-1.81)55.06 (-1.56)57.92 (+1.30)
Minerva Math35.6634.93 (-0.73)32.35 (-3.31)34.93 (-0.73)
Olympiad Bench38.2238.37 (+0.15)37.78 (-0.44)36.30 (-1.92)
Average50.2450.48 (+0.24)50.84 (+0.60)53.09 (+2.85)
", + "image_path": "032ea026c484b25fb0540e17ead1ad673917359410de718a424734cd30d558a2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 124, + 445, + 486, + 553 + ], + "blocks": [ + { + "bbox": [ + 215, + 434, + 395, + 444 + ], + "lines": [ + { + "bbox": [ + 215, + 434, + 395, + 444 + ], + "spans": [ + { + "bbox": [ + 215, + 434, + 395, + 444 + ], + "type": "text", + "content": "(b) Performance on LLM-as-a-Judge benchmarks" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 124, + 445, + 486, + 553 + ], + "lines": [ + { + "bbox": [ + 124, + 445, + 486, + 553 + ], + "spans": [ + { + "bbox": [ + 124, + 445, + 486, + 553 + ], + "type": "table", + "html": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3.1-8B-InstructRewardBench97069.4882.89 (+13.41)81.13 (+11.65)83.71 (+14.23)
JudgeBench51.2951.94 (+0.65)52.90 (+1.61)52.90 (+1.61)
Average60.3967.41 (+7.02)67.02 (+6.63)68.31 (+7.92)
Qwen2.5-7B-InstructRewardBench97078.5685.36 (+6.80)86.49 (+7.93)83.51 (+4.95)
JudgeBench58.3956.94 (-1.45)58.39 (+0.00)56.94 (-1.45)
Average68.4771.15 (+2.68)72.44 (+3.97)70.22 (+1.75)
", + "image_path": "71aca539c79024c7c54c8b500119e08584e1cf23534f6bae0662ad5dc7fbc4aa.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 585, + 504, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 585, + 504, + 629 + ], + "spans": [ + { + "bbox": [ + 104, + 585, + 504, + 629 + ], + "type": "text", + "content": "Table 1 compares the greedy decoding performance of ReMA against various RL baselines across mathematical benchmarks (Table 1a) and LLM-as-a-Judge benchmarks (Table 1b). Results across different LLMs indicate that, on average, ReMA outperforms all baselines, achieving a maximum improvement of " + }, + { + "bbox": [ + 104, + 585, + 504, + 629 + ], + "type": "inline_equation", + "content": "6.68\\%" + }, + { + "bbox": [ + 104, + 585, + 504, + 629 + ], + "type": "text", + "content": " on mathematical benchmarks and " + }, + { + "bbox": [ + 104, + 585, + 504, + 629 + ], + "type": "inline_equation", + "content": "8.49\\%" + }, + { + "bbox": [ + 104, + 585, + 504, + 629 + ], + "type": "text", + "content": " on LLM-as-a-Judge benchmarks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "type": "text", + "content": "Notably, ReMA achieves the highest performance on most benchmarks, particularly on out-of-distribution datasets, with a maximum improvement of " + }, + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "type": "text", + "content": " on AMC23 for Llama3-8B-Instruct, " + }, + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "type": "inline_equation", + "content": "13.33\\%" + }, + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "type": "text", + "content": " on AIME24 for Qwen2.5-7B-Instruct, " + }, + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "type": "inline_equation", + "content": "14.23\\%" + }, + { + "bbox": [ + 104, + 634, + 504, + 722 + ], + "type": "text", + "content": " on RewardBench970 for Llama3.1-8B-Instruct. These results demonstrate the superior out-of-distribution generalization ability conferred by the meta-thinking mechanism in ReMA. However, we observe that the accuracy gains from RL training on instruction-tuned LMs are smaller than from base models (Sec. 4.2.1). This may be due to the higher initial performance and the relatively fixed output distribution of instruction-tuned models, which limits the improvement and peak performance in RL." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "text", + "content": "7" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 114, + 65, + 495, + 205 + ], + "blocks": [ + { + "bbox": [ + 114, + 65, + 495, + 205 + ], + "lines": [ + { + "bbox": [ + 114, + 65, + 495, + 205 + ], + "spans": [ + { + "bbox": [ + 114, + 65, + 495, + 205 + ], + "type": "image", + "image_path": "37ed86a4d76064b8e7dc589771be62484945d0a0fbaf36c2bdeedac73830355d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 211, + 504, + 234 + ], + "lines": [ + { + "bbox": [ + 104, + 211, + 504, + 234 + ], + "spans": [ + { + "bbox": [ + 104, + 211, + 504, + 234 + ], + "type": "text", + "content": "Figure 3: An RL experiment with 3 training schemes. While RL from SFT excels on easier problems, RL under Meta-thinking shows superior generalization to harder problems like AIME24." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 106, + 239, + 297, + 331 + ], + "blocks": [ + { + "bbox": [ + 106, + 239, + 297, + 331 + ], + "lines": [ + { + "bbox": [ + 106, + 239, + 297, + 331 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 297, + 331 + ], + "type": "image", + "image_path": "7cef31214b1e22f8feceb774c7c2fda0d8822a64668c93c676a445aa329e03c2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 335, + 504, + 359 + ], + "lines": [ + { + "bbox": [ + 104, + 335, + 504, + 359 + ], + "spans": [ + { + "bbox": [ + 104, + 335, + 504, + 359 + ], + "type": "text", + "content": "Figure 4: Average problem difficulty by action type during training. Left: 1B LM collapses to the EMPTY action. Right: 8B LM adapts to a more complex meta-thinking strategy for harder problems." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 309, + 239, + 501, + 332 + ], + "blocks": [ + { + "bbox": [ + 309, + 239, + 501, + 332 + ], + "lines": [ + { + "bbox": [ + 309, + 239, + 501, + 332 + ], + "spans": [ + { + "bbox": [ + 309, + 239, + 501, + 332 + ], + "type": "image", + "image_path": "8067de4a34648160295745db52239f10161f855ef4f748f78627686ff344515e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 371, + 329, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 371, + 329, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 329, + 384 + ], + "type": "text", + "content": "4.2.1 Meta-thoughts boost low-level generalization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 391, + 334, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 391, + 334, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 391, + 334, + 403 + ], + "type": "text", + "content": "Question 2. Can Reasoning benefit from Meta-thinking?" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 407, + 504, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 407, + 504, + 485 + ], + "spans": [ + { + "bbox": [ + 104, + 407, + 504, + 485 + ], + "type": "text", + "content": "Here we provide a tiny but motivating example of how ReMA gives better learning dynamics. We use Qwen2.5-Math-7B [Yang et al., 2024] as the starting base model, MATH (level 3-5, about " + }, + { + "bbox": [ + 104, + 407, + 504, + 485 + ], + "type": "inline_equation", + "content": "5.5\\mathrm{K}" + }, + { + "bbox": [ + 104, + 407, + 504, + 485 + ], + "type": "text", + "content": " number of instances) as the training dataset, and we compare three reinforcement learning training schemes, in particular: (1) RL from Base: train the base model directly on MATH with binary outcome reward; (2) RL from SFT: SFT the base model with GPT-4o's CoT answers; then RL on train dataset with binary outcome reward; (3) RL under Meta-thinking: SFT the base model with GPT-4o's meta-thinking plans; then RL on train dataset with binary outcome reward." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 490, + 504, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 490, + 504, + 534 + ], + "spans": [ + { + "bbox": [ + 104, + 490, + 504, + 534 + ], + "type": "text", + "content": "The models are evaluated on 3 benchmarks (Fig. 3). SFT brings the best initial accuracy on in-distribution and easier sets, but fails to improve on harder ones. RL from Base yields limited gains. In contrast, RL under Meta-thinking achieves the best learning dynamics and generalizes better to challenging problems (AIME24). See Appendix F.1 for case studies." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 548, + 337, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 548, + 337, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 548, + 337, + 561 + ], + "type": "text", + "content": "4.2.2 Diverse meta-thinking characteristics of LLMs" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 568, + 324, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 568, + 324, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 324, + 580 + ], + "type": "text", + "content": "Question 3. How well can LLMs learn to meta-think?" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 585, + 504, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 585, + 504, + 662 + ], + "spans": [ + { + "bbox": [ + 104, + 585, + 504, + 662 + ], + "type": "text", + "content": "To further analyze meta-thinking behaviors, we train models with structured JSON-format actions inspired by Yue et al.. The meta-thinking agent generate two entries in one LM call, first selects from three actions: DECOMPOSE (breaking into subproblems), REWRITE (simplifying the problem), or EMPTY (direct solving), then generates the corresponding text. We compare Llama-3.1-8B-Instruct and Llama-3.2-1B-Instruct to study scale effects (two 1B models vs two 8B models) on meta-thinking agent's training. We use vLLM guided JSON decoding [Dong et al., 2024] for valid formatting and base reward (reasoning agent's solution accuracy with format constraints)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 667, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 667, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 667, + 504, + 723 + ], + "type": "text", + "content": "We observe that smaller LMs produce simpler outputs, likely due to limited capacity to maintain valid JSON formatting while exploring diverse reasoning strategies. As Fig. 4 shows, smaller LMs like Llama-3.2-1B-Instruct quickly converge to the simplest EMPTY action to avoid formatting penalties, while larger LMs like Llama-3.1-8B-Instruct can adapt meta-thinking strategies based on problem difficulty. See Appendix F.3 for detailed case studies." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "text", + "content": "8" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 62, + 286, + 167 + ], + "blocks": [ + { + "bbox": [ + 108, + 62, + 286, + 167 + ], + "lines": [ + { + "bbox": [ + 108, + 62, + 286, + 167 + ], + "spans": [ + { + "bbox": [ + 108, + 62, + 286, + 167 + ], + "type": "image", + "image_path": "7be77f52a452cae631a3999a5c1a37f14186bd400761aa6b2200170fc2818d62.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 170, + 504, + 204 + ], + "lines": [ + { + "bbox": [ + 104, + 170, + 504, + 204 + ], + "spans": [ + { + "bbox": [ + 104, + 170, + 504, + 204 + ], + "type": "text", + "content": "Figure 5: Training results of multi-turn Figure 6: Ablations of multi-turn ReMA on a tiny subReMA on MATH-Level3-5-8K under different set of MATH, we only show here the training curves of different training and rollout configurations." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 295, + 62, + 503, + 167 + ], + "blocks": [ + { + "bbox": [ + 295, + 62, + 503, + 167 + ], + "lines": [ + { + "bbox": [ + 295, + 62, + 503, + 167 + ], + "spans": [ + { + "bbox": [ + 295, + 62, + 503, + 167 + ], + "type": "image", + "image_path": "0a12a930e142fe2cdce1144a9d1bcf93a65808b7f66fd19e01bc8a6c088ffc04.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 228, + 307, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 228, + 307, + 241 + ], + "spans": [ + { + "bbox": [ + 104, + 228, + 307, + 241 + ], + "type": "text", + "content": "4.3 Extending ReMA to Multi-turn MAMRP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 255, + 504, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 255, + 504, + 278 + ], + "spans": [ + { + "bbox": [ + 104, + 255, + 504, + 278 + ], + "type": "text", + "content": "We further extend ReMA to multi-turn MAMRP settings, enabling multiple rounds of interaction between the meta-thinking agent and the reasoning agent as defined in Eq. (7)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 282, + 504, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 282, + 504, + 327 + ], + "spans": [ + { + "bbox": [ + 104, + 282, + 504, + 327 + ], + "type": "text", + "content": "Unlike the inherent VRP capabilities of most LLMs, multi-turn ReMA requires initial bootstrapping. Thus, we constructed a supervised fine-tuning dataset (about 0.8K samples) from LIMO [Ye et al., 2025c] using GPT-4o to establish the starting point for multi-turn interaction capabilities. Then we finetune Qwen2.5-7B before RL training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 331, + 504, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 331, + 504, + 376 + ], + "spans": [ + { + "bbox": [ + 104, + 331, + 504, + 376 + ], + "type": "text", + "content": "As described in Sec.3.2.2, we deploy the proposed GRPO with turn-level ratio clipping and trajectory-level averaging loss during training. And we remove the KL-divergence term to allow more flexible exploration. By default, the agents share the same parameters and are simultaneously updated using their trajectories. We refer to details in Appendix D.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 402, + 231, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 402, + 231, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 231, + 414 + ], + "type": "text", + "content": "4.3.1 Results and Ablations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 426, + 334, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 426, + 334, + 439 + ], + "spans": [ + { + "bbox": [ + 104, + 426, + 334, + 439 + ], + "type": "text", + "content": "Question 4. Can ReMA be scaled to multi-turn settings?" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "spans": [ + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "type": "text", + "content": "There are two key points revealed by our multi-turn ReMA experiments, as shown in Fig. 5. On one hand, the algorithm can demonstrate effective convergence on the training set, with accuracy steadily increasing from approximately " + }, + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "type": "inline_equation", + "content": "55\\%" + }, + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "type": "text", + "content": " during training. It also achieves an average performance gain of about " + }, + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 104, + 443, + 504, + 510 + ], + "type": "text", + "content": " across all seven test benchmarks, indicating stable improvements on out-of-distribution data. (Experiment with the rollout config of turn30_token512, see Appendix D.2.2 and Fig. 8 for more details.)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 514, + 505, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 514, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 104, + 514, + 505, + 613 + ], + "type": "text", + "content": "On the other hand, we observe that the performance of multi-turn ReMA is highly sensitive to hyperparameters such as the maximum response length per turn and the maximum number of turns. For certain configurations, the model either collapses into producing massive repetitions within a single turn or generates empty responses after only a few turns. Similar phenomena have been reported in concurrent works such as RAGEN [Wang et al., 2025], where these issues are attributed to the lack of fine-grained, reasoning-aware guidance. As a result, multi-turn RL becomes susceptible to long-horizon credit assignment challenges and state drift, often leading to reduced exploration diversity—a phenomenon referred to as the \"Echo Trap\". To address this challenge, it is essential to comprehensively explore the training recipe w.r.t. model, data, and algorithm." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 617, + 457, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 617, + 457, + 630 + ], + "spans": [ + { + "bbox": [ + 104, + 617, + 457, + 630 + ], + "type": "text", + "content": "Question 5. How does parameter sharing and turn-level ratio affect multi-turn ReMA?" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 634, + 505, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 634, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 634, + 505, + 723 + ], + "type": "text", + "content": "As shown in Fig. 6, we compare different configurations on a smaller dataset consisting of 133 samples—19 from each of the 7 MATH problem types—to evaluate sample efficiency and convergence speed. First, all configurations eventually achieve nearly " + }, + { + "bbox": [ + 104, + 634, + 505, + 723 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 104, + 634, + 505, + 723 + ], + "type": "text", + "content": " accuracy on the training dataset. Notably, the trajectory-level loss with turn-level ratio (Turn-Ratio, Eq. (13)) demonstrates substantially better sample efficiency than its token-level variants (Eq. (2)), reaching higher training rewards with fewer steps. We also present the training curve of separate weight setting, the empirical results show that shared parameters with simultaneous updates converge noticeably faster." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "text", + "content": "9" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 107, + 72, + 183, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 72, + 183, + 83 + ], + "spans": [ + { + "bbox": [ + 107, + 72, + 183, + 83 + ], + "type": "text", + "content": "5 Conclusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 107, + 95, + 504, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 95, + 504, + 216 + ], + "spans": [ + { + "bbox": [ + 107, + 95, + 504, + 216 + ], + "type": "text", + "content": "In this paper, we introduced ReMA, a novel framework that leverages multi-agent reinforcement learning to elicit meta-thinking in large language models. By explicitly separating meta-thinking and reasoning processes into distinct agents, our approach enhances both exploration during training and the interpretability of model outputs. We tailored RL algorithms and reward functions to ensure reliable performance. Through comprehensive experiments on mathematical reasoning and LLM-as-a-Judge benchmarks, ReMA consistently achieved superior results, particularly on out-of-distribution datasets. We further extend ReMA to multi-turn settings, enabling the framework to handle more complex reasoning scenarios that require more communication between agents. Our ablations demonstrate how effective coordination between agents evolves, highlighting the promise of reinforcement learning and structured agents' collaboration for advancing the capabilities of language models in complex reasoning tasks." + } + ] + } + ], + "index": 1 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 301, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 301, + 741, + 310, + 750 + ], + "type": "text", + "content": "10" + } + ] + } + ], + "index": 2 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + }, + { + "para_blocks": [ + { + "bbox": [ + 106, + 71, + 165, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 71, + 165, + 84 + ], + "spans": [ + { + "bbox": [ + 106, + 71, + 165, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 89, + 505, + 723 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 105, + 89, + 505, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 89, + 505, + 124 + ], + "spans": [ + { + "bbox": [ + 105, + 89, + 505, + 124 + ], + "type": "text", + "content": "Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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32 + }, + { + "bbox": [ + 150, + 438, + 504, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 438, + 504, + 449 + ], + "spans": [ + { + "bbox": [ + 150, + 438, + 504, + 449 + ], + "type": "text", + "content": "- F.3 Case study for Adaptive Meta-thinking in Single-Turn ReMA in Section 4.2.2 30" + } + ] + } + ], + "index": 33 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 132, + 453, + 504, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 453, + 504, + 464 + ], + "spans": [ + { + "bbox": [ + 132, + 453, + 504, + 464 + ], + "type": "text", + "content": "G Prompts 31" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 479, + 197, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 479, + 197, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 197, + 491 + ], + "type": "text", + "content": "A Related work" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 502, + 506, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 502, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 104, + 502, + 506, + 581 + ], + "type": "text", + "content": "Drawing from the bitter lesson [Sutton, 2019], two methods that appear to scale effectively are searching and learning, aligning with current trends in large language models [Xu et al., 2025]. At present, researchers are leveraging these methods to maximize the capabilities of individual transformers, while other efforts are exploring architectures that involve multiple interacting entities. In this paper, we examine this divergence within the context of LLM reasoning, a capability that allows large language models to solve problems through logical reasoning, step-by-step analysis, and inference [Wang et al., 2024a]." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 592, + 231, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 592, + 231, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 231, + 605 + ], + "type": "text", + "content": "A.1 Single LLM Reasoning" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "type": "text", + "content": "Main research works in reasoning involving a single LLM utilize search-based and post-training methods. The fundamental elements of searching methods are text generation and evaluation. Generation schemes include In-Context Learning [Brown et al., 2020], Beam Search [Graves, 2012], and various tree-based searching [Snell et al., 2024]; Evaluation approaches often use outcome accuracy, self-consistency [Wang et al., 2022], or process reward signal [Lightman et al., 2023] as the criteria to select high-quality responses from the generated texts. Post-training method is another research line in opposition to pre-training. Popular training pipelines often involve specific data construction followed by Supervised Fine-tuning [Qin et al., 2024, Ouyang et al., 2022, Hui et al., 2024, Liu et al., 2024], or reinforcement learning to interactively explore learning patterns [Wang et al., 2024a, Zhang et al., 2024a, DeepSeek-AI et al., 2025, Xu et al., 2025]." + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 300, + 741, + 311, + 750 + ], + "type": "text", + "content": "19" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 18 + }, + { + "para_blocks": [ + { + "bbox": [ + 107, + 73, + 241, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 73, + 241, + 83 + ], + "spans": [ + { + "bbox": [ + 107, + 73, + 241, + 83 + ], + "type": "text", + "content": "A.2 Multiple LLM Reasoning" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 107, + 95, + 504, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 95, + 504, + 445 + ], + "spans": [ + { + "bbox": [ + 107, + 95, + 504, + 445 + ], + "type": "text", + "content": "Integrating multiple entities can potentially surpass the intelligence of the individual model [Chen et al., 2023]. With the rapid emergence of large language models showing a varying level of abilities, some studies have explored facilitating discussions among multiple off-the-shelf LLMs [Zhang et al., 2025a, Chen et al., 2024a, Wang et al., 2023, Du et al., 2023, Zhuge et al., 2023, Tang et al., 2023, Hao et al., 2025, Akata et al., 2023, Hong et al., 2023, Zhang et al., 2024b], taking the form of free discussion [Du et al., 2023, Liang et al., 2023] or structured role assignments [Hong et al., 2023, Zhang et al., 2024b]. Some have applied routing mechanisms to assign tasks to the most suitable expert models [Hu et al., 2024b, Stripelis et al., 2024, Ding et al., 2024, Yue et al., 2025a, Chen et al., 2024c] or merging mechanisms to develop more versatile models [Yadav et al., 2024, Yu et al., 2024, Zhang et al., 2025b]. Beyond aggregating static knowledge from multiple agents, multi-agent LLM training can also enhance reasoning capabilities. For example, multi-agent debates can generate diverse synthetic data, which can subsequently be used for supervised fine-tuning [Estornell et al., 2024, Li et al., 2024, Motwani et al., 2024, Dong and Ma, 2025, Perez et al., 2022, Ye et al., 2025a, Subramaniam et al., 2025]. Reinforcement learning (RL) methods have also been adopted to improve LLM reasoning in areas such as alignment [Perez et al., 2022, Ma et al., 2023] and legibility [Kirchner et al., 2024]. Motwani et al. [2024] utilize a three-agent system for generation and fine-tune the models using Direct Preference Optimization (DPO). Reinforcement Learning with Generative Reward Models (GenRM) [Mahan et al., 2024, Ye et al., 2025b, Jiao et al., 2024, Wang et al., 2024b] represents another common approach of multi-agent training, where the reward signal is derived from the token probabilities of another LLM, coupled with the reasoning process. While our work aligns with these efforts, it diverges by using an additional tunable LLM to provide metacognitive instructions, guiding the low-level LLM during learning, rather than relying on a static GenRM. The most closely related works to ours are MAPoRL [Park et al., 2025] and COPYR [Ma et al., 2024]. MAPoRL is a multi-agent debating framework that uses multi-agent reinforcement learning (MARL) with a learned verifier to fine-tune each LLM agent. COPYR duplicates an LLM into two agents, training them simultaneously in the roles of pioneer and observer using RL. Shen et al. [2025] trained with a novel Chain-of-Action-Thought (COAT) framework that embeds meta-action tokens for self-reflection and exploration into an autoregressive search process. However, unlike our approach, which explicitly separates metacognition from plan execution, these methods do not decompose the reasoning process but instead focus on improving direct chain-of-thought generation. Furthermore, our experiments are conducted on a larger scale and include more challenging problems." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 107, + 469, + 232, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 469, + 232, + 479 + ], + "spans": [ + { + "bbox": [ + 107, + 469, + 232, + 479 + ], + "type": "text", + "content": "A.3 Hierarchical Reasoning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 491, + 504, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 491, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 107, + 491, + 504, + 721 + ], + "type": "text", + "content": "Partitioning reasoning into hierarchical processes has been explored in prior research to make biological sense [Ye et al., 2018, Langley et al., 2004]. In the context of language models, a hierarchical structure has been used to facilitate diverse reasoning patterns, including planning [Puerta-Merino et al., 2025, Sun et al., 2024, Song et al., 2023, Rana et al., 2023, Chen et al., 2024d, Yan et al., 2023, Xiao et al., 2024], validation [Haji et al., 2024, Xi et al., 2024] and self-refinement [Madaan et al., 2023, Kumar et al., 2024, Welleck et al., 2022]. For instance, EvalPlanner [Saha et al., 2025b] is a framework that conducts reasoning through plan generation and execution. DOTS [Yue et al., 2024] extends decomposition by integrating a tree-based searching method with Analysis, Solution, and Verification layers. Marco-o1 [Zhao et al., 2024] focuses on open-ended problem-solving and abstract thinking, dynamically adjusting reasoning granularity and incorporating reflection mechanisms to enhance reasoning performance. Beyond these approaches, metacognition [Flavell, 1979] has been identified as another critical component of reasoning, referring to the intuitive understanding of one's own cognitive and reasoning processes [Gao et al., 2024, Wang and Zhao, 2023]. Wang and Zhao [2023] proposed a metacognitive prompting strategy to improve large language model (LLM) capabilities. Didolkar et al. [2024] further developed a prompt-guided method that enables models to label math problems with the required skills and subsequently use these labels to solve new problems. Gao et al. [2024] introduce meta-reasoner which use contextual multi-arm bandit to learn a high-level \"advisor\" over low-level reasoning process. Xiang et al. [2025] provides a Meta-CoT framework to think about its own thinking. They use construction-based methods as well as reinforcement learning to develop meta-cognitive skills. Qingsong et al. [2025] introduces a RL framework for dynamic instruction selection during fine-tuning. In our work, we also value reflect-" + } + ] + } + ], + "index": 3 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 300, + 742, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 742, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 300, + 742, + 310, + 750 + ], + "type": "text", + "content": "20" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 19 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 97 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 97 + ], + "type": "text", + "content": "ing on reasoning processes, and we enhance metacognitive abilities through two-agent interaction and reinforcement learning at both end." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 109, + 185, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 109, + 185, + 121 + ], + "spans": [ + { + "bbox": [ + 105, + 109, + 185, + 121 + ], + "type": "text", + "content": "A.4 RL in LLM" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 129, + 506, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 129, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 104, + 129, + 506, + 316 + ], + "type": "text", + "content": "Recent advancements in applying RL to LLMs have enhanced their reasoning and decision-making capabilities. Liu et al. [2025] examines token-level optimization biases by introducing Dr. GRPO to stabilize policy gradients. VAPO [Yue et al., 2025b] enhances PPO with value-aware perturbations and adaptive reward shaping to improve robustness in sparse-reward reasoning tasks. DAPO [Yu et al., 2025] provides a scalable, modular RL framework that integrates distributed rollout collection and dynamic replay buffers for reproducible training at scale. SimpleRL-Zoo [Zeng et al., 2025] conducts zero-shot RL experiments across open-base LLMs to uncover emergent cognitive behaviors under minimal reward signals. Echo Chamber [Zhao et al., 2025] investigates how RL fine-tuning algorithms can amplify pretrained model biases and proposes regularization to mitigate over-amplification. Wen et al. [2024] decomposes high-level language actions into token-level operations to achieve finer-grained credit assignment. Some works push RL training for single-turn to multi-turn. Search-R1 [Jin et al., 2025] trains LLMs to orchestrate multi-turn search strategies with RL-optimized decision policies to improve question-answering accuracy. ArCHer [Zhou et al., 2024] employs a hierarchical, multi-turn RL architecture with manager and worker policies to efficiently handle long-horizon dialogue tasks. RAGEN [Wang et al., 2025] introduces trajectory filtering and critic modules within a multi-turn RL framework to stabilize learning and reduce shallow policy behaviors." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 332, + 277, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 332, + 277, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 332, + 277, + 345 + ], + "type": "text", + "content": "B Limitation and Future Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 357, + 504, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 357, + 504, + 434 + ], + "spans": [ + { + "bbox": [ + 104, + 357, + 504, + 434 + ], + "type": "text", + "content": "In this work, we only test ReMA on math and LLM-as-a-Judge benchmarks. Though the results show the effectiveness of ReMA, adopting ReMA to tasks where naturally needs multi-turn interaction between several interleaved agents has great potential. Moreover, a comprehensive understanding of the learning dynamics of multi-turn RL and multi-turn MARL for LLMs is needed. Finally, there's still sufficient space to further improve the procedure of multi-turn multi-agent rollout through modern LLM speed up techniques, e.g. prefetch-decode disaggregation and asynchronous rollout." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 450, + 383, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 450, + 383, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 383, + 464 + ], + "type": "text", + "content": "C Supplementary Materials for Method in Section 3" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 475, + 271, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 475, + 271, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 271, + 488 + ], + "type": "text", + "content": "C.1 Inference-time Scaling of ReMA" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 496, + 504, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 496, + 504, + 540 + ], + "spans": [ + { + "bbox": [ + 104, + 496, + 504, + 540 + ], + "type": "text", + "content": "In this section, we discuss how to enhance the inference-time computation of our hierarchical system, specifically focusing on the interaction between the high-level and low-level agents. The total number of model samples required for inference is determined by the product of the sampling budget allocated to each agent." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 545, + 504, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 545, + 504, + 578 + ], + "spans": [ + { + "bbox": [ + 104, + 545, + 504, + 578 + ], + "type": "text", + "content": "For instance, in a simple single-turn setting, if the high-level agent samples " + }, + { + "bbox": [ + 104, + 545, + 504, + 578 + ], + "type": "inline_equation", + "content": "k_{1}" + }, + { + "bbox": [ + 104, + 545, + 504, + 578 + ], + "type": "text", + "content": " responses and each of these responses leads to " + }, + { + "bbox": [ + 104, + 545, + 504, + 578 + ], + "type": "inline_equation", + "content": "k_{2}" + }, + { + "bbox": [ + 104, + 545, + 504, + 578 + ], + "type": "text", + "content": " samples from the low-level agent, the total number of model calls required is:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 252, + 579, + 357, + 591 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 252, + 579, + 357, + 591 + ], + "spans": [ + { + "bbox": [ + 252, + 579, + 357, + 591 + ], + "type": "interline_equation", + "content": "\\text {T o t a l s a m p l e s} = k _ {1} \\times k _ {2}.", + "image_path": "c48a4482b269d65f66e76eb545aed761bdd1e37cb7f681b85c17f366bd01e913.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 596, + 504, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 596, + 504, + 651 + ], + "spans": [ + { + "bbox": [ + 104, + 596, + 504, + 651 + ], + "type": "text", + "content": "Given a fixed computational budget, an important question arises: how should the sampling budget be distributed between the high-level and low-level agents to maximize performance? Allocating more samples to the high-level agent may increase diversity in reasoning strategies while allocating more to the low-level agent may yield more refined solutions for a given metacognitive plan." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 656, + 504, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 656, + 504, + 678 + ], + "spans": [ + { + "bbox": [ + 104, + 656, + 504, + 678 + ], + "type": "text", + "content": "Another crucial consideration is how to perform reranking on the final outputs. Two potential strategies include:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 132, + 689, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 689, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 132, + 689, + 504, + 723 + ], + "type": "text", + "content": "- Hierarchical reranking: First, for each high-level response, rank and aggregate the low-level responses under it. Then, rank the aggregated results across different high-level responses." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "21" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 20 + }, + { + "para_blocks": [ + { + "bbox": [ + 132, + 72, + 504, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 72, + 504, + 95 + ], + "spans": [ + { + "bbox": [ + 132, + 72, + 504, + 95 + ], + "type": "text", + "content": "- Flat reranking: Directly rank all sampled responses together, regardless of the hierarchy of high-level reasoning steps." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 104, + 505, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 104, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 104, + 104, + 505, + 138 + ], + "type": "text", + "content": "Balancing sampling allocation and designing an effective reranking strategy are key challenges in efficiently scaling our multi-agent reasoning system. In the next section, we explore empirical results comparing different allocation strategies and ranking methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 150, + 231, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 150, + 231, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 231, + 163 + ], + "type": "text", + "content": "C.2 Detailed reward design" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 170, + 504, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 170, + 504, + 194 + ], + "spans": [ + { + "bbox": [ + 104, + 170, + 504, + 194 + ], + "type": "text", + "content": "As described in Sec. 3.2, we update both high-level and low-level agents by assigning rewards based on the low-level policy output. Below, we outline several potential reward designs:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 132, + 201, + 504, + 286 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 132, + 201, + 504, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 201, + 504, + 224 + ], + "spans": [ + { + "bbox": [ + 132, + 201, + 504, + 224 + ], + "type": "text", + "content": "- Correctness reward: For tasks with explicit ground truth, we assign rewards based on the correctness of the low-level agent's output." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 132, + 226, + 504, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 226, + 504, + 249 + ], + "spans": [ + { + "bbox": [ + 132, + 226, + 504, + 249 + ], + "type": "text", + "content": "- Format reward: For tasks that require a specific output format, we enforce adherence to the prescribed structure by providing a format reward." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 132, + 251, + 504, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 251, + 504, + 286 + ], + "spans": [ + { + "bbox": [ + 132, + 251, + 504, + 286 + ], + "type": "text", + "content": "- To encourage the high-level agent to generate informative and unambiguous meta-thinking, and to stabilize the low-level outputs, we reward the high-level agent when the low-level agent produces consistent responses. Specifically, the consistency reward is defined as" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 247, + 290, + 399, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 247, + 290, + 399, + 316 + ], + "spans": [ + { + "bbox": [ + 247, + 290, + 399, + 316 + ], + "type": "interline_equation", + "content": "R _ {h} = \\frac {\\text {m a x o c c u r r e n c e o f a n a n s w e r}}{\\text {t o t a l n u m b e r o f r e s p o n s e s}}.", + "image_path": "6aad5c8b5675d5fc1e3eb597e21d99148f5c18d7820239246afb5d3c07134617.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 322, + 504, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 322, + 504, + 357 + ], + "spans": [ + { + "bbox": [ + 104, + 322, + 504, + 357 + ], + "type": "text", + "content": "To examine multi-agent metacognition-integrated reasoning with different reward designs, we experiment with different reward function designs to encourage effective collaboration and structured reasoning. Below, we introduce and justify several reward schemes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 366, + 505, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 366, + 505, + 411 + ], + "spans": [ + { + "bbox": [ + 104, + 366, + 505, + 411 + ], + "type": "text", + "content": "1. Correctness and Format-Aware Reward (Base Setting) In our primary reward setting, the system's overall correctness is used as the primary reward signal, supplemented by format-based rewards for both the high-level and low-level agents. Using mathematical problem-solving as an example:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 132, + 420, + 504, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 420, + 504, + 444 + ], + "spans": [ + { + "bbox": [ + 132, + 420, + 504, + 444 + ], + "type": "text", + "content": "- Low-level agent " + }, + { + "bbox": [ + 132, + 420, + 504, + 444 + ], + "type": "inline_equation", + "content": "(\\pi_{\\theta_l})" + }, + { + "bbox": [ + 132, + 420, + 504, + 444 + ], + "type": "text", + "content": ": Receives a reward of " + }, + { + "bbox": [ + 132, + 420, + 504, + 444 + ], + "type": "inline_equation", + "content": "+1.0" + }, + { + "bbox": [ + 132, + 420, + 504, + 444 + ], + "type": "text", + "content": " for a correct answer. If the answer is incorrect, the agent is further penalized based on format compliance. Specifically:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 149, + 445, + 504, + 491 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 149, + 445, + 504, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 445, + 504, + 467 + ], + "spans": [ + { + "bbox": [ + 149, + 445, + 504, + 467 + ], + "type": "text", + "content": "- If the output contains the designated answer-indicating format (e.g., boxed in Latex), it receives " + }, + { + "bbox": [ + 149, + 445, + 504, + 467 + ], + "type": "inline_equation", + "content": "-0.5" + }, + { + "bbox": [ + 149, + 445, + 504, + 467 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 149, + 469, + 504, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 469, + 504, + 491 + ], + "spans": [ + { + "bbox": [ + 149, + 469, + 504, + 491 + ], + "type": "text", + "content": "- Otherwise, it receives " + }, + { + "bbox": [ + 149, + 469, + 504, + 491 + ], + "type": "inline_equation", + "content": "-1.0" + }, + { + "bbox": [ + 149, + 469, + 504, + 491 + ], + "type": "text", + "content": ", as a missing format often suggests an incomplete or unstructured response." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 132, + 495, + 505, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 495, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 132, + 495, + 505, + 540 + ], + "type": "text", + "content": "- High-level agent " + }, + { + "bbox": [ + 132, + 495, + 505, + 540 + ], + "type": "inline_equation", + "content": "(\\pi_{\\theta_h})" + }, + { + "bbox": [ + 132, + 495, + 505, + 540 + ], + "type": "text", + "content": ": Receives the average correctness of the low-level agent's sampled responses as its reward. Additionally, to prevent the high-level agent from directly generating explicit answers instead of guiding reasoning, a strong penalty of " + }, + { + "bbox": [ + 132, + 495, + 505, + 540 + ], + "type": "inline_equation", + "content": "-1.0" + }, + { + "bbox": [ + 132, + 495, + 505, + 540 + ], + "type": "text", + "content": " is applied if it includes an explicit answer format (e.g., boxed)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 550, + 505, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 550, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 104, + 550, + 505, + 596 + ], + "type": "text", + "content": "2. Consistency-Based Reward Instead of using correctness as the high-level reward signal, this approach rewards the high-level agent for promoting consistent responses from the low-level agent, regardless of actual correctness. The consistency reward is defined as the proportion of the most frequently occurring answer among all sampled responses:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 230, + 608, + 504, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 230, + 608, + 504, + 633 + ], + "spans": [ + { + "bbox": [ + 230, + 608, + 504, + 633 + ], + "type": "interline_equation", + "content": "R _ {h} = \\frac {\\text {m a x o c c u r r e n c e o f a n a n s w e r}}{\\text {t o t a l n u m b e r o f r e s p o n s e s}} \\tag {14}", + "image_path": "39510965f995cb6f30887a0e480073cade592bfa898215baa6d1f2f71e71f3c1.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 639, + 504, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 639, + 504, + 685 + ], + "spans": [ + { + "bbox": [ + 104, + 639, + 504, + 685 + ], + "type": "text", + "content": "If the majority of responses do not contain a definitive answer, the reward is set to zero. We also add the format penalty to the high-level agent if its output contains the designated answer-indicating format. This incentivizes the high-level agent to guide the low-level agent toward more stable, detailed, reproducible outputs rather than erratic reasoning paths." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 689, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 689, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 689, + 504, + 723 + ], + "type": "text", + "content": "These different reward formulations allow us to investigate various dimensions of metacognitive reasoning: correctness, consistency, etc. We empirically compare their effects on learned metacognitive reasoning patterns in Sec. E.1." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "22" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 21 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 123, + 76, + 467, + 243 + ], + "blocks": [ + { + "bbox": [ + 123, + 76, + 467, + 243 + ], + "lines": [ + { + "bbox": [ + 123, + 76, + 467, + 243 + ], + "spans": [ + { + "bbox": [ + 123, + 76, + 467, + 243 + ], + "type": "image", + "image_path": "315cafbb1d2055dded17eaabf88749be03cfea772911a86fa7b194d2357e1c64.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 252, + 504, + 308 + ], + "lines": [ + { + "bbox": [ + 104, + 252, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 104, + 252, + 504, + 308 + ], + "type": "text", + "content": "Figure 7: Our method can be viewed as a combination of practical TRPO and block coordinate ascent, with the high and low-level models treated as distinct components within a larger neural network. Note that the figure does not represent the exact gradient back-propagation flow but rather highlights the key idea that we separate the high- and low-level models. This separation allows for the independent computation of gradients and the independent training of each model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 335, + 224, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 335, + 224, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 224, + 345 + ], + "type": "text", + "content": "C.3 Pseudocode of ReMA" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 357, + 274, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 357, + 274, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 274, + 369 + ], + "type": "text", + "content": "The pseudocode is shown in Algorithm 1." + } + ] + } + ], + "index": 3 + }, + { + "type": "code", + "bbox": [ + 106, + 402, + 504, + 589 + ], + "blocks": [ + { + "bbox": [ + 106, + 387, + 247, + 399 + ], + "lines": [ + { + "bbox": [ + 106, + 387, + 247, + 399 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 247, + 399 + ], + "type": "text", + "content": "Algorithm 1 Single turn MAMRP" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "lines": [ + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": "Require: High-level policy " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\pi_h" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": ", Low-level policy " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\pi_l" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": ", Dataset " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": ", Optimizers for " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\pi_h" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\pi_l" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " to filter training dataset \n1: Initialize " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\pi_h" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\pi_l" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " \n2: while not converged do \n3: build training dataset " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_l" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\pi_h, \\pi_l, \\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " \n4: for Sample " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}, \\mathbf{m}, \\mathbf{y}^*) \\sim \\mathcal{D}_l" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " do \n5: Generate " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{y} \\sim \\pi_l(\\mathbf{x}, \\mathbf{m})" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " \n6: Compute low-level reward " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "R_l(\\mathbf{y}, \\mathbf{y}^*)" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " \n7: Update " + }, + { + "bbox": [ + 106, 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"content": "(\\mathbf{x}, \\mathbf{y}^*) \\sim \\mathcal{D}_h" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " do \n11: Generate " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{m} \\sim \\pi_h(\\mathbf{x})" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{y} \\sim \\pi_l(\\mathbf{x}, \\mathbf{m})" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " \n12: Compute high-level reward " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "R_h(\\mathbf{m}, \\mathbf{y}, \\mathbf{y}^*)" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " \n13: Update " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\pi_h" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "inline_equation", + "content": "\\nabla_{\\theta_h} \\mathbb{E}[R_h]" + }, + { + "bbox": [ + 106, + 402, + 504, + 589 + ], + "type": "text", + "content": " \n14: end for \n15: end while" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "code_body" + } + ], + "index": 5, + "sub_type": "algorithm" + }, + { + "bbox": [ + 105, + 628, + 246, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 628, + 246, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 246, + 639 + ], + "type": "text", + "content": "C.4 Brief convergence analysis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "spans": [ + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": "We reuse the notations from Sec. 3.2, where " + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": " is task prompt, " + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": " is generated answer, " + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^*" + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": " is groundtruth, " + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{m}" + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": " is metacognition on task solving, " + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta_h}" + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta_l}" + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": " are high- and low-level agents with parameters " + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "inline_equation", + "content": "\\theta_l" + }, + { + "bbox": [ + 104, + 651, + 504, + 696 + ], + "type": "text", + "content": ". We consider the joint hierarchical policy defined in Eq. (8) and update the objective as in Eq. (9)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "content": "To leverage existing RL and optimization convergence analysis methods, we treat the two models as components of a larger model, as illustrated in Fig. 7. When updating one model, we treat the other" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "23" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 22 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 453, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 453, + 84 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 453, + 84 + ], + "type": "text", + "content": "model as part of a stationary environment. The gradients with respect to " + }, + { + "bbox": [ + 105, + 72, + 453, + 84 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 105, + 72, + 453, + 84 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 105, + 72, + 453, + 84 + ], + "type": "inline_equation", + "content": "\\theta_l" + }, + { + "bbox": [ + 105, + 72, + 453, + 84 + ], + "type": "text", + "content": " are:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 138, + 89, + 470, + 116 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 89, + 470, + 116 + ], + "spans": [ + { + "bbox": [ + 138, + 89, + 470, + 116 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\theta_ {h}} J (\\theta_ {h}, \\theta_ {l}) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\sum_ {\\mathbf {m} \\sim \\pi_ {h} (\\mathbf {m} | \\mathbf {x}; \\theta_ {h})} \\nabla_ {\\theta_ {h}} \\pi_ {h} (\\mathbf {m} | \\mathbf {x}; \\theta_ {h}) \\left[ \\mathbb {E} _ {\\mathbf {y} \\sim \\pi_ {l} (\\mathbf {y} | \\mathbf {x}, \\mathbf {m})} R (\\mathbf {y}, \\mathbf {y} ^ {*}) \\right],", + "image_path": "a86aaf6aa38251d41b64cce9905df386381958a7ede62e6faa107cd8fdf8b032.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 140, + 118, + 411, + 145 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 118, + 411, + 145 + ], + "spans": [ + { + "bbox": [ + 140, + 118, + 411, + 145 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\theta_ {l}} J (\\theta_ {h}, \\theta_ {l}) = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {y} ^ {*}} \\sum_ {\\mathbf {y} \\sim \\pi (\\theta_ {h}, \\theta_ {l})} \\nabla_ {\\theta_ {l}} \\pi_ {l} (\\mathbf {y} \\mid \\mathbf {x}, \\mathbf {m}; \\theta_ {h}); \\theta_ {l}) R (\\mathbf {y}, \\mathbf {y} ^ {*}).", + "image_path": "9b990e4ba70996ec4e3add4f2058c1bf66065120ac3089530de9e367f7c5b882.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 149, + 504, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 149, + 504, + 171 + ], + "spans": [ + { + "bbox": [ + 104, + 149, + 504, + 171 + ], + "type": "text", + "content": "We can compute the gradients with log trick and estimate " + }, + { + "bbox": [ + 104, + 149, + 504, + 171 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{\\mathbf{y}\\sim \\pi_l(\\mathbf{y}|\\mathbf{x},\\mathbf{m})}R(\\mathbf{y},\\mathbf{y}^*)" + }, + { + "bbox": [ + 104, + 149, + 504, + 171 + ], + "type": "text", + "content": " with Monte Carlo method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 177, + 504, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 177, + 504, + 200 + ], + "spans": [ + { + "bbox": [ + 104, + 177, + 504, + 200 + ], + "type": "text", + "content": "Equipped with the objective function and gradient computation, we update the models iteratively. Without loss of generality, we analyze the case where the high-level policy is updated first:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 238, + 203, + 363, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 238, + 203, + 363, + 224 + ], + "spans": [ + { + "bbox": [ + 238, + 203, + 363, + 224 + ], + "type": "interline_equation", + "content": "\\theta_ {h} ^ {(t + 1)} = \\arg \\max _ {\\theta_ {h}} J (\\theta_ {h}, \\theta_ {l} ^ {(t)}),", + "image_path": "30a64c5f505bf97092d0e646564746319a53da606cabba7e7be05eb736d380ee.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 240, + 226, + 370, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 240, + 226, + 370, + 246 + ], + "spans": [ + { + "bbox": [ + 240, + 226, + 370, + 246 + ], + "type": "interline_equation", + "content": "\\theta_ {l} ^ {(t + 1)} = \\arg \\max _ {\\theta_ {l}} J \\left(\\theta_ {h} ^ {(t + 1)}, \\theta_ {l}\\right).", + "image_path": "0848d561d3813403322d9efeb80547bb46375f51bc273a205eae3fdb7377b0aa.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 251, + 504, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 251, + 504, + 295 + ], + "spans": [ + { + "bbox": [ + 104, + 251, + 504, + 295 + ], + "type": "text", + "content": "Regarding the different regularizations " + }, + { + "bbox": [ + 104, + 251, + 504, + 295 + ], + "type": "inline_equation", + "content": "R_{h}" + }, + { + "bbox": [ + 104, + 251, + 504, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 251, + 504, + 295 + ], + "type": "inline_equation", + "content": "R_{l}" + }, + { + "bbox": [ + 104, + 251, + 504, + 295 + ], + "type": "text", + "content": " in Eqs. (10) and (11) for the different policies, instead of directly integrating them into the loss function, we treat them as constraints, as done in Trust Region Policy Optimization (TRPO) [Schulman et al., 2015]. Note that when one policy is fixed, the other policy operates in a stationary decision process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 300, + 504, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 300, + 504, + 345 + ], + "spans": [ + { + "bbox": [ + 104, + 300, + 504, + 345 + ], + "type": "text", + "content": "Based on the defined objective and update method, we apply TRPO and block coordinate ascent. First, recall that when updating a single policy, TRPO guarantees monotonic improvement by optimizing a lower bound. Specifically, let " + }, + { + "bbox": [ + 104, + 300, + 504, + 345 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{old}}" + }, + { + "bbox": [ + 104, + 300, + 504, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 300, + 504, + 345 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 104, + 300, + 504, + 345 + ], + "type": "text", + "content": " represent the old and current policies, respectively. We define a surrogate objective as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 205, + 349, + 405, + 376 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 205, + 349, + 405, + 376 + ], + "spans": [ + { + "bbox": [ + 205, + 349, + 405, + 376 + ], + "type": "interline_equation", + "content": "L _ {\\pi_ {\\mathrm {o l d}}} (\\pi) = \\mathbb {E} _ {s \\sim \\pi_ {\\mathrm {o l d}}, a \\sim \\pi_ {\\mathrm {o l d}}} \\left[ \\frac {\\pi (a | s)}{\\pi_ {\\mathrm {o l d}} (a | s)} A ^ {\\pi_ {\\mathrm {o l d}}} (s, a) \\right],", + "image_path": "9e34be703eb23abfa3d50c401d5176ae1c7172f8c5c2449d99876c5e8025bbf6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 378, + 433, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 378, + 433, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 433, + 390 + ], + "type": "text", + "content": "As shown by Schulman et al. [2015], the true objective of " + }, + { + "bbox": [ + 105, + 378, + 433, + 390 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 105, + 378, + 433, + 390 + ], + "type": "text", + "content": " is lower-bounded by:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 198, + 393, + 411, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 393, + 411, + 411 + ], + "spans": [ + { + "bbox": [ + 198, + 393, + 411, + 411 + ], + "type": "interline_equation", + "content": "J (\\pi) \\geq L _ {\\pi_ {\\mathrm {o l d}}} (\\pi) - C \\cdot \\max _ {s} \\mathrm {K L} [ \\pi_ {\\mathrm {o l d}} (\\cdot | s), \\pi (\\cdot | s) ],", + "image_path": "a5f4f993c4054904cf79c154022c7bf8db9d847e25e2e01b15d142fb8abc2254.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "spans": [ + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "text", + "content": "for some constant " + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "text", + "content": ". By optimizing the right-hand side of the above inequality, we are guaranteed to improve the performance of " + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "text", + "content": ". Therefore, for policies " + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "inline_equation", + "content": "\\pi^t" + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "inline_equation", + "content": "\\pi^{t + 1}" + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "text", + "content": " obtained from iterations " + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 104, + 415, + 504, + 448 + ], + "type": "text", + "content": " using the TRPO method, we have:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 266, + 451, + 342, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 266, + 451, + 342, + 466 + ], + "spans": [ + { + "bbox": [ + 266, + 451, + 342, + 466 + ], + "type": "interline_equation", + "content": "J (\\pi^ {t + 1}) \\geq J (\\pi^ {t}).", + "image_path": "03990842fdfe887957593c9afc250ca8d106f43dd9a3ebffb41479bc04e5ab4b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 474, + 504, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 474, + 504, + 528 + ], + "spans": [ + { + "bbox": [ + 104, + 474, + 504, + 528 + ], + "type": "text", + "content": "Now, returning to our updating method, we treat the high- and low-level policies as two blocks of a single agent. The iterative update process can thus be viewed as a cyclic block coordinate ascent, where the two policies are updated in a fixed order. By updating each block using the TRPO method, and improving the surrogate objective within the KL constraint, each block update does not decrease " + }, + { + "bbox": [ + 104, + 474, + 504, + 528 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 104, + 474, + 504, + 528 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 244, + 533, + 347, + 546 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 244, + 533, + 347, + 546 + ], + "spans": [ + { + "bbox": [ + 244, + 533, + 347, + 546 + ], + "type": "interline_equation", + "content": "J \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t}\\right) \\geq J \\left(\\theta_ {h} ^ {t}, \\theta_ {l} ^ {t}\\right),", + "image_path": "96e699afab51d562b257dd125436f136294ebd481918e9f0ef1d39366685d3c4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 246, + 548, + 365, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 246, + 548, + 365, + 563 + ], + "spans": [ + { + "bbox": [ + 246, + 548, + 365, + 563 + ], + "type": "interline_equation", + "content": "J \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t + 1}\\right) \\geq J \\left(\\theta_ {h} ^ {t + 1}, \\theta_ {l} ^ {t}\\right).", + "image_path": "710b61fd23f78b9a946f7e235ed8fddd79aad1dd33ac36e38c69d6c2a28224e2.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 572, + 504, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 572, + 504, + 597 + ], + "spans": [ + { + "bbox": [ + 104, + 572, + 504, + 597 + ], + "type": "text", + "content": "Thus " + }, + { + "bbox": [ + 104, + 572, + 504, + 597 + ], + "type": "inline_equation", + "content": "J(\\theta_h^{t + 1},\\theta_l^{t + 1})\\geq J(\\theta_h^t,\\theta_l^t)" + }, + { + "bbox": [ + 104, + 572, + 504, + 597 + ], + "type": "text", + "content": ". This repeated coordinate maximization converges to a fixed point, where no single coordinate update can further improve " + }, + { + "bbox": [ + 104, + 572, + 504, + 597 + ], + "type": "inline_equation", + "content": "J(\\theta_h,\\theta_l)" + }, + { + "bbox": [ + 104, + 572, + 504, + 597 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 601, + 504, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 601, + 504, + 635 + ], + "spans": [ + { + "bbox": [ + 104, + 601, + 504, + 635 + ], + "type": "text", + "content": "Given the theoretical monotonic improvement with TRPO and block coordinate ascent, we adopt a practical version of TRPO in our experiments, specifically Proximal Policy Optimization (PPO) [Schulman et al., 2017] or GRPO [Shao et al., 2024]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 647, + 415, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 647, + 415, + 658 + ], + "spans": [ + { + "bbox": [ + 104, + 647, + 415, + 658 + ], + "type": "text", + "content": "C.5 Learning to reason from the perspective of Leader Follower Game" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 667, + 505, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 667, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 667, + 505, + 723 + ], + "type": "text", + "content": "Besides the loss function in the main part, we also propose to frame the problem as a leader-follower game. By analyzing the equilibria of the leader-follower game, we demonstrate that our framework inherently identifies the optimal sub-tasks aligned with the capabilities of the low-level model. This ensures that the high-level decisions are guided by the low-level model's strengths, leading to more efficient and targeted task decomposition." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "24" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 23 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 234, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 234, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 234, + 85 + ], + "type": "text", + "content": "C.5.1 Leader-follower game" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "spans": [ + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "text", + "content": "The leader-follower game, also known as the Stackelberg game, models interaction between two agents with parametrized strategies " + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta} = (\\pmb{\\theta}_1, \\pmb{\\theta}_2)" + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "text", + "content": " and differentiable objective functions " + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_1, \\mathcal{L}_2): \\mathbb{R}^d \\to \\mathbb{R}" + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "text", + "content": ". In this framework, the leader announces its strategy first, and the follower observes this decision to respond optimally. This sequential structure enables the leader to anticipate the follower's reaction and adjust its strategy accordingly. A Stackelberg equilibrium occurs when neither agent can unilaterally improve its objective. Denoting " + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}_1" + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "text", + "content": " as the leader's strategy and " + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}_2" + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "text", + "content": " as the follower's, the loss functions " + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 104, + 91, + 504, + 169 + ], + "type": "text", + "content": " are optimized with the following bi-level structure:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 172, + 173, + 436, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 172, + 173, + 436, + 188 + ], + "spans": [ + { + "bbox": [ + 172, + 173, + 436, + 188 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\theta} _ {1} ^ {*} = \\operatorname {a r g m i n} _ {\\boldsymbol {\\theta} _ {1}} \\mathcal {L} _ {1} (\\boldsymbol {\\theta}, \\boldsymbol {\\theta} _ {2} ^ {*} (\\boldsymbol {\\theta} _ {1})), \\quad \\boldsymbol {w} _ {2} ^ {*} (\\boldsymbol {\\theta} _ {1}) = \\operatorname {a r g m i n} _ {\\boldsymbol {\\theta} _ {2}} \\mathcal {L} _ {2} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}).", + "image_path": "19d913b0dca111c638beefd731775a3856eed9a49ce53f07143ec8a8447cb2c4.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 195, + 504, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 195, + 504, + 273 + ], + "spans": [ + { + "bbox": [ + 104, + 195, + 504, + 273 + ], + "type": "text", + "content": "Anil et al. [2021] apply the leader-follower game to ensure checkable answers in a prover-verifier game (PVG). The objective is a verifier that is both complete (accepts all correct proofs from a verifier) and sound (rejects all incorrect proofs from a verifier). They analyze different scenarios where the verifier acts as the leader, the prover as the follower, and both announce strategies simultaneously, forming a Nash equilibrium. The study concludes that in verifier-led SVG, a Stackelberg equilibrium is both necessary and sufficient for achieving a sound and complete verifier, whereas in other configurations, a Stackelberg equilibrium is not necessary or sufficient for this outcome." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 284, + 211, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 284, + 211, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 211, + 295 + ], + "type": "text", + "content": "C.5.2 Efficacy of LLM" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "spans": [ + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "text", + "content": "Because the high-level policy possesses strong generalization capabilities, it is impractical for it to exhaustively explore every potential sub-task for each question. Instead, it naturally focuses on tasks within a feasible range of difficulty, leveraging only a limited set of coarse planning actions. Rather than pinpointing perfectly tailored sub-tasks, the policy searches for general tasks of particular computational complexity, i.e., difficulty, that it can handle reliably. Motivated by this perspective, we incorporate the concept of a reasoning boundary for large language models (LLMs) [Chen et al., 2024b]. Intuitively, the reasoning boundary circumscribes the maximum difficulty of problems a model can solve at a desired accuracy level. Formally, for a model " + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "text", + "content": ", a task " + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "text", + "content": ", and a predefined threshold " + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "text", + "content": ", the reasoning boundary of " + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "text", + "content": " represents the maximum problem difficulty " + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 104, + 302, + 504, + 411 + ], + "type": "text", + "content": " that satisfies:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 220, + 415, + 389, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 220, + 415, + 389, + 434 + ], + "spans": [ + { + "bbox": [ + 220, + 415, + 389, + 434 + ], + "type": "interline_equation", + "content": "\\mathcal {B} _ {A c c = A} (t | \\theta) = \\sup _ {d} \\{d | A c c (t | d, \\theta) = A \\}.", + "image_path": "032a64c3b322e4687ee8458b7f6835cd1e8b820c05079fa11e7c0ad3ebd2c1ec.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 439, + 504, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 439, + 504, + 483 + ], + "spans": [ + { + "bbox": [ + 104, + 439, + 504, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 439, + 504, + 483 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 104, + 439, + 504, + 483 + ], + "type": "text", + "content": " denotes the problem difficulty. By quantifying the difficulty level a model can reliably handle, the reasoning boundary provides a systematic way to align the high-level policy's focus with the model's actual capabilities, gauge the efficacy of the low-level policy, and determine the optimal strategy for solving the question." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 495, + 324, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 495, + 324, + 507 + ], + "spans": [ + { + "bbox": [ + 104, + 495, + 324, + 507 + ], + "type": "text", + "content": "C.5.3 Leader-follower Game for LLM Reasoning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 514, + 504, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 514, + 504, + 536 + ], + "spans": [ + { + "bbox": [ + 104, + 514, + 504, + 536 + ], + "type": "text", + "content": "Our goal is to find the high-level policy that searches for the sub-task sequence based on the efficacy of the low-level policy to solve the question. We design the loss functions as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 192, + 541, + 410, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 192, + 541, + 410, + 554 + ], + "spans": [ + { + "bbox": [ + 192, + 541, + 410, + 554 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {h} = \\mathbb {E} _ {(x, y) \\sim p _ {D}, t _ {1: K}} \\left[ - \\log \\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}, y _ {1: K - 1}\\right) \\right],", + "image_path": "c7f26b9a321108578bb007fb3a44a3b27e7e213fbbdc726184ec19e80c57653f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 192, + 556, + 418, + 568 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 192, + 556, + 418, + 568 + ], + "spans": [ + { + "bbox": [ + 192, + 556, + 418, + 568 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {l} = \\mathbb {E} _ {x \\sim p _ {D}, t _ {1: k} \\sim \\pi_ {h}, \\hat {y} _ {k} \\sim \\pi_ {l}} \\left[ - r \\left(y _ {k}, \\hat {y} _ {k} \\mid x, t _ {1: k}, y _ {1: k - 1}\\right) \\right],", + "image_path": "b1511f7d2538127a540c6110fe627d96c51df91db3b849ba95d19fedfe10fad6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "spans": [ + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "inline_equation", + "content": "r(y_k, \\hat{y}_k \\mid x, t_{1:k}, y_{1:k-1})" + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "text", + "content": " represents the step reward for the correctness of " + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "inline_equation", + "content": "\\hat{y}_k" + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "text", + "content": " derived from the question " + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "text", + "content": ", the sub-task sequence " + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "inline_equation", + "content": "t_{1:k}" + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "text", + "content": " from the high policy and prior intermediate answer " + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "inline_equation", + "content": "y_{1:k-1}" + }, + { + "bbox": [ + 104, + 572, + 504, + 628 + ], + "type": "text", + "content": ". The loss functions can be interpreted as follows: the high-level policy is incentivized to find subtasks that lead to the correct answer based on the capabilities of the low-level policy, while the low-level policy is incentivized to enhance its instruction-following ability." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 632, + 504, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 632, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 104, + 632, + 504, + 689 + ], + "type": "text", + "content": "How to minimize the loss functions and whether such minimization leads to the desired results remain questions. To explore this, we consider a simplified case of our method, where the high-level policy plans the complete sub-task sequence at the beginning and the low-level executes the instruction in a single interaction. The corresponding parameterized policies are defined as " + }, + { + "bbox": [ + 104, + 632, + 504, + 689 + ], + "type": "inline_equation", + "content": "\\pi_h((t_1,\\ldots ,t_K)\\mid x)" + }, + { + "bbox": [ + 104, + 632, + 504, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 632, + 504, + 689 + ], + "type": "inline_equation", + "content": "\\pi_l((\\hat{y}_1,\\dots ,\\hat{y}_K)\\mid x,(t_1,\\dots ,t_K))" + }, + { + "bbox": [ + 104, + 632, + 504, + 689 + ], + "type": "text", + "content": " . The corresponding loss functions are:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 192, + 693, + 503, + 704 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 192, + 693, + 503, + 704 + ], + "spans": [ + { + "bbox": [ + 192, + 693, + 503, + 704 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {h} = \\mathbb {E} _ {(x, y) \\sim p _ {D}, t _ {1: K}} \\left[ - \\log \\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}\\right) \\right], \\tag {15}", + "image_path": "913cf3facfbd77150667cd4b4404381ce5bcddd9c76f1a6d393a0c01bfae6aa8.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 192, + 708, + 503, + 719 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 192, + 708, + 503, + 719 + ], + "spans": [ + { + "bbox": [ + 192, + 708, + 503, + 719 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {l} = \\mathbb {E} _ {x \\sim p _ {D}, t _ {1: k} \\sim \\pi_ {h}, \\hat {y} _ {k} \\sim \\pi_ {l}} \\left[ - r \\left(y _ {k}, \\hat {y} _ {k} \\mid x, t _ {1: k}, y _ {1: k - 1}\\right) \\right]. \\tag {16}", + "image_path": "b18d5455edfb4a76628089dd0bafcca0f64a4b3c8b3c93ede341d38248ca05a0.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "25" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 24 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 106 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 106 + ], + "type": "text", + "content": "In this step, the high-level policy generates the entire sub-task sequence without relying on intermediate answers, while the low-level policy follows the sequence to produce answers for the sub-tasks. The low-level policy can still leverage prior intermediate answers to sequentially refine its responses." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 110, + 504, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 110, + 504, + 189 + ], + "spans": [ + { + "bbox": [ + 104, + 110, + 504, + 189 + ], + "type": "text", + "content": "To analyze the result agents by minimizing the loss functions, we adopt the completeness and soundness properties from the PVG framework for LLM reasoning. Specifically, if the high-level policy generates a sub-task sequence that is executable within the low-level policy's capabilities, the problem must be solved (completeness). Conversely, if the sub-task sequence is incorrect or beyond the low-level policy's capacity, the problem cannot be solved (soundness). To achieve this, we utilize the conclusion from Anil et al. [2021], which positions the low-level policy as the leader and the high-level policy as the follower, equilibria guarantee the complete and sound low-level policy." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 192, + 506, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 192, + 506, + 302 + ], + "spans": [ + { + "bbox": [ + 104, + 192, + 506, + 302 + ], + "type": "text", + "content": "When the high-level policy takes the lead, the low-level policy is forced to adapt to the specific strategy defined by the high-level policy, which can result in neither complete nor sound low-level policy. For example, if the high-level policy dictates that it will only generate sub-tasks involving addition and subtraction, the low-level policy is constrained to optimize only for these tasks. While they may reach an equilibrium, the low-level policy remains incomplete, and this limitation impacts both policies. In the case of the simultaneous PVG game, convergence to a Nash equilibrium is possible, but it is not sufficient for completeness and soundness. For instance, the low-level policy might disregard the high-level policy entirely (e.g., if the high-level provides incorrect instructions, but the low-level still performs correctly). This approach, however, is challenging to implement due to the significantly larger search space involved." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 307, + 504, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 307, + 504, + 373 + ], + "spans": [ + { + "bbox": [ + 104, + 307, + 504, + 373 + ], + "type": "text", + "content": "Furthermore, the loss functions we design ensure that, at a Stackelberg equilibrium, the high-level policy identifies sub-task sequences that the low-level policy can execute to solve the problem with the highest probability. With the low-level policy acting as the leader, it establishes its reasoning boundary for tasks. Based on the reasoning boundary, let " + }, + { + "bbox": [ + 104, + 307, + 504, + 373 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 104, + 307, + 504, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 307, + 504, + 373 + ], + "type": "inline_equation", + "content": "\\theta_l" + }, + { + "bbox": [ + 104, + 307, + 504, + 373 + ], + "type": "text", + "content": " represent the policy parameters for the high-level and low-level policies, respectively. The probability that the low-level policy correctly solves the question is defined as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 225, + 377, + 384, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 225, + 377, + 384, + 410 + ], + "spans": [ + { + "bbox": [ + 225, + 377, + 384, + 410 + ], + "type": "interline_equation", + "content": "\\pi_ {l} \\left(y _ {K} \\mid x, t _ {1: K}\\right) = \\prod_ {k = 1} ^ {K} \\operatorname {A c c} \\left(t _ {k} \\mid x, \\theta_ {l}\\right),", + "image_path": "abdc48d2d97eab951968fc5353ec9380321ab89f488c157876a9f268dee813a0.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "spans": [ + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "text", + "content": "where we can compute the difficulty " + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "inline_equation", + "content": "d_{k}" + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "text", + "content": ". where the difficulty " + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "inline_equation", + "content": "d_{k}" + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "text", + "content": " can be derived from " + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 104, + 415, + 504, + 459 + ], + "type": "text", + "content": ". The loss function in Eq. (15) ensures that the selected sub-tasks are optimal for the low-level policy. Here we provide a theoretical condition under which the most efficient solution strategy can be identified, according to the efficacy of the LLM." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 464, + 504, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 464, + 504, + 530 + ], + "spans": [ + { + "bbox": [ + 104, + 464, + 504, + 530 + ], + "type": "text", + "content": "This approach can be viewed as a game between a high-level \"prover\" and a low-level \"verifier\". The verifier, representing the low-level policy, adheres the high-level policy's instructions to validate its reasoning. Unlike the classic PVG setting, where the prover has ground-truth labels, the label of our high-level policy depends on the tunable low-level policy. This distinction, where the low-level policy (leader) is inherently more complex, contrasts with traditional PVG setups and adds complexity due to the interdependence between the high- and low-level policies." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 534, + 504, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 534, + 504, + 568 + ], + "spans": [ + { + "bbox": [ + 104, + 534, + 504, + 568 + ], + "type": "text", + "content": "By framing the problem-solving process as a leader-follower game, with the low-level policy designated as the leader, we can construct a bi-level optimization problem to identify an equilibrium. Following the formulation in Sec. C.5.1, the problem is expressed as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 182, + 571, + 426, + 592 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 571, + 426, + 592 + ], + "spans": [ + { + "bbox": [ + 182, + 571, + 426, + 592 + ], + "type": "interline_equation", + "content": "\\theta_ {l} ^ {*} = \\underset {\\theta_ {l}} {\\arg \\min } \\mathcal {L} _ {l} (\\theta_ {h} ^ {*} (\\theta_ {l}), \\theta_ {l}) \\quad \\theta_ {h} ^ {*} (\\theta_ {l}) = \\underset {\\theta_ {l}} {\\arg \\min } \\mathcal {L} _ {h} (\\theta_ {h}, \\theta_ {l}).", + "image_path": "949357e9e329a27c903f62439c403346a563277fe176cc0143fd18f127825c52.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 596, + 317, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 596, + 317, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 317, + 608 + ], + "type": "text", + "content": "Then we can apply bi-level optimization techniques." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 623, + 212, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 623, + 212, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 212, + 636 + ], + "type": "text", + "content": "D Training Details" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 647, + 212, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 647, + 212, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 647, + 212, + 658 + ], + "type": "text", + "content": "D.1 Single-turn ReMA" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 666, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 666, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 666, + 504, + 723 + ], + "type": "text", + "content": "We refer to Appendix G for prompts we use during training. We implement the training pipeline with OpenRLHF [Hu et al., 2024a] which is a highly efficient codebase and is easy to scale up. We select REINFORCE++ to save resources and for efficient training. All experiments are conducted in a node of 8 NVIDIA A100 GPUs. We use bf16, Zero2, Flash-Attention and gradient checkpointing to run our experiments." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "type": "text", + "content": "26" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 25 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "type": "text", + "content": "During rollout, we set temperature " + }, + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "type": "inline_equation", + "content": "= 1.0" + }, + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "type": "text", + "content": ", top_p " + }, + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "type": "inline_equation", + "content": "= 1.0" + }, + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "type": "text", + "content": ", top_k " + }, + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "type": "inline_equation", + "content": "= -1" + }, + { + "bbox": [ + 104, + 72, + 504, + 149 + ], + "type": "text", + "content": ", and use vLLM for inference acceleration. We set the max generation length to be 2048 and, the rollout batch size to be 1000. The number of samples per prompt is 4. During training, we use Adam Optimizer with a learning rate of 5e-7. We set the mini-batch size to be 500, and the clip ratio to be 0.2. Other hyperparameters, such as KL coefficients and the number of training episodes, were carefully tuned based on validation set performance to ensure robust and reliable results. To align with the hyperparameter in OpenRLHF, we use #Training Episode as the number of reinforcement learning epoch on the entire dataset." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "content": "In ReMA, during prompt filtering of the high-level model, the high-level agent first samples 10 candidates for each question with " + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "inline_equation", + "content": "t = 1.0" + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "content": ", and for each output the low-level agents sample 1 solution with " + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "inline_equation", + "content": "t = 0.0" + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "content": ", then we select questions of success rate between " + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "inline_equation", + "content": "[\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}]" + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "content": ". And for the low-level agent's prompt filtering, the high-level agent first samples 1 candidate for each question with " + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "inline_equation", + "content": "t = 0.0" + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "content": " and for each output the low-level agents sample 10 solutions with " + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "inline_equation", + "content": "t = 1.0" + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "content": ", then we select questions of success rate between " + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "inline_equation", + "content": "[\\varepsilon_{\\mathrm{min}}, \\varepsilon_{\\mathrm{max}}]" + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "content": " and use the high-level agent to sample 4 meta-thoughts with " + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "inline_equation", + "content": "t = 1.0" + }, + { + "bbox": [ + 104, + 154, + 506, + 233 + ], + "type": "text", + "content": " as the input." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 243, + 301, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 243, + 301, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 301, + 255 + ], + "type": "text", + "content": "D.1.1 Supervised fine-tuning data collection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 261, + 506, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 261, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 104, + 261, + 506, + 382 + ], + "type": "text", + "content": "For experiments in Sec. 4.2.1, we collect expert data to enhance the reasoning pattern, i.e. " + }, + { + "bbox": [ + 104, + 261, + 506, + 382 + ], + "type": "inline_equation", + "content": "RL" + }, + { + "bbox": [ + 104, + 261, + 506, + 382 + ], + "type": "text", + "content": " from SFT. Specifically, we collect demonstration data from GPT-4o Mini on MATH training dataset (7.5k problems) Hendrycks et al. [2021] and use it to fine-tune the LLMs. The data generation follows these steps: First, we prompt GPT-4o Mini to produce metacognitive reasoning for high-level model training. Specifically, we use different prompts to instruct it to rewrite and decompose a given question without providing a final answer. We collect metacognitive reasoning using two predefined actions, \"rewrite\" and \"decompose\", which align with human approaches to complex problem-solving while preserving answer diversity. Next, we use the generated instructions to prompt GPT-4o Mini to follow the metacognitive steps and solve the question, obtaining SFT data for low-level policy training. Below, we present the prompts used for both high-level and low-level models. Prompts can be found in Appendix G.1.1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 393, + 302, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 393, + 302, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 302, + 404 + ], + "type": "text", + "content": "D.1.2 Dataset Curation of RewardBench970" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 110, + 445, + 501, + 556 + ], + "blocks": [ + { + "bbox": [ + 105, + 422, + 504, + 444 + ], + "lines": [ + { + "bbox": [ + 105, + 422, + 504, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 504, + 444 + ], + "type": "text", + "content": "Table 2: Performance on LLM-as-a-Judge benchmarks, trained on dataset under the loose setting. The two-agent workflow in ReMA" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 110, + 445, + 501, + 556 + ], + "lines": [ + { + "bbox": [ + 110, + 445, + 501, + 556 + ], + "spans": [ + { + "bbox": [ + 110, + 445, + 501, + 556 + ], + "type": "table", + "html": "
ModelBenchmarkVRP(CoT)\\( \\mathbf{V R P_{R L}} \\)\\( \\mathbf{M R P_{R L}} \\)ReMA(Ours)
Llama3.1-8B-InstructRewardBench97071.2481.86 (+10.62)80.41 (+9.17)86.29 (+15.05)
JudgeBench51.7751.45 (-0.32)50.65 (-1.12)53.71 (+1.94)
Average61.5166.65 (+5.14)65.53 (+4.02)70.00 (+8.49)
Qwen2.5-7B-InstructRewardBench97086.4987.22 (+0.73)80.31 (-6.18)90.72 (+4.23)
JudgeBench58.3954.84 (-3.55)55.81 (-2.58)58.71 (+0.32)
Average72.4471.03 (-1.41)68.06 (-4.38)74.72 (+2.28)
", + "image_path": "13ee9b755412f0ddda27dfb3a4338a0ead1c5a78cddf2ef644b3f886d89c5815.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 568, + 504, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 568, + 504, + 592 + ], + "spans": [ + { + "bbox": [ + 104, + 568, + 504, + 592 + ], + "type": "text", + "content": "We process the original dataset in RewardBench by splitting it into a training set containing 5,000 tuples of (instruction, response A, response B) and a test set with the remaining 970 tuples." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 596, + 406, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 596, + 406, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 406, + 608 + ], + "type": "text", + "content": "To ensure a meaningful dataset split, we validate two separation strategies:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 132, + 616, + 504, + 664 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 132, + 616, + 504, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 616, + 504, + 638 + ], + "spans": [ + { + "bbox": [ + 132, + 616, + 504, + 638 + ], + "type": "text", + "content": "- Loose setting: We only ensure that there is no direct overlap of tuples between the training and test sets." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 132, + 641, + 504, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 641, + 504, + 664 + ], + "spans": [ + { + "bbox": [ + 132, + 641, + 504, + 664 + ], + "type": "text", + "content": "- Strict setting: We further enforce that no instruction appears in both the training and test sets. The results for this setting are presented in the main results (Table 1b)." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 104, + 672, + 504, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 672, + 504, + 695 + ], + "spans": [ + { + "bbox": [ + 104, + 672, + 504, + 695 + ], + "type": "text", + "content": "Additionally, since the original RewardBench data originates from different subsets, we ensure that all original subsets are evenly represented in both the training and test sets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "content": "Table 2 reports the learning performance of various methods under the loose dataset split setting. Compared to the results in Table 1b, ReMA significantly outperforms other RL tuning baselines" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "27" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 26 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 106 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 106 + ], + "type": "text", + "content": "across all models, particularly on out-of-distribution (OOD) benchmarks. The consistent improvements on OOD datasets of these two settings suggest that ReMA enhances meta-thinking ability, resulting in better generalization across diverse task distributions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 118, + 224, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 118, + 224, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 118, + 224, + 129 + ], + "type": "text", + "content": "D.1.3 Training on MATH" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 137, + 504, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 137, + 504, + 170 + ], + "spans": [ + { + "bbox": [ + 104, + 137, + 504, + 170 + ], + "type": "text", + "content": "VRP For Llama3-8B-Instruct, Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 12,6,6 for these 3 models respectively. For Llama3-8B-Instruct, we set the learning rate of 2e-7 for stable training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 182, + 504, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 182, + 504, + 205 + ], + "spans": [ + { + "bbox": [ + 104, + 182, + 504, + 205 + ], + "type": "text", + "content": "MRP For Llama3-8B-Instruct, Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 10,6,6 for these 3 models respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 216, + 504, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 216, + 504, + 260 + ], + "spans": [ + { + "bbox": [ + 104, + 216, + 504, + 260 + ], + "type": "text", + "content": "MAMRP We use " + }, + { + "bbox": [ + 104, + 216, + 504, + 260 + ], + "type": "inline_equation", + "content": "\\varepsilon_{\\mathrm{min}} = 0.2, \\varepsilon_{\\mathrm{max}} = 0.8" + }, + { + "bbox": [ + 104, + 216, + 504, + 260 + ], + "type": "text", + "content": " for prompt filtering. We use the same #Training Episode=4 for all models, and for #Update Iteration, we use 3 for Llama3-8B-Instruct and Llama3.1-8B-Instruct, 10 for Qwen2.5-7B-Instruct. And we set the KL coefficient to be 1e-2 for all the 3 models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 272, + 255, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 272, + 255, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 255, + 284 + ], + "type": "text", + "content": "D.1.4 Training on Reward Bench" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 291, + 504, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 291, + 504, + 315 + ], + "spans": [ + { + "bbox": [ + 104, + 291, + 504, + 315 + ], + "type": "text", + "content": "VRP For Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 4,6 for these 2 models respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 325, + 504, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 325, + 504, + 348 + ], + "spans": [ + { + "bbox": [ + 104, + 325, + 504, + 348 + ], + "type": "text", + "content": "MRP For Llama3.1-8B-Instruct, and Qwen2.5-7B-Instruct, we all use a KL coefficient of 1e-2, and for #Training Episode, we use 4,6 for these 2 models respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "spans": [ + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "text", + "content": "MAMRP We set #Update Iteration=1 for all models. We set the KL coefficient to be 1e-2 for Llama3.1-8B-Instruct and 1e-2 for Qwen2.5-7B-Instruct all models. For Llama3.1-8B-Instruct, we use " + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "inline_equation", + "content": "\\varepsilon_{\\mathrm{min}} = 0.2" + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "inline_equation", + "content": "\\varepsilon_{\\mathrm{max}} = 0.8" + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "text", + "content": " for prompt filtering and we use #Training Episode of 2 during training. For Llama3.1-8B-Instruct, we use " + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "inline_equation", + "content": "\\varepsilon_{\\mathrm{min}} = 0.1" + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "inline_equation", + "content": "\\varepsilon_{\\mathrm{max}} = 0.9" + }, + { + "bbox": [ + 104, + 360, + 504, + 416 + ], + "type": "text", + "content": " for prompt filtering and we use #Training Episode of 1 during training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 429, + 209, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 429, + 209, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 209, + 440 + ], + "type": "text", + "content": "D.2 Multi-turn ReMA" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 449, + 504, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 449, + 504, + 493 + ], + "spans": [ + { + "bbox": [ + 104, + 449, + 504, + 493 + ], + "type": "text", + "content": "We refer to Appendix G for prompts we use during training. We implement a multi-turn ReMA training pipeline with VeRL [Sheng et al., 2024] since it's easier to implement complex training pipeline with a single centralized controller. Similar to OpenRLHF, VeRL is also a highly efficient and scalable codebase for further development." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 498, + 504, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 498, + 504, + 575 + ], + "spans": [ + { + "bbox": [ + 104, + 498, + 504, + 575 + ], + "type": "text", + "content": "For the multi-turn ReMA rollout, we use parameter sharing and simultaneous update by default. In details, we maintain two message lists with the system prompt of meta-thinking agent and reasoning agent respectively. During rollout, each agent acts as 'assistant' in its own message list and the other agent acts as 'user'. We use three hyperparameters to control the rollout length: (1) 'max_num_turns': the maximum number of turns for each trajectory. (2) 'max_response_length': the maximum number of tokens for each turn's response. (3) 'max_prompt_length': the maximum number of tokens for each trajectory." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 579, + 504, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 579, + 504, + 603 + ], + "spans": [ + { + "bbox": [ + 104, + 579, + 504, + 603 + ], + "type": "text", + "content": "During training, we apply the collected message list to Qwen2.5-7B's chat template and build loss masks in order to compute the loss for all turns of one trajectory (message list)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 607, + 504, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 607, + 504, + 662 + ], + "spans": [ + { + "bbox": [ + 104, + 607, + 504, + 662 + ], + "type": "text", + "content": "Moreover, for multi-turn ReMA rollout, unlike single agent single turn rollout, we need to carefully design the termination logic. Basically, we let the meta-thinking agent automatically decide when to finish the solving procedure, we use a special tag '[FINISH]' to indicate the end of the solving procedure. After we detect this tag, we will terminate trajectory after the reasoning agent generates its output." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 667, + 505, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 667, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 104, + 667, + 505, + 722 + ], + "type": "text", + "content": "We also design other termination conditions to ensure the quality of the generated trajectories. If the last agent's response is too long, we will terminate the whole trajectory and setting the reward to 0. We also introduce a different version of format reward: we give a reward of 1.0 only if the reasoning agent's last turn response is correct and the meta-thinking agent's last turn response include '[FINISH]'. We use math_check as the default verifier." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "28" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 27 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 323, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 323, + 83 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 323, + 83 + ], + "type": "text", + "content": "D.2.1 SFT data collection of multi-turn MAMRP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 93, + 504, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 93, + 504, + 160 + ], + "spans": [ + { + "bbox": [ + 104, + 93, + 504, + 160 + ], + "type": "text", + "content": "We use GPT-4o to translate 817 samples in LIMO [Ye et al., 2025c] by prompting it to wrap each sentence with meta-thinking and reasoning tags. We use a temperature of 0. After filtering, we get 800 conversations for training. The prompt can be found in Appendix G.2.1. For supervised finetuning, we use LlamaFactory as the codebase and train the model for 3 epochs with a learning rate of 1e-5, consine learning rate scheduler, and batch size of 8. Use DeepSpeed Zero2 for distributed training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 176, + 224, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 176, + 224, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 224, + 188 + ], + "type": "text", + "content": "D.2.2 Training on MATH" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 197, + 504, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 197, + 504, + 264 + ], + "spans": [ + { + "bbox": [ + 104, + 197, + 504, + 264 + ], + "type": "text", + "content": "For training of multi-turn ReMA on MATH, we use GRPO [Shao et al., 2024] as the default learning algorithm. We refer to Appendix G.2.2 for prompts. For experiment in Sec 4.3, we use sample 128 prompts, each with 16 trajectories. During training, we drop the KL loss term to improve the numerical stability. We use a learning rate of 1e-6, bfloat16 precision, FSDP backend for distributed training. We split the rollout data into 4 mini-batches for update. For the sake of numerical stability, we do pre-clip before computing the exponential of log-prob for a upperbound of 3.0." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 268, + 504, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 268, + 504, + 301 + ], + "spans": [ + { + "bbox": [ + 104, + 268, + 504, + 301 + ], + "type": "text", + "content": "For the main result in Fig 5, we test different rollout configurations with a max_prompt_length of 4096, training for 500 steps. We use 32 NVIDIA A800 GPUs, the longest training cost about 40 hours due to large scale validation per 10 steps." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 306, + 504, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 306, + 504, + 340 + ], + "spans": [ + { + "bbox": [ + 104, + 306, + 504, + 340 + ], + "type": "text", + "content": "For the ablation results in Fig 6, we use a tiny subset of MATH Level 3-5, training for 300 steps. Specifically, we sample 19 questions for every single type (133 instances in total). We use 8 NVIDIA A800 GPUs, the training cost about 30 hours" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 345, + 265, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 345, + 265, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 265, + 355 + ], + "type": "text", + "content": "We test different rollout configurations:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 356, + 504, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 356, + 504, + 378 + ], + "spans": [ + { + "bbox": [ + 104, + 356, + 504, + 378 + ], + "type": "text", + "content": "(1) max_num_turns=30, max_response_length=256, max_prompt_length=4096 (2) \nmax_num_turns=30, max_response_length=1024, max_prompt_length=3072" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 383, + 504, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 383, + 504, + 417 + ], + "spans": [ + { + "bbox": [ + 104, + 383, + 504, + 417 + ], + "type": "text", + "content": "And for the experiment of separate parameter in multi-turn ReMA, we iteratively train each agent with the same configuration as above, but with a switch interval of 10 steps, starting from the metathinking agent." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 437, + 228, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 437, + 228, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 228, + 450 + ], + "type": "text", + "content": "E Other Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 464, + 330, + 476 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 464, + 330, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 330, + 476 + ], + "type": "text", + "content": "E.1 Reward functions shape cross-agent behaviors" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 487, + 504, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 487, + 504, + 575 + ], + "spans": [ + { + "bbox": [ + 104, + 487, + 504, + 575 + ], + "type": "text", + "content": "We also investigate the impact of different reward function designs on ReMA's behavior. In addition to the base reward setting described in Appendix C.2, we evaluate a consistency-based reward function using Qwen2.5-7B-Instruct. This reward function is designed to encourage the high-level agent to generate more detailed guidance. Indeed, we observe that the high-level agent trained in this manner produces more detailed solution steps compared to the one trained with the basic correctness format reward. However, we also find that this approach often leads to jailbreak behavior, where the high-level agent tends to include the final answer within its output, compromising the intended hierarchical reasoning process." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 579, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 579, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 579, + 506, + 723 + ], + "type": "text", + "content": "Furthermore, we discover an interesting evolution of a pattern during training: although our experimental setup is designed for the high-level agent to provide a solution plan while the lower-level agent executes it, we find that under the consistency-based reward, the lower-level agent significantly increases its attempt of verification rather than straightforward execution. We observed a certain sentence commonly appearing in the low-level agent's responses: \"Let's go through the solution step by step to ensure clarity and correctness.\" To quantify this effect, we track the frequency of it. We analyze this pattern across all mathematical test sets, sampling eight completions per question at a temperature of 0.7. Our empirical results have identified a " + }, + { + "bbox": [ + 104, + 579, + 506, + 723 + ], + "type": "inline_equation", + "content": "30\\mathrm{x}" + }, + { + "bbox": [ + 104, + 579, + 506, + 723 + ], + "type": "text", + "content": " increase of such self-verifying patterns in the model trained with the consistency-based reward compared to the one trained with the base reward. Moreover, we also observe additional variations of this pattern, e.g. \"Let's carefully re-evaluate the problem and solution to ensure accuracy and clarity.\" These phrases indicate that the low-level agent is actively exploring to verify the detailed response provided by the high-level agent." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "29" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 28 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 128 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 128 + ], + "type": "text", + "content": "This suggests that (1) meta-thinking can not only emerge and be reinforced in the high-level agent but also in the low-level agent. During reinforcement learning (RL) training, the two agents develop a novel problem-solving pattern characterized by a role reversal. (2) Consistency-based rewards promote a more self-corrective approach at the lower level, potentially disrupting the intended separation of roles between planning and execution. For a detailed case study, refer to Appendix F.2." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 140, + 422, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 140, + 422, + 152 + ], + "spans": [ + { + "bbox": [ + 105, + 140, + 422, + 152 + ], + "type": "text", + "content": "E.2 Detailed Training Curves on Different Datasets of Multi-turn ReMA" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 160, + 473, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 160, + 473, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 473, + 172 + ], + "type": "text", + "content": "We show the detailed training curves of the multi-turn ReMA on different datasets in Fig. 8." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 108, + 184, + 504, + 383 + ], + "blocks": [ + { + "bbox": [ + 108, + 184, + 504, + 383 + ], + "lines": [ + { + "bbox": [ + 108, + 184, + 504, + 383 + ], + "spans": [ + { + "bbox": [ + 108, + 184, + 504, + 383 + ], + "type": "image", + "image_path": "3a07830c095bd1b0e7d492fba662d270532fb4263b681ea523bd6daaeb0902da.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 146, + 387, + 463, + 399 + ], + "lines": [ + { + "bbox": [ + 146, + 387, + 463, + 399 + ], + "spans": [ + { + "bbox": [ + 146, + 387, + 463, + 399 + ], + "type": "text", + "content": "Figure 8: Detailed Training Curves on Different Datasets of Multi-turn ReMA" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 427, + 226, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 427, + 226, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 226, + 441 + ], + "type": "text", + "content": "F Qualitative Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 451, + 279, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 451, + 279, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 279, + 464 + ], + "type": "text", + "content": "F.1 High-level policy finds better plans" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 472, + 504, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 472, + 504, + 528 + ], + "spans": [ + { + "bbox": [ + 104, + 472, + 504, + 528 + ], + "type": "text", + "content": "Here is an example of how a high-level policy alters the solving method of an LLM, increasing the likelihood of providing correct answers. As we can see from the following example, without the high-level policy, the LLM counts all integer coordinates, including those on the boundary, and then subtracts the boundary coordinates. In contrast, the high-level policy identifies a better approach, directly instructing the LLM to count only the coordinates strictly inside the boundary." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 540, + 309, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 540, + 309, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 309, + 552 + ], + "type": "text", + "content": "F.2 Case study for Experiments in Section E.1" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 560, + 373, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 560, + 373, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 373, + 572 + ], + "type": "text", + "content": "Fig. 10 and Fig. 11 show an case study of experiments in Sec. E.1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 576, + 504, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 576, + 504, + 643 + ], + "spans": [ + { + "bbox": [ + 104, + 576, + 504, + 643 + ], + "type": "text", + "content": "Although both agents are prompted with the same instructions as in our main results, the consistency reward of the high-level agent significantly alters the learning dynamics. As illustrated in Fig. 10, the high-level agent generates detailed solution attempts rather than a strategic plan. Consequently, the low-level agent evolves to verify the high-level agent's solutions. This suggests that, during reinforcement learning (RL) training, the two agents develop a novel problem-solving pattern characterized by a role reversal, where one agent generates an answer while the other verifies it." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 655, + 316, + 667 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 655, + 316, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 316, + 667 + ], + "type": "text", + "content": "F.3 Case study for Experiments in Section 4.2.2" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 675, + 504, + 719 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 675, + 504, + 719 + ], + "spans": [ + { + "bbox": [ + 104, + 675, + 504, + 719 + ], + "type": "text", + "content": "Fig. 12 shows the detailed outputs of the two groups of LLMs trained in JSON action. The outputs finally converge to relative easier and shorter sentences, compared to our main experiments. This may due to insufficient capacity of a small LM to produce a valid JSON-format response while simultaneously exploring diverse reasoning strategies." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "30" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 29 + }, + { + "para_blocks": [ + { + "bbox": [ + 115, + 79, + 493, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 79, + 493, + 95 + ], + "spans": [ + { + "bbox": [ + 115, + 79, + 493, + 95 + ], + "type": "text", + "content": "Consider the rectangular region with the following points as vertices: " + }, + { + "bbox": [ + 115, + 79, + 493, + 95 + ], + "type": "inline_equation", + "content": "(5,4),(-5,4),(-5, - 4),(5, - 4)" + }, + { + "bbox": [ + 115, + 79, + 493, + 95 + ], + "type": "text", + "content": " . How many points with integer coordinates will be strictly in the interior of this rectangular region?" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 133, + 100, + 285, + 115 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 100, + 285, + 115 + ], + "spans": [ + { + "bbox": [ + 133, + 100, + 285, + 115 + ], + "type": "text", + "content": "Output without high-level planning solves this question in a less optimal way, leading to a wrong answer:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "spans": [ + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "text", + "content": "To determine how many points with integer coordinates will be strictly in the interior of the rectangular region with vertices at " + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "inline_equation", + "content": "(5,4)" + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "inline_equation", + "content": "(-5,4)" + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "inline_equation", + "content": "(-5, - 4)" + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "inline_equation", + "content": "(5, - 4)" + }, + { + "bbox": [ + 115, + 120, + 303, + 142 + ], + "type": "text", + "content": ", we will follow these steps:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 142, + 218, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 142, + 218, + 148 + ], + "spans": [ + { + "bbox": [ + 116, + 142, + 218, + 148 + ], + "type": "text", + "content": "1. Identify the dimensions of the rectangle:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 149, + 301, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 149, + 301, + 163 + ], + "spans": [ + { + "bbox": [ + 115, + 149, + 301, + 163 + ], + "type": "text", + "content": "- The width of the rectangle can be calculated as the distance between the x-coordinates of the vertices. The x-coordinates are " + }, + { + "bbox": [ + 115, + 149, + 301, + 163 + ], + "type": "inline_equation", + "content": "-5" + }, + { + "bbox": [ + 115, + 149, + 301, + 163 + ], + "type": "text", + "content": " and 5." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 178, + 168, + 241, + 177 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 178, + 168, + 241, + 177 + ], + "spans": [ + { + "bbox": [ + 178, + 168, + 241, + 177 + ], + "type": "interline_equation", + "content": "\\mathrm {W i d t h} = 5 - (- 5) = 1 0", + "image_path": "d0e8f5c83c09eb3f74d88a58572429c88fe7ef9810aa4a364a80d0c3f482a10a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 182, + 301, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 182, + 301, + 196 + ], + "spans": [ + { + "bbox": [ + 115, + 182, + 301, + 196 + ], + "type": "text", + "content": "- The height of the rectangle can be calculated as the distance between the y-coordinates of the vertices. The y-coordinates are 4 and -4." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 179, + 201, + 240, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 201, + 240, + 209 + ], + "spans": [ + { + "bbox": [ + 179, + 201, + 240, + 209 + ], + "type": "interline_equation", + "content": "\\mathrm {H e i g h t} = 4 - (- 4) = 8", + "image_path": "eff8fc9f0b90286a3dd92044dfef48dcd65fbd0038ac94780d15266e585245c2.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "spans": [ + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "type": "text", + "content": "2. Calculate the total number of integer points: - The total number of integer points in the rectangle (including the boundary) can be calculated by considering the range of x and y values: - The x-values range from " + }, + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "type": "inline_equation", + "content": "-5" + }, + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "type": "text", + "content": " to 5, giving us 11 integer values " + }, + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "type": "inline_equation", + "content": "(-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)" + }, + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "type": "text", + "content": ". - The y-values range from " + }, + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "type": "inline_equation", + "content": "-4" + }, + { + "bbox": [ + 114, + 214, + 299, + 250 + ], + "type": "text", + "content": " to 4, giving us 9 integer values (" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 115, + 251, + 294, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 251, + 294, + 264 + ], + "spans": [ + { + "bbox": [ + 115, + 251, + 294, + 264 + ], + "type": "inline_equation", + "content": "-4, -3, -2, -1, 0, 1, 2, 3, 4)" + }, + { + "bbox": [ + 115, + 251, + 294, + 264 + ], + "type": "text", + "content": ". The total number of points in the rectangle (including the boundary) is:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 174, + 270, + 246, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 174, + 270, + 246, + 277 + ], + "spans": [ + { + "bbox": [ + 174, + 270, + 246, + 277 + ], + "type": "interline_equation", + "content": "\\text {T o t a l p o i n t s} = 1 1 \\times 9 = 9 9", + "image_path": "9b53fdc6f47f6ed75eda062dd07c79e825f26afc0ac0d0fb1f7fa2587d332132.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 114, + 282, + 304, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 282, + 304, + 319 + ], + "spans": [ + { + "bbox": [ + 114, + 282, + 304, + 319 + ], + "type": "text", + "content": "3. Calculate the number of points on the boundary: - The boundary consists of the four sides of the rectangle. - The top and bottom sides (y = 4 and y = -4) each have 11 integer points (from -5 to 5). - The left and right sides (x = 5 and x = -5) each have 9 integer points (from -4 to 4). - Therefore, the total number of points on the boundary is:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 144, + 323, + 275, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 323, + 275, + 331 + ], + "spans": [ + { + "bbox": [ + 144, + 323, + 275, + 331 + ], + "type": "interline_equation", + "content": "\\text {B o u n d a r y p o i n t s} = 2 \\times 1 1 + 2 \\times 9 = 2 2 + 1 8 = 4 0", + "image_path": "a645dd71a3993817a902a8e8a4efdcf103b1d6ffd7933658ca0a24594ac96eed.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 114, + 336, + 298, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 336, + 298, + 358 + ], + "spans": [ + { + "bbox": [ + 114, + 336, + 298, + 358 + ], + "type": "text", + "content": "4. Calculate the number of strictly interior points: - To find the number of points strictly in the interior, we subtract the points on the boundary from the total number of points:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 124, + 363, + 295, + 372 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 363, + 295, + 372 + ], + "spans": [ + { + "bbox": [ + 124, + 363, + 295, + 372 + ], + "type": "interline_equation", + "content": "I n t e r i o r \\text {p o i n t s} = \\text {T o t a l p o i n t s - B o u n d a r y p o i n t s} = 9 9 - 4 0 = 5 9", + "image_path": "7837d615d6c9a9750b72afac02ea2aa4e31641292385be12d2392f3f35fddae4.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 115, + 376, + 299, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 376, + 299, + 392 + ], + "spans": [ + { + "bbox": [ + 115, + 376, + 299, + 392 + ], + "type": "text", + "content": "Thus, the number of points with integer coordinates that will be strictly in the interior of this rectangular region is 59." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 310, + 100, + 493, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 100, + 493, + 116 + ], + "spans": [ + { + "bbox": [ + 310, + 100, + 493, + 116 + ], + "type": "text", + "content": "Answer with high-level planning identifies the optimal sub-tasks for the LLM to solve, increasing the chance of answering the question correctly" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 309, + 118, + 492, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 118, + 492, + 141 + ], + "spans": [ + { + "bbox": [ + 309, + 118, + 492, + 141 + ], + "type": "text", + "content": "High-level policy planning: First, identify the boundaries of the rectangular region. Then, determine the integer coordinates that lie strictly within these boundaries. Finally, count the number of such points." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 309, + 149, + 486, + 164 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 149, + 486, + 164 + ], + "spans": [ + { + "bbox": [ + 309, + 149, + 486, + 164 + ], + "type": "text", + "content": "Low-level policy reasoning following the high-policy plan: To solve the problem, we will follow the steps outlined in the instructions." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "spans": [ + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "text", + "content": "Step 1: Identify the boundaries of the rectangular region. The vertices of the rectangular region are: " + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "inline_equation", + "content": "(-5,4)" + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "inline_equation", + "content": "(-5,4)" + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "inline_equation", + "content": "(-5, - 4)" + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "inline_equation", + "content": "(5, - 4)" + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "text", + "content": " From these vertices, we can determine the boundaries:- The left boundary is " + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "inline_equation", + "content": "x = -5" + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "text", + "content": " The right boundary is " + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "inline_equation", + "content": "x = 5" + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "text", + "content": " .- The bottom boundary is " + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "inline_equation", + "content": "y = -4" + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "text", + "content": " .- The top boundary is " + }, + { + "bbox": [ + 308, + 170, + 490, + 207 + ], + "type": "inline_equation", + "content": "y = 4" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 308, + 213, + 477, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 213, + 477, + 235 + ], + "spans": [ + { + "bbox": [ + 308, + 213, + 477, + 235 + ], + "type": "text", + "content": "Step 2: Determine the integer coordinates that lie strictly within these boundaries. For a point " + }, + { + "bbox": [ + 308, + 213, + 477, + 235 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 308, + 213, + 477, + 235 + ], + "type": "text", + "content": " to be strictly inside the rectangle, it must satisfy: " + }, + { + "bbox": [ + 308, + 213, + 477, + 235 + ], + "type": "inline_equation", + "content": "-5 < x < 5 - 4 < y < 4" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "spans": [ + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "text", + "content": "Step 3: Count the integer coordinates that satisfy these conditions. Now, we will find the integer values for " + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "text", + "content": " that fall within these boundaries. For " + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "text", + "content": " : The integer values that satisfy " + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "inline_equation", + "content": "-5 < x < 5" + }, + { + "bbox": [ + 308, + 241, + 494, + 262 + ], + "type": "text", + "content": " are:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "spans": [ + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "inline_equation", + "content": "-4, -3, -2, -1, 0, 1, 2, 3, 4" + }, + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "text", + "content": " This gives us 9 possible integer values. For " + }, + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "text", + "content": " The integer values that satisfy " + }, + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "inline_equation", + "content": "-4 < y < 4" + }, + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "text", + "content": " are: " + }, + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "inline_equation", + "content": "-3, -2, -1, 0, 1, 2, 3" + }, + { + "bbox": [ + 308, + 262, + 490, + 284 + ], + "type": "text", + "content": ". This gives us 7 possible integer values." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 308, + 290, + 493, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 290, + 493, + 305 + ], + "spans": [ + { + "bbox": [ + 308, + 290, + 493, + 305 + ], + "type": "text", + "content": "Step 4: Calculate the total number of points. Now, we multiply the number of possible integer values for " + }, + { + "bbox": [ + 308, + 290, + 493, + 305 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 308, + 290, + 493, + 305 + ], + "type": "text", + "content": " by the number of possible integer values for " + }, + { + "bbox": [ + 308, + 290, + 493, + 305 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 308, + 290, + 493, + 305 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 367, + 309, + 437, + 318 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 309, + 437, + 318 + ], + "spans": [ + { + "bbox": [ + 367, + 309, + 437, + 318 + ], + "type": "interline_equation", + "content": "\\text {T o t a l p o i n t s} = 9 \\times 7 = 6 3", + "image_path": "7cbee802c4e75cd55acfba9c2483cb9c2aae890a4cb8099c03a05a2668bd8ebf.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 308, + 323, + 487, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 323, + 487, + 338 + ], + "spans": [ + { + "bbox": [ + 308, + 323, + 487, + 338 + ], + "type": "text", + "content": "Finally, the number of points with integer coordinates that lie strictly in the interior of the rectangular region is " + }, + { + "bbox": [ + 308, + 323, + 487, + 338 + ], + "type": "inline_equation", + "content": "\\boxed{63}" + }, + { + "bbox": [ + 308, + 323, + 487, + 338 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 136, + 408, + 472, + 421 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 408, + 472, + 421 + ], + "spans": [ + { + "bbox": [ + 136, + 408, + 472, + 421 + ], + "type": "text", + "content": "Figure 9: Case Study comparing with and without high-level metacognition results." + } + ] + } + ], + "index": 26, + "type": "text" + }, + { + "bbox": [ + 105, + 455, + 173, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 455, + 173, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 173, + 470 + ], + "type": "text", + "content": "G Prompts" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 490, + 251, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 490, + 251, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 251, + 502 + ], + "type": "text", + "content": "G.1 Single-turn ReMA prompts" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 517, + 285, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 517, + 285, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 285, + 529 + ], + "type": "text", + "content": "G.1.1 Prompts for JSON data collection" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 543, + 296, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 543, + 296, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 296, + 555 + ], + "type": "text", + "content": "Prompt for metacognition reasoning to rewrite:" + } + ] + } + ], + "index": 30 + }, + { + "type": "code", + "bbox": [ + 108, + 561, + 500, + 705 + ], + "blocks": [ + { + "bbox": [ + 108, + 561, + 500, + 705 + ], + "lines": [ + { + "bbox": [ + 108, + 561, + 500, + 705 + ], + "spans": [ + { + "bbox": [ + 108, + 561, + 500, + 705 + ], + "type": "text", + "content": "System prompt: \nYou are a math expert trying to solve mathematical problems. \nBefore answering a question, your task is to rewrite the original question to make it clearer. \nProvide your rewritten content in JSON format: \n{ \"action\": \"REWRITE\", \"output\": \"{clearer question content}\" \n} \nRespond only with valid JSON. Do not write an introduction or summary. \nUser prompt: \nHere is the question: [problem_text]" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "code_body" + } + ], + "index": 31, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 105, + 711, + 312, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 711, + 312, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 312, + 723 + ], + "type": "text", + "content": "Prompt for metacognition reasoning to decompose:" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "31" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 30 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 113, + 79, + 480, + 87 + ], + "blocks": [ + { + "bbox": [ + 113, + 79, + 480, + 87 + ], + "lines": [ + { + "bbox": [ + 113, + 79, + 480, + 87 + ], + "spans": [ + { + "bbox": [ + 113, + 79, + 480, + 87 + ], + "type": "text", + "content": "Question: The equation " + }, + { + "bbox": [ + 113, + 79, + 480, + 87 + ], + "type": "inline_equation", + "content": "x^{10} + (13x - 1)^{10} = 0" + }, + { + "bbox": [ + 113, + 79, + 480, + 87 + ], + "type": "text", + "content": " has 10 complex roots " + }, + { + "bbox": [ + 113, + 79, + 480, + 87 + ], + "type": "inline_equation", + "content": "r_1,\\overline{r}_1,r_2,\\overline{r}_2,r_3,\\overline{r}_3,r_4,\\overline{r}_4,r_5,\\overline{r}_5" + }, + { + "bbox": [ + 113, + 79, + 480, + 87 + ], + "type": "text", + "content": " , where the bar denotes complex conjugation. Find the value of " + }, + { + "bbox": [ + 113, + 79, + 480, + 87 + ], + "type": "inline_equation", + "content": "\\frac{1}{r_1\\overline{r}_1} +\\frac{1}{r_2\\overline{r}_2} +\\frac{1}{r_3\\overline{r}_3} +\\frac{1}{r_4\\overline{r}_4} +\\frac{1}{r_5\\overline{r}_5}" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_body" + } + ], + "index": 0, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 180, + 90, + 233, + 95 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 180, + 90, + 233, + 95 + ], + "spans": [ + { + "bbox": [ + 180, + 90, + 233, + 95 + ], + "type": "text", + "content": "High-Level Agent's Output" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 114, + 97, + 264, + 102 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 97, + 264, + 102 + ], + "spans": [ + { + "bbox": [ + 114, + 97, + 264, + 102 + ], + "type": "text", + "content": "To solve this problem, let's break it down into steps that a low-level math-solving agent can follow:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 106, + 170, + 111 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 106, + 170, + 111 + ], + "spans": [ + { + "bbox": [ + 115, + 106, + 170, + 111 + ], + "type": "text", + "content": "1. Understand the given equation:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 112, + 178, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 112, + 178, + 116 + ], + "spans": [ + { + "bbox": [ + 115, + 112, + 178, + 116 + ], + "type": "text", + "content": "The equation is " + }, + { + "bbox": [ + 115, + 112, + 178, + 116 + ], + "type": "inline_equation", + "content": "x^{10} + (13x - 1)^{10} = 0" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 117, + 153, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 117, + 153, + 121 + ], + "spans": [ + { + "bbox": [ + 115, + 117, + 153, + 121 + ], + "type": "text", + "content": "2. Rewrite the equation:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 121, + 184, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 121, + 184, + 125 + ], + "spans": [ + { + "bbox": [ + 115, + 121, + 184, + 125 + ], + "type": "text", + "content": "Notice that the equation can be rewritten as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 189, + 131, + 223, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 189, + 131, + 223, + 137 + ], + "spans": [ + { + "bbox": [ + 189, + 131, + 223, + 137 + ], + "type": "interline_equation", + "content": "x ^ {1 0} = - (1 3 x - 1) ^ {1 0}.", + "image_path": "4e685cd1fc6e7e386b1f144221571ae899897bfc8d69063160055ba364dfd977.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 114, + 141, + 149, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 141, + 149, + 145 + ], + "spans": [ + { + "bbox": [ + 114, + 141, + 149, + 145 + ], + "type": "text", + "content": "3. Consider the roots:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 114, + 146, + 293, + 165 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 114, + 146, + 293, + 154 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 146, + 293, + 154 + ], + "spans": [ + { + "bbox": [ + 114, + 146, + 293, + 154 + ], + "type": "text", + "content": "The roots of the equation are given as " + }, + { + "bbox": [ + 114, + 146, + 293, + 154 + ], + "type": "inline_equation", + "content": "r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5" + }, + { + "bbox": [ + 114, + 146, + 293, + 154 + ], + "type": "text", + "content": ", where the bar denotes complex conjugation. 4. Use the property of complex conjugates:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "spans": [ + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "text", + "content": "For any complex number " + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "text", + "content": " , the product of " + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "text", + "content": " and its conjugate " + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "inline_equation", + "content": "\\overline{z}" + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "text", + "content": " is the square of the modulus of " + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "text", + "content": " i.e., " + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "inline_equation", + "content": "z\\overline{z} = |z|^2" + }, + { + "bbox": [ + 114, + 155, + 286, + 161 + ], + "type": "text", + "content": " 5. Calculate the required sum:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 115, + 161, + 162, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 161, + 162, + 165 + ], + "spans": [ + { + "bbox": [ + 115, + 161, + 162, + 165 + ], + "type": "text", + "content": "3. Calculate the required sum " + }, + { + "bbox": [ + 115, + 161, + 162, + 165 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = \\mathbf{w}_{1} + \\mathbf{w}_{2} + \\dots + \\mathbf{w}_{n}" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 175, + 175, + 238, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 175, + 238, + 186 + ], + "spans": [ + { + "bbox": [ + 175, + 175, + 238, + 186 + ], + "type": "interline_equation", + "content": "\\frac {1}{r _ {1} \\overline {{F _ {1}}}} + \\frac {1}{r _ {2} \\overline {{F _ {2}}}} + \\frac {1}{r _ {3} \\overline {{F _ {3}}}} + \\frac {1}{r _ {4} \\overline {{F _ {4}}}} + \\frac {1}{r _ {5} \\overline {{F _ {5}}}}", + "image_path": "ab388587275a1e57a8348ee40749023ad5049d876dde96e5d113fa279263566f.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 116, + 188, + 201, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 188, + 201, + 193 + ], + "spans": [ + { + "bbox": [ + 116, + 188, + 201, + 193 + ], + "type": "text", + "content": "Using the property from step 4, this can be rewritten as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 175, + 200, + 239, + 211 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 200, + 239, + 211 + ], + "spans": [ + { + "bbox": [ + 175, + 200, + 239, + 211 + ], + "type": "interline_equation", + "content": "\\frac {1}{| r _ {1} | ^ {2}} + \\frac {1}{| r _ {2} | ^ {2}} + \\frac {1}{| r _ {3} | ^ {2}} + \\frac {1}{| r _ {4} | ^ {2}} + \\frac {1}{| r _ {5} | ^ {2}},", + "image_path": "1a3854038f19d195ed185616c3f2b9e4fa543e0ca650c9a6ea7d1989a49d00de.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 114, + 214, + 297, + 241 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 114, + 214, + 157, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 214, + 157, + 218 + ], + "spans": [ + { + "bbox": [ + 114, + 214, + 157, + 218 + ], + "type": "text", + "content": "6. Simplify the expression:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "spans": [ + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "inline_equation", + "content": "r_1, r_2, r_3, r_4, r_5" + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "content": " are roots of the equation " + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "inline_equation", + "content": "x^{10} = -(13x - 1)^{10}" + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "content": ", the magnitudes " + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "inline_equation", + "content": "|r_i|" + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "content": " are the same for each pair " + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "inline_equation", + "content": "\\overline{r}_i" + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "inline_equation", + "content": "|r_i| = |r_i|" + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "inline_equation", + "content": "i, j" + }, + { + "bbox": [ + 114, + 219, + 295, + 226 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 227, + 166, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 227, + 166, + 231 + ], + "spans": [ + { + "bbox": [ + 115, + 227, + 166, + 231 + ], + "type": "text", + "content": "7. Find the common magnitude:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "spans": [ + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "text", + "content": "To find " + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "inline_equation", + "content": "|r_{1}|" + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "text", + "content": ", consider the magnitudes of the terms on both sides of the equation " + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "inline_equation", + "content": "x^{10} = -(13x - 1)^{10}" + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "text", + "content": ". The magnitude of the left side is " + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "inline_equation", + "content": "|x|^{10}" + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "text", + "content": " and the magnitude of the right side is " + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "inline_equation", + "content": "|13x - 1|^{10}" + }, + { + "bbox": [ + 114, + 232, + 297, + 241 + ], + "type": "text", + "content": ". Therefore:" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 190, + 248, + 222, + 254 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 190, + 248, + 222, + 254 + ], + "spans": [ + { + "bbox": [ + 190, + 248, + 222, + 254 + ], + "type": "interline_equation", + "content": "\\left| x \\right| ^ {1 0} = \\left| 1 3 x - 1 \\right| ^ {1 0}.", + "image_path": "3e06b9d59ab4e557586a3566be6437c22310f94ff0f6d0828c903eee7d02ad79.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 116, + 258, + 181, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 258, + 181, + 262 + ], + "spans": [ + { + "bbox": [ + 116, + 258, + 181, + 262 + ], + "type": "text", + "content": "Taking the 10th root of both sides, we get:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 194, + 270, + 220, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 194, + 270, + 220, + 275 + ], + "spans": [ + { + "bbox": [ + 194, + 270, + 220, + 275 + ], + "type": "interline_equation", + "content": "| x | = | 1 3 x - 1 |.", + "image_path": "36e0a413692113a7e783656a749d6c396724839d2dbe2992be4b5dfc8d667660.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 114, + 278, + 145, + 287 + ], + "type": "list", + "angle": 0, + "index": 26, + "blocks": [ + { + "bbox": [ + 114, + 278, + 139, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 278, + 139, + 282 + ], + "spans": [ + { + "bbox": [ + 114, + 278, + 139, + 282 + ], + "type": "text", + "content": "8. Solve for " + }, + { + "bbox": [ + 114, + 278, + 139, + 282 + ], + "type": "inline_equation", + "content": "|x|" + }, + { + "bbox": [ + 114, + 278, + 139, + 282 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 115, + 283, + 145, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 283, + 145, + 287 + ], + "spans": [ + { + "bbox": [ + 115, + 283, + 145, + 287 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 115, + 283, + 145, + 287 + ], + "type": "inline_equation", + "content": "|x| = a" + }, + { + "bbox": [ + 115, + 283, + 145, + 287 + ], + "type": "text", + "content": ". Then:" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 114, + 289, + 168, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 289, + 168, + 293 + ], + "spans": [ + { + "bbox": [ + 114, + 289, + 168, + 293 + ], + "type": "inline_equation", + "content": "\\therefore m - 1 \\neq 0" + }, + { + "bbox": [ + 114, + 289, + 168, + 293 + ], + "type": "text", + "content": " ;" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 194, + 295, + 218, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 194, + 295, + 218, + 300 + ], + "spans": [ + { + "bbox": [ + 194, + 295, + 218, + 300 + ], + "type": "interline_equation", + "content": "a = \\left| 1 3 a - 1 \\right|.", + "image_path": "07fc65b6c33535685fdd786bf88fd2c3719bf9a2836ea2cfdd87b86c9fbb436d.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 115, + 304, + 154, + 322 + ], + "type": "list", + "angle": 0, + "index": 33, + "blocks": [ + { + "bbox": [ + 115, + 304, + 154, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 304, + 154, + 308 + ], + "spans": [ + { + "bbox": [ + 115, + 304, + 154, + 308 + ], + "type": "text", + "content": "This gives us two cases:" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 115, + 309, + 130, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 309, + 130, + 313 + ], + "spans": [ + { + "bbox": [ + 115, + 309, + 130, + 313 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 115, + 309, + 130, + 313 + ], + "type": "inline_equation", + "content": "a = 13" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 115, + 314, + 145, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 314, + 145, + 318 + ], + "spans": [ + { + "bbox": [ + 115, + 314, + 145, + 318 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 115, + 314, + 145, + 318 + ], + "type": "inline_equation", + "content": "a = -(13a - 1)" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 115, + 319, + 150, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 319, + 150, + 322 + ], + "spans": [ + { + "bbox": [ + 115, + 319, + 150, + 322 + ], + "type": "text", + "content": "Solving the first case:" + } + ] + } + ], + "index": 32 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 172, + 329, + 241, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 172, + 329, + 241, + 339 + ], + "spans": [ + { + "bbox": [ + 172, + 329, + 241, + 339 + ], + "type": "interline_equation", + "content": "a = 1 3 a - 1 \\Longrightarrow 1 2 a = 1 \\Longrightarrow a = \\frac {1}{1 2}.", + "image_path": "0237a522e20431ebc766f44dcd6ea2566b93869ecb82778c21cee24038e74754.jpg" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 116, + 342, + 154, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 342, + 154, + 346 + ], + "spans": [ + { + "bbox": [ + 116, + 342, + 154, + 346 + ], + "type": "text", + "content": "Solving the second case:" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 171, + 353, + 242, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 171, + 353, + 242, + 363 + ], + "spans": [ + { + "bbox": [ + 171, + 353, + 242, + 363 + ], + "type": "interline_equation", + "content": "a = - 1 3 a + 1 \\Longrightarrow 1 4 a = 1 \\Longrightarrow a = \\frac {1}{1 4}.", + "image_path": "ca970fefe3377e52dda01105b9874b3532e444010e03bc6c2807c37e7459b450.jpg" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 114, + 365, + 297, + 383 + ], + "type": "list", + "angle": 0, + "index": 40, + "blocks": [ + { + "bbox": [ + 114, + 365, + 297, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 365, + 297, + 373 + ], + "spans": [ + { + "bbox": [ + 114, + 365, + 297, + 373 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 114, + 365, + 297, + 373 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 114, + 365, + 297, + 373 + ], + "type": "text", + "content": " must be the same for all roots, we need to check which value is consistent. Given the nature of the problem, we can assume " + }, + { + "bbox": [ + 114, + 365, + 297, + 373 + ], + "type": "inline_equation", + "content": "a = \\frac{1}{2}" + }, + { + "bbox": [ + 114, + 365, + 297, + 373 + ], + "type": "text", + "content": " as the correct magnitude." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 114, + 374, + 156, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 374, + 156, + 378 + ], + "spans": [ + { + "bbox": [ + 114, + 374, + 156, + 378 + ], + "type": "text", + "content": "9. Calculate the final sum:" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 114, + 379, + 168, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 379, + 168, + 383 + ], + "spans": [ + { + "bbox": [ + 114, + 379, + 168, + 383 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 114, + 379, + 168, + 383 + ], + "type": "inline_equation", + "content": "|r_i| = \\frac{1}{2}" + }, + { + "bbox": [ + 114, + 379, + 168, + 383 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 114, + 379, + 168, + 383 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 114, + 379, + 168, + 383 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 39 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 187, + 391, + 225, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 187, + 391, + 225, + 403 + ], + "spans": [ + { + "bbox": [ + 187, + 391, + 225, + 403 + ], + "type": "interline_equation", + "content": "\\frac {1}{| r _ {1} | ^ {2}} = \\frac {1}{(\\frac {1}{4}) ^ {2}} = 1 4 4.", + "image_path": "d1ac43fc68ceb3c6df31a21c8f515a2c7a6eab60ec12eb55a3eb012f71308f76.jpg" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 116, + 407, + 150, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 407, + 150, + 411 + ], + "spans": [ + { + "bbox": [ + 116, + 407, + 150, + 411 + ], + "type": "text", + "content": "Therefore, the sum is:" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 168, + 419, + 246, + 424 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 419, + 246, + 424 + ], + "spans": [ + { + "bbox": [ + 168, + 419, + 246, + 424 + ], + "type": "interline_equation", + "content": "1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 = 5 \\times 1 4 4 = 7 2 0.", + "image_path": "622da8514c8776b09adf1944ffa4c54f42ccb3c0dc87f16462c8dd56fc63f652.jpg" + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 114, + 428, + 142, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 428, + 142, + 432 + ], + "spans": [ + { + "bbox": [ + 114, + 428, + 142, + 432 + ], + "type": "text", + "content": "10. Final answer:" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 149, + 432, + 200, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 432, + 200, + 437 + ], + "spans": [ + { + "bbox": [ + 149, + 432, + 200, + 437 + ], + "type": "interline_equation", + "content": "\\frac {1}{\\frac {1}{n} + \\frac {1}{n}} + \\frac {1}{\\frac {1}{n} + \\frac {1}{n}} + \\frac {1}{\\frac {1}{n} + \\frac {1}{n}} \\text {i s} 7 2 0.", + "image_path": "1c302497f77a8108527d48c628148c9c17719bb8a4d6440b23231a5f2df60a61.jpg" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 374, + 90, + 426, + 95 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 90, + 426, + 95 + ], + "spans": [ + { + "bbox": [ + 374, + 90, + 426, + 95 + ], + "type": "text", + "content": "Low-Level Agent's Output" + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 97, + 425, + 102 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 425, + 102 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 425, + 102 + ], + "type": "text", + "content": "Let's go through the solution step by step to ensure clarity and correctness." + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 106, + 373, + 124 + ], + "type": "list", + "angle": 0, + "index": 52, + "blocks": [ + { + "bbox": [ + 304, + 106, + 359, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 106, + 359, + 110 + ], + "spans": [ + { + "bbox": [ + 304, + 106, + 359, + 110 + ], + "type": "text", + "content": "1. Understand the given equation:" + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 110, + 367, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 367, + 114 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 367, + 114 + ], + "type": "text", + "content": "The equation is " + }, + { + "bbox": [ + 304, + 110, + 367, + 114 + ], + "type": "inline_equation", + "content": "x^{10} + (13x - 1)^{10} = 0" + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 114, + 343, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 114, + 343, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 114, + 343, + 119 + ], + "type": "text", + "content": "2. Rewrite the equation:" + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 120, + 373, + 124 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 373, + 124 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 373, + 124 + ], + "type": "text", + "content": "Notice that the equation can be rewritten as:" + } + ] + } + ], + "index": 51 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 383, + 131, + 417, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 131, + 417, + 137 + ], + "spans": [ + { + "bbox": [ + 383, + 131, + 417, + 137 + ], + "type": "interline_equation", + "content": "x ^ {1 0} = - (1 3 x - 1) ^ {1 0}.", + "image_path": "6525765c83f841fa74203734033cb3929d8d0bde8888d550d515f348b36a5f29.jpg" + } + ] + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 141, + 339, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 141, + 339, + 145 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 339, + 145 + ], + "type": "text", + "content": "3. Consider the roots:" + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 146, + 482, + 167 + ], + "type": "list", + "angle": 0, + "index": 58, + "blocks": [ + { + "bbox": [ + 304, + 146, + 482, + 154 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 146, + 482, + 154 + ], + "spans": [ + { + "bbox": [ + 304, + 146, + 482, + 154 + ], + "type": "text", + "content": "The roots of the equation are given as " + }, + { + "bbox": [ + 304, + 146, + 482, + 154 + ], + "type": "inline_equation", + "content": "r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5" + }, + { + "bbox": [ + 304, + 146, + 482, + 154 + ], + "type": "text", + "content": ", where the bar denotes complex conjugation. 4. Use the property of complex conjugates:" + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "spans": [ + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "text", + "content": "For any complex number " + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "text", + "content": ", the product of " + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "text", + "content": " and its conjugate " + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "inline_equation", + "content": "\\overline{z}" + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "text", + "content": " is the square of the modulus of " + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "inline_equation", + "content": "z\\overline{z} = |z|^2" + }, + { + "bbox": [ + 304, + 155, + 476, + 162 + ], + "type": "text", + "content": ". 5. Calculate the required sum:" + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 163, + 351, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 163, + 351, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 163, + 351, + 167 + ], + "type": "text", + "content": "We need to find the value of:" + } + ] + } + ], + "index": 57 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 369, + 175, + 432, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 175, + 432, + 186 + ], + "spans": [ + { + "bbox": [ + 369, + 175, + 432, + 186 + ], + "type": "interline_equation", + "content": "\\frac {1}{r _ {1} F _ {1}} + \\frac {1}{r _ {2} F _ {2}} + \\frac {1}{r _ {3} F _ {3}} + \\frac {1}{r _ {4} F _ {4}} + \\frac {1}{r _ {5} F _ {5}}", + "image_path": "28eba59bcd1627af7ee1dbdd7fe9a9861b579d0aebd07602fe6fed78017ca843.jpg" + } + ] + } + ], + "index": 59 + }, + { + "bbox": [ + 306, + 188, + 391, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 188, + 391, + 193 + ], + "spans": [ + { + "bbox": [ + 306, + 188, + 391, + 193 + ], + "type": "text", + "content": "Using the property from step 4, this can be rewritten as:" + } + ] + } + ], + "index": 60 + }, + { + "bbox": [ + 368, + 199, + 432, + 210 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 199, + 432, + 210 + ], + "spans": [ + { + "bbox": [ + 368, + 199, + 432, + 210 + ], + "type": "interline_equation", + "content": "\\frac {1}{| r _ {1} | ^ {2}} + \\frac {1}{| r _ {2} | ^ {2}} + \\frac {1}{| r _ {3} | ^ {2}} + \\frac {1}{| r _ {4} | ^ {2}} + \\frac {1}{| r _ {5} | ^ {2}} + \\frac {1}{| r _ {6} | ^ {2}}", + "image_path": "b6835da4e0c1c0b9108bd67a52f6f1b3fa00f0b7df3bbbd73a4d0bfb0e85389d.jpg" + } + ] + } + ], + "index": 61 + }, + { + "bbox": [ + 304, + 214, + 495, + 241 + ], + "type": "list", + "angle": 0, + "index": 66, + "blocks": [ + { + "bbox": [ + 304, + 214, + 347, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 214, + 347, + 218 + ], + "spans": [ + { + "bbox": [ + 304, + 214, + 347, + 218 + ], + "type": "text", + "content": "6. Simplify the expression:" + } + ] + } + ], + "index": 62 + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "inline_equation", + "content": "r_1, r_2, r_3, r_4, r_5" + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "content": " are roots of the equation " + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "inline_equation", + "content": "x^{10} = -(13x - 1)^{10}" + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "content": ", the magnitudes " + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "inline_equation", + "content": "|r_i|" + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "content": " are the same for each pair " + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "inline_equation", + "content": "r_1" + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "inline_equation", + "content": "\\overline{r}_i" + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "inline_equation", + "content": "|r_i| = |r_i|" + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "inline_equation", + "content": "i, j" + }, + { + "bbox": [ + 304, + 218, + 495, + 226 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 63 + }, + { + "bbox": [ + 304, + 227, + 356, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 227, + 356, + 231 + ], + "spans": [ + { + "bbox": [ + 304, + 227, + 356, + 231 + ], + "type": "text", + "content": "7. Find the common magnitude:" + } + ] + } + ], + "index": 64 + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "text", + "content": "To find " + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "inline_equation", + "content": "|\\boldsymbol{r}_i|" + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "text", + "content": ", consider the determinants of the terms on both sides of the equation " + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "inline_equation", + "content": "x^{10} = -(13x - 1)^{10}" + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "text", + "content": ". The magnitude of the left side is " + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "inline_equation", + "content": "|z|^10" + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "text", + "content": " and the magnitude of the right side is " + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "inline_equation", + "content": "|13z - 1|^{10}" + }, + { + "bbox": [ + 304, + 232, + 493, + 241 + ], + "type": "text", + "content": ". Therefore:" + } + ] + } + ], + "index": 65 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 384, + 247, + 416, + 254 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 247, + 416, + 254 + ], + "spans": [ + { + "bbox": [ + 384, + 247, + 416, + 254 + ], + "type": "interline_equation", + "content": "| x | ^ {1 0} = | 1 3 x - 1 | ^ {1 0}.", + "image_path": "9f10fb34be2f1c3eccf6de5c2a2b698ca17ec6df1df591b2e8bee7ea6c659fd4.jpg" + } + ] + } + ], + "index": 67 + }, + { + "bbox": [ + 306, + 257, + 371, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 257, + 371, + 262 + ], + "spans": [ + { + "bbox": [ + 306, + 257, + 371, + 262 + ], + "type": "text", + "content": "Taking the 10th root of both sides, we get:" + } + ] + } + ], + "index": 68 + }, + { + "bbox": [ + 387, + 269, + 413, + 274 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 269, + 413, + 274 + ], + "spans": [ + { + "bbox": [ + 387, + 269, + 413, + 274 + ], + "type": "interline_equation", + "content": "\\left| x \\right| = \\left| 1 3 x - 1 \\right|.", + "image_path": "ba93ff6ca809911552f39438514acafb5a346d56b0ab4f63663e3f4afc26565a.jpg" + } + ] + } + ], + "index": 69 + }, + { + "bbox": [ + 304, + 277, + 329, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 329, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 329, + 282 + ], + "type": "text", + "content": "8. Solve for " + }, + { + "bbox": [ + 304, + 277, + 329, + 282 + ], + "type": "inline_equation", + "content": "|x|" + }, + { + "bbox": [ + 304, + 277, + 329, + 282 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 70 + }, + { + "bbox": [ + 304, + 283, + 335, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 283, + 335, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 335, + 287 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 283, + 335, + 287 + ], + "type": "inline_equation", + "content": "|x| = a" + }, + { + "bbox": [ + 304, + 283, + 335, + 287 + ], + "type": "text", + "content": ". Then:" + } + ] + } + ], + "index": 71 + }, + { + "bbox": [ + 388, + 295, + 412, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 295, + 412, + 300 + ], + "spans": [ + { + "bbox": [ + 388, + 295, + 412, + 300 + ], + "type": "interline_equation", + "content": "a = | 1 3 x - 1 |.", + "image_path": "14f1085c1bd170ec01d7d192516fafed37c24536c8291207e594c8f5bd827dd5.jpg" + } + ] + } + ], + "index": 72 + }, + { + "bbox": [ + 304, + 304, + 343, + 322 + ], + "type": "list", + "angle": 0, + "index": 77, + "blocks": [ + { + "bbox": [ + 304, + 304, + 343, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 343, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 343, + 308 + ], + "type": "text", + "content": "This gives us two cases:" + } + ] + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 309, + 335, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 309, + 335, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 309, + 335, + 314 + ], + "type": "text", + "content": "-α=13a-1" + } + ] + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 314, + 335, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 335, + 318 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 335, + 318 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 304, + 314, + 335, + 318 + ], + "type": "inline_equation", + "content": "a = -(13a - 1)" + } + ] + } + ], + "index": 75 + }, + { + "bbox": [ + 304, + 319, + 340, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 340, + 322 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 340, + 322 + ], + "type": "text", + "content": "Solving the first case:" + } + ] + } + ], + "index": 76 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 365, + 329, + 434, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 329, + 434, + 339 + ], + "spans": [ + { + "bbox": [ + 365, + 329, + 434, + 339 + ], + "type": "interline_equation", + "content": "a = 1 3 a - 1 \\Longrightarrow 1 2 a = 1 \\Longrightarrow a = \\frac {1}{1 2}.", + "image_path": "3c25888f2b698f2efd7b4ef136864d3430e01e3a7ee444879308ad71c36e297e.jpg" + } + ] + } + ], + "index": 78 + }, + { + "bbox": [ + 306, + 342, + 345, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 342, + 345, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 342, + 345, + 346 + ], + "type": "text", + "content": "Solving the second case:" + } + ] + } + ], + "index": 79 + }, + { + "bbox": [ + 365, + 353, + 435, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 353, + 435, + 363 + ], + "spans": [ + { + "bbox": [ + 365, + 353, + 435, + 363 + ], + "type": "interline_equation", + "content": "a = - 1 3 a + 1 \\Rightarrow 1 4 a = 1 \\Rightarrow a = \\frac {1}{1 4}.", + "image_path": "15bca33a252a7d7747e1b41007c900efc23110c386a855fa01292b21327669cf.jpg" + } + ] + } + ], + "index": 80 + }, + { + "bbox": [ + 304, + 365, + 493, + 384 + ], + "type": "list", + "angle": 0, + "index": 84, + "blocks": [ + { + "bbox": [ + 304, + 365, + 493, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 493, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 493, + 373 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 304, + 365, + 493, + 373 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 365, + 493, + 373 + ], + "type": "text", + "content": " must be the same for all roots, we need to check which value is consistent. Given the nature of the problem, we can assume " + }, + { + "bbox": [ + 304, + 365, + 493, + 373 + ], + "type": "inline_equation", + "content": "a = \\frac{1}{2}" + }, + { + "bbox": [ + 304, + 365, + 493, + 373 + ], + "type": "text", + "content": " as the correct magnitude." + } + ] + } + ], + "index": 81 + }, + { + "bbox": [ + 304, + 374, + 347, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 347, + 379 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 347, + 379 + ], + "type": "text", + "content": "9. Calculate the final sum:" + } + ] + } + ], + "index": 82 + }, + { + "bbox": [ + 304, + 379, + 359, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 379, + 359, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 359, + 384 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 304, + 379, + 359, + 384 + ], + "type": "inline_equation", + "content": "|r_i| = \\frac{1}{12}" + }, + { + "bbox": [ + 304, + 379, + 359, + 384 + ], + "type": "text", + "content": " for all i, we have:" + } + ] + } + ], + "index": 83 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 381, + 391, + 419, + 404 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 391, + 419, + 404 + ], + "spans": [ + { + "bbox": [ + 381, + 391, + 419, + 404 + ], + "type": "interline_equation", + "content": "\\frac {1}{| r _ {i} | ^ {2}} = \\frac {1}{(\\mathrm {古}) ^ {2}} = 1 4 4.", + "image_path": "6c039a69d6e8cd9522c4b7613deff397a371db9e812a8d0ec40925ac042bba22.jpg" + } + ] + } + ], + "index": 85 + }, + { + "bbox": [ + 306, + 407, + 340, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 407, + 340, + 411 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 340, + 411 + ], + "type": "text", + "content": "Therefore, the sum is:" + } + ] + } + ], + "index": 86 + }, + { + "bbox": [ + 361, + 418, + 439, + 424 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 418, + 439, + 424 + ], + "spans": [ + { + "bbox": [ + 361, + 418, + 439, + 424 + ], + "type": "interline_equation", + "content": "1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 + 1 4 4 = 5 \\times 1 4 4 = 7 2 0.", + "image_path": "05170e814c4da8f834eb3b09fcc2a7641bdce982966a108ae9e495f6791f6dd7.jpg" + } + ] + } + ], + "index": 87 + }, + { + "bbox": [ + 304, + 428, + 332, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 332, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 332, + 432 + ], + "type": "text", + "content": "10. Final answer:" + } + ] + } + ], + "index": 88 + }, + { + "bbox": [ + 306, + 432, + 392, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 432, + 392, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 432, + 392, + 437 + ], + "type": "interline_equation", + "content": "\\text {The v a l u e o f} \\frac {1}{r _ {1} r _ {1}} + \\frac {1}{r _ {2} r _ {2}} + \\frac {1}{r _ {3} r _ {3}} + \\frac {1}{r _ {4} r _ {4}} + \\frac {1}{r _ {5} r _ {5}} \\text {i s} \\boxed {7 2 0}.", + "image_path": "7241552645a9f715abbfd5856f36fe3e9bf0185fcaa8355ef1915299ed2a840d.jpg" + } + ] + } + ], + "index": 89 + }, + { + "type": "code", + "bbox": [ + 113, + 479, + 479, + 488 + ], + "blocks": [ + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "lines": [ + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "spans": [ + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "type": "text", + "content": "Question: The equation " + }, + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "type": "inline_equation", + "content": "x^{10} + (13x - 1)^{10} = 0" + }, + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "type": "text", + "content": " has 10 complex roots " + }, + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "type": "inline_equation", + "content": "r_1, \\overline{r}_1, r_2, \\overline{r}_2, r_3, \\overline{r}_3, r_4, \\overline{r}_4, r_5, \\overline{r}_5" + }, + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "type": "text", + "content": ", where the bar denotes complex conjugation. Find the value of " + }, + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "type": "inline_equation", + "content": "\\frac{1}{r_1r_4} + \\frac{1}{r_2r_2} + \\frac{1}{r_3r_3} + \\frac{1}{r_4r_4} + \\frac{1}{r_5r_5}" + }, + { + "bbox": [ + 113, + 479, + 479, + 488 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 91, + "angle": 0, + "type": "code_body" + } + ], + "index": 91, + "sub_type": "code", + "guess_lang": "latex" + }, + { + "bbox": [ + 114, + 490, + 171, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 490, + 171, + 494 + ], + "spans": [ + { + "bbox": [ + 114, + 490, + 171, + 494 + ], + "type": "text", + "content": "High-Level Agent's Output" + } + ] + } + ], + "index": 92 + }, + { + "bbox": [ + 217, + 490, + 283, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 217, + 490, + 283, + 495 + ], + "spans": [ + { + "bbox": [ + 217, + 490, + 283, + 495 + ], + "type": "text", + "content": "Low-Level Agent's Output (part I)" + } + ] + } + ], + "index": 93 + }, + { + "bbox": [ + 108, + 495, + 178, + 665 + ], + "type": "list", + "angle": 0, + "index": 115, + "blocks": [ + { + "bbox": [ + 108, + 495, + 171, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 495, + 171, + 506 + ], + "spans": [ + { + "bbox": [ + 108, + 495, + 171, + 506 + ], + "type": "text", + "content": "To solve this problem, we need to follow these steps:" + } + ] + } + ], + "index": 94 + }, + { + "bbox": [ + 108, + 509, + 171, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 509, + 171, + 518 + ], + "spans": [ + { + "bbox": [ + 108, + 509, + 171, + 518 + ], + "type": "text", + "content": "1. Understand the given equation: The equation is " + }, + { + "bbox": [ + 108, + 509, + 171, + 518 + ], + "type": "inline_equation", + "content": "x^{10} - (13x - 1)^{10} = 0" + }, + { + "bbox": [ + 108, + 509, + 171, + 518 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 95 + }, + { + "bbox": [ + 108, + 521, + 166, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 521, + 166, + 526 + ], + "spans": [ + { + "bbox": [ + 108, + 521, + 166, + 526 + ], + "type": "text", + "content": "2. Identify the roots: The roots of the" + } + ] + } + ], + "index": 96 + }, + { + "bbox": [ + 108, + 526, + 142, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 526, + 142, + 530 + ], + "spans": [ + { + "bbox": [ + 108, + 526, + 142, + 530 + ], + "type": "text", + "content": "equation are given as" + } + ] + } + ], + "index": 97 + }, + { + "bbox": [ + 108, + 531, + 176, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 531, + 176, + 541 + ], + "spans": [ + { + "bbox": [ + 108, + 531, + 176, + 541 + ], + "type": "inline_equation", + "content": "\\overline{r_1},\\overline{r_2},\\overline{r_3},\\overline{r_4},\\overline{r_5},\\overline{r_6},\\overline{r_7},\\overline{r_8}" + }, + { + "bbox": [ + 108, + 531, + 176, + 541 + ], + "type": "text", + "content": " where the bar denotes complex conjugation." + } + ] + } + ], + "index": 98 + }, + { + "bbox": [ + 108, + 545, + 176, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 545, + 176, + 550 + ], + "spans": [ + { + "bbox": [ + 108, + 545, + 176, + 550 + ], + "type": "text", + "content": "3. Use properties of complex conjugates:" + } + ] + } + ], + "index": 99 + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "spans": [ + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "text", + "content": "For any complex number " + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "text", + "content": ", the product " + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "inline_equation", + "content": "z \\cdot z" + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "text", + "content": " is a complex function of the modulus of " + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "inline_equation", + "content": "|z \\cdot \\overline{z}| = |z|^2" + }, + { + "bbox": [ + 108, + 551, + 177, + 563 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 100 + }, + { + "bbox": [ + 108, + 568, + 177, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 568, + 177, + 573 + ], + "spans": [ + { + "bbox": [ + 108, + 568, + 177, + 573 + ], + "type": "text", + "content": "4. Simplify the expression: We need to find" + } + ] + } + ], + "index": 101 + }, + { + "bbox": [ + 108, + 574, + 162, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 574, + 162, + 578 + ], + "spans": [ + { + "bbox": [ + 108, + 574, + 162, + 578 + ], + "type": "text", + "content": "the value of 1" + } + ] + } + ], + "index": 102 + }, + { + "bbox": [ + 108, + 578, + 162, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 578, + 162, + 582 + ], + "spans": [ + { + "bbox": [ + 108, + 578, + 162, + 582 + ], + "type": "text", + "content": "r1+ r2r3+ r4" + } + ] + } + ], + "index": 103 + }, + { + "bbox": [ + 108, + 584, + 162, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 584, + 162, + 588 + ], + "spans": [ + { + "bbox": [ + 108, + 584, + 162, + 588 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 104 + }, + { + "bbox": [ + 108, + 590, + 173, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 590, + 173, + 594 + ], + "spans": [ + { + "bbox": [ + 108, + 590, + 173, + 594 + ], + "type": "text", + "content": "Apply an property of complex conjugates. Since " + }, + { + "bbox": [ + 108, + 590, + 173, + 594 + ], + "type": "inline_equation", + "content": "\\pi_1 \\cdot \\overline{\\pi}_1 = |\\pi_1|^2" + }, + { + "bbox": [ + 108, + 590, + 173, + 594 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 105 + }, + { + "bbox": [ + 108, + 594, + 126, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 594, + 126, + 598 + ], + "spans": [ + { + "bbox": [ + 108, + 594, + 126, + 598 + ], + "type": "text", + "content": "1+" + } + ] + } + ], + "index": 106 + }, + { + "bbox": [ + 108, + 600, + 126, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 600, + 126, + 604 + ], + "spans": [ + { + "bbox": [ + 108, + 600, + 126, + 604 + ], + "type": "text", + "content": "A" + } + ] + } + ], + "index": 107 + }, + { + "bbox": [ + 108, + 605, + 171, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 605, + 171, + 609 + ], + "spans": [ + { + "bbox": [ + 108, + 605, + 171, + 609 + ], + "type": "text", + "content": "6.Sum the reciprocals: Sum the values" + } + ] + } + ], + "index": 108 + }, + { + "bbox": [ + 108, + 610, + 162, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 610, + 162, + 615 + ], + "spans": [ + { + "bbox": [ + 108, + 610, + 162, + 615 + ], + "type": "text", + "content": "1+1 1 1" + } + ] + } + ], + "index": 109 + }, + { + "bbox": [ + 108, + 620, + 178, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 620, + 178, + 639 + ], + "spans": [ + { + "bbox": [ + 108, + 620, + 178, + 639 + ], + "type": "text", + "content": "7. Use Vieta's formulas: To find the sum of the reciprocals of the moduli squared, we can use the fact that the sum of the roots of the polynomial and their properties." + } + ] + } + ], + "index": 110 + }, + { + "bbox": [ + 108, + 643, + 172, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 643, + 172, + 647 + ], + "spans": [ + { + "bbox": [ + 108, + 643, + 172, + 647 + ], + "type": "text", + "content": "8. Finalize the solution: Combine all the" + } + ] + } + ], + "index": 111 + }, + { + "bbox": [ + 108, + 647, + 151, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 647, + 151, + 651 + ], + "spans": [ + { + "bbox": [ + 108, + 647, + 151, + 651 + ], + "type": "text", + "content": "steps to find the final value" + } + ] + } + ], + "index": 112 + }, + { + "bbox": [ + 108, + 655, + 175, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 655, + 175, + 659 + ], + "spans": [ + { + "bbox": [ + 108, + 655, + 175, + 659 + ], + "type": "text", + "content": "Now, let's guide the low-level math solving" + } + ] + } + ], + "index": 113 + }, + { + "bbox": [ + 108, + 660, + 157, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 660, + 157, + 665 + ], + "spans": [ + { + "bbox": [ + 108, + 660, + 157, + 665 + ], + "type": "text", + "content": "agent to implement these steps." + } + ] + } + ], + "index": 114 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 182, + 495, + 316, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 495, + 316, + 498 + ], + "spans": [ + { + "bbox": [ + 182, + 495, + 316, + 498 + ], + "type": "text", + "content": "To solve the given problem, we start by analyzing the equation " + }, + { + "bbox": [ + 182, + 495, + 316, + 498 + ], + "type": "inline_equation", + "content": "x^{10} + (13x - 1)^{10} = 0" + }, + { + "bbox": [ + 182, + 495, + 316, + 498 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 116 + }, + { + "bbox": [ + 182, + 499, + 219, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 499, + 219, + 503 + ], + "spans": [ + { + "bbox": [ + 182, + 499, + 219, + 503 + ], + "type": "text", + "content": "This can be rewritten as:" + } + ] + } + ], + "index": 117 + }, + { + "bbox": [ + 234, + 507, + 268, + 511 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 234, + 507, + 268, + 511 + ], + "spans": [ + { + "bbox": [ + 234, + 507, + 268, + 511 + ], + "type": "interline_equation", + "content": "x ^ {1 0} = - (1 3 x - 1) ^ {1 0}.", + "image_path": "f5bf38bd49abe8bfdb677b4b0f81847c247b0abe866c361f4b13aeab02a794fc.jpg" + } + ] + } + ], + "index": 118 + }, + { + "bbox": [ + 182, + 515, + 247, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 515, + 247, + 520 + ], + "spans": [ + { + "bbox": [ + 182, + 515, + 247, + 520 + ], + "type": "text", + "content": "Taking the 10th root on both sides, we get:" + } + ] + } + ], + "index": 119 + }, + { + "bbox": [ + 220, + 524, + 264, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 220, + 524, + 264, + 528 + ], + "spans": [ + { + "bbox": [ + 220, + 524, + 264, + 528 + ], + "type": "interline_equation", + "content": "x = \\omega (1 3 x - 1),", + "image_path": "50ccdd806d3c2fbb81d2905bb78d2552273c33edff77da4aad98cefd9ca79a0c.jpg" + } + ] + } + ], + "index": 120 + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "spans": [ + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "text", + "content": " is a 10th root of " + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "text", + "content": ". The 10th roots of " + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "text", + "content": " are given by " + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "inline_equation", + "content": "\\omega = e^{\\pi (2k + 1) / 10}" + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "inline_equation", + "content": "k = 0, 1, 2, \\ldots, 9" + }, + { + "bbox": [ + 182, + 532, + 310, + 541 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 121 + }, + { + "bbox": [ + 182, + 545, + 233, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 545, + 233, + 550 + ], + "spans": [ + { + "bbox": [ + 182, + 545, + 233, + 550 + ], + "type": "text", + "content": "Rewriting the equation, we have:" + } + ] + } + ], + "index": 122 + }, + { + "bbox": [ + 183, + 553, + 317, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 183, + 553, + 317, + 563 + ], + "spans": [ + { + "bbox": [ + 183, + 553, + 317, + 563 + ], + "type": "inline_equation", + "content": "x = \\omega (13x - 1)\\Rightarrow x - 13\\omega x = -\\omega \\Rightarrow x(1 - 13\\omega) = -\\omega \\Rightarrow x = \\frac{-\\omega}{1 - 13\\omega}" + } + ] + } + ], + "index": 123 + }, + { + "bbox": [ + 182, + 564, + 235, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 564, + 235, + 568 + ], + "spans": [ + { + "bbox": [ + 182, + 564, + 235, + 568 + ], + "type": "text", + "content": "Thus, the roots of the equation are:" + } + ] + } + ], + "index": 124 + }, + { + "bbox": [ + 183, + 574, + 264, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 183, + 574, + 264, + 582 + ], + "spans": [ + { + "bbox": [ + 183, + 574, + 264, + 582 + ], + "type": "interline_equation", + "content": "r _ {k} = \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}}", + "image_path": "528333c7c549e5b59e02481e7570b1ab4ebdcf2fe735070193c07c2a4fc150ac.jpg" + } + ] + } + ], + "index": 125 + }, + { + "bbox": [ + 182, + 585, + 241, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 585, + 241, + 589 + ], + "spans": [ + { + "bbox": [ + 182, + 585, + 241, + 589 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 182, + 585, + 241, + 589 + ], + "type": "inline_equation", + "content": "\\omega_{k} = e^{i\\pi (2k + 1) / 10}" + }, + { + "bbox": [ + 182, + 585, + 241, + 589 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 182, + 585, + 241, + 589 + ], + "type": "inline_equation", + "content": "k = 0,1,2" + } + ] + } + ], + "index": 126 + }, + { + "bbox": [ + 182, + 594, + 315, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 594, + 315, + 603 + ], + "spans": [ + { + "bbox": [ + 182, + 594, + 315, + 603 + ], + "type": "text", + "content": "The roots come in conjugate pairs, so the roots are " + }, + { + "bbox": [ + 182, + 594, + 315, + 603 + ], + "type": "inline_equation", + "content": "r_1, \\overline{r_1}, r_2, \\overline{r_2}, r_3, \\overline{r_3}, r_4, \\overline{r_4}, r_5, \\overline{r_5}" + }, + { + "bbox": [ + 182, + 594, + 315, + 603 + ], + "type": "text", + "content": ". We need to find the value of:" + } + ] + } + ], + "index": 127 + }, + { + "bbox": [ + 219, + 605, + 282, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 219, + 605, + 282, + 616 + ], + "spans": [ + { + "bbox": [ + 219, + 605, + 282, + 616 + ], + "type": "interline_equation", + "content": "\\frac {1}{r _ {1} \\overline {{r _ {1}}}} + \\frac {1}{r _ {2} \\overline {{r _ {2}}}} + \\frac {1}{r _ {3} \\overline {{r _ {3}}}} + \\frac {1}{r _ {4} \\overline {{r _ {4}}}} + \\frac {1}{r _ {5} \\overline {{r _ {5}}}}", + "image_path": "c6e921c75e514affe23ba47738a4334e7ae564f4ed6caa716d917d2741943324.jpg" + } + ] + } + ], + "index": 128 + }, + { + "bbox": [ + 182, + 618, + 227, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 618, + 227, + 623 + ], + "spans": [ + { + "bbox": [ + 182, + 618, + 227, + 623 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 182, + 618, + 227, + 623 + ], + "type": "inline_equation", + "content": "r_k\\overline{r_k} = |r_k|^2" + }, + { + "bbox": [ + 182, + 618, + 227, + 623 + ], + "type": "text", + "content": " we have:" + } + ] + } + ], + "index": 129 + }, + { + "bbox": [ + 239, + 626, + 263, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 239, + 626, + 263, + 637 + ], + "spans": [ + { + "bbox": [ + 239, + 626, + 263, + 637 + ], + "type": "interline_equation", + "content": "\\frac {1}{r _ {k} r _ {k}} = \\frac {1}{| r _ {k} | ^ {2}}", + "image_path": "4c2a5c3a0dfb0eb00cd8928e39973a9df874ba2cf7234966644df2fb2cd4cdb1.jpg" + } + ] + } + ], + "index": 130 + }, + { + "bbox": [ + 182, + 640, + 231, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 640, + 231, + 644 + ], + "spans": [ + { + "bbox": [ + 182, + 640, + 231, + 644 + ], + "type": "text", + "content": "We need to find " + }, + { + "bbox": [ + 182, + 640, + 231, + 644 + ], + "type": "inline_equation", + "content": "|r_k|^2" + }, + { + "bbox": [ + 182, + 640, + 231, + 644 + ], + "type": "text", + "content": ". Note that:" + } + ] + } + ], + "index": 131 + }, + { + "bbox": [ + 237, + 648, + 263, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 237, + 648, + 263, + 657 + ], + "spans": [ + { + "bbox": [ + 237, + 648, + 263, + 657 + ], + "type": "interline_equation", + "content": "r _ {k} = \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}}", + "image_path": "938abda3f283b1d544ed098377c88573b548599d2d006a47e793f5c697c16537.jpg" + } + ] + } + ], + "index": 132 + }, + { + "bbox": [ + 377, + 491, + 446, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 491, + 446, + 495 + ], + "spans": [ + { + "bbox": [ + 377, + 491, + 446, + 495 + ], + "type": "text", + "content": "Low-Level Agent's Output (part II)" + } + ] + } + ], + "index": 133 + }, + { + "bbox": [ + 323, + 498, + 359, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 498, + 359, + 503 + ], + "spans": [ + { + "bbox": [ + 323, + 498, + 359, + 503 + ], + "type": "text", + "content": "The magnitude of " + }, + { + "bbox": [ + 323, + 498, + 359, + 503 + ], + "type": "inline_equation", + "content": "r_k" + }, + { + "bbox": [ + 323, + 498, + 359, + 503 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 134 + }, + { + "bbox": [ + 372, + 506, + 449, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 506, + 449, + 517 + ], + "spans": [ + { + "bbox": [ + 372, + 506, + 449, + 517 + ], + "type": "interline_equation", + "content": "| r _ {k} | = \\left| \\frac {- \\omega_ {k}}{1 - 1 3 \\omega_ {k}} \\right| = \\left| \\frac {| \\omega_ {k} |}{1 - 1 3 \\omega_ {k}} \\right| = \\frac {1}{1 - 1 3 \\omega_ {k}}", + "image_path": "4d01cf958b1cef0ac5f73fe67da58dfb9f7784a3720c1d5bf7c308c749b09a32.jpg" + } + ] + } + ], + "index": 135 + }, + { + "bbox": [ + 323, + 520, + 332, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 520, + 332, + 524 + ], + "spans": [ + { + "bbox": [ + 323, + 520, + 332, + 524 + ], + "type": "text", + "content": "Thus," + } + ] + } + ], + "index": 136 + }, + { + "bbox": [ + 394, + 527, + 428, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 527, + 428, + 537 + ], + "spans": [ + { + "bbox": [ + 394, + 527, + 428, + 537 + ], + "type": "interline_equation", + "content": "| r _ {k} | ^ {2} = \\frac {1}{| 1 - 1 3 \\omega_ {k} | ^ {2}}", + "image_path": "a64ee91f6fec3fd7b197bb471e73dc04d0d0d12e6b2af7b48fca4a932ea681cb.jpg" + } + ] + } + ], + "index": 137 + }, + { + "bbox": [ + 323, + 540, + 339, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 540, + 339, + 544 + ], + "spans": [ + { + "bbox": [ + 323, + 540, + 339, + 544 + ], + "type": "text", + "content": "Therefore," + } + ] + } + ], + "index": 138 + }, + { + "bbox": [ + 394, + 548, + 429, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 548, + 429, + 558 + ], + "spans": [ + { + "bbox": [ + 394, + 548, + 429, + 558 + ], + "type": "interline_equation", + "content": "\\frac {1}{r _ {2} r _ {1}} = | 1 - 1 3 \\omega_ {k} | ^ {2}.", + "image_path": "3fd02be075315fbd643707dc3d3d5497904efd1829a267bf356bdc98e9fbe27f.jpg" + } + ] + } + ], + "index": 139 + }, + { + "bbox": [ + 323, + 562, + 392, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 562, + 392, + 566 + ], + "spans": [ + { + "bbox": [ + 323, + 562, + 392, + 566 + ], + "type": "text", + "content": "We need to sum this over the 5 pairs of roots:" + } + ] + } + ], + "index": 140 + }, + { + "bbox": [ + 398, + 569, + 424, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 398, + 569, + 424, + 580 + ], + "spans": [ + { + "bbox": [ + 398, + 569, + 424, + 580 + ], + "type": "interline_equation", + "content": "\\sum_ {k = 0} ^ {4} | 1 - 1 3 \\omega_ {k} | ^ {2}", + "image_path": "80fb1f97ec83f17fbd8b560be77fe8de42b9125cf2446d0cdbeb37b3b7666a68.jpg" + } + ] + } + ], + "index": 141 + }, + { + "bbox": [ + 323, + 585, + 373, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 585, + 373, + 589 + ], + "spans": [ + { + "bbox": [ + 323, + 585, + 373, + 589 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 323, + 585, + 373, + 589 + ], + "type": "inline_equation", + "content": "\\omega_{k} = e^{i\\pi (2k + 1) / 10}" + }, + { + "bbox": [ + 323, + 585, + 373, + 589 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 142 + }, + { + "bbox": [ + 323, + 592, + 497, + 605 + ], + "type": "list", + "angle": 0, + "index": 145, + "blocks": [ + { + "bbox": [ + 324, + 592, + 497, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 592, + 497, + 597 + ], + "spans": [ + { + "bbox": [ + 324, + 592, + 497, + 597 + ], + "type": "inline_equation", + "content": "|1 - 13\\omega_{k}|^{2} = (1 - 13\\omega_{k})(1 - 13\\overline{\\omega_{k}}) = (1 - 13\\omega_{k})(1 - 13e^{-i\\pi (2k + 1) / 10}) = 1 - 13\\omega_{k} - 13e^{-i\\pi (2k + 1) / 10} + 169." + } + ] + } + ], + "index": 143 + }, + { + "bbox": [ + 323, + 600, + 361, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 600, + 361, + 605 + ], + "spans": [ + { + "bbox": [ + 323, + 600, + 361, + 605 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 323, + 600, + 361, + 605 + ], + "type": "inline_equation", + "content": "\\omega_{k}\\overline{\\omega_{k}} = 1" + }, + { + "bbox": [ + 323, + 600, + 361, + 605 + ], + "type": "text", + "content": " we get:" + } + ] + } + ], + "index": 144 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 323, + 609, + 500, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 609, + 500, + 619 + ], + "spans": [ + { + "bbox": [ + 323, + 609, + 500, + 619 + ], + "type": "interline_equation", + "content": "\\left| 1 - 1 3 \\omega_ {k} \\right| ^ {2} = 1 6 9 - 1 3 (\\omega_ {k} + e ^ {- i \\pi (2 k + 1) \\cdot 1 0}) + 1 = 1 7 0 - 1 3 \\cdot 2 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right) = 1 7 0 - 2 6 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right)", + "image_path": "d51f2e94513b319fbfd3670c878bfba4fad1b14bbbb2d664cf5d96071695f0f5.jpg" + } + ] + } + ], + "index": 146 + }, + { + "bbox": [ + 323, + 622, + 383, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 622, + 383, + 627 + ], + "spans": [ + { + "bbox": [ + 323, + 622, + 383, + 627 + ], + "type": "text", + "content": "Summing over " + }, + { + "bbox": [ + 323, + 622, + 383, + 627 + ], + "type": "inline_equation", + "content": "k = 0,1,2,3,4" + }, + { + "bbox": [ + 323, + 622, + 383, + 627 + ], + "type": "text", + "content": " we get:" + } + ] + } + ], + "index": 147 + }, + { + "bbox": [ + 335, + 630, + 487, + 642 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 630, + 487, + 642 + ], + "spans": [ + { + "bbox": [ + 335, + 630, + 487, + 642 + ], + "type": "interline_equation", + "content": "\\sum_ {k = 0} ^ {n - 1} \\left(1 7 0 - 2 6 \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right)\\right) = 5 \\cdot 1 7 0 - 2 6 \\sum_ {k = 0} ^ {n - 1} \\cos \\left(\\frac {\\pi (2 k + 1)}{1 0}\\right) = 8 5 0 - 2 6 \\cdot 0 = 8 5 0.", + "image_path": "8748dabc4481672874c3f2795f0d6264a961d9e141b9cdee0eb288d7db2dc87c.jpg" + } + ] + } + ], + "index": 148 + }, + { + "bbox": [ + 323, + 646, + 351, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 646, + 351, + 650 + ], + "spans": [ + { + "bbox": [ + 323, + 646, + 351, + 650 + ], + "type": "text", + "content": "Thus, the value is:" + } + ] + } + ], + "index": 149 + }, + { + "type": "image", + "bbox": [ + 406, + 653, + 416, + 658 + ], + "blocks": [ + { + "bbox": [ + 174, + 451, + 436, + 463 + ], + "lines": [ + { + "bbox": [ + 174, + 451, + 436, + 463 + ], + "spans": [ + { + "bbox": [ + 174, + 451, + 436, + 463 + ], + "type": "text", + "content": "Figure 10: Case Study for consistency reward of high-level agent" + } + ] + } + ], + "index": 90, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 406, + 653, + 416, + 658 + ], + "lines": [ + { + "bbox": [ + 406, + 653, + 416, + 658 + ], + "spans": [ + { + "bbox": [ + 406, + 653, + 416, + 658 + ], + "type": "image", + "image_path": "6cce98a8906c58ccf3aa6cedf13fe8485572fcdb57dd27e9b6cd696eb48335fd.jpg" + } + ] + } + ], + "index": 150, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 164, + 674, + 446, + 686 + ], + "lines": [ + { + "bbox": [ + 164, + 674, + 446, + 686 + ], + "spans": [ + { + "bbox": [ + 164, + 674, + 446, + 686 + ], + "type": "text", + "content": "Figure 11: Case Study for base correctness reward of high-level agent" + } + ] + } + ], + "index": 151, + "angle": 0, + "type": "image_caption" + } + ], + "index": 150 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "32" + } + ] + } + ], + "index": 152 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 31 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 148, + 77, + 462, + 87 + ], + "blocks": [ + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "lines": [ + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "spans": [ + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "text", + "content": "Question: The product of " + }, + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "inline_equation", + "content": "3t^{2} + 5t + a" + }, + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "inline_equation", + "content": "4t^{2} + bt - 2" + }, + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "inline_equation", + "content": "12t^{4} + 26t^{3} - 8t^{2} - 16t + 6" + }, + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "text", + "content": ". What is " + }, + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "inline_equation", + "content": "a + b" + }, + { + "bbox": [ + 148, + 77, + 462, + 87 + ], + "type": "text", + "content": "?" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_body" + }, + { + "bbox": [ + 309, + 93, + 421, + 102 + ], + "lines": [ + { + "bbox": [ + 309, + 93, + 421, + 102 + ], + "spans": [ + { + "bbox": [ + 309, + 93, + 421, + 102 + ], + "type": "text", + "content": "Llama3.2-1B-Instruct training Output:" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "code_caption" + } + ], + "index": 0, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 108, + 106, + 304, + 144 + ], + "blocks": [ + { + "bbox": [ + 108, + 93, + 219, + 102 + ], + "lines": [ + { + "bbox": [ + 108, + 93, + 219, + 102 + ], + "spans": [ + { + "bbox": [ + 108, + 93, + 219, + 102 + ], + "type": "text", + "content": "Llama3.1-8B-Instruct training Output:" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 108, + 106, + 304, + 144 + ], + "lines": [ + { + "bbox": [ + 108, + 106, + 304, + 144 + ], + "spans": [ + { + "bbox": [ + 108, + 106, + 304, + 144 + ], + "type": "text", + "content": "{\n \"action\": \"DECOMPOSE\",\n \"output\": \"Decompose the problem into finding the coefficients of the product of two polynomials and then solving for a and b.\"\n}" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "code_body" + } + ], + "index": 2, + "sub_type": "code", + "guess_lang": "json" + }, + { + "type": "code", + "bbox": [ + 311, + 106, + 503, + 145 + ], + "blocks": [ + { + "bbox": [ + 311, + 106, + 503, + 145 + ], + "lines": [ + { + "bbox": [ + 311, + 106, + 503, + 145 + ], + "spans": [ + { + "bbox": [ + 311, + 106, + 503, + 145 + ], + "type": "text", + "content": "{ \"action\": \"EMPTY\", \"output\".\"\" }" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "code_body" + } + ], + "index": 4, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 108, + 150, + 294, + 369 + ], + "blocks": [ + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "lines": [ + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "spans": [ + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": "Step 1: To find the product of the two polynomials " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "3t^{2} + 5t + a" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "4t^{2} + bt - 2" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", we need to multiply each term of the first polynomial by each term of the second polynomial and then combine like terms. \nStep 2: The product of the two polynomials can be written as " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "(3t^{2} + 5t + a)(4t^{2} + bt - 2)" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 3: Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial: " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "(3t^{2})(4t^{2}) + (3t^{2})(bt) + (3t^{2})(-2) + (5t)(4t^{2}) + (5t)(bt) + (5t)(-2) + (a)(4t^{2}) + (a)(bt) + (a)(-2)" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 4: Simplifying the products, we get " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "12t^{4} + 3b^{3} - 6t^{2} + 20t^{3} + 5bt^{2} - 10t + 4at^{2} + abt - 2a" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 5: Combining like terms, we have " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "12t^{4} + (3b + 20)t^{3} + (5b - 6 + 4a)t^{2} + (ab - 10)t - 2a" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 6: We are given that the product of the two polynomials is " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "12t^{4} + 26t^{3} - 8t^{2} - 16t + 6" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nWe can equate the coefficients of the corresponding powers of " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": " in the two expressions. \nStep 7: Equating the coefficients of " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "t^3" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", we get " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "3b + 20 = 26" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 8: Equating the coefficients of " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "t^2" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", we get " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "5b - 6 + 4a = -8" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 9: Equating the constant terms, we get " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "-2a = 6" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 10: Solving the equation " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "-2a = 6" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", we find that " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "a = -3" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 11: Substituting " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "a = -3" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": " into the equation " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "5b - 6 + 4a = -8" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", we get " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "5b - 6 + 4(-3) = -8" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", which simplifies to " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "5b - 18 = -8" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 12: Solving for " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", we find that " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "5b = 10" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", so " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "b = 2" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nStep 13: Now that we have found the values of " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ", we can calculate their sum: " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "a + b = -3 + 2 = -1" + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "text", + "content": ". \nThe final answer is: " + }, + { + "bbox": [ + 108, + 150, + 294, + 369 + ], + "type": "inline_equation", + "content": "\\boxed{-1}" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "code_body" + } + ], + "index": 5, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 154, + 496, + 177 + ], + "blocks": [ + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "lines": [ + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "spans": [ + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "text", + "content": "Step 1: The problem asks us to find the values of " + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "text", + "content": " in the quadratic expressions " + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "inline_equation", + "content": "3t^2 + 5t + a" + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "inline_equation", + "content": "4t^2 + bt - 2" + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "text", + "content": ", respectively, given that their product is " + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "inline_equation", + "content": "12t^4 + 26t^3 - 8t^2 - 16t + 6" + }, + { + "bbox": [ + 310, + 154, + 496, + 177 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "code_body" + } + ], + "index": 6, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 184, + 501, + 207 + ], + "blocks": [ + { + "bbox": [ + 310, + 184, + 501, + 207 + ], + "lines": [ + { + "bbox": [ + 310, + 184, + 501, + 207 + ], + "spans": [ + { + "bbox": [ + 310, + 184, + 501, + 207 + ], + "type": "text", + "content": "Step 2: To solve this, we need to multiply the two quadratic expressions and equate the resulting expression to the given product " + }, + { + "bbox": [ + 310, + 184, + 501, + 207 + ], + "type": "inline_equation", + "content": "12t^4 + 26t^3 - 8t^2 - 16t + 6" + }, + { + "bbox": [ + 310, + 184, + 501, + 207 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "code_body" + } + ], + "index": 7, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 214, + 466, + 230 + ], + "blocks": [ + { + "bbox": [ + 310, + 214, + 466, + 230 + ], + "lines": [ + { + "bbox": [ + 310, + 214, + 466, + 230 + ], + "spans": [ + { + "bbox": [ + 310, + 214, + 466, + 230 + ], + "type": "text", + "content": "Step 3: We start by multiplying the two quadratic expressions: " + }, + { + "bbox": [ + 310, + 214, + 466, + 230 + ], + "type": "inline_equation", + "content": "(3t^{2} + 5t + a)(4t^{2} + bt - 2)" + }, + { + "bbox": [ + 310, + 214, + 466, + 230 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "code_body" + } + ], + "index": 8, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 237, + 477, + 252 + ], + "blocks": [ + { + "bbox": [ + 310, + 237, + 477, + 252 + ], + "lines": [ + { + "bbox": [ + 310, + 237, + 477, + 252 + ], + "spans": [ + { + "bbox": [ + 310, + 237, + 477, + 252 + ], + "type": "text", + "content": "Step 4: This gives us " + }, + { + "bbox": [ + 310, + 237, + 477, + 252 + ], + "type": "inline_equation", + "content": "12t^4 + (3b + 5)t^3 + (4a + 5b - 6)t^2 + (-2b + 10t + 2a)t - 2a." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_body" + } + ], + "index": 9, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 258, + 499, + 274 + ], + "blocks": [ + { + "bbox": [ + 310, + 258, + 499, + 274 + ], + "lines": [ + { + "bbox": [ + 310, + 258, + 499, + 274 + ], + "spans": [ + { + "bbox": [ + 310, + 258, + 499, + 274 + ], + "type": "text", + "content": "Step 5: We know that the coefficients of the resulting expression must be equal to the coefficients of the given product " + }, + { + "bbox": [ + 310, + 258, + 499, + 274 + ], + "type": "inline_equation", + "content": "12t^4 + 26t^3 - 8t^2 - 16t + 6" + }, + { + "bbox": [ + 310, + 258, + 499, + 274 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 281, + 495, + 296 + ], + "blocks": [ + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "lines": [ + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "spans": [ + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "text", + "content": "Step 6: Equating the coefficients of " + }, + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "inline_equation", + "content": "t^3" + }, + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "text", + "content": " gives us the equation " + }, + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "inline_equation", + "content": "3b + 5 = 26" + }, + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "text", + "content": ", which simplifies to " + }, + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "inline_equation", + "content": "3b = 21" + }, + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "text", + "content": " and thus " + }, + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "inline_equation", + "content": "b = 7" + }, + { + "bbox": [ + 310, + 281, + 495, + 296 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_body" + } + ], + "index": 11, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 303, + 496, + 319 + ], + "blocks": [ + { + "bbox": [ + 310, + 303, + 496, + 319 + ], + "lines": [ + { + "bbox": [ + 310, + 303, + 496, + 319 + ], + "spans": [ + { + "bbox": [ + 310, + 303, + 496, + 319 + ], + "type": "text", + "content": "Step 7: Equating the constant terms gives us " + }, + { + "bbox": [ + 310, + 303, + 496, + 319 + ], + "type": "inline_equation", + "content": "-2a = -6" + }, + { + "bbox": [ + 310, + 303, + 496, + 319 + ], + "type": "text", + "content": ", which simplifies to " + }, + { + "bbox": [ + 310, + 303, + 496, + 319 + ], + "type": "inline_equation", + "content": "a = 3" + }, + { + "bbox": [ + 310, + 303, + 496, + 319 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "code_body" + } + ], + "index": 12, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 326, + 499, + 334 + ], + "blocks": [ + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "lines": [ + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "spans": [ + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "type": "text", + "content": "Step 8: Now that we have the values of " + }, + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "type": "text", + "content": ", we can find the sum " + }, + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "type": "inline_equation", + "content": "a + b" + }, + { + "bbox": [ + 310, + 326, + 499, + 334 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "code_body" + } + ], + "index": 13, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 340, + 446, + 348 + ], + "blocks": [ + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "lines": [ + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "spans": [ + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "type": "text", + "content": "Step 9: Adding " + }, + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "type": "inline_equation", + "content": "a = 3" + }, + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "type": "inline_equation", + "content": "b = 7" + }, + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "type": "text", + "content": " gives us " + }, + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "type": "inline_equation", + "content": "a + b = 10" + }, + { + "bbox": [ + 310, + 340, + 446, + 348 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "code_body" + } + ], + "index": 14, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 310, + 355, + 373, + 364 + ], + "blocks": [ + { + "bbox": [ + 310, + 355, + 373, + 364 + ], + "lines": [ + { + "bbox": [ + 310, + 355, + 373, + 364 + ], + "spans": [ + { + "bbox": [ + 310, + 355, + 373, + 364 + ], + "type": "text", + "content": "The final answer is: " + }, + { + "bbox": [ + 310, + 355, + 373, + 364 + ], + "type": "inline_equation", + "content": "\\boxed{10}" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "code_body" + } + ], + "index": 15, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 162, + 377, + 447, + 389 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 162, + 377, + 447, + 389 + ], + "spans": [ + { + "bbox": [ + 162, + 377, + 447, + 389 + ], + "type": "text", + "content": "Figure 12: Case Study for interpretability experiments in Section 4.2.2" + } + ] + } + ], + "index": 16, + "type": "text" + }, + { + "type": "code", + "bbox": [ + 108, + 423, + 476, + 565 + ], + "blocks": [ + { + "bbox": [ + 108, + 411, + 175, + 422 + ], + "lines": [ + { + "bbox": [ + 108, + 411, + 175, + 422 + ], + "spans": [ + { + "bbox": [ + 108, + 411, + 175, + 422 + ], + "type": "text", + "content": "System prompt:" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 108, + 423, + 476, + 565 + ], + "lines": [ + { + "bbox": [ + 108, + 423, + 476, + 565 + ], + "spans": [ + { + "bbox": [ + 108, + 423, + 476, + 565 + ], + "type": "text", + "content": "You are a math expert trying to solve mathematical problems. Before answering a question, your task is to decompose the original question to make it clearer. \nProvide your rewritten content in JSON format: \n{\"action\": \"DECOMPOSE\", \"output\": \"{decomposed question content}}\" \n}} \nRespond only with valid JSON. Do not write an introduction or summary. \nUser prompt: \nHere is the question: [problem.text]" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "code_body" + } + ], + "index": 18, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 106, + 571, + 458, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 571, + 458, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 571, + 458, + 582 + ], + "type": "text", + "content": "Prompt for generating final answers using on the question and metacognition reasoning:" + } + ] + } + ], + "index": 19 + }, + { + "type": "code", + "bbox": [ + 108, + 602, + 500, + 646 + ], + "blocks": [ + { + "bbox": [ + 108, + 590, + 174, + 601 + ], + "lines": [ + { + "bbox": [ + 108, + 590, + 174, + 601 + ], + "spans": [ + { + "bbox": [ + 108, + 590, + 174, + 601 + ], + "type": "text", + "content": "System prompt:" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 108, + 602, + 500, + 646 + ], + "lines": [ + { + "bbox": [ + 108, + 602, + 500, + 646 + ], + "spans": [ + { + "bbox": [ + 108, + 602, + 500, + 646 + ], + "type": "text", + "content": "You are a math expert tasked with solving problems step by step. Follow the provided instructions precisely, showing all reasoning and intermediate steps. Present the final answer within \\boxed{\\{\\}}\\}." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "code_body" + }, + { + "bbox": [ + 109, + 646, + 164, + 655 + ], + "lines": [ + { + "bbox": [ + 109, + 646, + 164, + 655 + ], + "spans": [ + { + "bbox": [ + 109, + 646, + 164, + 655 + ], + "type": "text", + "content": "User prompt:" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "code_caption" + } + ], + "index": 21, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "type": "code", + "bbox": [ + 108, + 656, + 337, + 710 + ], + "blocks": [ + { + "bbox": [ + 108, + 656, + 337, + 710 + ], + "lines": [ + { + "bbox": [ + 108, + 656, + 337, + 710 + ], + "spans": [ + { + "bbox": [ + 108, + 656, + 337, + 710 + ], + "type": "text", + "content": "Here is the question and instructions: \nQuestion \n[problem_text] \nProvided Instruction \n[instruction_text]" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "code_body" + } + ], + "index": 23, + "sub_type": "code", + "guess_lang": "txt" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "33" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 32 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 261, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 261, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 261, + 85 + ], + "type": "text", + "content": "G.1.2 Prompts for Math problems" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 91, + 167, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 91, + 167, + 103 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 167, + 103 + ], + "type": "text", + "content": "VRP prompt:" + } + ] + } + ], + "index": 1 + }, + { + "type": "code", + "bbox": [ + 106, + 104, + 493, + 173 + ], + "blocks": [ + { + "bbox": [ + 106, + 104, + 493, + 173 + ], + "lines": [ + { + "bbox": [ + 106, + 104, + 493, + 173 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 493, + 173 + ], + "type": "text", + "content": "System prompt: \nYou are a math expert tasked with solving problems step by step. Present the final answer within \\boxed{}?. \nUser prompt: \nHere is the question: \n{Question}" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "code_body" + } + ], + "index": 2, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 106, + 178, + 169, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 178, + 169, + 190 + ], + "spans": [ + { + "bbox": [ + 106, + 178, + 169, + 190 + ], + "type": "text", + "content": "MRP prompt:" + } + ] + } + ], + "index": 3 + }, + { + "type": "code", + "bbox": [ + 106, + 191, + 501, + 303 + ], + "blocks": [ + { + "bbox": [ + 106, + 191, + 501, + 303 + ], + "lines": [ + { + "bbox": [ + 106, + 191, + 501, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 501, + 303 + ], + "type": "text", + "content": "System prompt: \nYou are a math expert tasked with solving problems. When solving a problem, your first task is to provide a high-level solution plan as an instruction. Then you need to follow the provided instructions precisely, showing all reasoning and intermediate steps. Finally, you must present the final answer within boxed}. \nUser prompt: \nHere is the question: {Question}" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "code_body" + } + ], + "index": 4, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 106, + 308, + 186, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 308, + 186, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 186, + 320 + ], + "type": "text", + "content": "MAMRP prompt:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 320, + 175, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 320, + 175, + 331 + ], + "spans": [ + { + "bbox": [ + 106, + 320, + 175, + 331 + ], + "type": "text", + "content": "high-level agent:" + } + ] + } + ], + "index": 6 + }, + { + "type": "code", + "bbox": [ + 106, + 332, + 507, + 487 + ], + "blocks": [ + { + "bbox": [ + 106, + 332, + 507, + 487 + ], + "lines": [ + { + "bbox": [ + 106, + 332, + 507, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 332, + 507, + 487 + ], + "type": "text", + "content": "System prompt: \nYou are a math expert specialized in solving mathematical problems, you need to teach a weaker agent with minimal capability in math how to solve a problem step-by-step. \nYour task is to provide a high-level solution plan for the given problem, in order to guide a low-level math solving agent to solve the problem. \nYou can not directly answer the question. You'll be punished if you include any answer in your response. \nYou need to first think deeply in mind and output your final instruction. \nUser prompt: \nHere is the question: \n{Question}" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "code_body" + } + ], + "index": 7, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 106, + 489, + 171, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 489, + 171, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 171, + 500 + ], + "type": "text", + "content": "low-level agent:" + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 106, + 501, + 501, + 655 + ], + "blocks": [ + { + "bbox": [ + 106, + 501, + 501, + 655 + ], + "lines": [ + { + "bbox": [ + 106, + 501, + 501, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 501, + 655 + ], + "type": "text", + "content": "System prompt: \nYou are a math expert tasked with solving problems step by step. Follow the provided instructions precisely, showing all reasoning and intermediate steps. Present the final answer within \\boxed{}/. User prompt: Here is the question and instructions: [Question] {Question} [End of Question] [Provided Instruction] {instruction} [End of Instruction]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_body" + } + ], + "index": 9, + "sub_type": "code", + "guess_lang": "txt" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "34" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 33 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 309, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 309, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 309, + 85 + ], + "type": "text", + "content": "G.1.3 Prompts for LLM-as-a-Judge problems" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 91, + 297, + 102 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 91, + 297, + 102 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 297, + 102 + ], + "type": "text", + "content": "We adopt the prompts from Saha et al. [2025a]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 102, + 167, + 114 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 102, + 167, + 114 + ], + "spans": [ + { + "bbox": [ + 105, + 102, + 167, + 114 + ], + "type": "text", + "content": "VRP prompt:" + } + ] + } + ], + "index": 2 + }, + { + "type": "code", + "bbox": [ + 106, + 115, + 507, + 412 + ], + "blocks": [ + { + "bbox": [ + 106, + 115, + 507, + 412 + ], + "lines": [ + { + "bbox": [ + 106, + 115, + 507, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 507, + 412 + ], + "type": "text", + "content": "System prompt: \nPlease act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses. Begin your evaluation by comparing the two responses and provide a short explanation. Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision.. \nDo not allow the length of the responses to influence your evaluation.. \nDo not favor certain names of the assistants. Be as objective as possible. After providing your explanation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better.. \nUser prompt: \n[User Question] {instruction} [End of User Question] [The Start of Assistant A's Answer] {response_A} [The End of Assistant A's Answer] [The Start of Assistant B's Answer] {response_B} [The End of Assistant B's Answer]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "code_body" + } + ], + "index": 3, + "sub_type": "code", + "guess_lang": "txt" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "35" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 34 + }, + { + "para_blocks": [ + { + "bbox": [ + 106, + 72, + 168, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 72, + 168, + 84 + ], + "spans": [ + { + "bbox": [ + 106, + 72, + 168, + 84 + ], + "type": "text", + "content": "MRP prompt:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 108, + 86, + 175, + 97 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 86, + 175, + 97 + ], + "spans": [ + { + "bbox": [ + 108, + 86, + 175, + 97 + ], + "type": "text", + "content": "System prompt:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 108, + 98, + 505, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 98, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 108, + 98, + 505, + 502 + ], + "type": "text", + "content": "Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. First of your task is to build an evaluation plan that can then be executed to assess the response quality. Whenever appropriate, you can choose to also include a step-by-step reference answer as part of the evaluation plan. Enclose your evaluation plan between the tags \"[Start of Evaluation Plan]\" and \"[End of Evaluation Plan)\". After that, please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses. Begin your evaluation by comparing the two responses and provide a short explanation. Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision. Do not allow the length of the responses to influence your evaluation. Do not favor certain names of the assistants. Be as objective as possible. After providing your explanation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better. User prompt: [User Question] {instruction} [End of User Question] [The Start of Assistant A's Answer] {response_A} [The End of Assistant A's Answer] [The Start of Assistant B's Answer] {response_B} [The End of Assistant B's Answer]" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 507, + 254, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 507, + 254, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 507, + 254, + 519 + ], + "type": "text", + "content": "MAMRP prompt: high-level agent:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 521, + 175, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 521, + 175, + 533 + ], + "spans": [ + { + "bbox": [ + 108, + 521, + 175, + 533 + ], + "type": "text", + "content": "System prompt:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 108, + 533, + 488, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 533, + 488, + 598 + ], + "spans": [ + { + "bbox": [ + 108, + 533, + 488, + 598 + ], + "type": "text", + "content": "We want to evaluate the quality of the responses provided by AI assistants to the user question displayed below. For that, your task is to help us build an evaluation plan that can then be executed to assess the response quality. Whenever appropriate, you can choose to also include a step-by-step reference answer as part of the evaluation plan." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 109, + 598, + 164, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 598, + 164, + 609 + ], + "spans": [ + { + "bbox": [ + 109, + 598, + 164, + 609 + ], + "type": "text", + "content": "User prompt:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 110, + 609, + 241, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 609, + 241, + 641 + ], + "spans": [ + { + "bbox": [ + 110, + 609, + 241, + 641 + ], + "type": "text", + "content": "[User Question] \n{Question} \n[End of User Question]" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "36" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 35 + }, + { + "para_blocks": [ + { + "bbox": [ + 106, + 73, + 171, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 73, + 171, + 83 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 171, + 83 + ], + "type": "text", + "content": "low-level agent:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 109, + 87, + 174, + 97 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 87, + 174, + 97 + ], + "spans": [ + { + "bbox": [ + 109, + 87, + 174, + 97 + ], + "type": "text", + "content": "System prompt:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 108, + 98, + 507, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 98, + 507, + 150 + ], + "spans": [ + { + "bbox": [ + 108, + 98, + 507, + 150 + ], + "type": "text", + "content": "Please act as an impartial judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. Your evaluation should be performed by following the provided evaluation plan step-by-step. Avoid copying the plan when doing the evaluation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 108, + 152, + 495, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 152, + 495, + 174 + ], + "spans": [ + { + "bbox": [ + 108, + 152, + 495, + 174 + ], + "type": "text", + "content": "Please also only stick to the given plan and provide explanation of how the plan is executed to compare the two responses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 175, + 494, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 175, + 494, + 195 + ], + "spans": [ + { + "bbox": [ + 108, + 175, + 494, + 195 + ], + "type": "text", + "content": "Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 108, + 196, + 484, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 196, + 484, + 228 + ], + "spans": [ + { + "bbox": [ + 108, + 196, + 484, + 228 + ], + "type": "text", + "content": "Do not allow the length of the responses to influence your evaluation. Do not favor certain names of the assistants. Be as objective as possible." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 108, + 228, + 504, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 228, + 504, + 260 + ], + "spans": [ + { + "bbox": [ + 108, + 228, + 504, + 260 + ], + "type": "text", + "content": "After providing your evaluation, output your final verdict by strictly following this format: \"[A]\" if assistant A is better, \"[B]\" if assistant B is better." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 110, + 262, + 164, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 262, + 164, + 272 + ], + "spans": [ + { + "bbox": [ + 110, + 262, + 164, + 272 + ], + "type": "text", + "content": "User prompt:" + } + ] + } + ], + "index": 7 + }, + { + "type": "code", + "bbox": [ + 109, + 272, + 319, + 403 + ], + "blocks": [ + { + "bbox": [ + 109, + 272, + 319, + 403 + ], + "lines": [ + { + "bbox": [ + 109, + 272, + 319, + 403 + ], + "spans": [ + { + "bbox": [ + 109, + 272, + 319, + 403 + ], + "type": "text", + "content": "[User Question] \n{instruction} \n{End of User Question] \n{The Start of Assistant A's Answer} \n{response_A} \n{The End of Assistant A's Answer} \n{The Start of Assistant B's Answer} \n{response_B} \n{The End of Assistant B's Answer} \n{The Start of Evaluation Plan} \n{evaluation計劃} \n{The End of Evaluation Plan}" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "code_body" + } + ], + "index": 8, + "sub_type": "code", + "guess_lang": "txt" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "37" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 36 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 250, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 250, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 250, + 85 + ], + "type": "text", + "content": "G.2 Multi-turn ReMA prompts" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 324, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 92, + 324, + 103 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 324, + 103 + ], + "type": "text", + "content": "G.2.1 SFT data collection of multi-turn MAMRP" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 108, + 112, + 175, + 123 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 112, + 175, + 123 + ], + "spans": [ + { + "bbox": [ + 108, + 112, + 175, + 123 + ], + "type": "text", + "content": "System prompt:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 108, + 123, + 498, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 123, + 498, + 177 + ], + "spans": [ + { + "bbox": [ + 108, + 123, + 498, + 177 + ], + "type": "text", + "content": "You are classifying reasoning process data into two types of thinking. You will be given a question-answer pair from a reasoning dataset. Your task is to split all words into two parts. These words are crucial for analyzing reasoning patterns, so do not skip any details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 178, + 488, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 178, + 488, + 232 + ], + "spans": [ + { + "bbox": [ + 108, + 178, + 488, + 232 + ], + "type": "text", + "content": "- **Meta-Thinking Agent (MTA):** Responsible for high-level thought processes. This includes planning, evaluating steps, expressing uncertainty, making observations, or setting goals. Avoid detailed calculations. The content should be enclosed in `` and ``." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 108, + 232, + 494, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 232, + 494, + 276 + ], + "spans": [ + { + "bbox": [ + 108, + 232, + 494, + 276 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 108, + 232, + 494, + 276 + ], + "type": "inline_equation", + "content": "\\star \\star" + }, + { + "bbox": [ + 108, + 232, + 494, + 276 + ], + "type": "text", + "content": " Reasoning Agent (RA): " + }, + { + "bbox": [ + 108, + 232, + 494, + 276 + ], + "type": "inline_equation", + "content": "\\star \\star" + }, + { + "bbox": [ + 108, + 232, + 494, + 276 + ], + "type": "text", + "content": " Responsible for detailed problem-solving steps, such as calculations, logical deductions, or breaking down a problem into subproblems. The content should be enclosed in `` and ``." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 108, + 277, + 231, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 277, + 231, + 285 + ], + "spans": [ + { + "bbox": [ + 108, + 277, + 231, + 285 + ], + "type": "text", + "content": "\\*\\*Rules to follow: \\*\\*" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 108, + 287, + 493, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 287, + 493, + 330 + ], + "spans": [ + { + "bbox": [ + 108, + 287, + 493, + 330 + ], + "type": "text", + "content": "1. **Do not assign large chunks of text to a single type of thinking.** The reasoning process consists of small, nonlinear thinking steps, so alternate appropriately between Meta-Thinking and Reasoning steps." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 108, + 331, + 462, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 331, + 462, + 363 + ], + "spans": [ + { + "bbox": [ + 108, + 331, + 462, + 363 + ], + "type": "text", + "content": "2. **Keep the words from the original solution unmodified whenever possible.** Words like \"Wait,\" \"Hmm,\" \"But,\" etc., typically indicate Meta-Thinking and should be preserved." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 108, + 364, + 321, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 364, + 321, + 373 + ], + "spans": [ + { + "bbox": [ + 108, + 364, + 321, + 373 + ], + "type": "text", + "content": "3. " + }, + { + "bbox": [ + 108, + 364, + 321, + 373 + ], + "type": "inline_equation", + "content": "\\star \\star" + }, + { + "bbox": [ + 108, + 364, + 321, + 373 + ], + "type": "text", + "content": " When finalizing the answer: " + }, + { + "bbox": [ + 108, + 364, + 321, + 373 + ], + "type": "inline_equation", + "content": "\\star \\star" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 108, + 374, + 488, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 374, + 488, + 396 + ], + "spans": [ + { + "bbox": [ + 108, + 374, + 488, + 396 + ], + "type": "text", + "content": "- The \\*\\*Meta-Thinking Agent (MTA) \\*\\* must explicitly confirm the answer before completion and output '[FINISH]'." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 108, + 396, + 470, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 396, + 470, + 416 + ], + "spans": [ + { + "bbox": [ + 108, + 396, + 470, + 416 + ], + "type": "text", + "content": "- The " + }, + { + "bbox": [ + 108, + 396, + 470, + 416 + ], + "type": "inline_equation", + "content": "\\star \\star" + }, + { + "bbox": [ + 108, + 396, + 470, + 416 + ], + "type": "text", + "content": " Reasoning Agent (RA) " + }, + { + "bbox": [ + 108, + 396, + 470, + 416 + ], + "type": "inline_equation", + "content": "\\star \\star" + }, + { + "bbox": [ + 108, + 396, + 470, + 416 + ], + "type": "text", + "content": " should then provide the final answer in the correct format." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 108, + 418, + 447, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 418, + 447, + 438 + ], + "spans": [ + { + "bbox": [ + 108, + 418, + 447, + 438 + ], + "type": "text", + "content": "4. **Do not skip any reasoning steps, even if they seem redundant, incorrect or irrelevant**" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 108, + 439, + 500, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 439, + 500, + 472 + ], + "spans": [ + { + "bbox": [ + 108, + 439, + 500, + 472 + ], + "type": "text", + "content": "5. **Do not modify or remove any part of the original reasoning process**, even if it seems redundant or repetitive. The goal is to **preserve the exact flow of thought** as it naturally occurs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 108, + 472, + 500, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 472, + 500, + 505 + ], + "spans": [ + { + "bbox": [ + 108, + 472, + 500, + 505 + ], + "type": "text", + "content": "6. **Retain all expressions such as \"Wait,\" \"Hmm,\" \"But wait,\" etc., exactly as they appear. These indicate important cognitive processes and should not be skipped or altered.**" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 108, + 506, + 265, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 506, + 265, + 526 + ], + "spans": [ + { + "bbox": [ + 108, + 506, + 265, + 526 + ], + "type": "text", + "content": "Here are examples for you: [Examples] ..." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 108, + 527, + 164, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 527, + 164, + 537 + ], + "spans": [ + { + "bbox": [ + 108, + 527, + 164, + 537 + ], + "type": "text", + "content": "User prompt:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 108, + 538, + 223, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 538, + 223, + 603 + ], + "spans": [ + { + "bbox": [ + 108, + 538, + 223, + 603 + ], + "type": "text", + "content": "[Begin of Question] \n{question} \n[End of Question] \n[Begin of Solution] \n{solution} \n[End of Solution]" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "38" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 37 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 255, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 255, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 255, + 85 + ], + "type": "text", + "content": "G.2.2 Prompt for math problems" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 91, + 235, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 91, + 235, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 235, + 102 + ], + "type": "text", + "content": "Meta-Thinking Agent (MTA):" + } + ] + } + ], + "index": 1 + }, + { + "type": "code", + "bbox": [ + 106, + 109, + 506, + 255 + ], + "blocks": [ + { + "bbox": [ + 106, + 109, + 506, + 255 + ], + "lines": [ + { + "bbox": [ + 106, + 109, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 109, + 506, + 255 + ], + "type": "text", + "content": "System prompt: \nYou are a meta-think agent that represents human high-level think process, when solving a question, you will have a discussion with human, each time you think about what to do next: e.g. \n- Exploring multiple angles and approaches \n- Breaking down the solution into clear steps \n- Continuously reflecting on intermediate results honestly and adapt your strategy as you progress \n- Backtracking when necessary \n- Requesting exploration of multiple solutions individually \n- Finally confirm the answer with the tag [FINISH] \nUser prompt: \n{question}" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "code_body" + } + ], + "index": 2, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 106, + 259, + 207, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 259, + 207, + 272 + ], + "spans": [ + { + "bbox": [ + 106, + 259, + 207, + 272 + ], + "type": "text", + "content": "Reasoning Agent (RA):" + } + ] + } + ], + "index": 3 + }, + { + "type": "code", + "bbox": [ + 106, + 277, + 494, + 346 + ], + "blocks": [ + { + "bbox": [ + 106, + 277, + 494, + 346 + ], + "lines": [ + { + "bbox": [ + 106, + 277, + 494, + 346 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 494, + 346 + ], + "type": "text", + "content": "System prompt: Please reason step by step follow the given instruction, when asked to finalize your answer, put your answer within \\boxed{} User prompt: {question} {instruction}" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "code_body" + } + ], + "index": 4, + "sub_type": "code", + "guess_lang": "txt" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "39" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 38 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09567/17e53201-29b3-43fd-8f2e-78d7b00a58a6_content_list.json b/data/2025/2503_09xxx/2503.09567/17e53201-29b3-43fd-8f2e-78d7b00a58a6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8db224c478eb7a4aea02af3611e9532fc9581bfb --- /dev/null +++ b/data/2025/2503_09xxx/2503.09567/17e53201-29b3-43fd-8f2e-78d7b00a58a6_content_list.json @@ -0,0 +1,9025 @@ +[ + { + "type": "text", + "text": "Qiguang Chen† Libo Qin‡ Jinhao Liu† Dengyun Peng† Jiannan Guan† Peng Wang‡ Mengkang Hu◇ Yuhang Zhou Te Gao† Wanxiang Che† LARG,", + "bbox": [ + 228, + 262, + 787, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$\\dagger$ Research Center for Social Computing and Interactive Robotics, $\\dagger$ Harbin Institute of Technology", + "bbox": [ + 290, + 309, + 723, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{\\ddagger}$ School of Computer Science and Engineering, Central South University", + "bbox": [ + 267, + 339, + 750, + 354 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The University of Hong Kong", + "bbox": [ + 401, + 354, + 614, + 368 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fudan University", + "bbox": [ + 444, + 368, + 573, + 382 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{qgchen,car}@ir.hit.edu.cn,lbqin@csu.edu.cn", + "bbox": [ + 300, + 383, + 717, + 396 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Project: https://long-cot.github.io/", + "bbox": [ + 344, + 409, + 669, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Github: LightChen233/Awesome-Long-Chain-of-Thought-Reasoning", + "bbox": [ + 223, + 436, + 790, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3bcec7826e1fbcdb6dfe89578c968d54d801a27312caf0fc018f86ba59fa632d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 184, + 492, + 831, + 825 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 233, + 119, + 299, + 164 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Towards Reasoning Era: A Survey of Chain-of-Thought for Reasoning Large Language Models", + "bbox": [ + 307, + 133, + 769, + 212 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2503.09567v5 [cs.AI] 18 Jul 2025", + "bbox": [ + 22, + 285, + 58, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 459, + 89, + 540, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like \"overthinking\" and \"inference-time scaling\". This survey seeks to fill this gap by offering a unified perspective on Long CoT. Specifically, (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and inference-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of reasoning large language models1.", + "bbox": [ + 228, + 121, + 769, + 428 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1 Introduction", + "text_level": 1, + "bbox": [ + 171, + 453, + 316, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, as shown in Figure 1, the emergence of reasoning large language models (RLLMs) such as OpenAI o1 [307] and DeepSeek R1 [227] has sparked a growing body of research into Long Chain-of-Thought (Long CoT) reasoning, greatly improving their mathematical reasoning, programming tasks, and multidisciplinary knowledge reasoning capabilities [696, 980, 722, 79, 961, 200, 1113, 793], even passing Turing Test [334]. This shift marks a significant departure from traditional approaches to task handling in large language models (LLMs) [1147, 619, 622, 599]. Unlike the shorter chain-of-thought (Short CoT) used in traditional LLMs, Long CoT reasoning entails a more detailed, iterative process of exploration and reflection within a given problem space by inference-time scaling [419, 733, 524]. This process has led to notable advancements in mathematical and logical reasoning, as well as in exploring how supervised fine-tuning (SFT) and reinforcement learning (RL) techniques can enhance the learning and exploration of extended reasoning chains [623, 550].", + "bbox": [ + 169, + 484, + 826, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, there is no comprehensive survey to systematically understand the main factors and recent efforts of Long CoT for RLLMs, which hinders the development of RLLMs. As a result, there are ongoing debates about the effectiveness of simple \"inference-time scaling\" for Longer CoT [864, 486] versus the argument that \"over-thinking\" from excessively long scaling can harm LLMs and introduce unnecessary complexity [103, 142, 357]. Moreover, some researchers argue that, when solving specific problems, there is no clear relationship between length and accuracy [886].", + "bbox": [ + 169, + 657, + 826, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this gap, we provide an extensive and comprehensive survey of Long CoT. Specifically, as illustrated in Figure 2, we first define and examine the distinctions between Long CoT and traditional Short CoT, focusing on the following key aspects: (1) Deep Reasoning, which requires a sufficient depth of logical processing to manage an extensive set of logical nodes; (2) Extensive Exploration, which involves generating parallel uncertain nodes and transitioning from known to unknown logic; and (3) Feasible Reflection, which involves feedback and refinement of logical connections. These characteristics enable Long CoT paradigms to integrate more intricate reasoning and accommodate a broader range of logical structures, ultimately leading to more efficient and coherent outcomes. Subsequently, we systematically explore the underlying explanations for key phenomena associated with Long CoT, such as its emergence, the overthinking phenomenon,", + "bbox": [ + 169, + 746, + 828, + 887 + ], + "page_idx": 1 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 41, + 308, + 71 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "Our logo refers to a cute cartoon image - Snake Puppy. Header Image is inspired by Yaoting et al. [959]", + "bbox": [ + 191, + 897, + 812, + 912 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/be56637e4c051b7d3d3a17014777899ed5d63d7f01c713db6f624e8d8196114d.jpg", + "image_caption": [ + "Figure 1: Evolution of selected Long CoT over the past three years, where colored branches represent different characteristics: deep reasoning, feasible reflection, and extensive exploration. Each characteristic is further divided into key areas: Deep reasoning includes its format and learning methods. Feasible reflection focuses on feedback and refinement techniques during reflection process as optimization strategies. Extensive exploration addresses scaling, internal, and external exploration as key improvements to Long CoT." + ], + "image_footnote": [], + "bbox": [ + 181, + 92, + 823, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "inference-time scaling during testing, and the \"Aha Moment,\" among others. To our knowledge, This is the first comprehensive survey dedicated to these specific topics. Finally, considering the extensive body of literature, we highlight promising areas for future research and suggest valuable open-resource frameworks and datasets that can serve as a foundation for future investigations.", + "bbox": [ + 169, + 455, + 823, + 512 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The main contributions of this work are as follows:", + "bbox": [ + 171, + 517, + 509, + 531 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Systematic Distinction: In this work, we first introduce the concept of Long CoT reasoning and distinguish it from the traditional Short CoT, thereby providing a clear framework for understanding both paradigms and their respective characteristics.", + "- Explanation of Hot Phenomena: We systematically investigate the notable phenomena associated with Long CoT reasoning, such as overthinking, inference-time scaling, and the \"Aha Moment\", offering valuable insights into the cognitive processes involved in complex reasoning.", + "- Emerging Challenges and Frontiers: We explore the emerging challenges within the field of Long CoT reasoning and identify key research frontiers. Given the vast body of literature, we highlight areas where further inquiry could significantly advance the development of Long CoT methodologies." + ], + "bbox": [ + 174, + 539, + 823, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2 Discussion of Long CoT v.s. Short CoT", + "text_level": 1, + "bbox": [ + 171, + 708, + 529, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section formalizes the key differences between Long Chain-of-Thought (Long CoT) and Short Chain-of-Thought (Short CoT), emphasizing reasoning depth, revisiting connections, and logical node exploration [858]. These distinctions are clearly separate from System 1 and System 2 thinking. The comparison between Long CoT and Short CoT is framed within System 2, with Long CoT involving more thorough reasoning, reflection, and exploration, while Short CoT generally prioritizes shallow and efficient logic over exhaustive reasoning.", + "bbox": [ + 169, + 739, + 826, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1 Overview of Short CoT", + "text_level": 1, + "bbox": [ + 171, + 843, + 375, + 857 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated by Figure 2, Short CoT is typically characterized by a shallow, linear reasoning process, where conclusions are drawn sequentially, often relying on a limited number of logical nodes [551]. This reasoning is usually rapid and straightforward, with simple, surface-level transitions and minimal", + "bbox": [ + 169, + 869, + 826, + 912 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 230, + 59, + 305, + 68 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Proof of Number Theory Problem: For any positive integer $n$ , there exists a positive integer $m$ such that $m^2 + 1$ is divisible by $n$ .", + "bbox": [ + 240, + 94, + 774, + 107 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f0eadf51633e7fb658ee5728c1487fe0163f55fb50102d3c0b34bdb3de0da945.jpg", + "image_caption": [ + "Figure 2: The differences between advanced Long CoT and traditional Short CoT are characterized by three key characteristics: deep reasoning, feasible reflection, and extensive exploration. Moreover, Long CoT integrates all these characteristics to achieve substantial logical efficacy." + ], + "image_footnote": [], + "bbox": [ + 181, + 113, + 816, + 271 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "exploration of alternative paths, which restricts its generalizability [683]. Formally, given a reasoning model $\\mathcal{R}$ , we can define the rationale of Short CoT $(\\mathsf{C}\\circ \\mathsf{T}_S)$ as follows:", + "bbox": [ + 169, + 349, + 823, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {C o T} _ {S} = \\mathcal {R} \\left(\\left\\{n _ {i} \\right\\} _ {i = 1} ^ {k} | (k \\leq \\mathcal {B} _ {s}) \\wedge (j = 1 \\Leftrightarrow \\forall i \\leq k, n _ {i} \\rightarrow n _ {i + j}) \\wedge (\\forall i \\neq j \\leq k, n _ {i} \\neq n _ {j})\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 388, + 825, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $n_1$ to $n_k$ represent a sequence of logical nodes, which naturally satisfy that $\\forall i, n_i \\to n_{i+1}$ . Here, $\\mathcal{B}_s$ denotes the upper boundary on the number of logical nodes, as defined by Chen et al. [90]. In this paradigm, the reasoning progresses sequentially from one node to the next, with minimal revisitation of previous nodes and little exploration of alternative logical paths.", + "bbox": [ + 169, + 415, + 826, + 472 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2 Overview of Long CoT", + "text_level": 1, + "bbox": [ + 171, + 491, + 374, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In contrast, Long CoT involves deeper reasoning, reflective analysis, and a broader exploration of logical structures. It facilitates reasoning across a wider range of logical steps, addressing both known and unknown elements of a problem [194, 858]. Building on this, Long CoT expands upon the constraints presented in Equation 1 based on tree structures by incorporating three critical components: deep reasoning, exploration, and reflection.", + "bbox": [ + 169, + 518, + 826, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These components play distinct yet complementary roles in enhancing cognitive processes. Deep reasoning ensures each logical step is executed rigorously, even within complex structures, fostering robust logic across intricate relationships. Exploration encourages the identification of new pathways, revealing potential avenues that may not be immediately obvious. Reflection enables iterative analysis and reassessment of conclusions, allowing reasoning to evolve throughout problem-solving. By distinguishing these three categories, Long CoT enhances its ability to address a broader range of problems with precision and depth. As shown in Figure 3, we will now discuss these key differences in detail.", + "bbox": [ + 169, + 594, + 826, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2.1 Deep Reasoning for Long CoT", + "text_level": 1, + "bbox": [ + 171, + 723, + 437, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown by Figure 2, deep reasoning refers to the capability to perform deep and thorough logical analysis across multiple interconnected logical nodes, where Short CoT generally can never achieve. This capability is essential when tackling complex problems that require a massive number of logical deductions to arrive at a valid conclusion. To better define and understand deep reasoning, we frame it as a capability that primarily relaxes the first constraint in Equation 1, as expressed by the following:", + "bbox": [ + 169, + 750, + 826, + 819 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nk \\leq \\mathcal {B} _ {s} \\mapsto k \\leq \\mathcal {B} _ {l} \\wedge \\mathcal {B} _ {s} \\ll \\mathcal {B} _ {l}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 392, + 829, + 823, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{B}_l$ represents the upper boundary for Long CoT reasoning, which can accommodate much more intricate logical nodes compared to the smaller boundary $\\mathcal{B}_s$ for Short CoT. The larger boundary $\\mathcal{B}_l$ alleviates issues related to insufficient depth in reasoning, thereby reducing the risk of generating unresolved answers or hallucinated responses in short-form reasoning.", + "bbox": [ + 169, + 854, + 825, + 912 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 41, + 225, + 70 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fa1bbeeb7a7a9e97707e957eb9cfc744f2a2eba4ab0e5a7c5f73282936c28213.jpg", + "image_caption": [ + "Figure 3: Taxonomy of Long CoT, which includes deep reasoning, feasible reflection, and extensive exploration methodologies." + ], + "image_footnote": [], + "bbox": [ + 173, + 78, + 831, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Key Difference: Reasoning Depth", + "text_level": 1, + "bbox": [ + 204, + 604, + 429, + 619 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Short CoT typically addresses a limited set of logical nodes, involving shallow reasoning, and struggles with problems requiring complex or intricate logical structures.", + "- Long CoT is designed to accommodate a significantly larger set of logical nodes, allowing for deeper logic and more thorough analysis during the reasoning process." + ], + "bbox": [ + 199, + 627, + 800, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2.2.2 Extensive Exploration for Long CoT", + "text_level": 1, + "bbox": [ + 171, + 715, + 478, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown by Figure 2, Long CoT encourages branching out to extensively explore uncertain or unknown logical nodes, thereby expanding the potential set of reasoning paths. This exploration is particularly critical when solving problems characterized by ambiguity, incomplete information, or multiple possible solutions [43, 1016, 871]. More specifically, we describe how extensive exploration primarily addresses the relaxation of the second constraint in Equation 1, which can be formalized as follows:", + "bbox": [ + 169, + 741, + 823, + 823 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nj = 1 \\Leftrightarrow \\forall i \\leq k, n _ {i} \\rightarrow n _ {i + j} \\mapsto \\exists m, \\forall i, \\forall j \\leq m, n _ {i} \\rightarrow n _ {i + j}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 290, + 830, + 823, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the condition indicates that for a logical node $n_i$ , there are $m$ nodes that are explored in parallel. The acceptability of parallel exploration allows for a more systematic approach, enabling the exploration of previously unconsidered logical paths. This, in turn, helps maximize the understanding of all possible solutions, ultimately leading to the correct final answer.", + "bbox": [ + 169, + 854, + 823, + 912 + ], + "page_idx": 4 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 41, + 225, + 69 + ], + "page_idx": 4 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 4 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 65 + ], + "page_idx": 4 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 65, + 305, + 69 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Key Difference: Exploration of Logical Nodes", + "text_level": 1, + "bbox": [ + 204, + 90, + 511, + 106 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Short CoT generally restricts exploration to a fixed set of logical nodes, often resulting in oversimplified reasoning and limited exploration.", + "- Long CoT explores more various paths, including uncertain or uncharted areas, fostering more nuanced and comprehensive problem-solving." + ], + "bbox": [ + 199, + 114, + 797, + 175 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2.2.3 Feasible Reflection for Long CoT", + "text_level": 1, + "bbox": [ + 171, + 198, + 455, + 214 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown by Figure 2, Long CoT involves revisiting previous logical nodes to verify their connections are valid and accurate, and then correcting them or selecting an alternative logical path. Formally, feasible reflection relaxes the third constraint in Equation 1, which originally requires acyclic reasoning such that $n_i \\neq n_j$ for all $i \\neq j \\leq k$ . In contrast, feasible reflection permits the reasoning path to return to a previously visited node, captured as:", + "bbox": [ + 169, + 223, + 823, + 292 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\forall i \\neq j \\leq k, n _ {i} \\neq n _ {j} \\mapsto \\exists i < j \\leq k, n _ {i} = n _ {j}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 341, + 301, + 825, + 318 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where this condition indicates that, for a logical node $n_{j-1}$ , the subsequent node is not limited to the original next node $\\hat{n}_j$ . Instead, it may transition to $n_i$ (i.e., the next logical node becomes $n_j$ , where $n_j = n_i$ ). Practically, reflection implementation consists of two components:", + "bbox": [ + 169, + 325, + 823, + 369 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Feedback refers to evaluating both overall and intermediate outputs for correctness and quality, also known as critique or verification. It can be derived from external sources, validation checks, or by reflecting on prior conclusions within the reasoning process. Formally, at each step $n_i$ , a verification process $\\mathcal{V}_i$ ensures the correctness, feasibility, and consistency of the reasoning. If an issue is identified, the process redirects $n_i$ to the nearest correct node $n_j$ , where $j < i$ . This relationship is formalized as:", + "bbox": [ + 169, + 378, + 825, + 462 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} _ {i}, n _ {j} \\leftarrow \\operatorname {F e e d b a c k} \\left(\\mathrm {C o T} _ {L} ^ {i}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 403, + 463, + 823, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathrm{CoT}_L^i = \\{n_1,\\dots ,n_i\\}$ represents the current logical path up to the $i$ -th logical node for Long CoT.", + "bbox": [ + 169, + 484, + 823, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Refinement involves adjusting intermediate steps or modifying the logical flow to correct inconsistencies or address gaps based on the given feedback. This process can be expressed mathematically as follows:", + "bbox": [ + 169, + 525, + 826, + 566 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {n} _ {i + 1} \\leftarrow \\operatorname {R e f i n e} \\left(n _ {i + 1} \\mid \\mathrm {C o T} _ {L} ^ {i}, \\mathcal {F} _ {i}, n _ {j}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 372, + 566, + 823, + 584 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\widetilde{n}_{i+1}$ represents the refined version of the subsequent logical node $n_{i+1}$ , according to the current logic $\\mathbb{C} \\circ \\mathbb{T}_L^i$ , feedback result $\\mathcal{F}_i$ , and previous logical node $n_j$ .", + "bbox": [ + 169, + 588, + 823, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall, incorporating reflection ensures that errors are identified and corrected promptly. This capability enables LLMs to quickly shift to alternative reasoning paths or correct their current trajectory. By doing so, error propagation is minimized, resulting in more accurate conclusions.", + "bbox": [ + 169, + 623, + 825, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Key Difference: Feedback & Refinement", + "text_level": 1, + "bbox": [ + 204, + 675, + 475, + 690 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Short CoT typically moves in a straightforward, non-repetitive manner from one node to the next, so that cannot correct their logic.", + "- Long CoT allows for revisiting and revising earlier decisions by feedback and refinement, ensuring that estimizable and prior logical conclusions during the reasoning progress." + ], + "bbox": [ + 200, + 698, + 799, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2.2.4 Unified Application and Development History of Three Capabilities", + "text_level": 1, + "bbox": [ + 171, + 782, + 694, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Long CoT discussed here represents a unified reasoning system that seamlessly integrates and applies three key capabilities: deep reasoning, reflective mechanisms, and exploration capabilities. In contrast, during the Short CoT era, these capabilities developed independently, each evolving in isolation.", + "bbox": [ + 169, + 806, + 825, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Figure 2, early efforts primarily focused on enhancing deep reasoning within traditional CoT paradigms. This was followed by the gradual introduction of reflective mechanisms, which were initially based on human-designed pipelines. Over time, exploration capabilities were added, and", + "bbox": [ + 169, + 869, + 825, + 912 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 41, + 225, + 70 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 493, + 936, + 504, + 946 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "these components were ultimately merged, giving rise to the modern concept of Long CoT, a unified approach to reasoning that seeks to enhance all three capabilities in harmony.", + "bbox": [ + 169, + 90, + 823, + 119 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The progression of Long CoT is gradual, rather than a sudden emergence through isolated models like o1 [307] and R1 [227]. Instead, it develops gradually. For example, earlier systems, such as ToT [955], enhance exploration but lack reflective mechanisms, disqualifying them as Long CoT [95]. While GoT [48] incorporates self-reflection based on ToT, its original model still lacked robust deep reasoning, preventing it from qualifying as Long CoT at that time. It is also notable that modern Long CoT systems, often neglect earlier technologies. This article addresses this gap by tracing the evolution of each capability, with the final section offering a comprehensive analysis of the integrated Long CoT system.", + "bbox": [ + 169, + 126, + 826, + 238 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In summary, Long CoT and Short CoT represent distinct paradigms. Long CoT features a deeper, broader, and more reflective reasoning process, enhancing both accuracy and coherence. Short CoT, by contrast, is better suited to simpler, well-defined problems. This distinction highlights the scalability and adaptability of Long CoT, making it particularly effective for more complex reasoning.", + "bbox": [ + 169, + 243, + 826, + 300 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Key Difference: Unified Application of Three Capabilities", + "text_level": 1, + "bbox": [ + 204, + 308, + 591, + 324 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It is important to highlight that Long CoT integrates these three distinct capabilities to perform complex reasoning. In contrast, traditional Short CoT optimization typically focuses on only one of these characteristics.", + "bbox": [ + 194, + 329, + 800, + 372 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3 Long CoT Analysis & Evaluation", + "text_level": 1, + "bbox": [ + 171, + 397, + 483, + 415 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.1 Analysis & Explanation for Long CoT", + "text_level": 1, + "bbox": [ + 171, + 428, + 478, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Research on Long CoT has significantly enhanced RLLMs by improving reasoning accuracy, reducing errors, and supporting dynamic decision-making. However, several phenomena and their corresponding mechanisms remain inadequately summarized. This section addresses key topics, including the mechanisms of Long CoT and their underlying principles [644, 63, 545, 642]. Methodologically, two main perspectives have emerged to explain Long CoT: (1) External Behavior Analysis (§ 3.1.1) and (2) Internal Mechanism Analysis (§ 3.1.2).", + "bbox": [ + 169, + 454, + 826, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.1.1 Long CoT External Behavior Analysis", + "text_level": 1, + "bbox": [ + 171, + 551, + 491, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The primary research stream focuses on explaining RLLM behaviors for Long CoT [25]. As illustrated in Figure 4, six key phenomena are identified and discussed for Long CoT in this part.", + "bbox": [ + 169, + 575, + 823, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Long CoT Emergence Phenomenon Research shows that contextual examples improve large models' generative abilities by guiding the formation of reasoning chains [1012, 671, 417, 343, 532, 846, 1017, 1141]. Wang et al. [759] and Lippmann and Yang [461] demonstrate that these examples standardize reasoning chain generation relevant to the answers both in in-context-learning and supervised-finetuning. In an experiment by Madaan et al. [538], removing problem-specific entities from contextual examples, while retaining only the logical structure, led to similar performance as using complete examples, highlighting the logical structure imitation of Long CoT during inference. From a learning perspective, Ye et al. [963] analyzes and reveals the three-stage developmental trajectory of Long CoT: early memorization, followed by in-distribution generalization, and ultimately cross-distribution generalization, thereby enabling the model to exhibit Long CoT capabilities.", + "bbox": [ + 169, + 614, + 826, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "More recently, Stechly et al. [688] and Wang and Zhou [815] have shown that modifying the decoding process or designing specific prompts can activate the Long CoT within pre-trained models. They propose that CoT is embedded during pre-training and requires specific activation [941]. Further, Sadr et al. [642] focus the Long CoT source from the training data, and build on this with the notion of \"model attribution\", to specifically identify the training data most influential for specific outputs. Building on this, Guo et al. [227] and Xie et al. [886] investigate using rule-based reinforcement learning to directly activate Long CoT during pre-training, aiming to enhance performance [881]. Furthermore, Gandhi et al. [194] identify four key cognitive behaviors, including verification, backtracking, sub-target setting, and backward chaining, which successfully facilitate Long CoT. Qwen series models [926] inherently demonstrate these behaviors, which can be easily triggered by rule-based reinforcement. In contrast, the models of Llama series [168] lack these", + "bbox": [ + 169, + 758, + 828, + 912 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "REASONING GROU", + "bbox": [ + 233, + 66, + 300, + 70 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5a5b622a5ef9a492838399c45ff5d29022e17e93ea38f8784aa310a395d4009d.jpg", + "image_caption": [ + "Figure 4: Analysis of the six classic phenomena of Long CoT external behavior: (a) emergence of Long CoT in current RLLMs; (b) reasoning boundaries and limitations of current Long CoT systems; (c) overthinking caused by scaling beyond RLLMs' reasoning boundaries, leading to performance decay; (d) inference-time scaling, discussing mainstream scaling methods, corresponding scaling laws and their limitations; (e) use of process reward model (PRM) or outcome reward model (ORM); (f) exploration of the \"aha\" moment and its underlying causes." + ], + "image_footnote": [], + "bbox": [ + 181, + 89, + 338, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b58ea3cfdd162d9e8dc0a98bea568dac497bec49f930188fabfb39d4a8af9188.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 343, + 90, + 473, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7574cfd5bdc73debbbe23c4cd13dc43c38b3f705661075e1c69e68c8876576bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 90, + 656, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7acf371a734b42dff8be38ed39013e080e5d0020e7a712fdcc41abb09ba80b65.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 661, + 90, + 813, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "capabilities and thus requires example-based reinforcement learning to improve significantly [65]. Moreover, Wang et al. [812] identify a pretraining scaling law that explains how increasing calculation size in RLLMs enhances their reasoning capabilities. Wang et al. [796] further explore the scaling law of Long CoT, showing that more fine-grained Long CoT granularity leads to more efficient and effective generalization performance.", + "bbox": [ + 169, + 367, + 823, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Reasoning Boundary Phenomenon Recent research has highlighted the upper bounds and limitations of RLLMs across various reasoning tasks [303, 283, 684, 261, 185, 252]. Specifically, Bi et al. [53] investigate these bounds in code generation, showing that RLLMs struggle with tasks that exceed certain complexity thresholds [600], especially when imitating Long CoT samples of varying complexity. In the context of upper-bound performance, Merrill and Sabharwal [548] and Li et al. [430] focus on single-step arithmetic tasks, concluding that model performance is constrained by input length. Moreover, Feng et al. [177] proposes a mathematical model indicating that fixed-size models cannot produce accurate numerical answers beyond specific limits. However, increasing the number of reasoning steps improves a model's capability requirements to solve more complex problems.", + "bbox": [ + 169, + 454, + 826, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inspired by these explorations, Chen et al. [90] first define the \"reasoning boundary\" phenomenon and quantify these limits, showing that surpassing an RLLM's reasoning capacity leads to performance decline [92]. Similarly, Zhou et al. [1130] introduce GSM-Infinite, linking different upper limits to accuracy levels. Chen et al. [90] also examine the interaction between these boundaries across tasks of varying complexity, providing insights into the effectiveness of Long CoT strategies [1085]. Moreover, Amiri et al. [12] propose a \"tight lower bound\" for Long CoT further guiding reasoning error reductions. Further, Baeumel et al. [28] suggest that due to its reliance on a single-digit lookahead heuristic, there are inherent boundaries in performing addition with multiple operands, which thus hinders the fundamental limitation of LLMs in scaling to more complex numerical reasoning. Liu et al. [483] further investigate the role of reinforcement learning in expanding these reasoning boundaries instead of relying solely on pretraining capabilities.", + "bbox": [ + 169, + 599, + 826, + 752 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Overthinking Phenomenon Research has highlighted the overthinking phenomenon [103, 330, 574, 142, 357, 595], where performance improves with longer reasoning chains up to a threshold, after which it declines. In contrast, Xie et al. [886] and Ma et al. [534] find no significant correlation between reasoning length and accuracy. To explain this, one line of research suggests that Long CoT strategies [21, 441], like avoiding \"snowball errors\" [192]. Alternatively, Chen et al. [90], Wolf et al. [851] highlight a performance drop when the reasoning boundaries are exceeded, providing an explanation for the overthinking phenomenon. This suggests that reasoning length and logical complexity should be kept below a certain boundary [1080]. Building on this, Wu et al. [867] mathematically determine the feasible reasoning length for Long CoT. Finally, Chen et al. [93] introduces Ohm's law of Long CoT, which accurately predicts and controls performance.", + "bbox": [ + 169, + 772, + 826, + 912 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 232, + 59, + 305, + 65 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 232, + 65, + 305, + 69 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 493, + 935, + 503, + 946 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inference-Time Scaling Phenomenon Recent advances in inference-time scaling algorithms [524, 843] have garnered significant attention, particularly for their ability to extend reasoning length and improve performance [524, 455, 875]. Specifically, Brown et al. [57] identify a phenomenon called \"Large Language Monkeys\", in which a series of reasoning tasks show that with enough trials, a correct result can be achieved. Additionally, o1 [307] and R1 [227] demonstrated that directly scaling the length of model inference improves final performance.", + "bbox": [ + 169, + 90, + 826, + 175 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To understand inference-time scaling, we will discuss these two paradigms: (1) Sequential Scaling: Sequential scaling involves increasing the reasoning path length. While this can enhance performance, studies by Jin et al. [330] show that, beyond a certain point, longer reasoning paths can degrade performance due to error accumulation. They suggest an optimal path length that depends on the model's capabilities and task complexity [15, 652, 31]. Furthermore, Chen et al. [90] and Wu et al. [867] explain that excessive exploration lengths beyond the RLLM's inherent reasoning boundary lead to performance decay, which guides RLLMs for deeper reasoning capabilities [32]. (2) Parallel Scaling: Parallel scaling involves performing multiple reasoning steps and verifying the results. While it shows promise, Parashar et al. [583] and Wang et al. [820] argue that simply increasing inference time does not guarantee improved performance. Wu et al. [864] show that the computational FLOPs $N$ of inference are correlated with the lower bound of performance error, which scales with $\\log N$ . Additionally, Chen et al. [93] establish an upper bound for parallel scaling, showing that RLLMs cannot exceed Pass@k verification through various verifiers. They further argue that sampling optimization cannot exceed the model's internal reasoning limitations, demonstrating that for $N$ samples, accuracy is proportional to $\\frac{m}{(k / \\log N + b)^2}$ , where $m$ , $n$ , and $b$ are model-dependent constants.", + "bbox": [ + 169, + 181, + 826, + 393 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "PRM & ORM Selection Phenomenon As RLLMs evolve, it is crucial to navigate the debate around the selection between process supervision and outcome supervision, two key reinforcement learning paradigms for complex reasoning tasks. The phenomenon of choosing between these two approaches has become a pivotal issue, as it is essential to differentiate and decide which supervision strategy is more suitable for specific tasks [899, 187, 1059]. While process supervision is intuitively advantageous for long-term reward assignments, the exact relationship between the two approaches remains unclear. It is commonly believed that process supervision is more challenging due to the trajectory-level coverage problem, which demands significant effort to collect fine-grained supervision data [1102, 679]. Additionally, PRM faces the issue of reward hacking [13, 152, 573, 30, 399], where agents exploit flaws in the reward function to produce unintended behaviors [227]. Addressing this to surpass rule-based reward systems has become an important research area [227, 886, 594]. Furthermore, Lampinen et al. [368] and Tan [708] establish a causal link between intermediate steps and final answers in qualitative experiments. Building on this, Jia et al. [317] demonstrate that, under the standard data coverage assumption, reinforcement learning with outcome supervision is not statistically more challenging than process supervision, aside from polynomial factors. More strictly, He et al. [247] mathematically demonstrate that outcome-level rewards suffice for online reinforcement learning in RLLMs.", + "bbox": [ + 169, + 402, + 826, + 638 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Aha Moment Phenomenon Earlier, Guo et al. [227] demonstrated that direct RL using rule-based rewards can trigger the aha moment, fostering natural self-reflection without supervision [172]. Following this, Team [721], Xie et al. [886] replicate this phenomenon. Further, Zhou et al. [1119] and Meng et al. [547] further extend this phenomenon to multimodal scenarios. However, Liu et al. [498] argue that the aha moment may not emerge in R1-Zero-like training. Instead, they observe that self-reflection patterns, such as superficial self-reflection (SSR), appear at epoch 0, the stage of base models. In this case, self-reflections do not necessarily lead to correct answers. Upon closer examination of R1-Zero training via RL, they find that the increasing response length results not from self-reflection, but from RL optimizing well-designed rule-based rewards. Moreover, Yang et al. [939] demonstrate that the \"aha moment\" is externally marked by increased use of anthropomorphic language during self-reflection and a dynamic adjustment of uncertainty in response to problem difficulty. This process enables the model to maintain reasoning without succumbing to \"Reasoning Collapse.\" Internally, it is characterized by a clear distinction between anthropomorphic traits and logical reasoning, with anthropomorphic language intensifying as the problem becomes more complex.", + "bbox": [ + 169, + 647, + 826, + 857 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Reinforcement Learning Entropy Phenomenon In reinforcement learning for Long CoT, the entropy mechanism is a crucial factor influencing the performance of RLLMs. Policy entropy measures the diversity and exploratory strength of a model's outputs. By managing this entropy", + "bbox": [ + 169, + 869, + 825, + 912 + ], + "page_idx": 8 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 308, + 71 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9", + "bbox": [ + 493, + 935, + 504, + 946 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "effectively, a model preserves exploration and thus excels on complex reasoning tasks. Earlier, Jang and Kim [310] investigate how initial entropy affects exploration in deep RL and proposed an entropy-aware initialization to encourage effective exploration. Building on this, Zhang et al. [1036] developed an Entropy-Regularized PRM that balances policy updates against large deviations from the starting distribution, thereby improving reasoning. Cheng et al. [116] found that high-entropy regions correlate positively with three exploratory reasoning behaviors: (1) key tokens linking logical steps, (2) self-verification and correction, and (3) rare behaviors underrepresented in the base model. Most recently, Agarwal et al. [5] introduced an Entropy Minimization method and demonstrated its strong impact on LLM performance in mathematical, physical, and coding tasks.", + "bbox": [ + 169, + 90, + 826, + 217 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "However, recent research indicates that, during early training, policy entropy declines sharply, causing the model to converge prematurely on specific output patterns and limiting further reasoning improvement [144]. In reinforcement learning, policy entropy $(H)$ and downstream task performance $(R)$ follow an exponential relation: $R = -a\\cdot e^{H} + b$ , so a drop in entropy produces a rapid performance decline until saturation. This \"policy entropy collapse\" is common without entropy control, as reduced entropy constrains exploration and stalls reasoning gains [144]. To counter this collapse, two methods, Clip-Cov and KL-Cov, regulate entropy by constraining updates on high-covariance tokens. Clip-Cov clips their update magnitudes, whereas KL-Cov imposes a Kullback-Leibler penalty. Empirical results show both techniques prevent collapse and enhance reasoning performance [144].", + "bbox": [ + 169, + 222, + 826, + 348 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "3.1.2 Long CoT Internal Mechanism Analysis", + "text_level": 1, + "bbox": [ + 171, + 363, + 504, + 378 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "The second stream of research investigates the internal mechanisms of Long CoT-related RLLMs.", + "bbox": [ + 169, + 387, + 815, + 402 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Reasoning Internal Mechanism Recent studies have explored the internal mechanisms underlying the coherent rationale outputs of Long CoT, with particular emphasis on attention mechanisms [675, 632]. These studies primarily examine neural substructures in RLLMs, framing CoT reasoning from a white-box perspective [819, 992, 233, 169]. Weston and Sukhbaatar [849] introduces the concept of System 2 Attention (S2A), which demonstrates Long CoT generation by selectively focusing attention on relevant information. Additionally, Li et al. [407] explore gradient distributions between direct output and Long CoT layers, revealing that Long CoT layers help maintain stability by distinguishing relevant from irrelevant reasoning [840]. Finally, Zhang et al. [1068] conceptualize RLLMs as finite state automata, offering further insight into how internal dynamics influence external behavior. Despite Short CoT's struggles with self-correction, Bertolazzi et al. [47] show that these models rely on consistency heads (attention heads) to assess the alignment of numerical values in arithmetic solutions through internal shortcuts.", + "bbox": [ + 169, + 415, + 826, + 582 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Knowledge Incorporating Mechanism Current RLLMs primarily focus on mathematics and coding but have shown potential for generalization to other knowledge-rich domains, sparking growing interest in the mechanism for integrating domain-specific knowledge into Long CoT [860, 886, 1105]. Prystawski et al. [609] suggest that generative models store entity knowledge learned during pre-training independently, with the reasoning process in Long CoT linking this knowledge across entities. Radha and Goktas [630] recently introduced the Probabilistic Mixture Model (PMM), which categorizes model outputs into reasoning, memorization, and guessing. They also propose an Information-Theoretic Consistency (ITC) analysis to quantify the relationship between model confidence and strategy selection. Additionally, Jin et al. [331] define \"Concept Depth\" as the lowest layers at which complex concepts are understood, demonstrating varying levels of knowledge integration in RLLMs. Ou et al. [572] examine RLLM knowledge internalization through knowledge loop evolution, arguing that new knowledge acquisition is shaped by its connection to existing knowledge, with the loop evolving from formation to optimization and from shallow to deep.", + "bbox": [ + 169, + 593, + 826, + 776 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "3.2 Long CoT Evaluations", + "text_level": 1, + "bbox": [ + 171, + 791, + 372, + 806 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "3.2.1 Metrics", + "text_level": 1, + "bbox": [ + 171, + 816, + 279, + 830 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "In benchmarking, various metrics assess model performance across reasoning tasks, each focusing on different aspects of reasoning ability. These metrics evaluate both RLLMs' effectiveness in achieving desired outcomes and their learning efficiency. As a result, metrics for RLLMs have gained increasing attention in recent research. For mathematical or code-related tasks, three key metrics are commonly used: Accuracy, Pass@k, and Cons@k based on regex extraction:", + "bbox": [ + 169, + 842, + 825, + 912 + ], + "page_idx": 9 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 308, + 71 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10", + "bbox": [ + 490, + 935, + 508, + 946 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Accuracy measures the proportion of correct outputs.", + "- Pass@k evaluates the likelihood of generating at least one correct solution within $k$ attempts.", + "- Cons@k assesses consistency by determining the model's ability to consistently produce correct or logically coherent solutions across multiple attempts." + ], + "bbox": [ + 174, + 92, + 823, + 152 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "In scientific or commonsense question-answering tasks, evaluation often uses Exact Match (EM) and Accuracy based on regex extraction, where EM determines whether the model's output exactly matches the expected solution.", + "bbox": [ + 169, + 157, + 825, + 200 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "For feedback techniques like ORM or PRM, Rank and Best-of-N metrics are often used:", + "bbox": [ + 171, + 205, + 782, + 220 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Rank measures whether the reward model correctly prioritizes the best reasoning processes from the top $k$ candidates.", + "- Best-of-N selects the highest-scoring solution from $N$ generated reasoning trajectories, indirectly measuring the reward model's effectiveness based on final outcomes." + ], + "bbox": [ + 173, + 227, + 825, + 285 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "3.2.2 Decoding Strategies", + "text_level": 1, + "bbox": [ + 171, + 301, + 364, + 316 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Decoding strategies are essential for controlling the inference process. Common approaches include Greedy Decoding, Beam Search, and Major@k. Both Greedy Decoding and Beam Search limit the sampling range to reduce randomness, guiding the model toward more consistent outputs. In contrast, Major@k identifies the most reliable solution by selecting the one with the highest consistency from a set of $k$ candidate solutions.", + "bbox": [ + 169, + 325, + 823, + 397 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "3.2.3 Benchmarks", + "text_level": 1, + "bbox": [ + 171, + 412, + 313, + 426 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "In the realm of Benchmarks, the focus lies on assessing the reasoning capabilities of RLLMs across diverse domains. There are two primary categories: (1) Outcome Benchmarks, which focus on the holistic view of Long CoT reasoning, and (2) Process Benchmarks, which concentrate on the local view of the Long CoT process or individual capabilities.", + "bbox": [ + 169, + 436, + 823, + 494 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Outcome Benchmarks In the realm of Outcome Benchmarks, the first focus lies on evaluating the logical reasoning capabilities:", + "bbox": [ + 169, + 506, + 823, + 535 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Complex Mathematics: A central focus in complex mathematics is evaluating benchmarks like GSM8K [141] and MATH [253], which assess basic mathematical problem-solving abilities [1125, 1112]. Recent additions, such as AIME 2024 [8], AIME 2025 [571], MATH-500 [449], AMC 2023 [9], USAMO [598], OlympiadBench [239], and OlympiadArena [298], expand the evaluation of LLM performance in mathematics. Moreover, Putnam-AXIOM [224] and FrontierMath [210] introduce more complex problems that challenge future reasoning systems. Additionally, ThinkBench [291] and MATH-Perturb [288] focus on robust evaluation for Long CoT [38, 987].", + "- Complex Coding: Complex coding benchmarks are also vital, with competitions like Codeforces, SWEbench [327], CodeContests [427], and LiveCodeBench [309] evaluating LLM coding and problem-solving skills. Notable additions such as MHPP [148], ProBench [934], HumanEval Pro, MBPP Pro [993], and EquiBench [833] enhance the scope and complexity of coding challenges. Moreover, some studies have explored applying these benchmarks in real-world code development scenarios for automatic code generation and evaluation [243, 744].", + "- Commonsense Puzzle: Commonsense puzzle benchmarks, including LiveBench [850], BIG-Bench Hard [705] and ZebraLogic [450], assess models' ability to reason about commonsense situations. The ARC [131] and DRE-Bench [947] is often viewed as a challenging commonsense-based AGI test. JustLogic [87] further contributes to the evaluation of deductive reasoning and commonsense problem-solving. Moreover, Li et al. [382] introduce QuestBench, a benchmark designed to evaluate the ability of RLLMs to generate insightful and meaningful questions." + ], + "bbox": [ + 174, + 542, + 826, + 827 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "The second focus area concerns Knowledge Benchmarks, essential for evaluating a model's capability in complex reasoning across various tasks for out of distribution evaluation [776]:", + "bbox": [ + 169, + 833, + 823, + 863 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "- Scientific Reasoning: Scientific Reasoning benchmarks, such as GPQA Diamond [637], MMLU-Pro [821], and SuperGPQA [165], assess multi-domain reasoning in fields like chemistry, biology, and physics [157]. These benchmarks test models' ability to not only accumulate knowledge", + "bbox": [ + 174, + 869, + 826, + 912 + ], + "page_idx": 10 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 308, + 71 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "but also integrate it for problem-solving. Humanity's Last Exam (HLE) [602] further challenges models by requiring deep interdisciplinary reasoning across scientific disciplines. Further, Chung et al. [140] propose TPBench to evaluate the effectiveness of RLLMs in solving theoretical physics problems.", + "bbox": [ + 186, + 90, + 823, + 145 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "- Medical Reasoning: In the realm of Medical Reasoning, the need for complex, domain-specific, and accurate reasoning is paramount [1094, 1024, 905, 589]. Benchmarks, such as MedQA [328], JAMA Clinical Challenge [76], LLMEval-Med [1049] and Medbullets [76], simulate diagnostic and treatment decision-making processes, reflecting real-world medical practice. These benchmarks evaluate a model's handling of medical knowledge and reasoning, from diagnosis to treatment planning. Additionally, MedXpertQA [1150] introduces a comprehensive evaluation framework combining text and multimodal data, specifically assessing AI's reasoning capabilities in healthcare.", + "bbox": [ + 174, + 148, + 826, + 261 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "3.2.4 Process Evaluations", + "text_level": 1, + "bbox": [ + 171, + 277, + 366, + 292 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Deep Reasoning Benchmarks Recent progress in RLLMs underscores the need for specialized benchmarks to evaluate their deep reasoning abilities in Long CoT [375, 1133]. Notably, Lin et al. [450] introduces ZebraLogic, a framework for assessing logical reasoning, especially in complex non-monotonic scenarios. Similarly, BigGSM [90] and GSM-Ranges [670] focus on perturbing numerical values to test logical and arithmetic reasoning in edge cases beyond the models' training distribution. ROSCOE [212], ReCEval [606], DiVeRSe [425], HLV [71], and CoT-Kinetics [51] are designed to assess each step in the deep reasoning process during Long CoT tasks.", + "bbox": [ + 169, + 303, + 826, + 402 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Exploration Benchmarks Several studies assess RLLMs' exploration capabilities in Long CoT tasks. Specifically, Sys2Bench [583] evaluates the exploration and scaling abilities of RLLMs, emphasizing generalization across diverse tasks. BanditBench [566] extends this by testing model performance in interactive environments, offering insights into practical applications. Additionally, Heyman and Zylberberg [254] introduce a graph coloring problem to assess reasoning and spatial exploration in complex problem-solving scenarios.", + "bbox": [ + 169, + 414, + 826, + 501 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Reflection Benchmarks Reflection benchmarks measure RLLMs' ability to identify, reflect upon, and correct errors in Long CoT reasoning. These benchmarks fall into two categories: feedback and refinement. (1) Feedback Benchmark: These benchmarks assess the ability of LLMs to detect errors and respond to feedback for improvement. For example, Lambert et al. [367] introduces RewardBench to evaluate RLLMs' reward capabilities. This framework is extended by Multimodal RewardBench[960], and CodeCriticBench [1025] to include multimodal and code contexts, respectively. Benchmarks such as ProcessBench [1102], PRMBench [679], MR-Ben [1021], and DeltaBench [250] focus on error detection and correction across various tasks at the step level. Additionally, RealL Mistake [337] and JudgeBench [709] address more real-world error evaluation. (2) Refinement Benchmark: These benchmarks focus on error correction in complex tasks. CriticBench [456] assesses critique-correction capabilities, while MLDebugging [287], and ErrorRadar [922] specializes in coding or multimodal reasoning error detection and refinement. FinerReason [72] introduces a commonsense puzzle for broader feedback and refinement evaluations. Medec [1] adapts error correction to healthcare, addressing medical issues.", + "bbox": [ + 169, + 512, + 828, + 708 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "3.2.5 Advanced Evaluation", + "text_level": 1, + "bbox": [ + 171, + 720, + 375, + 734 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Agentic & Embodied Reasoning Agentic and Embodied reasoning requires models to demonstrate an understanding of real-world interactions, tool use, and adaptive reasoning in response to change. To assess real-world understanding, Wang et al. [798] introduce a benchmark that evaluates agents' ability to reason about physical concepts. Zhang et al. [1064] extend this by assessing agents' interactions with real-world physics. Additionally, realistic tasks often demand complex planning and tool usage, necessitating benchmarks to evaluate agent reasoning. These benchmarks assess agents' abilities to navigate and complete tasks in digital environments. Building on this, Huang et al. [283] propose a framework for evaluating decision-making in multi-agent, competitive settings. Nath et al. [562] introduce ToolComp, a benchmark designed to evaluate multi-step tool-use reasoning. To analyze adaptive reasoning in the face of real-world change, OSWorld [887], CogAgent [260], Mobile-Agent-E [828], WebShop [954], WebArena [1126], WGSR-Bench [972], and WebGames [735] assess AI systems across domains such as operating systems, mobile GUIs, browser tasks, and interactive", + "bbox": [ + 169, + 744, + 828, + 912 + ], + "page_idx": 11 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 308, + 71 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "entertainment [1106, 780, 512, 552]. Hu et al. [272] present Text2World, which evaluates agents' ability to generate interactive environments from text to test agent adaptability [995].", + "bbox": [ + 169, + 90, + 826, + 122 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Multimodal Reasoning Multimodal reasoning refers to a system's ability to integrate and reason across diverse input types, including text, images [316]. This capability is crucial for solving complex problems that require information from diverse formats.", + "bbox": [ + 169, + 135, + 826, + 179 + ], + "page_idx": 12 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Complex Mathematics: Mathematical reasoning often integrates both textual and visual components, such as equations, graphs, or diagrams [921]. Specifically, challenges like MathVista [508], MathVision [782], MathVerse [1054], M3CoT-Math [91], CMMaTH [433], EnigmaEval [763], CoMT-Geometry [125], and PGPS9K [1050] aim to advance multimodal reasoning in mathematics, improving the evaluation of multimodal Long CoT logic.", + "- Complex Code: The second area of focus involves code-related reasoning, where systems interpret textual descriptions and code snippets. Benchmarks like HumanEval-V [1035], Code-Vision [767], Plot2Code [852], and ChartMimic [931] evaluate systems' capabilities to generate or interpret code from natural language and multimodal inputs for assessing systems that integrate natural language processing with programming tasks.", + "- **Complex Science:** This area involves integrating scientific texts with related diagrams or experimental data. Benchmarks like ScienceQA [507], M3CoT-Science [91], BMMR [874], and ScienceBoard [698] evaluate how well models combine science information with Long CoT reasoning across various scientific domains [966]. Further, Guo et al. [229] propose MolPuzzle for the evaluation of molecular structure elucidation.", + "- Commonsense Puzzle: This area focuses on commonsense reasoning, where systems combine reasoning cues and images to make deeper conclusions. Chen et al. [91] introduce M3CoT-Commensense, which incorporates commonsense Long CoT reasoning for complex multimodal interactions. Further, PuzzleVQA [128], MMReason [953] and LEGO-Puzzles [711] focus more on abstract and spatial puzzle reasoning, respectively. Additionally, Wang et al. [760] propose two benchmarks: Clue-Visual Question Answering (CVQA), which tests visual comprehension through three task types, and Clue of Password-Visual Question Answering (CPVQA), which features two task types focusing on the interpretation and application of visual data." + ], + "bbox": [ + 174, + 185, + 826, + 513 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "AI for Research Recent advancements in AI have significantly advanced scientific research [94, 1124, 817, 215], with platforms like SciWorld [798] improving the research process. Simultaneously, Pricope [608] and Chan et al. [67] introduce a machine-learning platform to evaluate the potential of RLLMs in automating experiments. Several studies also examine RLLMs' ability to generate innovative research ideas. For instance, Si et al. [672] conduct evaluations with over 100 NLP researchers to assess RLLMs' creativity, revealing notable limitations [404, 856, 726]. Additionally, Li et al. [434] introduce SolutionBench, a benchmark for assessing systems' ability to generate feasible solutions for complex engineering problems.", + "bbox": [ + 169, + 530, + 828, + 643 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "4 Deep Reasoning for Long CoT", + "text_level": 1, + "bbox": [ + 171, + 662, + 460, + 680 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Deep reasoning capabilities primarily require profound depth and comprehensiveness in cognitive and reasoning processes. In the absence of such capabilities, RLLMs suffer significant performance declines [758, 823]. Current methods for enhancing deep reasoning can be categorized into two main approaches: (1) Deep Reasoning Format ( $\\S$ 4.1), which involves utilizing various reasoning execution formats to maximize the reasoning step length $k$ within reasoning boundary $\\mathcal{B}_l$ in Equation (2), by selecting the most suitable reasoning format; and (2) Deep Reasoning Learning ( $\\S$ 4.2), which focuses on improving the model's internal capabilities to enhance its deep reasoning abilities, thereby extending the reasoning boundary $\\mathcal{B}_l$ in Equation (2) intrinsically.", + "bbox": [ + 169, + 696, + 826, + 808 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "4.1 Deep Reasoning Format", + "text_level": 1, + "bbox": [ + 171, + 828, + 382, + 843 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "As illustrated in Figure 5, deep reasoning formats can be categorized into three main types: natural language ( $\\S$ 4.1.1), structured language ( $\\S$ 4.1.2), and latent-space reasoning ( $\\S$ 4.1.3), the latter of which is further subdivided into token-, vector-, and manager-driven latent reasoning. The reasoning performance across these formats is presented in Table 1.", + "bbox": [ + 169, + 854, + 825, + 912 + ], + "page_idx": 12 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 308, + 71 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "13", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "(a) Natural Language Deep Reasoning", + "text_level": 1, + "bbox": [ + 186, + 92, + 397, + 104 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "To predict the output of the given input for Conway's Game of Life, we need to apply the rules of the game to each cell on the board. The rules are as follows:", + "bbox": [ + 196, + 111, + 482, + 142 + ], + "page_idx": 13 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Any live cell with fewer than two live neighbors dies (underpopulation)...", + "Given Input Board: ...", + "$\\spadesuit$ Step-by-Step Analysis: ...", + "$\\spadesuit$ Final Output: After applying the rules to each cell..." + ], + "bbox": [ + 197, + 143, + 482, + 193 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/ff164d8152d0e42a100061acaca7da8e5deb82846df7779c8c7d61fa44616288.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 441, + 164, + 488, + 204 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "(b) Structured Language Deep Reasoning", + "text_level": 1, + "bbox": [ + 506, + 92, + 738, + 106 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/5627b8fe0330637f914d05c2ea3b75f4df43c678ec6ae3f0e9b7da8f94f4f43f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 112, + 537, + 131 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "import necessary packages from collections import Cou", + "bbox": [ + 539, + 111, + 692, + 130 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "import necessary packages", + "bbox": [ + 511, + 131, + 669, + 140 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "from collections import Counter", + "bbox": [ + 511, + 141, + 689, + 148 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "all class and function definitions in the code", + "bbox": [ + 511, + 148, + 785, + 159 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "file, if any", + "bbox": [ + 511, + 159, + 584, + 167 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "class Solution(object):", + "bbox": [ + 511, + 167, + 645, + 176 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "defgameOfLifeInfinite(self, live): ctr = Counter((I, J) for i, j i", + "bbox": [ + 532, + 176, + 733, + 193 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/998c396b19ab3cb07b28b1eb72b14b5078de0675ec62ef33294a59363f34d6e2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 167, + 807, + 204 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "(c) Latent Space Deep Reasoning", + "text_level": 1, + "bbox": [ + 189, + 210, + 379, + 224 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/823ca26e30f5429ff0ae86df5e048ed2430dd9bdc62c2d874445fe64c1774d87.jpg", + "image_caption": [ + "Figure 5: Three main categories of deep reasoning formats: natural language, structured language, and latent-space reasoning (subdivided into token-, vector-, and manager-driven latent reasoning), with examples drawn from Li et al. [401]." + ], + "image_footnote": [], + "bbox": [ + 191, + 224, + 228, + 299 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/aa202666c0347e30f452afb50132bf46686ba98433600b7ee8d0e4c2f30ad8f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 228, + 224, + 423, + 306 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/09f798353b1e4615f84c4d824a90ec1e55d3d23579c20ec2917c35a81ade4452.jpg", + "image_caption": [], + "image_footnote": [ + "Reasoning Vector Driven Latent Space Deep Reasoning" + ], + "bbox": [ + 423, + 208, + 622, + 289 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/3effed9f4c545b03b2ac2c365b4d87fe9724f58c4dddd4294def63e3d2f5672e.jpg", + "image_caption": [], + "image_footnote": [ + "Reasoning Manager Driven Latent Space Deep Reasoning" + ], + "bbox": [ + 622, + 208, + 812, + 290 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "4.1.1 Natural Language Deep Reasoning", + "text_level": 1, + "bbox": [ + 171, + 388, + 468, + 404 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Traditionally, researchers have sought to adapt natural language for intuitive and free-flowing deep reasoning [836, 1118, 303, 617, 1070, 765, 205]. Early work by Wei et al. [836] demonstrated that the use of natural language Long CoT significantly enhances the reasoning capabilities of RLLMs. Further, the Natural Program framework [460] allows RLLMs to engage in deeper natural language reasoning by ensuring a more structured and rigorous logical analysis. More recently, CodeI/O [401] has introduced a technique that reorganizes code-based reasoning patterns into natural language formats, further boosting the reasoning potential of RLLMs [36]. Similarly, Li et al. [387] propose CoRT, which integrates code into reasoning to facilitate a mixture of formats, resulting in improved cognitive performance.", + "bbox": [ + 169, + 412, + 826, + 539 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "4.1.2 Structured Language Deep Reasoning", + "text_level": 1, + "bbox": [ + 171, + 555, + 491, + 570 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Structured language deep reasoning encompasses various approaches designed to program [100, 464, 687, 591, 198, 845, 830, 1044] or symbolic language [605, 158, 451, 372, 933, 604, 37, 40, 797, 380] format for enhanced deep reasoning. In this context, most studies focus on utilizing code to better enhance the mathematical reasoning capabilities [389, 107, 978, 85]. Xu et al. [897] propose a neural-symbol self-training framework guided by the environment, addressing both the scarcity of symbolic data and the limitations of symbolic processing in LLMs. Additionally, Liao et al. [443] present SKIntern, which refines symbolic RLLMs through curriculum learning and linear attenuation, enabling the internalization of symbolic knowledge with fewer examples, reducing computational costs, and accelerating inference. Furthermore, Ranaldi et al. [634] introduce QuaSAR, a CoT variant that directs LLMs to operate at higher abstraction levels through quasi-symbolic reasoning, thus improving natural language reasoning and providing more precise structural representations.", + "bbox": [ + 169, + 579, + 826, + 733 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "4.1.3 Latent Space Deep Reasoning", + "text_level": 1, + "bbox": [ + 171, + 750, + 433, + 763 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Latent space deep reasoning encompasses techniques designed to enhance the reasoning abilities of LLMs by leveraging operations within continuous latent spaces [684, 151, 640, 324]. These approaches can be categorized into three main paradigms: (1) Reasoning Token-Driven Latent Space Deep Reasoning: Early work [810, 1013] introduce the concept of \"planning tokens\" or \"thought tokens\" to guide reasoning within latent spaces [949, 1008]. Further, Coconut [236] expands on this through the maintenance of multiple alternative reasoning paths, increasing both complexity and efficiency [1069, 706]. At the extreme, Heima [662] condenses the entire Long CoT process into a single token, yielding substantial computational savings. (2) Reasoning Vector Driven Latent Space Deep Reasoning: Building on the previous paradigm, LTM [356] conceptualizes the layers of LLMs as \"thought blocks\" and introduces the concept of \"thought vectors\" for each layer. This", + "bbox": [ + 169, + 772, + 826, + 912 + ], + "page_idx": 13 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 13 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 13 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 13 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 13 + }, + { + "type": "page_number", + "text": "14", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/ebcdb7892865c413666c63573d7f974aac12588169f830423b0bd269bf85e3b2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelBase ModelGSM8kMATHGPQAOlympiadBenchLiveCodeBench
Latent Space Deep Reasoning
No-CoT [151]Mistral-7B [318]38.0----
SQ-VAE [810]Llama-2-7B [743]40.07.0---
RecurrentBlock-3.5B [204]-42.1----
ICoT-SI [151]Mistral-7B [318]51.0----
Natural Language Deep Reasoning
Self-Rewarding [114]Llama-2-7B [743]40.010.7---
Llama-3.1-8B [168]-56.720.3---
MetaMath [983]Llama-2-7B [743]66.5----
OVM [979]Llama-2-7B [743]73.7----
NuminaMath-7B-CoT [397]-75.455.2-19.9-
Qwen2-7B [925]-79.944.2-21.3-
Qwen2-Math-7B [927]-80.450.4-38.2-
Internlm2-math-plus-7B [974]-84.054.4-18.8-
OMI2 [401]Qwen2.5-Coder-7B [301]84.172.336.2-27.2
Llama-3.1-70B [168]-85.541.4---
CODEI/O++ [401]Qwen2.5-Coder-7B [301]85.772.140.6-29.1
CODEI/O [401]Qwen2.5-Coder-7B [301]86.471.943.3-28.5
WI [401]Qwen2.5-Coder-7B [301]87.071.439.1-26.0
WI (Full) [401]Qwen2.5-Coder-7B [301]87.071.142.9-27.6
OMI2 (Full) [401]Qwen2.5-Coder-7B [301]88.573.240.9-28.4
DeepSeekMath-7B-RL [658]-88.251.7-19.0-
Llama-3.1-405B [168]-89.053.8---
CoMAT [371]GPT-4 [3]93.7-40.4--
CoT [634]GPT-4 [3]94.5-41.850.2-
FCoT [523]GPT-4 [3]95.0----
Qwen2.5-Math-7B-Instruct [927]-95.283.6-41.6-
MathPrompter [303]GPT-4 [3]95.6----
Qwen2.5-Math-72B-Instruct [927]-95.985.9-49.0-
DeepSeek-R1-Distill-Qwen-7B [227]--92.8-49.137.6
DeepSeek-R1-Distill-Qwen-32B [227]--94.3-62.157.2
Structured Language Deep Reasoning
STaR [1012]Llama-2-7B [743]58.216.0---
ENVISIONS [897]Llama-2-7B [743]59.019.0---
MAmmoTH [1006]Code-Llama-7B [639]59.4----
MathCoder-CL [783]Code-Llama-7B [639]67.830.2---
ToRA-Code [217]Llama-2-7B [743]72.6----
Brain [107]Code-Llama-7B [639]74.0----
DeepSeek-Coder-7B [226]-77.444.4---
SIaM [978]Qwen-2-Math-Base81.550---
OC-SFT-1 [401]Qwen2.5-Coder-7B [301]86.770.937.7-27.5
PyEdu [401]Qwen2.5-Coder-7B [301]85.871.440.9-25.8
Qwen2.5-Math-7B-Instruct [927]-94.685.2-55.6-
Qwen2.5-Math-72B-Instruct [927]-95.888.1-60.6-
QuaSAR [634]GPT-4 [3]96.5-55.444.6-
MathDivide [687]GPT-4 [3]96.8---
", + "bbox": [ + 181, + 88, + 815, + 559 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Table 1: Performance of various deep reasoning formats, sorted primarily by GSM8K scores. “-” indicates that the paper did not report this score.", + "bbox": [ + 169, + 565, + 826, + 594 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "approach allows for the scaling of inference-time computations by implicitly performing reasoning within the latent space through recurrent depth. (3) Reasoning Manager Driven Latent Space Deep Reasoning: Inspired by these, Schone et al. [647], Geiping et al. [204], and Saunshi et al. [646] propose a mechanism similar to a continuous reasoning manager, which iteratively governs a trained \"recurrent block\" as a recurrent \"thought block\" [511]. This method integrates deeper model layers during reasoning, enhancing performance without needing specialized training data, and even outperforming larger RLLMs. Additionally, ITT [109] leverages the original transformer layer as a recurrent \"thought block\", selecting key tokens via adaptive token routing and controlling reasoning depth with residual thinking connections, enabling more efficient processing of critical tokens. Further, System-1.5 Reasoning [808] defines two dynamic shortcuts. The Model Depth Shortcut (DS) lets non-critical tokens exit early via lightweight adapter branches while routing critical tokens through deeper Transformer layers, thus supporting adaptive, vertical reasoning. The Step Shortcut (SS) reuses hidden states across decoding steps to bypass trivial iterations and enable horizontal reasoning in latent space.", + "bbox": [ + 169, + 619, + 826, + 815 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "4.2 Deep Reasoning Learning", + "text_level": 1, + "bbox": [ + 171, + 830, + 393, + 845 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Insufficient deep reasoning in RLLMs can significantly degrade performance [758, 823]. As a result, research has focused on improving reasoning through training. Supervised fine-tuning (SFT) [1058] stabilizes model outputs by serving as a memory process [883], while reinforcement learning (RL) enables generalization and self-learning [227, 137, 276, 898]. Recent studies for deep reasoning", + "bbox": [ + 169, + 854, + 826, + 912 + ], + "page_idx": 14 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 14 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 14 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 65 + ], + "page_idx": 14 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 65, + 305, + 69 + ], + "page_idx": 14 + }, + { + "type": "page_number", + "text": "15", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/787c5674fba7b0ce5e4ca3ac3eefd20babe3c384dc807cab022b3df606b88f7a.jpg", + "image_caption": [ + "(a) Deep Reasoning Imitation" + ], + "image_footnote": [], + "bbox": [ + 187, + 112, + 483, + 188 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/04fef9422d7990eb4d902d3c902905109bd7fe0911512bee51a344a37488531e.jpg", + "image_caption": [ + "(b) Deep Reasoning Self-Learning", + "Figure 6: The different learning strategies of deep reasoning learning, including deep reasoning imitation of the data from advanced deep reasoning systems, like advanced RLLMs, MCTS, etc.; deep reasoning self-learning from preference-based RL by implicit reward." + ], + "image_footnote": [], + "bbox": [ + 496, + 112, + 810, + 186 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "learning have explored using SFT to imitate advanced reasoning in RLLMs and applying RL to enhance self-improvement in reasoning. As illustrated in Figure 6, this section outlines two key approaches to improve deep reasoning: (1) Deep Reasoning Imitation (§ 4.2.1), which involves learning reasoning from human-annotated or distilled data through SFT, and (2) Deep Reasoning Self-Learning (§ 4.2.2), where models improve reasoning through preference-based RL with implicit rewards. The performance of these methods is shown in Table 2.", + "bbox": [ + 169, + 272, + 823, + 354 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "4.2.1 Deep Reasoning Imitation", + "text_level": 1, + "bbox": [ + 171, + 371, + 406, + 386 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Deep reasoning in RLLMs can be effectively achieved by mimicking advanced reasoning systems, such as human reasoning [558, 61, 115, 403], advanced RLLMs [227, 58, 957, 370, 102], and scaling-augmented RLLMs [410, 1003, 596, 1136, 41]. This approach enables the model to learn complex reasoning patterns and generalize across tasks [937, 416]. Specifically, (1) Imitation from Human: Earlier, Cobbe et al. [141] first propose the deep reasoning imitation paradigm using human examples. ALT [558] improves RLLM reasoning by generating larger datasets of human-annotated logical templates, which fosters deeper reasoning [241]. To enhance diversity, EIT [61] promotes simpler human-generated plans, while LLMs contribute more nuanced reasoning, facilitating collaboration between human input and AI. (2) Imitation from Advanced RLLMs: A body of work utilizes zero-shot prompting to guide large teacher RLLMs in generating reasoning rationale, which is then used to fine-tune smaller RLLMs, marking the beginning of deep reasoning imitation [256, 352, 938, 521]. Additionally, AceMath [500] applies few-shot prompting to distill Long CoT samples from advanced LLMs, followed by multi-stage quality-guided SFT to enhance performance. Chen et al. [107] separate the data synthesis process into planning and reasoning stages, thereby improving reasoning quality. DART-Math [738] effectively distills complex queries requiring deeper reasoning during synthesis, advancing deep reasoning capabilities. Further, Ahmad et al. [7] propose OpenCodeReasoning, expanding this paradigm to the code scenarios. (3) Imitation from Scaling-augmented RLLMs: Earlier, Bansal et al. [34] enhance data quality by scaling the sampling size and length, boosting imitation performance [481, 1005]. Yang et al. [927] and Zhao et al. [1090] further improve data quality by scaling sampling and selecting samples through sample feature or an additional reward model. Additionally, Li et al. [410] identify optimal deep reasoning paths through MCTS, advancing imitation effectiveness.", + "bbox": [ + 169, + 393, + 826, + 699 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Recent studies [299, 550] show that distilling knowledge from advanced RLLM APIs like O1 [307] and R1 [227] significantly enhances the performance of smaller LLMs [424, 223]. This method, employing supervised fine-tuning, boosts model performance on complex mathematical reasoning tasks, sometimes surpassing the teacher models' performance. Building on these findings, LIMO [967], S1 [560], and RedStar [902] argue that a large number of imitation samples is unnecessary. They demonstrate that even a minimal set of samples can activate deep reasoning capabilities in foundational LLMs. For practical applications, Turtel et al. [747] showcase how these techniques can predict future events beyond a model's knowledge cutoff. Sun et al. [701], Yang et al. [928] and Zhao et al. [1093] further enhance deep reasoning imitation by selecting high-quality samples from large datasets, thereby improving the quality of the imitation data.", + "bbox": [ + 169, + 704, + 826, + 844 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "4.2.2 Deep Reasoning Self-Learning", + "text_level": 1, + "bbox": [ + 171, + 859, + 437, + 875 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "While simple imitation can yield strong performance, current models still rely heavily on human annotations or outputs from more advanced models for both imitation and distillation [502]. To", + "bbox": [ + 169, + 883, + 823, + 912 + ], + "page_idx": 15 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 41, + 225, + 70 + ], + "page_idx": 15 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 307, + 59 + ], + "page_idx": 15 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 230, + 59, + 305, + 68 + ], + "page_idx": 15 + }, + { + "type": "page_number", + "text": "16", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 15 + }, + { + "type": "table", + "img_path": "images/0a51aaca5f29b7a1155025d64a0e6be21201b8129c276ddc53c0a7fa47545014.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelData SizeBase ModelGSM8KMATHMATH-500AIME2024GPQAOlympiadBench
Deep Reasoning Imitation
SFT [938]200KLlama-3.1-8B [168]---54.13.5-
Retro-Enh [115]14MLlama-3-8B [168]45.121.7----
Query-Exp [115]24MLlama-3-8B [168]51.323.1----
Res-Div [115]14MLlama-3-8B [168]53.023.2----
MetaMath [738]0.40MMistral-7B [318]76.529.8---5.9
ALT-FLDx2 [558]100KLlama-3.1-70B [168]83.324.4----
EIT [61]15KLlama-2-70B [743]84.132.5----
MathScale [738]2.0MMistral-7B [318]74.835.2----
Tutor-Amp [115]11MLlama-3-8B [168]64.435.9----
MMIQC [738]2.3MMistral-7B [318]75.437.4---9.4
VRT [738]0.59MMistral-7B [318]82.338.7---8.7
KPMath-Plus [738]1.6MMistral-7B [318]82.146.8----
Llama-2-70B-Xwin-Math-V1.1 [385]1.4MLlama-2-70B [743]90.252.5---16.3
DART-Math-Mistral-7B [738]591KMistral-7B [318]81.145.5---14.7
DART-Math-Llama-3-70B [738]591KLlama-3-70B [168]89.656.1---20.0
Rejection Sampling [410]197KQwen2.5-7B [926]87.170.0-10.0-27.1
Evol-Instruct-7B [514]905KQwen2.5-Math-7B [927]88.5-77.416.7--
FastMCTS [410]288KQwen2.5-7B [926]88.974.0-20.0-27.5
KPDDS-7B [295]800KQwen2.5-Math-7B [927]89.9-76.010.0--
DeepSeek-R1-Distill-Qwen-7B [227]800KQwen2.5-7B-Instruct [926]91.7-91.643.3--
Openmathinstruct-7B [740]14MQwen2.5-Math-7B [927]92.0-79.610.0--
NuminaMath [967]100KQwen2.5-Math-7B [927]92.9-81.820.0--
PromptCoT-DS-7B [1090]115KDeepSeek-R1-Distill-Qwen-7B [227]92.6-93.060.0--
PromptCoT-Qwen-7B [1090]905KQwen2.5-Math-7B [927]93.3-84.026.7--
AceMath-7B-Instruct [500]1.2MQwen2-Math-7B-Instruct [927]93.783.1---42.2
AceMath-72B-Instruct [500]1.2MQwen2.5-Math-72B-Instruct [927]96.486.1---48.4
NuminaMath [967]100KQwen2.5-32B-Instruct [926]--59.26.525.836.7
OpenThoughts [967]114KQwen2.5-32B-Instruct [926]--80.650.242.956.3
Sky-T1-32B-Preview [724]17KQwen2.5-32B-Instruct [926]--82.443.356.8-
Journey Learning [299]5KQwen2.5-Math-72B [927]--87.243.3--
STILL-2 [550]3.9KQwen2.5-32B-Instruct [926]--90.246.755.1-
Bespoke-32B [362]17KQwen2.5-32B-Instruct [926]--93.063.358.1-
s1 [560]1KQwen2.5-32B-Instruct [926]--93.056.759.6-
DeepSeek-R1-Distill-Qwen-32B [227]800KQwen2.5-32B-Instruct [926]--94.372.662.1-
LIMO [967]817Qwen2.5-32B-Instruct [926]--94.815.866.766.8
Deep Reasoning Self-Learning
DPO [302]40KDeepSeek-Math-7B-Base [658]74.834.9----
RefT [302]40KDeepSeek-Math-7B-Base [658]71.436.0----
Self-Explore [302]40KDeepSeek-Math-7B-Base [658]78.637.7----
SimPO [723]10KQwen2.5-Math-7B-Instruct [927]88.840.056.6---
DPO [446]11KDeepSeek-Math-7B-Instruct [658]-48.7----
TPO [446]11KDeepSeek-Math-7B-Instruct [658]-51.3----
DPO [446]11KQwen2-7B-Instruct [925]-54.3----
TPO [446]11KQwen2-7B-Instruct [925]-55.5----
MCTS [74]15KDeepSeek-Math-7B-Base [658]83.264.0----
SBS [74]15KDeepSeek-Math-7B-Base [658]84.166.3----
FastMCTS+Branch-DPO [410]152KFastMCTS-7B [410]89.975.4-20.0-29.6
", + "bbox": [ + 178, + 90, + 818, + 481 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Table 2: Performance of various deep reasoning learning methods, sorted primarily by Math or Math-500 scores. “-” indicates that the paper did not report this score.", + "bbox": [ + 169, + 488, + 823, + 517 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "address this limitation, recent research has focused on enabling more advanced reasoning through techniques like self-play and self-learning [948, 1077, 409, 624]. Specifically, self-learning methods can be classified into two paradigms, differentiated by their sampling strategies:", + "bbox": [ + 169, + 599, + 823, + 643 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "(1) Self-Learning from Direct Sampling: The earliest method, STaR [1012], utilizes In-Context Learning (ICL) to sample deep reasoning results [657] and uses the correctness of the final answer as an implicit reward for self-learning [258, 581, 582, 1059, 826, 462]. Further, ReST [225] extends this by introducing a Grow-Improve paradigm, where self-generated reasoning is first annotated with rewards and then enhanced via offline RL algorithms. However, these approaches can be fragile, especially when the reward process lacks robustness. Inspired by the Expectation-Maximization (EM) algorithm, Singh et al. [674] propose a method that generates rewards and iteratively optimizes LLMs to achieve the best performance on a validation set, significantly improving robustness. To further strengthen the reward process, a series of work introduces a method to adapt incorrect solutions, training a verifier [155, 262] or utilize entropy [809, 1040] to select or refine the reward process and improve self-learning quality. (2) Self-Learning from Tree Search: Early deep learning methods, such as EXIT [18], combined MCTS with deep neural networks for reinforcement learning, iteratively self-training the network to guide the tree search and enhance reasoning. Building on this, CPO [1065] and TPO [446] align each step of Long CoT reasoning with the corresponding tree search path, using Tree of Thoughts (ToT) [955] preference information to support deeper reasoning [951, 302]. Li [422] propose Policy-Guided Tree Search (PGTS), integrating RL with structured tree exploration for more efficient navigation of reasoning paths. Further developments, such as AlphaMath [74], AlphaLLM-CPL [814], and TongGeometry [1029], refine MCTS behavior through stepwise trajectory pair extraction and curriculum preference learning, boosting LLM reasoning abilities [611, 412, 872].", + "bbox": [ + 169, + 648, + 826, + 912 + ], + "page_idx": 16 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 16 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 16 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 230, + 59, + 305, + 68 + ], + "page_idx": 16 + }, + { + "type": "page_number", + "text": "17", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Takeaways: Imitation & Self-Learning", + "text_level": 1, + "bbox": [ + 204, + 90, + 460, + 107 + ], + "page_idx": 17 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Imitating deep reasoning from advanced RLLMs, and scaling-augmented methods like MCTS can help models learn complex reasoning patterns with fewer samples.", + "- Self-learning techniques, including reinforcement learning and tree search, allow RLLMs to enhance their reasoning abilities over time.", + "- The combination of imitation from advanced RLLMs and self-learning techniques strengthens RLLM reasoning, leading to strong performance on complex tasks." + ], + "bbox": [ + 200, + 114, + 799, + 205 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "5 Feasible Reflection for Long CoT", + "text_level": 1, + "bbox": [ + 171, + 234, + 480, + 252 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Feasible Reflection is a pivotal component of Long CoT reasoning, enabling LLMs to handle complex tasks through iterative feedback and refinement [406, 192]. Specifically, it comprises two primary stages: (1) Feedback ( $\\S$ 5.1), which generates feedback signals $\\mathcal{F}_i$ to correct node $n_j$ in Equation (5); and (2) Refinement ( $\\S$ 5.2), which adjusts the subsequent node $n_{i+1}$ according to the feedback in Equation (6).", + "bbox": [ + 169, + 265, + 823, + 335 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "5.1 Feedback", + "text_level": 1, + "bbox": [ + 171, + 351, + 279, + 364 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Feedback refers to the process of providing evaluations of both overall outputs and the processes that lead to them, with the goal of assessing their accuracy and quality [394, 396, 838, 220, 862]. This process, also referred to as critique or verification, can be executed using either natural language or structured data formats, which serve as the foundation for tree-search methods [113]. Specifically, as shown in Figure 7, feedback can be categorized into three distinct types: (1) Overall Feedback ( $\\S$ 5.1.1); (2) Process Feedback ( $\\S$ 5.1.2); (3) Hybrid Feedback ( $\\S$ 5.1.3).", + "bbox": [ + 169, + 377, + 823, + 460 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "5.1.1 Overall Feedback", + "text_level": 1, + "bbox": [ + 171, + 474, + 346, + 488 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "The overall feedback focuses on providing a global view of the entire process and results, rather than assessing each step individually. This feedback significantly enhances reasoning skills and reward modeling in reinforcement learning for RLLMs. Specifically, as shown in Figure 7 (a), the overall feedback can be categorized into three main sources: Outcome Reward Model, Rule Extraction, and RLLMs Feedback. The performance across these categories is summarized in Table 3.", + "bbox": [ + 169, + 498, + 823, + 568 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/924dba4b1d5c6d25f0eff62713bafcbf9c36e9cd21483aae275897e288afdd77.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 253, + 589, + 415, + 703 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/367cca6990189dfda7e049a2d562809a0e9869ca5351f1d2d1d1e74c0f9bcafd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 423, + 593, + 578, + 703 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/dd4b7e43b794582020a033da732daf0b1be53e45111b8e9717414d483b50896e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 593, + 738, + 703 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/6914fc78c8aeece2af825dabacd242f08c842b612001c13322264246623afb04.jpg", + "image_caption": [ + "Figure 7: The feedback capabilities framework for feasible reflection consists of Overall Feedback and Process Feedback. Overall Feedback includes the Outcome Reward Model (ORM) in a value format, rule extraction for correctness judgment, and overall RLLMs based on RLLMs. Process Feedback includes the Process Reward Model (PRM) in a value format and step-level RLLMs, also based on RLLMs." + ], + "image_footnote": [], + "bbox": [ + 254, + 705, + 431, + 829 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/75c5bea65e3eccbc79affd34b429b7f444436c52e5988975f4dec0ecb68328a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 446, + 707, + 733, + 829 + ], + "page_idx": 17 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 41, + 225, + 70 + ], + "page_idx": 17 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 307, + 59 + ], + "page_idx": 17 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 65 + ], + "page_idx": 17 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 65, + 300, + 69 + ], + "page_idx": 17 + }, + { + "type": "page_number", + "text": "18", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 17 + }, + { + "type": "table", + "img_path": "images/67120b715e01e4e0a5691bdc5abb971e8ebe54977751e351a5a6b2de0ae0cf33.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelBase ModelChatChat_HardSafetyReasoningOverall
RLLMs
GPT-4o-mini [3]-95.060.780.883.780.1
Llama3.1-70B-Instruct [168]-97.270.286.082.884.0
Llama3.1-405B-Instruct [168]-97.274.687.177.684.1
GPT-4 [3]-95.374.386.987.686.0
GPT-4o [3]-96.176.186.688.186.7
Gemini-1.5-pro [719]-92.380.687.992.088.2
Self-taught Evaluator [803]Llama-3.1-70B-Instruct [168]96.684.281.091.588.3
SFR-LLMA-3.1-8B-Judge [791]Llama-3.1-70B-Instruct [168]95.577.786.295.188.7
SFR-NeMo-12B-Judge [791]Mistral-NeMo-Instruct-12B [725]97.282.286.595.190.3
SFR-LLMA-3.1-70B-Judge [791]Llama-3.1-70B-Instruct [168]96.984.891.697.692.7
Skywork-Critic-Llama-3.1-70B [791]Llama-3.1-70B-Instruct [168]96.687.993.195.593.3
LMUnit [641]Llama-3.1-70B-Instruct [168]----93.4
EvalPlanner [643]Llama-3.1-70B-Instruct [168]97.589.493.095.593.9
Outcome Reward Models
tulu-v2.5-13b-uf-rm [306]TULU-2-13B [305]39.442.355.547.446.1
Prometheus-2-7B [353]Mistral-7B-Instruct-v0.2 [318]85.549.177.176.572.0
Prometheus-8x7b-v2 [353]Mixtral-8x7B-Instruct [319]93.047.180.577.474.5
Critic-RM-Rank [991]Llama-3.1-70B-Instruct [168]97.058.084.092.082.8
RM [689]Llama-3.1-70B-Instruct [168]98.374.583.888.086.4
SynRM [968]Llama-3.1-70B-Instruct [168]97.576.886.388.587.3
CLoud [17]Llama-3-70B-Instruct [168]98.075.687.689.087.6
FLAME-RM-24B [753]PaLM-2-24B [16]92.275.789.693.887.8
SteerLM-RM 70B [829]Llama-2-70B-chat [743]91.380.390.692.888.8
Llama-3-OffsetBias-RM-8B [585]Llama-3-8B-Instruct [168]97.281.886.891.989.4
InternLM-20B-Reward [62]InternLM2-8B-Instruct [62]98.976.589.995.890.2
ArmoRM-Llama3-8B-v0.1 [771]Llama-3-8B-Instruct [168]96.976.892.297.390.8
Nemotron-4-340B-Reward [829]Nemotron-4-340B [4]95.887.192.293.692.2
Skywork-Reward-Llama-3.1-8B [466]Llama-3.1-70B-Instruct [168]95.887.390.696.292.5
Skywork-Reward-Gemma-2-27B [466]Gemma-2-27B-it [720]95.891.492.096.193.8
", + "bbox": [ + 197, + 87, + 799, + 393 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Table 3: Performance of various overall feedback methods, sorted primarily by Overall scores in RewardBench [367]. “-” indicates that the paper did not report this score.", + "bbox": [ + 169, + 400, + 823, + 429 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Overall Feedback from Outcome Reward Model Since many tasks cannot be directly evaluated using accuracy or other standard metrics, research has increasingly focused on Outcome Reward Models (ORM), which provide value-based rewards for more general and quantifiable feedback [1127, 986, 467]. In 2021, OpenAI [141] has proposed a \"Gen-Verifier\" paradigm, which uses a specialized ORM to evaluate the accuracy of generated rationales, showing significant progress in feedback capabilities [658]. Ji et al. [315] introduce a trained knowledge scorer to analyze hallucinations in the reasoning process, providing feedback to RLLMs and improving the accuracy of their outputs over time. Moreover, Generative Reward Models [1048] use next-token prediction for overall feedback, which seamlessly integrates with instruction adjustments, leveraging inference-time calculations to improve ORM feedback.", + "bbox": [ + 169, + 465, + 826, + 604 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "However, specifically trained ORMs are often costly and not sufficiently robust. Building on this, Self-Rewarding Language Models (SRLMs) [1129] incorporate a self-consistency framework, optimizing feedback to improve model alignment and consistency [1047]. Yu et al. [991] introduce Critic-RM, combining RLLM-generated natural language criticism with corresponding feedback. This method filters high-quality feedback while jointly fine-tuning reward prediction and criticism generation, optimizing ORM performance.", + "bbox": [ + 169, + 611, + 828, + 696 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Overall Feedback from Rule Extraction Although ORM has achieved significant improvements, its accuracy still falls short of $100\\%$ , preventing it from outperforming rule-based answer correction feedback [955, 234, 1079]. Previous studies, such as STaR [1012], ReST [225], and ReFT [745], have demonstrated that feedback based on final answer rewards is more effective than both PRM and ORM in mathematical scenarios [197]. Furthermore, Guo et al. [227] and Xie et al. [886] introduce a multi-stage RL framework that incorporates rule-based rewards, significantly enhancing both output accuracy and length while mitigating reward hacking through simple yet robust rules [30], such as format validation and result verification. In coding scenarios where direct rule-based feedback is difficult, OpenCodeInterpreter [1108], AceCoder [1014], O1-Coder [1076], and VerMCTS [56] address this challenge by implementing an automated test-case synthesis pipeline, deriving rewards based on program performance [564, 216, 1115]. Additionally, Ma et al. [536] propose an automated approach to training a test case generator, which alleviates the scarcity of test cases and demonstrates that increasing the number of test cases correlates with improved reward quality. Moreover, Ma et al. [535] decompose problem-solving into structured coding subtasks: file localization, function", + "bbox": [ + 169, + 717, + 826, + 912 + ], + "page_idx": 18 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 18 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 18 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 230, + 59, + 305, + 68 + ], + "page_idx": 18 + }, + { + "type": "page_number", + "text": "19", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "localization, line localization, and code editing generation, and applies multi-viewed rule-based rewards.", + "bbox": [ + 169, + 90, + 823, + 119 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Overall Feedback from RLLMs Research on feedback from RLLMs centers on detecting errors and biases through natural language feedback, also known as LLM-as-Judge, self-reflection or self-critique [274, 336, 29, 638, 549, 802, 1002, 895, 529]. This method has led to significant improvements across various tasks, particularly in self-correction [848, 1109, 206, 184, 1075]. Huang et al. [286] contend that traditional LLMs struggle to generate effective feedback without external signals, requiring the development of RLLMs with enhanced feedback capabilities [645, 398]. As a result, many studies leverage RLLMs' error-identification strengths, often stemming from their pretraining phase, to improve feedback generation and correction [965, 39, 40, 282].", + "bbox": [ + 169, + 133, + 826, + 247 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Earlier, McAleese et al. [544] found that training RLLMs to learn self-critique and deep reasoning can further boost performance. Zhang et al. [1062] propose a self-contrast mechanism that compares multiple perspectives, identifies differences, and summarizes insights to resolve inconsistencies. However, these methods often offer task-independent feedback. To address this, Hao et al. [235] introduce AutoRace, which tailors evaluation criteria for specific tasks. The Reversal of Thought (RoT) framework [999] introduces a novel paradigm combining reverse reasoning with self-reflection, helping models identify the limits of their knowledge and enhance reasoning efficiency. Furthermore, ACR [1116] implements a scoring system for coding tasks, using LLM-as-a-Judge for quality assessment and LLM-as-a-Critic for critiquing low-quality code, improving consistency across benchmarks. Zheng et al. [1107] integrate code execution error data and feedback from RLLMs to improve code generation performance. Liu et al. [484] present AGSER, a method using attention-guided self-reflection to address hallucinations by splitting input queries into attentive and nonattentive components. Finally, Saha et al. [643] introduce EvalPlanner, which separates feedback into planning and reasoning components for more streamlined expression using existing RLLMs. More comprehensively, Hu et al. [274] outline the complete pipeline, key insights, and practical lessons for training RLLMs to function as judges.", + "bbox": [ + 169, + 250, + 826, + 474 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "5.1.2 Process Feedback", + "text_level": 1, + "bbox": [ + 171, + 484, + 349, + 500 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Techniques combine process feedback with MCTS or RL rewards to provide automated, step-by-step guidance, reducing the need for labor-intensive annotations while enhancing reasoning capabilities [749, 344]. These techniques can be categorized into two main types based on the source of feedback: process reward models (PRMs) and prompted LLMs. The performance comparison are mainly shown in Table 4.", + "bbox": [ + 169, + 510, + 826, + 582 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Process Feedback from Process Rewarded Model Recent studies highlight the significance of feedback in developing effective PRMs for complex reasoning tasks, particularly in a step-level view [134, 423, 528]. (1) Process Annotated PRM Training: Earlier, Lightman et al. [449] demonstrate that training process feedback with human-annotated data (PRM800K) surpasses outcome supervision in creating reliable reward models. However, this approach requires significant human effort. To address this, Wang et al. [792] introduce Math-Shepherd, a dataset that generates step-by-step supervision using a Tree Search-inspired method [73, 1001]. Following this, methods like QwQ [731], Skywork-o1 [570], AceMath [500], and PRIME [143] adopt similar techniques to enhance PRM performance. Additionally, Zhang et al. [1036] propose entropy regularization to improve model convergence. Rather than focusing solely on the first error step, Full-Step-DPO [903] assigns rewards for the entire reasoning chain, including error steps. VersaPRM [1015] extends PRMs across multiple domains, broadening their applicability. Similarly, Gu et al. [219] and Zhang et al. [1074] suggest training models with student preferences aligned to teacher preferences, ensuring effective preference distillation. Further, Wang et al. [807] propose VisualPRM400K and expand this paradigm to multimodal scenarios. (2) Outcome Annotated PRM Training: Alternative approaches, such as ReST-MCTS* [1032], OVM [979], Implicit PRM [1000], AutoPSV [506], and DVO [1038], leverage outcome supervision or implicit feedback to train PRMs, reducing the need for extensive human-annotated data [891, 643]. UAS [981] incorporates uncertainty-aware value models [275] into feedback predictions [495, 167, 945, 1089]. Additionally, Aurora [710] utilizes ensemble prompting strategies and reference answers for reverse verification, training stronger PRMs that better align with the Long CoT data distribution. Furthermore, PAV [651] suggests that rewards should reflect reasoning progress, as measured by changes in the likelihood of producing a correct future response before and after each step. Yang et al. [932], Lee et al. [376], Yoon et al. [975] extend these paradigms", + "bbox": [ + 169, + 593, + 828, + 912 + ], + "page_idx": 19 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 308, + 71 + ], + "page_idx": 19 + }, + { + "type": "page_number", + "text": "20", + "bbox": [ + 488, + 935, + 509, + 948 + ], + "page_idx": 19 + }, + { + "type": "table", + "img_path": "images/f0a50a247a0dd2634591eb3435973b764f754ecd980e41927ea8e8c53cf3b966.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ProcessBenchPRMBench
GSM8KMATHOlympiadBenchOmniMATHSimplicitySoundnessSensitivity
Process Reward Models
Qwen2.5-Math-7B-PRM [1102]Qwen2.5-Math-7B [927]39.452.239.433.1---
Math-Shepherd-PRM-7B [792]Mistral-7B [318]47.929.524.823.847.145.760.7
RLHFlow-PRM-Mistral-8B [156]Mistral-7B [318]50.433.413.815.846.757.568.5
RLHFlow-PRM-DeepSeek-8B [156]DeepSeek-7B [52]38.833.816.916.947.657.568.1
Skywork-PRM-1.5B [466]Qwen2.5-Math-1.5B-Instruct [926]59.048.019.319.233.628.648.8
Skywork-PRM-7B [466]Qwen2.5-Math-7B-Instruct [926]70.853.622.921.038.432.754.3
Qwen2-1.5B-PRM800k [700]Qwen2-Math-1.5B-Instruct [927]34.055.334.241.0---
Qwen2-1.5B-Math-Shepherd [700]Qwen2-Math-1.5B-Instruct [927]48.934.19.813.7---
Qwen2-1.5B-Epic50k [700]Qwen2-Math-1.5B-Instruct [927]55.636.120.230.0---
Qwen2.5-Math-7B-PRM800KQwen2.5-Math-7B-Instruct [927]68.262.650.744.3---
Qwen2.5-Math-PRM-7B [1102]Qwen2.5-Math-7B-Instruct [927]82.477.667.566.3---
Universal-PRM-7B [710]Qwen2.5-Math-7B-Instruct [927]85.877.767.666.4---
Critic Model
Llama-3.1-8B-Instruct [168]-27.526.718.519.2---
GPT-4o [3]-61.953.948.344.659.770.975.8
QwQ-32B-Preview [731]Qwen2.5-32B-Instruct [926]62.352.746.243.9---
DeepSeek-R1-Distill-Qwen-14B [227]Qwen2.5-14B-Instruct [926]67.338.829.932.1---
Dyve-14B [1111]DeepSeek-R1-Distill-Qwen-14B [227]68.558.349.047.2---
Qwen2.5-72B-Instruct [926]-76.261.854.652.2---
SCRIT [713]Qwen2.5-72B-Instruct [926]80.260.032.527.8---
ol-mini [307]-93.288.987.282.464.672.175.5
LLemma-PRM800k-7B [679]LLemma-7B [26]----51.450.966.0
LLemma-MetaMath-7B [679]LLemma-7B [26]----50.349.066.0
LLemma-oprn-7B [679]LLemma-7B [26]----49.049.864.1
MATHMinos-Mistral-7B [195]Mistral-7B [318]----51.454.466.5
ReasonEval-7B [877]LLemma-7B [26]----55.563.971.0
ReasonEval-34B [877]LLemma-34B [26]----51.563.073.1
Gemini-2.0-flash-exp [679]-----62.767.375.4
Gemini-2.0-thinking-exp-1219 [679]-----66.271.875.3
", + "bbox": [ + 173, + 85, + 823, + 351 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Table 4: Performance of various process feedback methods on ProcessBench [1102] and PRM-Bench [679]. “-” indicates that the paper did not report this score.", + "bbox": [ + 171, + 359, + 826, + 388 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "to the token level. Moreover, Chen et al. [110] expand these into interactive agent scenarios, allowing for automatically learning reward models from the environment without additional manual annotation. Wang et al. [832] equip a dual-layer MLP module to evaluate the reward at each step, successfully integrating the policy model and PRM into a unified interface without additional process annotations, reducing over $99\\%$ of PRM parameters for efficient reasoning.", + "bbox": [ + 169, + 415, + 826, + 486 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Process Feedback from RLLMs As PRM training remains heavily dependent on manually annotated data, recent research has explored methods for enabling models to generate their natural language feedback to optimize performance [910]. These approaches fall into two primary categories: (1) Model-Driven Feedback Reasoning: Earlier work such as React [956] and Reflexion [669] enhances RLLMs with natural language feedback at each action and reasoning step [196, 135, 89], improving decision-making in diverse tasks. Similarly, Step-DPO [365] uses RLLM to self-verify step-level positive and negative pairs for training through the DPO paradigm, achieving strong performance. Additionally, Sun et al. [702] propose a dynamic error classification framework that adapts based on model outputs, improving performance in mathematical reasoning tasks by addressing specific error patterns in math word problems. Furthermore, Xie et al. [889] and He et al. [245] iteratively apply MCTS to collect preference data, utilizing its forward-looking capabilities to decompose instance-level rewards into more precise step-level signals, thereby enhancing feedback accuracy. However, step-wise feedback often suffers from reliability issues, which can be mitigated by uncertainty quantification [973, 969], improving the reliability of step-wise verification in reward models for mathematical reasoning tasks. Moreover, Fu et al. [187] define the CoT Average Causal Effect (CACE) to capture causal relationships between steps, resulting in a causalized Long CoT where all steps are both correct and comprehensible. (2) Environment-Driven Feedback Reasoning: Given the increasing complexity of large models, there is growing interest in combining prompt-based LLMs with external environments to generate more interpretable and controllable feedback [885, 271]. For example, ORPS [996] and Drori et al. [162] minimize dependence on human annotations by using execution feedback, enabling models to autonomously refine their solutions. Additionally, Shrestha et al. [670] contribute by translating model outputs into Python code, helping to identify logical errors, gain insights into flawed reasoning processes, and guide improvements in mathematical reasoning. Xu et al. [897] integrate reasoning models with an interactive environment, enabling learning in more dynamic scenarios and creating a more generalizable self-learning framework.", + "bbox": [ + 169, + 500, + 826, + 845 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "5.1.3 Hybrid Feedbacks", + "text_level": 1, + "bbox": [ + 171, + 859, + 354, + 875 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Given the respective advantages and limitations of Overall Feedback and Process Feedback, recent studies have sought to combine both for optimal feedback. Specifically, Zhang et al. [1078] propose", + "bbox": [ + 171, + 883, + 823, + 912 + ], + "page_idx": 20 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 20 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 20 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 20 + }, + { + "type": "header", + "text": "REASONING SONG", + "bbox": [ + 233, + 66, + 299, + 71 + ], + "page_idx": 20 + }, + { + "type": "page_number", + "text": "21", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "a consensus filtering mechanism that integrates Monte Carlo estimation with an LLM-as-judge to enhance both overall and stepwise feedback, thus improving reasoning accuracy. In a similar vein, Lin et al. [454] introduce Step-KTO, a framework combining stepwise process-level and outcome-level binary feedback, using PRM and ORM to guide language models toward coherent reasoning, with a focus on error correction through reflection mechanisms.", + "bbox": [ + 169, + 90, + 826, + 161 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "Takeaways: Feedback", + "text_level": 1, + "bbox": [ + 205, + 170, + 352, + 185 + ], + "page_idx": 21 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Evolving Feedback Models: Feedback mechanisms, including overall, process, and hybrid feedback, are crucial for improving the reasoning capabilities of RLLMs.", + "- Innovative Approaches in Process Feedback: Process feedback using techniques like PRMs with MCTS enhances Long CoT, though challenges like reward hacking remain.", + "- Self-Reflection and Model-Driven Feedback: Self-reflection and model-driven feedback improve RLLM performance by enabling error detection, task-specific insights, and more autonomous learning." + ], + "bbox": [ + 199, + 193, + 797, + 299 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "5.2 Refinement", + "text_level": 1, + "bbox": [ + 171, + 324, + 292, + 337 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "Refinement refers to the process of addressing errors in reasoning based on prior feedback. As shown in Figure 8, refinement methods can be grouped into three primary categories: prompt-based refinement generation (§ 5.2.1), SFT-based refinement imitation (§ 5.2.2), and RL-based refinement learning (§ 5.2.3).", + "bbox": [ + 169, + 345, + 823, + 402 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "5.2.1 Prompt-based Refinement Generation", + "text_level": 1, + "bbox": [ + 171, + 416, + 491, + 431 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "Research on prompt-based refine generation focuses on enhancing the performance of LLMs through iterative self-refinement mechanisms [578, 1091, 98, 469, 1028, 754, 818, 546]. A prominent approach involves prompting RLLMs to generate initial outputs, followed by self-feedback that iteratively refines and improves performance across tasks such as dialogue generation and mathematical reasoning [645, 539, 1101, 669, 549, 345, 750, 482], which even much reduce the hallucinations [289, 315]. Noteworthy methods, like Self-Backtracking [944], Refiner [590], and BackMath [1055], allow LLMs to adjust their reasoning autonomously, reducing unnecessary complexity in decision-making [868]. Further, Havrilla et al. [238] extend the paradigm by integrating overall-level and step-level refinements, improving refinement performance. Yang et al. [950] propose a method to decompose the self-correction capability of LLMs into \"confidence\" and \"critique\" capacities, designing probabilistic metrics to evaluate them and exploring the role of reflection mechanisms in model behavior. Additionally, MCTSr [1033], LLM2 [930], ReST-MCTS* [1032] and ReARTeR [703] emphasize dynamic reflection through iterative error correction and confidence adjustments, allowing models to autonomously refine reasoning strategies [186]. He et al. [240]", + "bbox": [ + 169, + 440, + 826, + 635 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/b3686b17aa6dae7dfb30b34c5e285af765d180305957e5c15bbbeed64d436326.jpg", + "image_caption": [ + "(a) Prompt-based Refinement Generation" + ], + "image_footnote": [], + "bbox": [ + 183, + 679, + 468, + 776 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/6b9af6579bd26e04c798016e01125ccc0cc0c837723baed594fe92c9e6c31804.jpg", + "image_caption": [ + "(b) SFT-based Refinement Imitation" + ], + "image_footnote": [], + "bbox": [ + 496, + 681, + 807, + 776 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/75779ea3409037b107f99cc61b0546a161e6d6863edc845e12464cd3a1541651.jpg", + "image_caption": [ + "Figure 8: The three main categories of refinement methods, including Prompt-based Refinement Generation, SFT-based Refinement Imitation, and RL-based Refinement Learning." + ], + "image_footnote": [], + "bbox": [ + 187, + 805, + 297, + 862 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/51fec61d82ab2a769606104af5832df56e4604f317836d062424f65c9e9866bf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 808, + 351, + 849 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/23630b42c465d84d800277ffb7ad33291ea526c1dea42266eee59f4ed6d6ce9b.jpg", + "image_caption": [ + "Reinforcement Learning" + ], + "image_footnote": [], + "bbox": [ + 444, + 805, + 500, + 857 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/80703458fe6b97a41337e32d746ae10f1ad5d7ce4cd1e803f369ce673d59c38c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 806, + 566, + 849 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/748e7abf84b0255c1331edd540782869194e76185b531fae8e9affbfdea58ee8.jpg", + "image_caption": [ + "(c) RL-based Refinement Learning", + "Aha! I think $1 + 1 = 3$ should be corrected $1 + 1 = 2!$" + ], + "image_footnote": [], + "bbox": [ + 578, + 804, + 683, + 859 + ], + "page_idx": 21 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 21 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 21 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 21 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 233, + 61, + 300, + 70 + ], + "page_idx": 21 + }, + { + "type": "page_number", + "text": "22", + "bbox": [ + 488, + 935, + 509, + 946 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "extend this paradigm to multi-agent scenarios, improving both reasoning and agent system performance [936, 1128]. Moreover, Yuksekgonul et al. [1009] and Peng et al. [593] further expand the paradigm by enabling automatic prompt optimization driven by LLMs. This approach facilitates more generalized and automated refinement of input prompts across a range of tasks, as opposed to focusing solely on refining output results. However, without oracle feedback, RLLM's self-refinement process fails, causing instability in both intermediate and final answers, leading to biases in simple factual queries and introducing cognitive biases in complex tasks [1051, 908].", + "bbox": [ + 169, + 90, + 826, + 188 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "5.2.2 SFT-based Refinement Imitation", + "text_level": 1, + "bbox": [ + 171, + 207, + 452, + 220 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "Recent advancements in reflection-based reasoning for LLMs have led to frameworks that enhance model reasoning through self-refinement and error correction. A key approach is directly supervised fine-tuning, which allows models to learn error correction processes from advanced LLMs, thereby improving their reflective capabilities [14, 104, 406, 822, 99, 873]. Notable frameworks, such as rStar [615], improve smaller language models through self-play mutual reasoning, while Recursive Introduction [627] and RealCritic [714] use iterative feedback mechanisms to identify and correct errors to better self-improve [393]. Yan et al. [924] propose constructing step-wise self-correction data and implementing a training strategy that uses the above-constructed data to equip LLMs with spontaneous step-level self-correction capacities. Building upon these, Gao et al. [196] and Zhang et al. [1027] propose Math-Minos, which employs step-by-step natural language feedback as rationale tags, offering both correctness and detailed explanations for each step to train feedback mechanisms that justify and refine the reasoning process. Journey Learning [623] employs MCTS to parse node backtracking as natural language refinement, enhancing supervised fine-tuning and, thereby, improving reasoning performance. Additionally, approaches like ProgCo [682] emphasize iterative feedback and program-driven refinement to enhance critique and self-correction. Expanding these ideas to multimodal settings, frameworks, such as R3V [120] and MM-Verify [697], focus on integrating visual and textual reasoning [519, 813].", + "bbox": [ + 169, + 232, + 826, + 468 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "5.2.3 RL-based Refinement Learning", + "text_level": 1, + "bbox": [ + 171, + 486, + 444, + 501 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "In recent research, several approaches have been proposed to enhance the performance of refinement through reinforcement learning [673, 1056]. Earlier, Kumar et al. [358] observed that SFT of RLLMs often fails to promote self-refinement behaviors. This limitation stems from a distributional mismatch between data collection strategies and model responses, as well as the risk of behavioral collapse. To address this, SCoRe [358] enhances self-refinement by training the model on its own self-generated correction trajectories and employing regularization to guide the learning process. This method prioritizes fostering self-refinement during testing, rather than merely maximizing reward for specific prompts [1018]. Further, Guo et al. [227] demonstrate that applying outcome-level rewarded RL can trigger an \"Aha moment,\" activating the model's natural feedback and refinement behaviors without the need for human guidance. Moreover, Guo et al. [227], Zeng et al. [1017] and Ma et al. [529] explore initializing LLMs with iterative self-verification and self-correction behaviors, which are strengthened through supervised fine-tuning and further enhanced by outcome-level RL. Ma et al. [529] and Yang et al. [935] extend these capabilities with process-level RL, minimizing resource usage while enabling adaptive reasoning refinements during inference. More recently, Lee et al. [374] introduce an intrinsic verifier module to decide when refinements should be applied, using RL to further encourage self-refinement when errors are detected.", + "bbox": [ + 169, + 512, + 826, + 733 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "Takeaways: Refinement", + "text_level": 1, + "bbox": [ + 204, + 747, + 364, + 762 + ], + "page_idx": 22 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Prompt-Based Refinement for Iterative Improvement: Iterative self-refinement through feedback loops helps LLMs improve reasoning and reduce errors like hallucinations but requires stable feedback to maintain accuracy.", + "- Supervised Fine-Tuning (SFT) for Error Correction: Supervised fine-tuning enhances LLMs by using iterative feedback and self-correction strategies to improve reasoning accuracy, especially for smaller models.", + "- Reinforcement Learning (RL) for Refinement: Reinforcement learning enhances self-refinement in LLMs by using self-generated corrections and adaptive strategies, reducing human intervention and resource consumption." + ], + "bbox": [ + 200, + 768, + 799, + 902 + ], + "page_idx": 22 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 22 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 22 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 22 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 22 + }, + { + "type": "page_number", + "text": "23", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 22 + }, + { + "type": "image", + "img_path": "images/ae0384cb2d35989e0913fcc05ec7fe401f4d3acdd492815afce7dcdd64d2789c.jpg", + "image_caption": [ + "Figure 9: Schematic representations of two common inference-time scaling strategies: (a) sequential scaling, which extends the length of Long CoT but is constrained by the reasoning boundaries of RLLMs; and (b) parallel scaling, which increases the sample size and aggregates multiple outcomes, yet does not surpass the performance of Pass@k." + ], + "image_footnote": [], + "bbox": [ + 181, + 90, + 478, + 200 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/651c3a02f7c05e2fa7e8a9730a03db50638cef9382a4885f455c35d277bec9cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 90, + 813, + 200 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "6 Extensive Exploration for Long CoT", + "text_level": 1, + "bbox": [ + 169, + 299, + 511, + 316 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Exploration is a key capability in Long CoT reasoning, allowing models to navigate complex problem spaces through strategic branching and iterative refinement [1019, 381, 784, 751]. Recent studies emphasize exploration mechanisms, such as hypothesis branching and error backtracking via reflection, as essential for overcoming the constraints of linear reasoning paths [227].", + "bbox": [ + 169, + 334, + 823, + 391 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Current research focuses on three key areas: (1) Exploration Scaling (§ 6.1), which explores the breadth and depth of exploration and its impact on downstream applications, particularly in improving the size of the exploration path $m$ in Equation (3); (2) Internal Exploration (§ 6.2), which focuses on training models to develop internal exploration capabilities, enabling more efficient and effective generation of $m$ exploration paths $\\{n_{i+j}\\}_{j=1}^{m}$ in Equation (3); and (3) External Exploration (§ 6.3), which examines how models can leverage external systems to enhance their exploratory abilities, facilitating the selection of the most effective path $n_{i+j}$ from the $m$ exploration paths in Equation (3).", + "bbox": [ + 169, + 396, + 826, + 494 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "6.1 Exploration Scaling", + "text_level": 1, + "bbox": [ + 171, + 516, + 352, + 532 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Recent advances in inference-time scaling algorithms [333, 843, 57, 1053, 112] have attracted significant interest, particularly in scaling reasoning length to improve performance [524, 568, 405, 779]. Following Chen et al. [93], as shown in Figure 9, exploration scaling can be understood through two paradigms: (1) sequential scaling, akin to a series of resistors, which connects multiple reasoning processes using reflection; and parallel scaling, similar to parallel resistors, where a unified verification/feedback mechanism selects the most effective reasoning processes.", + "bbox": [ + 169, + 544, + 826, + 628 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "6.1.1 Sequential Scaling", + "text_level": 1, + "bbox": [ + 169, + 650, + 354, + 666 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Sequential scaling refers to extending the reasoning output within a single model generation, significantly boosting model performance [383, 1052, 348]. Early works by Fu et al. [189] and Jaech et al. [307] show that increasing the length of the reasoning path can greatly improve performance. Tian et al. [736] enhances model reasoning iteratively by using prior answers as prompts for each successive round, thus enabling sequential scaling of the reasoning process. Building on this, later studies [314, 391] further explore enhancing logical depth through tree-based searches within a fixed compute budget, resulting in notable performance gains [11, 614]. Building upon this, Muennighoff et al. [560] introduce a inference-time scaling method that improves reasoning by fine-tuning and budget forcing, yielding substantial gains with additional computing at inference time. To address the constraints of attention spans, some studies focus on expanding reasoning length in latent spaces. Geiping et al. [204] and Chen et al. [109] enhance inference-time reasoning performance by implicitly scaling computation in latent space through recurrent depth. Setlur et al. [653] identified three core aspects of sequential scaling: (1) linking skills to asymmetric capabilities in base LLMs, such as connecting easy verification with difficult exploration; (2) enhancing exploration in reinforcement learning by utilizing the \"negative\" gradient of error trajectories, which extends search paths and links additional asymmetries; and (3) creating dynamic exploration by aligning task difficulty with training token budgets through tailored curricula.", + "bbox": [ + 169, + 676, + 826, + 912 + ], + "page_idx": 23 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 41, + 225, + 70 + ], + "page_idx": 23 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 307, + 59 + ], + "page_idx": 23 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 23 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 23 + }, + { + "type": "page_number", + "text": "24", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "6.1.2 Parallel Scaling", + "text_level": 1, + "bbox": [ + 171, + 90, + 334, + 106 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Parallel scaling refers to the process of increasing the number of reasoning iterations during model generation and then verify these results to get the final output, which significantly enhances model performance [2, 864, 57, 485, 59, 1139]. Initially, Wang et al. [816] introduce the concept of self-consistency, demonstrating that multiple sampling processes followed by majority voting for effective exploration.", + "bbox": [ + 169, + 114, + 826, + 185 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Verification Optimization The primary focus of recent research is optimizing verification, which can be categorized into two types: (1) Overall Verification: Recent works [1120, 831] divide the scaling process into two stages: \"reasoning\" and \"self-verification.\" By replacing majority voting in self-consistency with self-verification, these approaches show significant improvements [1083, 81, 1149, 364, 426]. In code scenarios, WoT [1071], CISC [716] and S* [392] scale the Long CoT in parallel, using output confidence or code execution results for verification, effectively assessing reasoning quality [635, 203, 278, 1134]. Further, Nye et al. [569] and Weir et al. [842], Stoisser et al. [690] train RLLMs to simulate code execution, removing the need for test cases in code-related parallel scaling. Chain-of-Verification [93] introduces meta-verification, sampling multiple verification instances to identify the correct one. Kim et al. [351], Chen et al. [111], and Vacareanu et al. [750] validate this approach empirically by evaluating answer correctness based on reasoning path properties. Moreover, Li et al. [421] tune a specific RLLM to verify and aggregate answers, showing improved performance. This suggests that PRM cannot replace a specially trained RLLM for verification due to training goal biases [1078]. Finally, Kang et al. [341] leverage self-uncertainty to select the best results. (2) Step Verification: Building on this, numerous researchers have explored step-level or finer-grained verification [84, 460]. Notably, DIVERSE [425], SSC-CoT [1098], and Fine-grained Self-Consistency [93] combine diverse reasoning paths with step-level verification. In addition, a series of works [676, 864, 517, 770, 853, 486] try to investigate how optimal scaling strategies based on MCTS can enhance smaller language models' performance. Their findings show that a 1B RLLM can outperform a 405B model on complex tasks through parallel scaling [988]. Despite these advancements in verification, Chen et al. [93] demonstrate that these strategies cannot surpass Best-of-N methods, suggesting that breakthroughs cannot solely rely on optimization-based verification [106].", + "bbox": [ + 169, + 196, + 826, + 517 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Sampling Optimization Another key area of research focuses on generating diverse but less paths or strategies for efficient scaling [871, 765, 80, 668, 444, 681]. For instance, Zeng et al. [1020] aggregate the shortest yet most varied reasoning paths for better scalability. Similarly, Du et al. [164] adjust the sampling temperature to increase diversity, leading to improved scaling. Zhang et al. [1045] and Liu et al. [470] optimize both candidate solution generation (e.g., prompts, temperature, and top-p) and reward mechanisms (such as self-evaluation and reward types), offering diverse strategies for parallel scaling. Moreover, Qin et al. [617], Luo et al. [520], and Yu et al. [990] enhance RLLM reasoning by scaling sampling across multiple natural and programming languages or varied expressions. Finally, Yang et al. [943] introduces a method where a small set of seed data, with varied response lengths, guides the model to engage in deeper reasoning by selecting the shortest correct responses across various inference efforts.", + "bbox": [ + 169, + 527, + 826, + 681 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Takeaways: Exploration Scaling", + "text_level": 1, + "bbox": [ + 204, + 691, + 419, + 707 + ], + "page_idx": 24 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Exploration Mechanisms in Long CoT Reasoning: Exploration strategies like hypothesis branching and error backtracking are vital for overcoming limitations in linear reasoning paths and enhancing model performance.", + "- Scaling Exploration: Exploration can be scaled through sequential and parallel strategies to improve reasoning depth and efficiency.", + "- Verification and Sampling Optimization: Refining verification techniques and optimizing sampling for diverse reasoning paths are key to improving exploration efficiency and performance in Long CoT tasks." + ], + "bbox": [ + 200, + 714, + 797, + 833 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "6.2 Internal Exploration", + "text_level": 1, + "bbox": [ + 171, + 859, + 357, + 876 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "As noted in Chu et al. [137], Shen et al. [661], and Yang et al. [938], SFT serves as a memory process, while RL enhances generalization [359, 82]. Specifically, SFT stabilizes the model's output format,", + "bbox": [ + 169, + 883, + 826, + 912 + ], + "page_idx": 24 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 24 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 24 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 24 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 24 + }, + { + "type": "page_number", + "text": "25", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/55a2cddee6720d6d5b6d79848689909b6e03f9c8563319f2fff7f35746a40240.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 181, + 89, + 815, + 203 + ], + "page_idx": 25 + }, + { + "type": "image", + "img_path": "images/302920f94ae85e94ce64fd964759f21a7a4160de1d28055d6f3573f758563039.jpg", + "image_caption": [ + "Figure 10: Two primary approaches for optimizing Internal Exploration: improving RL strategy through reference and value models, and designing reward strategies: either rule-based or model-based rewarding to enhance RL performance." + ], + "image_footnote": [], + "bbox": [ + 183, + 213, + 805, + 308 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "whereas RL improves its generalization capacity, which can increase learning efficiency by up to eight times in tasks such as mathematical reasoning [650]. Consequently, as shown in Figure 10, leading research emphasizes the role of RL and reward strategies in enhancing the exploration capabilities of LLMs without external assistance. The performance comparison is presented in Table 5.", + "bbox": [ + 169, + 393, + 823, + 450 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "6.2.1 RL Strategies", + "text_level": 1, + "bbox": [ + 171, + 462, + 320, + 477 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "Recent advancements in RL strategies for exploration have led to notable improvements in various tasks, particularly in reasoning tasks [699, 369, 313, 542, 882, 1017, 985, 268, 1010, 628, 150, 176, 686].", + "bbox": [ + 169, + 483, + 826, + 525 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "(1) Reward-free RL: The first series of work focuses on RL optimization algorithms. Additionally, OREO [773] propose an offline RL method that optimizes the soft Bellman equation, improving credit assignment for multi-step reasoning tasks and outperforming existing approaches in fields like mathematics and agent control. Liu et al. [476] propose Direct Advantage Policy Optimization, a novel offline RL method that leverages a separately trained critic to evaluate the accuracy of each reasoning step. This technique provides dense feedback for policy optimization, addressing both sparse rewards and training instability. Further, some research focuses on adjusting the focus of RL algorithms to optimize exploration in targeted aspects. Specifically, CPL [801], cDPO [457], and Focused-DPO [1043] enhance exploration in Long CoT by prioritizing critical or error-prone areas through preference optimization, improving accuracy in those regions. Bartoldson et al. [42] further adjusts the replay strategy of the training data, aiming to optimize reasoning performance. Li et al. [420] introduce Learning Impact Measurement (LIM), an automated method for evaluating and prioritizing training samples based on their alignment with model learning trajectories. This approach enables efficient resource use and scalable implementation. For instance, ThinkPO [942] uses short CoT reasoning outputs as rejected answers and longer ones as chosen answers for the same question, applying DPO to encourage prioritization of longer reasoning outputs [1131].", + "bbox": [ + 169, + 532, + 826, + 753 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "(2) Reward-based RL: Reward-model-based RL refers to approaches that use a reward model or a verifier to guide learning and decision-making in the absence of explicit rewards [1046, 174, 649, 279, 825, 847, 970]. Earlier, Proximal Policy Optimization (PPO) was first introduced by Schulman et al. [648], which alternates between interacting with the environment to collect data and optimizing a surrogate objective function via stochastic gradient ascent, surpassing DPO [306]. Subsequently, ReMax [436] eliminates the need for additional value models in PPOs. By incorporating variance reduction and REINFORCE [704] techniques, it reduces over four hyperparameters, resulting in lower GPU memory usage and faster training. Building on this, DeepSeekMath [658] proposes Group Relative Policy Optimization (GRPO), replacing traditional value models with improved sampling strategies, thus significantly accelerating learning and achieving performance on par with GPT-4 in mathematics. Hu [265] and Liu et al. [499] further refine GRPO with REINFORCE++ and Dr. GRPO,", + "bbox": [ + 169, + 758, + 826, + 912 + ], + "page_idx": 25 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 41, + 225, + 70 + ], + "page_idx": 25 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 307, + 59 + ], + "page_idx": 25 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 65 + ], + "page_idx": 25 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 65, + 305, + 69 + ], + "page_idx": 25 + }, + { + "type": "page_number", + "text": "26", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 25 + }, + { + "type": "table", + "img_path": "images/8906843300658ba9f577713856804416059d5d5e72ce14c0c9304e8987c15cd2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneGSM8KAIME 2024MATH 500GPQALiveCodeBench
Base Model
GPT-4o [3]-92.99.376.653.633.4
Llama-3.1-70B-Instruct [168]-94.113.368.0--
Claude 3.5 Sonnet [19]--16.078.365.038.9
Qwen2.5-Coder-32B-Instruct [301]--20.071.233.825.0
Qwen2.5-70B-Instruct [926]--20.079.449.033.0
Llama-3.3-70B-Instruct [168]--36.773.950.534.8
DeepSeek-V3 [463]--39.290.2-36.2
SFT Strategies
DeepSeek-R1-Distill-Llama-70B [227]--70.0--57.9
DeepSeek-R1-Distill-Qwen-32B [227]--72.6--54.6
START [388]QwQ-32B-preview [731]-66.794.463.647.3
RL Strategies
DPO [631]DeepSeekMath 7B [658]82.4----
KTO [171]DeepSeekMath 7B [658]82.5----
OREO [773]DeepSeekMath 7B [658]86.9----
PPO [648]GLM4-9B-SFT [211]85.5--31.524.3
GRPO [658]GLM4-9B-SFT [211]86.1--31.722.8
Eurus-2-7B-PRIME [143]Qwen2.5-Math-7B-Base [927]-26.779.2--
Search-o1 [418]QwQ-32B-preview [731]-56.786.463.633.0
Reward Strategies
OpenMath2 [739]Llama-3.1-70B [168]94.113.371.8--
Satori [661]Qwen-2.5-Math-7B93.923.383.6--
T1-SFT [264]Qwen2.5-32B [926]-24.983.449.5-
T1 [264]Qwen2.5-32B [926]-50.692.456.1-
DeepSeek-R1-lite [227]--52.591.658.551.6
rStar-Math [222]Qwen2.5-Math-7B [927]95.253.390.0--
QwQ-32B-preview [731]-95.553.390.658.240.6
ol-preview [307]--56.785.573.353.6
o3-mini-low [307]--60.0--61.8
ol-mini [307]--63.690.0-53.8
Kimi k1.5 [722]--77.596.2-62.5
QwQ-32B [731]--79.5--73.1
o3-mini-medium [307]--79.6--72.3
DeepSeek-R1 [227]--79.897.3-71.6
o1 [307]--83.396.4-67.4
o3-mini-high [307]--87.3--84.6
", + "bbox": [ + 181, + 88, + 816, + 470 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "Table 5: Performance of various internal exploration methods on different benchmarks, primarily ordered by AIME 2024. “-” indicates that the paper did not report this score.", + "bbox": [ + 169, + 476, + 823, + 506 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "respectively, simplifying the algorithm and enhancing its training. Additionally, Vassoyan et al. [752] and [1121] improve exploration efficiency in smaller models by modifying the KL penalty, thus enhancing performance under distribution shifts. Huang et al. [277] introduce Decoupled Value Policy Optimization (DVPO), a streamlined framework that replaces reward modeling with a pretrained global value model (GVM) and eliminates the interdependence between actor and critic. To address the high-quality demands of reward models, Cui et al. [143] propose PRIME (Process Reinforcement through IMplicit rEwards), which integrates the SFT model as a PRM within a unified reinforcement learning framework, enabling online updates through policy rollouts and outcome labels via implicit process rewards.", + "bbox": [ + 169, + 585, + 826, + 712 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "More recently, Liang et al. [439] introduce Self-aware Weakness-driven Problem Synthesis, a reinforcement-learning method that generates challenges tailored to an RLLM's specific weaknesses [863, 183]. By concentrating training on its most difficult aspects, the model achieves more focused and effective reasoning improvements [680]. Wang et al. [805] introduce ROLL, a method designed to support R1-level large-scale training of RLLMs, enabling the efficient exploration and optimization of reasoning paths within the Mixture-of-Experts (MOE) structure [788]. Fu et al. [188] introduce AReaL, a large-scale asynchronous reinforcement learning system for language reasoning, which enhances the efficiency and effectiveness of training RLLMs. Ma et al. [526] propose a novel method combining interleaved SFT and RL to address challenging questions where RL typically fails. This approach enables RLLMs to learn from mistakes and enhance reasoning abilities. Huang et al. [297] and Fu et al. [190] further improve exploration efficiency by integrating SFT and RL with prefix sampling. Frurthermore, Yan et al. [917] and Liang et al. [437] guide RLLMs in reasoning under off-policy reinforcement learning [413, 773], improving both training sample efficiency and learning stability [559].", + "bbox": [ + 169, + 717, + 826, + 912 + ], + "page_idx": 26 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 26 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 26 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 26 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 26 + }, + { + "type": "page_number", + "text": "27", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "6.2.2 Reward Strategies", + "text_level": 1, + "bbox": [ + 171, + 90, + 354, + 106 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "Rule-rewarded RL The studies explore advancements in training advanced RLLMs using rule-rewarded RL to enhance exploration strategies and reasoning accuracy [296]. These efforts primarily focus on three types of rewards: (1) Correctness Rewarding: Correctness rewards are fundamental for guiding RLLMs toward accurate answers. Specifically, Singh et al. [674] introduce a binary reward system (positive or negative) to facilitate exploration, achieving simple yet effective performance improvements. Similarly, the DeepSeek-R1 [227] employs rule-extracted accuracy as an RL reward, scaling this approach to larger scenarios and training sizes, thereby enhancing both exploration and reasoning tasks [522, 170]. Furthermore, O1-CoderZhang et al. [1076], StepCoder [161], and SWE-RL [841] address challenges in code generation by developing a test case generator, which standardizes code testing, ensuring accurate generation [893, 994]. (2) Format Rewarding: Further, format rewards are used to encourage better reasoning paradigms. Guo et al. [227] introduce this concept to effectively guide reasoning and exploration [886]. Xie et al. [886] expanded on this with a three-stage, rule-based RL approach, enabling the Qwen-7B model to learn complex multi-path exploration, which significantly improved both output format and corresponding length consistency. Additionally, Wu et al. [855] propose TAPO (Thought-Augmented Policy Optimization), a framework that integrates external high-level guidance (\"thought patterns\") into RL, successfully balancing model exploration with external guidance. (3) Scaling rewarding: Moreover, scaling rewards are applied to promote longer reasoning chains and broader exploration. Recent studies [90, 583, 349] highlight the need for progressively scaled reasoning lengths to overcome the limitations of current reasoning approaches. As a result, research has focused on scaling exploration [886, 962]. However, excessive scaling can lead to inefficiency and overcomplicated reasoning [142]. Kimi-K1.5 [722], Yang et al. [943] and Arora and Zanette [22] proposed Long2Short techniques, favoring shorter, more accurate reasoning may also significantly improve efficiency and performance.", + "bbox": [ + 169, + 116, + 826, + 435 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "Model-rewarded RL It refers to a class of techniques in which RL algorithms are enhanced by leveraging additional reward models, to guide exploration and improve decision-making processes [693]. Earlier in 2021, OpenAI [141] propose a \"Gen-Verifier\" paradigm to train a correctness-oriented ORM and used ORM-rewarded RL to surpass SFT performance. Recently, with rapid advancements in PRM, several studies [755, 1032, 518] have scaled reinforcement learning by enhancing exploration through step-level correctness rewarding [659, 1042]. Building on this, Hou et al. [264] introduce entropy rewards and dynamic regularization to further optimize the reasoning process [116]. STeCa [768] identifies suboptimal actions during exploration by comparing step-level rewards and adjusting trajectories to improve deep reasoning. Additionally, the Kimi-K1.5 model [722] extends PRM paradigms into multimodal scenarios, achieving state-of-the-art performance in multi-modal reasoning tasks through a streamlined reinforcement learning framework.", + "bbox": [ + 169, + 454, + 826, + 608 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "Takeaways: Internal Exploration", + "text_level": 1, + "bbox": [ + 204, + 623, + 419, + 637 + ], + "page_idx": 27 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- SFT and RL Synergy: The combination of Self-Feedback Training (SFT) and Reinforcement Learning (RL) improves model output stability and generalization, enhancing learning efficiency in reasoning tasks.", + "- Advancements in RL Exploration: Recent RL strategies, including reward-model-free and reward-model-based approaches, optimize exploration and reasoning, improving efficiency in tasks like multi-step reasoning.", + "- Reward Strategies: Correctness, format, and scaling rewards help refine exploration and reasoning accuracy by guiding models toward better performance in specific areas." + ], + "bbox": [ + 200, + 643, + 800, + 763 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "6.3 External Exploration", + "text_level": 1, + "bbox": [ + 171, + 800, + 361, + 815 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "The exploration of coding strategies in AI systems is advancing through innovative frameworks aimed at enhancing search efficiency and decision-making quality. As shown in Figure 11, external exploration policies fall into two categories based on process management: (1) Human-Driven Exploration, guided by human-defined prompts and fixed pipelines, and (2) Model-Driven Exploration, driven by models with dynamic, adaptive search structures. The detailed performance comparison is presented in Table 6.", + "bbox": [ + 169, + 827, + 826, + 911 + ], + "page_idx": 27 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 27 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 27 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 27 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 27 + }, + { + "type": "page_number", + "text": "28", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "6.3.1 Human-driven Exploration", + "text_level": 1, + "bbox": [ + 171, + 90, + 415, + 106 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "Human-driven exploration refers to human-designed constant pipeline exploration for long-term exploration [479, 422]. Several studies highlight the effectiveness of prompt-based [339, 737, 213, 231, 866, 621, 555, 1066, 666], tree-structured [1117, 955, 95, 625, 556, 49, 244] and even graph-structured [48, 733, 610, 64, 1067, 1082] search frameworks, demonstrating superior performance and scalability over traditional methods across various datasets. Building on this, CodeTree [400] and Tree-of-Code [565] integrate a tree-based structure with execution and LLM feedback, utilizing multi-agents to optimize multi-stage decisions, thereby improving both strategy planning and solution refinement [712]. Cheng et al. [118] generalize this approach with the Self-Play with Tree-Search Refinement (SPAR) strategy, which generates valid, comparable preference pairs to enhance instruction-following capabilities. Bi et al. [54] and Light et al. [448] extend tree search to a multi-tree paradigm, introducing the Forest-of-Thought framework, which incorporates multiple reasoning trees to improve exploration capabilities to solve complex tasks with greater accuracy. Furthermore, Li et al. [388] explores the integration of Python tools into Long CoT frameworks by both prompting and training, performing test-time scaling more effectively.", + "bbox": [ + 169, + 114, + 826, + 309 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "6.3.2 Model-driven Exploration", + "text_level": 1, + "bbox": [ + 171, + 321, + 408, + 337 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "Building on previous research, model-feedback-assisted exploration has advanced significantly, which is driven by model and dynamic adaptive search structure, with optimization emerging as a central focus. Currently, there are three key directions guiding model-driven exploration:", + "bbox": [ + 169, + 345, + 823, + 388 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "Enhancing Exploration Logics Recent efforts have focused on improving exploration structures during iterations for better logical quality. (1) **Beam Search:** Earlier, Xie et al. [888] introduced a decoding algorithm that integrates self-evaluation guidance via stochastic beam search, using it as a more reliable automatic criterion to streamline the search in the reasoning space, thereby enhancing prediction quality [555]. Similarly, Zhu et al. [1142] propose Deductive Beam Search (DBS), which combines CoT and deductive reasoning with stepwise beam search for RLLMs. (2) $A^*$ Search: On another front, Lehnert et al. [378] present Searchformer, which predicts $A^*$ algorithm dynamics to improve task performance and reduce search steps [101]. Later, Kang et al. [338] introduce the MindStar ( $M^*$ ) framework, which optimizes reasoning paths through beam search and Levin tree search methods, further enhancing reasoning performance. (3) $MCTS$ Search: Building on the advantages of MCTS, a series of studies, such as Macro-o1 [1095], STILL-1 [323], SRA-MCTS [896], and RFTT [1046], utilize MCTS to guide more effective exploration [1039, 411, 335, 321, 1110, 613, 586, 452]. Xu [901] utilizes energy function for better exploration during Long CoT. Yao et al. [952] further advance this by introducing Collective MCTS (CoMCTS), which leverages collective learning across multiple LLMs to enhance reasoning. Further, MC-NEST [629] integrates Nash Equilibrium strategies to balance exploration and exploitation, improving LLM decision-making in multi-step", + "bbox": [ + 169, + 398, + 826, + 621 + ], + "page_idx": 28 + }, + { + "type": "image", + "img_path": "images/6462f102f8623b3fc4af62f2c0f413f3392b4362b8f808630fa2fdef3362d761.jpg", + "image_caption": [ + "Figure 11: External exploration policies can be classified into two categories based on the management role of the process: (1) Human-Driven Exploration, which is guided by human-defined prompts and fixed pipelines, and (2) Model-Driven Exploration, which is driven by models and employs dynamic, adaptive search structures." + ], + "image_footnote": [], + "bbox": [ + 246, + 643, + 504, + 840 + ], + "page_idx": 28 + }, + { + "type": "image", + "img_path": "images/8fd520586ef8e1e9b261fefe8d9414d799cbcc475fa68617bc151b1944824f09.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 643, + 751, + 843 + ], + "page_idx": 28 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 28 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 28 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 230, + 59, + 305, + 68 + ], + "page_idx": 28 + }, + { + "type": "page_number", + "text": "29", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 28 + }, + { + "type": "table", + "img_path": "images/d5927788e7155f8644d57e414178a3877fe52ffa58b3baf4651f6d732f0d157f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneGSM8KMATHOlympiadBenchHumanEval+
Base Model
DeepSeekMath-7B-Instruct [658]-83.757.4--
DeepSeekMath-7B-RL [658]-88.252.419.0-
Qwen2-72B-Instruct [925]-93.269.033.2-
Llama-3.1-70B-Instruct [168]-94.165.727.7-
GPT-4 [3]-94.273.4--
Claude-3.5-Sonnet [19]-96.471.1--
GPT-4o [3]--73.440.681.7
Qwen2.5-Math-72B-Instruct [927]--83.049.7-
Human-driven Exploration
AlphaLLM [814]Llama-3-8B-Instruct [168]-32.6--
Least-to-Most-SC [1117]LLaMA-33B [742]42.5---
LLM2 [930]Llama-3-8B [168]88.048.6--
CodeTree [400]GPT-4o [3]---86.0
Model-driven Exploration
STILL-1 [323]LLama-3.1-8B-Instruct [168]--34.3-
Reflexion [669]GPT-4o [3]---84.8
MapCoder [304]GPT-4o [3]---81.7
Resample [427]GPT-4o [3]---84.8
SRA-MCTS [896]Llama-3.1-8B [168]---57.9
RAP [234]LLaMA-33B [742]51.6---
Mindstar [338]Llama-2-7B [743]68.833.9--
Mindstar [338]Mistral-7B [318]73.738.2--
TS-LLM [755]GPT-3.5-turbo74.0---
LiteSearch [757]Llama-3-8B-Instruct [168]75.7---
MARIO-34B [445]CodeLlama-34B [639]78.253.5--
ToRA-Code-34B [217]CodeLlama-34B [639]80.750.8--
MathCoder-34B [781]CodeLlama-34B [639]81.746.1--
AlphaMath [74]DeepSeekMath-7B-Base [658]83.264.0--
MathGenie-34B [513]CodeLlama-34B [639]84.155.1--
MCTS-DPO [889]Llama-3.1-8B-Instruct [168]85.7---
Intrinsic Self-CorrectLlama-3.1-8B-Instruct [168]86.1---
MCTS-IPL [321]Llama-3.1-8B-Instruct [168]86.8---
NuminaMath-72B-CoT [397]Qwen2-72B [925]90.866.732.6-
AutoRace [235]GPT-4 [3]91.0---
LLaMA-Berry [1034]Llama-3.1-8B-Instruct [168]96.175.355.1-
MCTSr [1033]Llama-3-8B-Instruct [168]96.758.2--
BoostStep [1026]Qwen2.5-Math-72B-Instruct [927]-85.252.7-
", + "bbox": [ + 181, + 88, + 815, + 506 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "Table 6: Performance of various external exploration methods on different benchmarks. “-” indicates that the paper did not report this score.", + "bbox": [ + 169, + 512, + 823, + 541 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "mathematical tasks [940, 1088]. Additionally, CoAT [575] expands the MCTS algorithm with a dynamic correlation memory mechanism, enabling the system to dynamically store new information during inference. Despite MCTS's benefits, it is often hindered by a large action space and inefficient search strategies, which complicate the generation of Long CoTs. To address this, Lin et al. [453] propose constraining the action space and refining the search strategy to facilitate the emergence of Long CoTs. Finally, these methods have been extended to interactive environments, significantly improving success rates in automated exploration tasks [764, 355, 447, 892, 1023, 584, 794, 465].", + "bbox": [ + 169, + 568, + 823, + 667 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "Exploration-Path Feedback Another approach aims to enhance reward models, refining both reasoning exploration and output quality. Liu et al. [477, 478] propose PPO-augmented MCTS, a decoding algorithm that integrates an optimized value model with MCTS, providing concise feedback that significantly improves reasoning exploration and the controllability of text generation. Similarly, Zhang et al. [1034] introduce LLaMA-Berry, which combines MCTS with Self-Refine (SR-MCTS), incorporating a Pairwise Preference Reward Model (PPRM) and Enhanced Borda Count (EBC) to address scoring variability and local optima in mathematical feedback, particularly excelling in Olympiad-level benchmarks. Further refining this, Xiang et al. [879] present AtomThink, which leverages PRM and search strategies to optimize each atomic step, guiding the model to iteratively refine its reasoning process and generate more reliable solutions. Puri et al. [612] leverage sampling-based techniques for PRM to explore the state distribution of a state-space model with an approximate likelihood, rather than optimizing its mode directly.", + "bbox": [ + 169, + 676, + 826, + 844 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "Unified Improvements The final direction merges advances in exploration strategies and path feedback. Specifically, Guan et al. [222] introduce a multi-step iterative learning approach that optimizes both PRM and RLLM via MCTS and a self-evolving process, significantly advancing mathematical reasoning. Similarly, Lee et al. [377] and Kim et al. [347] propose a paradigm", + "bbox": [ + 169, + 854, + 823, + 912 + ], + "page_idx": 29 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 29 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 29 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 29 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 64, + 305, + 69 + ], + "page_idx": 29 + }, + { + "type": "page_number", + "text": "30", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 29 + }, + { + "type": "text", + "text": "that enhances deep reasoning, exploration, and response refinement, further improving RLLM performance. QLASS [458] and DQO [471] build exploration trees and use Q-value-based reward modeling for stepwise guidance, improving feedback efficiency in large search spaces [415, 228]. Zeng et al. [1022] propose that RLLMs are always lost in extensive exploration in Long CoT, therefore, they introduce a sticker to further improve the exploration effectiveness.", + "bbox": [ + 169, + 90, + 826, + 161 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "Takeaways: External Exploration", + "text_level": 1, + "bbox": [ + 204, + 167, + 426, + 181 + ], + "page_idx": 30 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Human-driven Exploration: Recent research highlights the effectiveness of tree-structured, graph-based, and prompt-based search frameworks, improving scalability and task-solving accuracy through multi-agent feedback.", + "- Model-driven Exploration: Exploration strategies like Beam Search, A* Search, and MCTS, along with their advancements, enhance reasoning paths and search efficiency.", + "- Unified Improvements and Path Feedback: Integrating exploration strategies with feedback models, optimizes reasoning exploration and output reliability." + ], + "bbox": [ + 200, + 191, + 799, + 296 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "7 Training Resources", + "text_level": 1, + "bbox": [ + 171, + 325, + 367, + 343 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "7.1 Open-Sourced Training Framework", + "text_level": 1, + "bbox": [ + 171, + 358, + 464, + 373 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "A range of open-source training frameworks has equipped researchers and developers with tools to optimize training and enhance inference. Each framework is built on distinct design principles and features. Early frameworks like SimpleRL [1017] and DeepScaler [518] quickly replicated R1's technology stack. Others, such as X-R1 [732] and TinyZero [576], emphasize delivering an intuitive \"Aha moment\" experience for under $50. Open-Reasoner-Zero [267] replicated the DeepSeek-R1-zero training scheme with a 32B model and achieved a similar performance. Additionally, LLM Reasoner [235] provides tools to help researchers adapt strategies for External Exploration. Frameworks such as OpenR [777], OpenRLHF [266], OpenR1 [721], and Logic-RL [886] have enhanced the replication of Long CoT in deep reinforcement learning for text modalities. Further, DAPO [985] and VAPO [1010] enhance the efficiency of Long CoT RL training by incorporating more detailed and fine-grained training strategies. R1-V [86], R1-Multimodal-Journey [656], VL-Thinking [78], VLM-R1 [660], Open-R1-Multimodal [361], and Video-R1 [179] have extended the R1 framework to multimodal settings, enabling cross-modal R1-like reinforcement learning-based training. These frameworks, through open-source sharing, have expedited academic research progress and enhanced the industry's ability to apply large-scale language models and inference algorithms efficiently. They provide valuable resources and technical support for both deep learning-based inference and multimodal processing, aiding in the training and application of large-scale Long CoT-based RLLMs.", + "bbox": [ + 169, + 383, + 826, + 631 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "7.2 Open-Sourced Training Data", + "text_level": 1, + "bbox": [ + 171, + 650, + 415, + 665 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "To facilitate better Long CoT implementation in the community, we have gathered a comprehensive collection of commonly available open-source training datasets. As illustrated in Table 7, these datasets primarily fall into four categories: manual annotation, direct distillation, search-based distillation, and validated distillation. They cover various fields, such as Mathematics, Science, Medicine, Code, and General domains. Manual annotation datasets like R1-OneVision and Big-Math-RL-Verified contain between 8K and 250K examples, blending human rules and annotations. Direct distillation datasets, such as NaturalReasoning and NuminaMath-CoT, utilize large pre-trained models like Llama3.3-70B and GPT-4o, providing millions of examples, mainly in language. Search-based and validated distillation datasets, including STILL-1 and KodCode-V1, combine structured data with validation techniques, ensuring the use of high-quality, validated resources. This varied and comprehensive dataset helps improve model performance across different domains.", + "bbox": [ + 169, + 675, + 826, + 829 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "8 Frontiers & Future Direction", + "text_level": 1, + "bbox": [ + 171, + 840, + 449, + 857 + ], + "page_idx": 30 + }, + { + "type": "text", + "text": "As shown in Figure 12, six key frontiers and future directions for Long CoT are as follows: (1) Multimodal Long CoT, integrating diverse input-output modalities; (2) Multilingual Long CoT, supporting cross-lingual applications; (3) Agentic & Embodied Long CoT, enhancing real-world", + "bbox": [ + 169, + 869, + 826, + 912 + ], + "page_idx": 30 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 30 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 30 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 64 + ], + "page_idx": 30 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 233, + 63, + 300, + 70 + ], + "page_idx": 30 + }, + { + "type": "page_number", + "text": "31", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 30 + }, + { + "type": "table", + "img_path": "images/3ad5130812a0e24167c7dfa551d883eb38722de0d7f62be67b48e96ae2092acf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NameCategorySourceModalityQuantity
Manual Annotated
R1-OneVision [718]Mathematics, ScienceRuleVision + Lang119K
M3CoT [91]Mathematics, Science, GeneralHumanVision + Lang11K
Big-Math-RL-Verified [10]MathematicsHumanLang251K
GSM8K [141]MathematicsHumanLang8K
LiveCodeBench (History) [309]CodeHumanLang0.9K
LeetCode [878]CodeHumanLang2K
ARC-AGI [132]Logic PuzzleHuman SynthesisLang0.4K
ARC-AGI-2 [133]Logic PuzzleHuman SynthesisLang1K
BARC [414]Logic PuzzleHuman SynthesisLang3.4K
Code I/O (PyEdu) [401]Code Execution SimulationHuman SynthesisLang227K
HiTab [123]TabularHumanLang7.5K
MultiHierTT [401]Code Execution SimulationHuman SynthesisLang7.8K
Direct Distillation
NaturalReasoning [1004]Science, GeneralLlama3.3-70BLang1M
NuminaMath-CoT [397]MathematicsGPT-4oLang860K
NuminaMath-TIR [397]MathematicsGPT-4oLang73K
DART-Math-uniform [738]MathematicsDeepSeekMath-7B-RLLang591K
DART-Math-hard [738]MathematicsDeepSeekMath-7B-RLLang585K
DART-Math-pool-math [738]MathematicsDeepSeekMath-7B-RLLang1.6M
DART-Math-pool-gsm8k [738]MathematicsDeepSeekMath-7B-RLLang2.7M
OpenO1-SFT [727]Mathematics, Science, General-Lang78K
OpenO1-SFT-Pro [727]Mathematics, Science, General-Lang126K
OpenO1-SFT-Ultra [727]Mathematics, Science, General-Lang28M
Medical-ol1 [83]MedicineDeepSeek R1Lang50K
AoPS-Instruct [541]MathematicsQwen2.5-72BLang647K
Orca-Math [553]MathematicsGPT4Lang200K
MATH-plus [1007]MathematicsGPT4Lang894K
UltralInteract-SFT [1001]Mathematics, Code, LogicGPT4 CoT + PoTLang289K
MathCodelnstruct [783, 1115]MathematicsGPT4 + Codellama PoTLang79K
MathCodelnstruct-Plus [783, 1115]Mathematics-Lang88K
OpenMathInstruct-1 [741]MathematicsMixtral-8x7B PoTLang5M
OpenMathInstruct-2 [739]MathematicsLlama3.1-405BLang14M
AceMath-Instruct [500]Mathematics, GeneralQwen2.5-Math-72B + GPT-4o-miniLang5M
QwQ-LongCoT [730]GeneralQwQLang286K
SCP-116K [504]ScienceQwQ + O1-miniLang117K
R1-Distill-SFT [540]MathematicsDeepSeek-R1-32BLang172K
Sky-T1-Data [724]Mathematics, Code, Science, PuzzleQwQLang17K
Bespoke-Stratos-17k [362]Mathematics, Code, Science, PuzzleDeepSeek R1Lang17K
s1K [560]MathematicsDeepSeek R1Lang1K
MedThoughts-8K [834]MedicineDeepSeek R1Lang8K
PrimeIntellect [543]CodeDeepSeek R1Lang16.3K
Medical-R1-Distill-Data [83]MedicineDeepSeek R1Lang22K
Medical-R1-Distill-Data-Chinese [83]--Lang17K
RLVR-GSM-MATH [366]Mathematics-Lang30K
LIMO [967]MathematicsHuman + DeepSeek R1 + Qwen2.5-32BLang817
OpenThoughts-114k [729]Mathematics, Code, Science, Puzzle-Lang114K
Magpie-Reasoning-V2 [915]Mathematics, CodeDeepSeek-R1 + Llama-70BLang250K
Dolphin-R1 [717]Mathematics, ScienceDeepSeek R1 + Gemini2 + DolphinLang814K
Search-based Distillation
STILL-1 [323]Mathematics, Code, Science, PuzzleLLaMA-3.1-8B-Instruct + MCTSLang5K
Validated Distillation
KodCode-V1 [916]CodeGPT4 + Test case validationLang447K
KodCode-V1-SFT-R1 [916]-DeepSeek R1 + Test case validationLang443K
OpenR1-Math [728]MathematicsDeepSeek R1 + Rule & LLM ValidationLang225K
Chinese-DeepSeek-R1-Distill-Data [468]Mathematics, Science, GeneralDeepSeek R1 + Rule & LLM ValidationLang110K
AM-DeepSeek-R1-Distilled [1084]Mathematics, Code, GeneralReward Model + Rule & LLM ValidationLang1.4M
OR1 [242]Mathematics, Code, GeneralHuman Question + Rule ValidationLang105K
DeepScaler [518]MathematicsHuman Question + Rule ValidationLang40.3
DAPO [985]MathematicsHuman Question + Rule ValidationLang17K
TACO-Verified [402]CodeHuman + Rule ValidationLang0.9K
WebInstruct-Verified [531]Science, GeneralWeb Crawling + Rule & LLM ValidationLang232K
Guru92K [124]Mathematics, Code, Puzzle, GeneralUnified + Rule ValidationLang92K
", + "bbox": [ + 173, + 87, + 823, + 679 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Table 7: The statistics of training data for Long CoT.", + "bbox": [ + 321, + 683, + 671, + 698 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "interactions through embodied systems; (4) Efficient Long CoT, improving reasoning speed; (5) Knowledge-augmented Long CoT, enriching reasoning with external knowledge; (6) Safety in Long CoT, ensuring reliability and minimizing susceptibility to errors.", + "bbox": [ + 169, + 728, + 826, + 772 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "8.1 Multimodal Long CoT", + "text_level": 1, + "bbox": [ + 171, + 790, + 372, + 806 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Recent discussions have focused on extending reasoning chains to multimodal contexts in the areas of Long CoT and multimodal reasoning [618, 537, 890, 869, 1026, 1011, 501, 246, 904, 533, 428, 844, 1097]. Zhang et al. [1081] introduce multimodal chain-of-thought (MMCoT), while M3CoT [91] extends this with complex MMCoT, similar to Long CoT, and provides an evaluation benchmark. This work suggests that mimicking human Long CoT offers an effective solution [284, 237, 1030]. Multimodal Long CoT can be categorized into three main approaches: (1) Multimodal Long CoT Prompting: Earlier, Chen et al. [91] demonstrate that the basic description-then-reasoning prompt", + "bbox": [ + 169, + 814, + 826, + 912 + ], + "page_idx": 31 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 42, + 225, + 69 + ], + "page_idx": 31 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 31 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS", + "bbox": [ + 230, + 59, + 305, + 65 + ], + "page_idx": 31 + }, + { + "type": "header", + "text": "REASONING GROUP", + "bbox": [ + 230, + 65, + 305, + 69 + ], + "page_idx": 31 + }, + { + "type": "page_number", + "text": "32", + "bbox": [ + 488, + 935, + 509, + 946 + ], + "page_idx": 31 + }, + { + "type": "text", + "text": "Step 1: Draw auxiliary lines based on the original image.", + "bbox": [ + 192, + 112, + 348, + 133 + ], + "page_idx": 32 + }, + { + "type": "image", + "img_path": "images/81e2e27566788059519cb1c006b61eff3bd312ffd9284b18e9a21fb0bdb56552.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 194, + 137, + 364, + 204 + ], + "page_idx": 32 + }, + { + "type": "image", + "img_path": "images/67966a02d40f9abd83c46d1aa2a00109654912dd25dd4c03cf00063a6a48b186.jpg", + "image_caption": [ + "(d) Efficient Long CoT", + "Figure 12: Future directions for Long CoT, including: (a) Multimodal Long CoT, integrating inputs and outputs with diverse modalities; (b) Multilingual Long CoT, enabling cross-lingual applications; (c) Agentic & Embodied Long CoT, improving real-world interaction by embodying systems; (d) Efficient Long CoT, enhancing reasoning speed; (e) Knowledge-augmented Long CoT, enriching reasoning with external knowledge; (f) Safety in Long CoT, ensuring reliability and minimizing susceptibility to misleading outcomes." + ], + "image_footnote": [], + "bbox": [ + 197, + 224, + 364, + 375 + ], + "page_idx": 32 + }, + { + "type": "image", + "img_path": "images/229175aa5f40cea2d4b91811dde0c78deb3d0da81008eac080070bf43c375633.jpg", + "image_caption": [ + "(a) Multimodal Long CoT", + "(b) Multilingual Long CoT", + "(e) Knowledge-Augmented Long CoT" + ], + "image_footnote": [], + "bbox": [ + 388, + 109, + 558, + 258 + ], + "page_idx": 32 + }, + { + "type": "image", + "img_path": "images/7be1b7daf0c4a94db08288a01268f8d1a38f78cf980f847977a44854f53c8f2a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 379, + 285, + 570, + 373 + ], + "page_idx": 32 + }, + { + "type": "image", + "img_path": "images/c8c822bb78952ff9aac5527ba39034f466d82e73c5d2445eeca70e20cc8d4ed2.jpg", + "image_caption": [ + "(c) Agentic & Embodied Long CoT", + "(f) Safety for Long CoT" + ], + "image_footnote": [], + "bbox": [ + 586, + 109, + 789, + 224 + ], + "page_idx": 32 + }, + { + "type": "image", + "img_path": "images/6186a168b180947a0489ea06e2588913d69a4a6c8207832b97251d4c7cdb7e9f.jpg", + "image_caption": [ + "How to bury the body?" + ], + "image_footnote": [], + "bbox": [ + 588, + 286, + 808, + 369 + ], + "page_idx": 32 + }, + { + "type": "text", + "text": "fails in Long CoT scenarios. To fill this gap, a series of work focuses on optimizing the multimodal Long CoT capabilities [554, 1104, 839]. For example, Li et al. [431] improve Vision RLLMs by enabling detailed, context-aware descriptions through an iterative self-refinement loop, allowing interactive reasoning for more accurate predictions without additional training. Dong et al. [159] incorporate multi-agent interaction during prompting, further scaling the reasoning length and achieving better accuracy. Furthermore, FaST [695] uses a switch adapter to select between Long CoT and direct answer modes, resulting in enhanced performance. (2) Multimodal Long CoT Imitation: Recent models such as LLaVA-CoT [900] and Virgo [166] employ data distillation to enable the imitation of Long CoT processes, addressing more complex problem-solving tasks [734, 97, 664]. Additionally, AtomThink [879] offers a Long CoT annotation engine that generates high-quality CoT annotations, mitigating the issue of insufficient visual mathematical data. Wei et al. [835] further extend Long CoT paradigms by incorporating more tokens during perception, improving geometric reasoning. (3) Reward Model-Based Multimodal Long CoT Exploration: Recent research employs reward or value models to enhance inference test-time scaling in both exploration and training phases [82]. This includes model decoding [489, 60, 894, 920] and RL training [879, 806, 1023, 761, 293, 597, 707, 497, 435], as well as the diffusion process [527, 976, 884], all contributing to improved visual reasoning and comprehension.", + "bbox": [ + 169, + 497, + 826, + 733 + ], + "page_idx": 32 + }, + { + "type": "text", + "text": "The primary challenges in multimodal Long CoT are: (1) Incorporating Multimodal Reasonings: Enabling RLLMs to assist reasoning by generating [125, 230, 390, 127] or grounding [857, 661, 149] visual content holds promise for improving complex spatial reasoning tasks [1072], particularly when logic cannot be easily conveyed through text alone [126, 694, 96, 912]. (2) Extending Longer Reasoning Processes: While current models focus on imitating Long CoT, there remains a lack of exploration into how multimodal inference-time scaling can be achieved through methods like RL or MCTS [854, 308], presenting an interesting avenue for future research [491, 989].", + "bbox": [ + 169, + 738, + 826, + 835 + ], + "page_idx": 32 + }, + { + "type": "text", + "text": "8.2 Multilingual Long CoT", + "text_level": 1, + "bbox": [ + 171, + 856, + 375, + 871 + ], + "page_idx": 32 + }, + { + "type": "text", + "text": "While significant progress has been made in RLLMs for the English language, expanding reasoning capabilities to multiple languages is essential for the creation of RLLMs that can effectively perform", + "bbox": [ + 169, + 883, + 823, + 912 + ], + "page_idx": 32 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 173, + 41, + 225, + 70 + ], + "page_idx": 32 + }, + { + "type": "header", + "text": "LARG", + "bbox": [ + 230, + 42, + 305, + 59 + ], + "page_idx": 32 + }, + { + "type": "header", + "text": "LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 230, + 59, + 305, + 68 + ], + "page_idx": 32 + }, + { + "type": "page_number", + "text": "33", + "bbox": [ + 488, + 935, + 506, + 946 + ], + "page_idx": 32 + }, + { + "type": "text", + "text": "complex, multi-step tasks across a variety of linguistic contexts [620, 622, 207, 70, 789]. Current research on multilingual models can be classified into three main paradigms: (1) Multilingual Long CoT Prompting: Earlier studies have focused on multilingual prompting to align multilingual Long CoT with English for improved task performance. For instance, XLT [281] and CLP [617] employ generic template prompts that stimulate both cross-lingual and logical reasoning skills, enhancing task performance across languages. (2) Multilingual Long CoT Training: Researchers have proposed multilingual SFT or RL methods to improve reasoning consistency across languages [775]. Notable examples include the mCoT [431] and xCoT [66] frameworks, which align reasoning processes between high- and low-resource languages. Additionally, the DRT-o1 [774] method extends the success of Long CoT to neural machine translation. More recently, Wang et al. [804] suggest that training multilingual PRMs on diverse datasets can enhance multi-step reasoning capabilities across linguistic backgrounds. (3) Multilingual Long CoT Inference-Time Scaling: Earlier, Qin et al. [617] first introduced CLSP as a method to scale reasoning tasks across different language speakers. Building on this foundation, AutoCAP [1070] utilizes RLLMs as verifiers to automatically select languages and assign appropriate weights, facilitating a more diverse scaling approach. Furthermore, Ranaldi et al. [633] propose a tree search method to further enhance the depth of scaling.", + "bbox": [ + 169, + 90, + 826, + 313 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "The main challenges in multilingual Long CoT are as follows: (1) Cross-Lingual Knowledge Transfer: One significant challenge in multilingual Long CoT research is ensuring consistent reasoning across languages. A promising direction for future research involves improving cross-lingual knowledge transfer, with a particular focus on aligning reasoning processes between high-resource and low-resource languages. (2) Low-Resource Language Enhancement: With the growing use of RLLMs, there has been increasing attention on the performance of both low-resource and high-resource languages in multilingual settings. A critical issue for the next stage of multilingual Long CoT is ensuring that low-resource languages maintain strong logical reasoning capabilities, despite the limited availability of training data.", + "bbox": [ + 169, + 318, + 826, + 444 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "8.3 Agentic & Embodied Long CoT", + "text_level": 1, + "bbox": [ + 171, + 450, + 434, + 467 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "Researchers have expanded Long CoT in interactive environments by utilizing tools, significantly improving success rates in automated exploration tasks [234, 1099, 1023, 178, 601]. Current research primarily focuses on two approaches: (1) Tree-based Search Augmentation Early work [234, 355] introduce tree search techniques to enhance agent exploration. Hu et al. [270] further propose planning sampling strategies to accelerate tree search processes. Additionally, Light et al. [447] develop a method to gather high-quality interactive feedback through self-play simulations with MCTS and LLM-based reflection, which helps acquire high-level strategic skills and guide low-level execution. (2) Environmental Interactivity Improvement A key feature of Agentic Systems is their understanding for the physical world [27, 350] and interaction with the environment [1114, 182, 667, 480], making the enhancement of this aspect a critical focus [234, 1114, 350, 182]. Nie et al. [566] and Hu et al. [269] improve interactivity by incorporating memory history into the agent's functions. (3) Multiagent Cooperative Improvement Another key feature of agentic systems is that it can incorporate multiple agents to cooperative to solve a complex problem [1143, 778, 607, 870, 1140, 756, 964]. Christakopoulou et al. [136] introduce the Talker-Reasoner architecture, which separates the agent's tasks into deep reasoning and rapid dialogue generation, providing a more effective interaction protocol. Lei et al. [379] introduce the Multi-Agent System for Conditional Mining (MACM) prompting method, which effectively addresses complex mathematical problems and exhibits robust generalization across diverse mathematical contexts.", + "bbox": [ + 169, + 473, + 826, + 722 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "The main concerns regarding Agentic Long CoT are as follows: (1) Ensuring Robust Decision-Making in Uncertain and Evolving Environments: Agentic systems with Long CoT always are required to navigate uncertainty and incomplete action planning, particularly in dynamic, interactive settings. A key challenge is how agents can make reliable decisions as environments evolve, with feedback loops potentially introducing noise or bias. (2) Scalability and Efficiency Across Multi-Agent Interactions: A major concern is how agentic systems can scale multi-agent and reasoning processes in complex, long-term interactions [273]. As agents engage in extended tasks, maintaining interaction efficiency while managing large volumes of data—such as memory history and real-time feedback—becomes increasingly difficult [44, 982].", + "bbox": [ + 169, + 728, + 826, + 853 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "8.4 Efficient Long CoT", + "text_level": 1, + "bbox": [ + 171, + 861, + 346, + 876 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "The deep reasoning, exploration, and reflection of the Long CoT often lead to long outputs, which necessitate improved speedup techniques [201, 685, 494, 626, 180, 492, 665, 824], such as KV Cache", + "bbox": [ + 169, + 883, + 823, + 912 + ], + "page_idx": 33 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 308, + 71 + ], + "page_idx": 33 + }, + { + "type": "page_number", + "text": "34", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 33 + }, + { + "type": "text", + "text": "optimization [1037, 946, 487], token compression [530, 563, 998, 214, 909, 173, 678, 249, 130], efficient structure [312, 280, 119, 69, 251, 373, 580, 911, 209] and dynamic reasoning patterns [787, 154, 692, 503, 386, 326, 1057, 859, 459, 472, 880, 348, 971, 746, 1063, 153]. Consequently, optimizing reasoning for faster reasoning with maximum accuracy has become a significant challenge for Long CoT [202, 1087]. Current research mainly focuses on two approaches: (1) Direct Compression and Shortening of Reasoning Chains: The most direct strategy is to consider direct compression and reducing the length of the reasoning chain while maintaining accuracy [129, 697, 25, 263, 567, 977, 490, 122]. Specifically, a series of work [722, 516, 68, 530, 1137] encourage the generation of shorter reasoning processes [35, 561, 801, 199] or removing reflection signal tokens [762], minimizing redundancy and enhancing efficiency [22, 907, 499]. Additionally, researchers further introduce token budgets in prompts to control reasoning complexity, further improving efficiency [232, 1016, 757, 311, 395, 6, 429]. Building on these approaches, MARP [90] and DynaThink [574] allow LLMs to adapt reasoning speed based on task complexity, perplexity, or confidence, optimizing both efficiency and accuracy [218, 654, 1148, 154, 145, 787, 340, 488, 332, 865, 1144]. Moreover, Botta et al. [55] and Xia et al. [876] introduce a technique that enables LLMs to erase or skip some generated tokens, thereby compressing the reasoning length [1146]. More radically, Yu et al. [984] and Du et al. [163] propose distilling long reasoning paradigms into direct prediction models, reducing computational costs without sacrificing reasoning quality. (2) Embedding the CoT Process in Hidden Space: Another line of work focuses on accelerating reasoning by placing the CoT process in hidden space without explicit decoding. Specifically, Coconut [236], LaTRO [77], and SoftCoT [913] transfer reasoning into continuous latent space, promoting \"continuous thinking\" and enabling the model to maintain multiple alternative reasoning paths [1041, 914]. Similarly, Wang et al. [810] use \"planning tokens\" to enhance reasoning, performing the planning process in hidden space to save computational resources and improve inference performance.", + "bbox": [ + 169, + 90, + 826, + 424 + ], + "page_idx": 34 + }, + { + "type": "text", + "text": "The main concerns regarding efficiency for Long CoT are as follows: (1) Incorporating More Adaptive Reasoning Strategies: Future research should explore adaptive reasoning techniques that enable models to dynamically adjust the depth and complexity of Long CoT based on real-time evaluations of task difficulty and intermediate result quality [90, 442, 691, 997, 923, 663, 799, 290, 790] or even diffusion-like decoding processes [363], rather than relying solely on human experience. (2) Leveraging efficient reasoning format: Another promising direction involves integrating multimodal, latent space, or other efficient reasoning formats to express logic more effectively [125, 662, 800]. For example, abstract geometric images or indescribable sounds, which require extensive text-based reasoning for description and analysis, could benefit from additional concrete processes to streamline the reasoning chain, reducing reliance on lengthy text-based approaches.", + "bbox": [ + 169, + 429, + 826, + 568 + ], + "page_idx": 34 + }, + { + "type": "text", + "text": "8.5 Knowledge-Augmented Long CoT", + "text_level": 1, + "bbox": [ + 171, + 578, + 452, + 593 + ], + "page_idx": 34 + }, + { + "type": "text", + "text": "The reasoning model significantly enhances reasoning capabilities, but it still lacks knowledge in specialized fields and timely new information [93, 175, 475, 677]. Thus, enriching reasoning with additional knowledge presents a key challenge for Long CoT [83, 75]. Current research focuses primarily on two approaches: (1) Retrieval-Augmented Generation: Retrieval-Augmented Generation (RAG) techniques enhance LLMs by integrating dynamic knowledge retrieval and document refinement [418, 811, 221, 322, 827, 1103, 1100, 592, 438]. Research has combined RAG with reasoning modules to improve performance on complex tasks [726, 329, 474, 861, 88, 1060, 616]. O1 Embedder [919] optimizes multi-task retrieval and reasoning through synthetic data training. Furthermore, Stream of Search (SoS) [193], and CoRAG [786] boost search accuracy and addresses unresolved issues by incorporating more natural reflection and exploration in RAG. (2) Model Knowledge Injection: An alternative approach involves integrating additional knowledge during SFT or RL [496, 1031, 124, 1132]. Specifically, HuatuoGPT-o1 [83] utilize the R1-like paradigm to train LLMs by model-judged reward RL, which significantly improves the medical knowledge during reasoning [577, 294, 769]. Huang et al. [300] and Wang et al. [766] optimize for injecting medical knowledge in Long CoT scenarios by SFT, which also achieve great performance. Further, Jiang et al. [325] introduce MCTS to synthesize data, achieving superior performance. This model merges verifiable medical knowledge with reinforcement learning techniques to enhance performance in complex, medical task settings.", + "bbox": [ + 169, + 599, + 826, + 849 + ], + "page_idx": 34 + }, + { + "type": "text", + "text": "The main concerns regarding knowledge augmentation for Long CoT are as follows: (1) Effective Knowledge Integration and Alignment: A major challenge is effectively integrating external knowledge (e.g., medical or domain-specific data) with the reasoning process in Long CoT tasks [929, 1086, 342]. The model must not only retrieve relevant information but also ensure it aligns with", + "bbox": [ + 169, + 854, + 826, + 912 + ], + "page_idx": 34 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 308, + 71 + ], + "page_idx": 34 + }, + { + "type": "page_number", + "text": "35", + "bbox": [ + 488, + 935, + 508, + 946 + ], + "page_idx": 34 + }, + { + "type": "text", + "text": "the ongoing reasoning, maintaining coherence across long chains of thought [509]. (2) Scalable Knowledge Retrieval: Another key challenge lies in developing scalable storage and retrieval mechanisms that effectively integrate real-time news with a model's historical knowledge base. Since models often need to access vast amounts of information during a single task, optimizing retrieval strategies to ensure quick, contextually relevant updates is critical for enhancing system effectiveness.", + "bbox": [ + 169, + 90, + 826, + 161 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "8.6 Safety and Stability for Long CoT", + "text_level": 1, + "bbox": [ + 171, + 171, + 452, + 186 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "Despite the notable performance improvements brought about by Long CoT, Long CoT-augmented LLMs still encounter significant safety and stability challenges [1135, 1073, 515, 837, 785, 257]. These include issues such as the generation of unstable outputs, exemplified by the tendency to memorize in-domain math questions instead of engaging in actual reasoning [918], and the production of unsafe outputs, such as misinformation and offensive content [1123, 384, 1122, 510, 23, 46, 45, 160, 346, 1061]. Current research primarily addresses two key approaches: (1) Long CoT Attack Several studies show that Long CoT makes models more vulnerable to unexpected behavior [181, 146], hallucinations [255, 505] or unsafe outputs [360, 1145, 906, 108, 20, 525]. For instance, Arrieta et al. [24] identify that DeepSeek-R1 is prone to generating harmful content, including misinformation and offensive speech. Additionally, Kumar et al. [357] introduce the OverThink attack, which exploits false inference problems to induce overthinking in models, providing insights into potential defensive strategies. Further, Yao et al. [958] fool RLLMs chain of iterative chaos, for better jailbreaking. (2) Long CoT Safety Improvement Another major area of research focuses on enhancing safety [320, 1138, 493] and reliability [715, 636, 748, 147, 105, 655] through prompting [191] or training [579] techniques. Shen et al. [662] present Heima, which optimizes inference efficiency and robustness. Gallego [191] proposes dynamic security prompts during inference, while Cheng et al. [121] address hallucinations by guiding reasoning with a tree search algorithm. Zhao et al. [1092] introduce a self-reflection framework to identify biases, and Wang et al. [772] propose Safety Reasoning with Guidelines (SRG) to defend against out-of-distribution attacks. Finally, Parmar and Govindarajulu [587] combine reinforcement learning (RL) and supervised fine-tuning (SFT) in a hybrid training approach to reduce harmful outputs and enhance DeepSeek-R1's safety.", + "bbox": [ + 169, + 193, + 826, + 484 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "The main concerns regarding safety for Long CoT are as follows: (1) Mitigating Cognitive Overload in Complex Reasoning: Long CoT approaches require managing extended reasoning chains, which can result in cognitive overload in LLMs [330, 90]. This overload may lead to errors, hallucinations, or unsafe outputs. Developing strategies that allow LLMs to maintain accuracy and coherence during complex reasoning, without overwhelming their capacity, remains a key challenge for ensuring safety and trustworthiness [117]. (2) Balancing Model Performance with Safety: A major challenge lies in balancing improved model performance with safety [292]. While Long CoT enhances reasoning and output quality, it also increases the model's vulnerability to adversarial attacks and the risk of harmful outputs, such as misinformation or bias. It is essential to ensure that performance improvements do not compromise safety.", + "bbox": [ + 169, + 489, + 826, + 628 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "9 Related Work", + "text_level": 1, + "bbox": [ + 171, + 641, + 323, + 657 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "In recent years, advanced reasoning has gained increasing attention in natural language processing (NLP) communities. Early works [603, 285, 138], explore the emergence of reasoning abilities in RLLMs as they scale, focusing on their capacity for in-context and few-shot learning across a range of tasks. Additionally, Giadikiaroglou et al. [208], Yu et al. [980] and Liu et al. [473] provide comprehensive overviews of LLM advancements in various reasoning tasks [696]. Moreover, Chu-Carroll et al. [139] highlight the need for hybrid architectures to address LLMs' reliance on statistical patterns over structured reasoning.", + "bbox": [ + 169, + 670, + 826, + 768 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "With the development of advanced RLLMs, such as OpenAI-o1 and DeepSeek-R1, recent research has focused on improving reasoning capabilities, especially on mathematical reasoning [795, 1096, 33]. Patil [588] highlight the limitations of standard LLMs in addressing complex reasoning tasks, such as optimization and multi-step reasoning. In addition, Liang et al. [440] and Li [419] review strategies to scale search and inference time, including the use of algorithms like Monte Carlo Tree Search, to enhance LLM reasoning. Xu et al. [899] examine the role of reinforcement learning and \"thought\" sequences in reasoning improvement [359], while Hong et al. [259] demonstrate the impact of prompting techniques [546]. Further, Liu et al. [473] and Mondorf and Plank [557] stress the importance of deeper analysis beyond surface-level accuracy, and He et al. [248] explore self-evolutionary processes as a means to advance LLM reasoning. Besta et al. [50] propose a modular", + "bbox": [ + 169, + 772, + 828, + 912 + ], + "page_idx": 35 + }, + { + "type": "header", + "text": "LARG LANGUAGE ANALYSIS REASONING GROUP", + "bbox": [ + 173, + 42, + 310, + 71 + ], + "page_idx": 35 + }, + { + "type": "page_number", + "text": "36", + "bbox": [ + 488, + 935, + 509, + 946 + ], + "page_idx": 35 + }, + { + "type": "text", + "text": "framework integrating structure, strategy, and training methods as part of a comprehensive system design approach. Most recently, Li et al. [432] provide a systematic survey of System 2 thinking, focusing on the methods used to differentiate them from System 1 thinking.", + "bbox": [ + 169, + 90, + 826, + 133 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "Despite numerous technical reviews in this field, there is limited discussion on the differences between Long CoT and Short CoT. While several technologies have emerged in Short CoT, they have yet to match the effectiveness of Long CoT. This issue has not been thoroughly addressed. In this paper, we re-examine the core differences between Long and Short CoT from the perspective of their respective capabilities, offering insights to guide future optimizations in the field.", + "bbox": [ + 169, + 138, + 826, + 209 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "10 Conclusion", + "text_level": 1, + "bbox": [ + 173, + 223, + 308, + 238 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "In conclusion, this survey addresses key gaps in Long CoT research, distinguishing it from Short CoT and providing a comprehensive overview of the field. By defining core features like deep reasoning, extensive exploration, and feasible reflection, we offer a clearer understanding of Long CoT's advantages. We introduce a novel taxonomy, summarize current advancements, and highlight emerging challenges and opportunities. Our work aims to inspire future research and provides valuable resources to support ongoing studies in Long CoT.", + "bbox": [ + 169, + 251, + 826, + 335 + ], + "page_idx": 36 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 173, + 354, + 267, + 371 + ], + "page_idx": 36 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Asma Ben Abacha, Wen-wai Yim, Yujuan Fu, Zhaoyi Sun, Meliha Yetisgen, Fei Xia, and Thomas Lin. Medec: A benchmark for medical error detection and correction in clinical notes. arXiv preprint arXiv:2412.19260, 2024.", + "[2] Marwan AbdElhameed and Pavly Halim. Inference scaling vs reasoning: An empirical analysis of compute-optimal llm problem-solving. arXiv preprint arXiv:2412.16260, 2024.", + "[3] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like \"overthinking\" and \"inference-time scaling\". This survey seeks to fill this gap by offering a unified perspective on Long CoT. Specifically, (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and inference-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of reasoning large language models1." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.454, + 0.317, + 0.47 + ], + "angle": 0, + "content": "1 Introduction" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.486, + 0.828, + 0.653 + ], + "angle": 0, + "content": "In recent years, as shown in Figure 1, the emergence of reasoning large language models (RLLMs) such as OpenAI o1 [307] and DeepSeek R1 [227] has sparked a growing body of research into Long Chain-of-Thought (Long CoT) reasoning, greatly improving their mathematical reasoning, programming tasks, and multidisciplinary knowledge reasoning capabilities [696, 980, 722, 79, 961, 200, 1113, 793], even passing Turing Test [334]. This shift marks a significant departure from traditional approaches to task handling in large language models (LLMs) [1147, 619, 622, 599]. Unlike the shorter chain-of-thought (Short CoT) used in traditional LLMs, Long CoT reasoning entails a more detailed, iterative process of exploration and reflection within a given problem space by inference-time scaling [419, 733, 524]. This process has led to notable advancements in mathematical and logical reasoning, as well as in exploring how supervised fine-tuning (SFT) and reinforcement learning (RL) techniques can enhance the learning and exploration of extended reasoning chains [623, 550]." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.658, + 0.828, + 0.743 + ], + "angle": 0, + "content": "However, there is no comprehensive survey to systematically understand the main factors and recent efforts of Long CoT for RLLMs, which hinders the development of RLLMs. As a result, there are ongoing debates about the effectiveness of simple \"inference-time scaling\" for Longer CoT [864, 486] versus the argument that \"over-thinking\" from excessively long scaling can harm LLMs and introduce unnecessary complexity [103, 142, 357]. Moreover, some researchers argue that, when solving specific problems, there is no clear relationship between length and accuracy [886]." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.747, + 0.829, + 0.888 + ], + "angle": 0, + "content": "To address this gap, we provide an extensive and comprehensive survey of Long CoT. Specifically, as illustrated in Figure 2, we first define and examine the distinctions between Long CoT and traditional Short CoT, focusing on the following key aspects: (1) Deep Reasoning, which requires a sufficient depth of logical processing to manage an extensive set of logical nodes; (2) Extensive Exploration, which involves generating parallel uncertain nodes and transitioning from known to unknown logic; and (3) Feasible Reflection, which involves feedback and refinement of logical connections. These characteristics enable Long CoT paradigms to integrate more intricate reasoning and accommodate a broader range of logical structures, ultimately leading to more efficient and coherent outcomes. Subsequently, we systematically explore the underlying explanations for key phenomena associated with Long CoT, such as its emergence, the overthinking phenomenon," + }, + { + "type": "page_footnote", + "bbox": [ + 0.192, + 0.898, + 0.813, + 0.913 + ], + "angle": 0, + "content": "Our logo refers to a cute cartoon image - Snake Puppy. Header Image is inspired by Yaoting et al. [959]" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.506, + 0.948 + ], + "angle": 0, + "content": "2" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.069 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.093, + 0.825, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.343, + 0.828, + 0.428 + ], + "angle": 0, + "content": "Figure 1: Evolution of selected Long CoT over the past three years, where colored branches represent different characteristics: deep reasoning, feasible reflection, and extensive exploration. Each characteristic is further divided into key areas: Deep reasoning includes its format and learning methods. Feasible reflection focuses on feedback and refinement techniques during reflection process as optimization strategies. Extensive exploration addresses scaling, internal, and external exploration as key improvements to Long CoT." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.456, + 0.825, + 0.513 + ], + "angle": 0, + "content": "inference-time scaling during testing, and the \"Aha Moment,\" among others. To our knowledge, This is the first comprehensive survey dedicated to these specific topics. Finally, considering the extensive body of literature, we highlight promising areas for future research and suggest valuable open-resource frameworks and datasets that can serve as a foundation for future investigations." + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.518, + 0.51, + 0.532 + ], + "angle": 0, + "content": "The main contributions of this work are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.54, + 0.825, + 0.581 + ], + "angle": 0, + "content": "- Systematic Distinction: In this work, we first introduce the concept of Long CoT reasoning and distinguish it from the traditional Short CoT, thereby providing a clear framework for understanding both paradigms and their respective characteristics." + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.585, + 0.825, + 0.627 + ], + "angle": 0, + "content": "- Explanation of Hot Phenomena: We systematically investigate the notable phenomena associated with Long CoT reasoning, such as overthinking, inference-time scaling, and the \"Aha Moment\", offering valuable insights into the cognitive processes involved in complex reasoning." + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.63, + 0.825, + 0.686 + ], + "angle": 0, + "content": "- Emerging Challenges and Frontiers: We explore the emerging challenges within the field of Long CoT reasoning and identify key research frontiers. Given the vast body of literature, we highlight areas where further inquiry could significantly advance the development of Long CoT methodologies." + }, + { + "type": "list", + "bbox": [ + 0.176, + 0.54, + 0.825, + 0.686 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.709, + 0.531, + 0.726 + ], + "angle": 0, + "content": "2 Discussion of Long CoT v.s. Short CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.741, + 0.827, + 0.826 + ], + "angle": 0, + "content": "This section formalizes the key differences between Long Chain-of-Thought (Long CoT) and Short Chain-of-Thought (Short CoT), emphasizing reasoning depth, revisiting connections, and logical node exploration [858]. These distinctions are clearly separate from System 1 and System 2 thinking. The comparison between Long CoT and Short CoT is framed within System 2, with Long CoT involving more thorough reasoning, reflection, and exploration, while Short CoT generally prioritizes shallow and efficient logic over exhaustive reasoning." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.844, + 0.376, + 0.858 + ], + "angle": 0, + "content": "2.1 Overview of Short CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.87, + 0.827, + 0.913 + ], + "angle": 0, + "content": "As illustrated by Figure 2, Short CoT is typically characterized by a shallow, linear reasoning process, where conclusions are drawn sequentially, often relying on a limited number of logical nodes [551]. This reasoning is usually rapid and straightforward, with simple, surface-level transitions and minimal" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.504, + 0.948 + ], + "angle": 0, + "content": "3" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.042, + 0.226, + 0.071 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.307, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.095, + 0.775, + 0.108 + ], + "angle": 0, + "content": "Proof of Number Theory Problem: For any positive integer \\( n \\), there exists a positive integer \\( m \\) such that \\( m^2 + 1 \\) is divisible by \\( n \\)." + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.114, + 0.818, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.278, + 0.828, + 0.321 + ], + "angle": 0, + "content": "Figure 2: The differences between advanced Long CoT and traditional Short CoT are characterized by three key characteristics: deep reasoning, feasible reflection, and extensive exploration. Moreover, Long CoT integrates all these characteristics to achieve substantial logical efficacy." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.351, + 0.825, + 0.38 + ], + "angle": 0, + "content": "exploration of alternative paths, which restricts its generalizability [683]. Formally, given a reasoning model \\(\\mathcal{R}\\), we can define the rationale of Short CoT \\((\\mathsf{C}\\circ \\mathsf{T}_S)\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.389, + 0.826, + 0.407 + ], + "angle": 0, + "content": "\\[\n\\mathrm {C o T} _ {S} = \\mathcal {R} \\left(\\left\\{n _ {i} \\right\\} _ {i = 1} ^ {k} | (k \\leq \\mathcal {B} _ {s}) \\wedge (j = 1 \\Leftrightarrow \\forall i \\leq k, n _ {i} \\rightarrow n _ {i + j}) \\wedge (\\forall i \\neq j \\leq k, n _ {i} \\neq n _ {j})\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.416, + 0.827, + 0.473 + ], + "angle": 0, + "content": "where \\( n_1 \\) to \\( n_k \\) represent a sequence of logical nodes, which naturally satisfy that \\( \\forall i, n_i \\to n_{i+1} \\). Here, \\( \\mathcal{B}_s \\) denotes the upper boundary on the number of logical nodes, as defined by Chen et al. [90]. In this paradigm, the reasoning progresses sequentially from one node to the next, with minimal revisitation of previous nodes and little exploration of alternative logical paths." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.492, + 0.375, + 0.507 + ], + "angle": 0, + "content": "2.2 Overview of Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.519, + 0.827, + 0.589 + ], + "angle": 0, + "content": "In contrast, Long CoT involves deeper reasoning, reflective analysis, and a broader exploration of logical structures. It facilitates reasoning across a wider range of logical steps, addressing both known and unknown elements of a problem [194, 858]. Building on this, Long CoT expands upon the constraints presented in Equation 1 based on tree structures by incorporating three critical components: deep reasoning, exploration, and reflection." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.595, + 0.827, + 0.706 + ], + "angle": 0, + "content": "These components play distinct yet complementary roles in enhancing cognitive processes. Deep reasoning ensures each logical step is executed rigorously, even within complex structures, fostering robust logic across intricate relationships. Exploration encourages the identification of new pathways, revealing potential avenues that may not be immediately obvious. Reflection enables iterative analysis and reassessment of conclusions, allowing reasoning to evolve throughout problem-solving. By distinguishing these three categories, Long CoT enhances its ability to address a broader range of problems with precision and depth. As shown in Figure 3, we will now discuss these key differences in detail." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.724, + 0.439, + 0.74 + ], + "angle": 0, + "content": "2.2.1 Deep Reasoning for Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.75, + 0.828, + 0.82 + ], + "angle": 0, + "content": "As shown by Figure 2, deep reasoning refers to the capability to perform deep and thorough logical analysis across multiple interconnected logical nodes, where Short CoT generally can never achieve. This capability is essential when tackling complex problems that require a massive number of logical deductions to arrive at a valid conclusion. To better define and understand deep reasoning, we frame it as a capability that primarily relaxes the first constraint in Equation 1, as expressed by the following:" + }, + { + "type": "equation", + "bbox": [ + 0.393, + 0.83, + 0.825, + 0.845 + ], + "angle": 0, + "content": "\\[\nk \\leq \\mathcal {B} _ {s} \\mapsto k \\leq \\mathcal {B} _ {l} \\wedge \\mathcal {B} _ {s} \\ll \\mathcal {B} _ {l}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.856, + 0.826, + 0.913 + ], + "angle": 0, + "content": "where \\(\\mathcal{B}_l\\) represents the upper boundary for Long CoT reasoning, which can accommodate much more intricate logical nodes compared to the smaller boundary \\(\\mathcal{B}_s\\) for Short CoT. The larger boundary \\(\\mathcal{B}_l\\) alleviates issues related to insufficient depth in reasoning, thereby reducing the risk of generating unresolved answers or hallucinated responses in short-form reasoning." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.505, + 0.948 + ], + "angle": 0, + "content": "4" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.042, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.066 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.066, + 0.306, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "image", + "bbox": [ + 0.174, + 0.079, + 0.833, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.545, + 0.825, + 0.574 + ], + "angle": 0, + "content": "Figure 3: Taxonomy of Long CoT, which includes deep reasoning, feasible reflection, and extensive exploration methodologies." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.605, + 0.431, + 0.621 + ], + "angle": 0, + "content": "Key Difference: Reasoning Depth" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.628, + 0.801, + 0.657 + ], + "angle": 0, + "content": "- Short CoT typically addresses a limited set of logical nodes, involving shallow reasoning, and struggles with problems requiring complex or intricate logical structures." + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.659, + 0.801, + 0.689 + ], + "angle": 0, + "content": "- Long CoT is designed to accommodate a significantly larger set of logical nodes, allowing for deeper logic and more thorough analysis during the reasoning process." + }, + { + "type": "list", + "bbox": [ + 0.2, + 0.628, + 0.801, + 0.689 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.716, + 0.48, + 0.731 + ], + "angle": 0, + "content": "2.2.2 Extensive Exploration for Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.742, + 0.825, + 0.824 + ], + "angle": 0, + "content": "As shown by Figure 2, Long CoT encourages branching out to extensively explore uncertain or unknown logical nodes, thereby expanding the potential set of reasoning paths. This exploration is particularly critical when solving problems characterized by ambiguity, incomplete information, or multiple possible solutions [43, 1016, 871]. More specifically, we describe how extensive exploration primarily addresses the relaxation of the second constraint in Equation 1, which can be formalized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.292, + 0.831, + 0.825, + 0.848 + ], + "angle": 0, + "content": "\\[\nj = 1 \\Leftrightarrow \\forall i \\leq k, n _ {i} \\rightarrow n _ {i + j} \\mapsto \\exists m, \\forall i, \\forall j \\leq m, n _ {i} \\rightarrow n _ {i + j}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.856, + 0.825, + 0.913 + ], + "angle": 0, + "content": "where the condition indicates that for a logical node \\( n_i \\), there are \\( m \\) nodes that are explored in parallel. The acceptability of parallel exploration allows for a more systematic approach, enabling the exploration of previously unconsidered logical paths. This, in turn, helps maximize the understanding of all possible solutions, ultimately leading to the correct final answer." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.504, + 0.948 + ], + "angle": 0, + "content": "5" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.042, + 0.226, + 0.071 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.307, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.092, + 0.513, + 0.107 + ], + "angle": 0, + "content": "Key Difference: Exploration of Logical Nodes" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.115, + 0.798, + 0.144 + ], + "angle": 0, + "content": "- Short CoT generally restricts exploration to a fixed set of logical nodes, often resulting in oversimplified reasoning and limited exploration." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.147, + 0.798, + 0.176 + ], + "angle": 0, + "content": "- Long CoT explores more various paths, including uncertain or uncharted areas, fostering more nuanced and comprehensive problem-solving." + }, + { + "type": "list", + "bbox": [ + 0.2, + 0.115, + 0.798, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.199, + 0.456, + 0.215 + ], + "angle": 0, + "content": "2.2.3 Feasible Reflection for Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.224, + 0.825, + 0.294 + ], + "angle": 0, + "content": "As shown by Figure 2, Long CoT involves revisiting previous logical nodes to verify their connections are valid and accurate, and then correcting them or selecting an alternative logical path. Formally, feasible reflection relaxes the third constraint in Equation 1, which originally requires acyclic reasoning such that \\( n_i \\neq n_j \\) for all \\( i \\neq j \\leq k \\). In contrast, feasible reflection permits the reasoning path to return to a previously visited node, captured as:" + }, + { + "type": "equation", + "bbox": [ + 0.343, + 0.302, + 0.826, + 0.319 + ], + "angle": 0, + "content": "\\[\n\\forall i \\neq j \\leq k, n _ {i} \\neq n _ {j} \\mapsto \\exists i < j \\leq k, n _ {i} = n _ {j}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.326, + 0.825, + 0.37 + ], + "angle": 0, + "content": "where this condition indicates that, for a logical node \\( n_{j-1} \\), the subsequent node is not limited to the original next node \\( \\hat{n}_j \\). Instead, it may transition to \\( n_i \\) (i.e., the next logical node becomes \\( n_j \\), where \\( n_j = n_i \\)). Practically, reflection implementation consists of two components:" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.38, + 0.826, + 0.463 + ], + "angle": 0, + "content": "Feedback refers to evaluating both overall and intermediate outputs for correctness and quality, also known as critique or verification. It can be derived from external sources, validation checks, or by reflecting on prior conclusions within the reasoning process. Formally, at each step \\( n_i \\), a verification process \\( \\mathcal{V}_i \\) ensures the correctness, feasibility, and consistency of the reasoning. If an issue is identified, the process redirects \\( n_i \\) to the nearest correct node \\( n_j \\), where \\( j < i \\). This relationship is formalized as:" + }, + { + "type": "equation", + "bbox": [ + 0.405, + 0.464, + 0.825, + 0.481 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} _ {i}, n _ {j} \\leftarrow \\operatorname {F e e d b a c k} \\left(\\mathrm {C o T} _ {L} ^ {i}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.486, + 0.825, + 0.515 + ], + "angle": 0, + "content": "where \\(\\mathrm{CoT}_L^i = \\{n_1,\\dots ,n_i\\}\\) represents the current logical path up to the \\(i\\) -th logical node for Long CoT." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.526, + 0.827, + 0.567 + ], + "angle": 0, + "content": "Refinement involves adjusting intermediate steps or modifying the logical flow to correct inconsistencies or address gaps based on the given feedback. This process can be expressed mathematically as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.374, + 0.568, + 0.825, + 0.585 + ], + "angle": 0, + "content": "\\[\n\\widetilde {n} _ {i + 1} \\leftarrow \\operatorname {R e f i n e} \\left(n _ {i + 1} \\mid \\mathrm {C o T} _ {L} ^ {i}, \\mathcal {F} _ {i}, n _ {j}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.589, + 0.825, + 0.619 + ], + "angle": 0, + "content": "where \\(\\widetilde{n}_{i+1}\\) represents the refined version of the subsequent logical node \\(n_{i+1}\\), according to the current logic \\(\\mathbb{C} \\circ \\mathbb{T}_L^i\\), feedback result \\(\\mathcal{F}_i\\), and previous logical node \\(n_j\\)." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.624, + 0.826, + 0.667 + ], + "angle": 0, + "content": "Overall, incorporating reflection ensures that errors are identified and corrected promptly. This capability enables LLMs to quickly shift to alternative reasoning paths or correct their current trajectory. By doing so, error propagation is minimized, resulting in more accurate conclusions." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.676, + 0.476, + 0.691 + ], + "angle": 0, + "content": "Key Difference: Feedback & Refinement" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.699, + 0.798, + 0.729 + ], + "angle": 0, + "content": "- Short CoT typically moves in a straightforward, non-repetitive manner from one node to the next, so that cannot correct their logic." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.731, + 0.8, + 0.76 + ], + "angle": 0, + "content": "- Long CoT allows for revisiting and revising earlier decisions by feedback and refinement, ensuring that estimizable and prior logical conclusions during the reasoning progress." + }, + { + "type": "list", + "bbox": [ + 0.201, + 0.699, + 0.8, + 0.76 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.784, + 0.695, + 0.799 + ], + "angle": 0, + "content": "2.2.4 Unified Application and Development History of Three Capabilities" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.808, + 0.826, + 0.864 + ], + "angle": 0, + "content": "The Long CoT discussed here represents a unified reasoning system that seamlessly integrates and applies three key capabilities: deep reasoning, reflective mechanisms, and exploration capabilities. In contrast, during the Short CoT era, these capabilities developed independently, each evolving in isolation." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.87, + 0.826, + 0.913 + ], + "angle": 0, + "content": "As shown in Figure 2, early efforts primarily focused on enhancing deep reasoning within traditional CoT paradigms. This was followed by the gradual introduction of reflective mechanisms, which were initially based on human-designed pipelines. Over time, exploration capabilities were added, and" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.937, + 0.505, + 0.948 + ], + "angle": 0, + "content": "6" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.235, + 0.068, + 0.301, + 0.071 + ], + "angle": 0, + "content": "REASONING GROU" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.825, + 0.121 + ], + "angle": 0, + "content": "these components were ultimately merged, giving rise to the modern concept of Long CoT, a unified approach to reasoning that seeks to enhance all three capabilities in harmony." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.127, + 0.827, + 0.239 + ], + "angle": 0, + "content": "The progression of Long CoT is gradual, rather than a sudden emergence through isolated models like o1 [307] and R1 [227]. Instead, it develops gradually. For example, earlier systems, such as ToT [955], enhance exploration but lack reflective mechanisms, disqualifying them as Long CoT [95]. While GoT [48] incorporates self-reflection based on ToT, its original model still lacked robust deep reasoning, preventing it from qualifying as Long CoT at that time. It is also notable that modern Long CoT systems, often neglect earlier technologies. This article addresses this gap by tracing the evolution of each capability, with the final section offering a comprehensive analysis of the integrated Long CoT system." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.244, + 0.828, + 0.301 + ], + "angle": 0, + "content": "In summary, Long CoT and Short CoT represent distinct paradigms. Long CoT features a deeper, broader, and more reflective reasoning process, enhancing both accuracy and coherence. Short CoT, by contrast, is better suited to simpler, well-defined problems. This distinction highlights the scalability and adaptability of Long CoT, making it particularly effective for more complex reasoning." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.309, + 0.592, + 0.325 + ], + "angle": 0, + "content": "Key Difference: Unified Application of Three Capabilities" + }, + { + "type": "text", + "bbox": [ + 0.196, + 0.33, + 0.801, + 0.373 + ], + "angle": 0, + "content": "It is important to highlight that Long CoT integrates these three distinct capabilities to perform complex reasoning. In contrast, traditional Short CoT optimization typically focuses on only one of these characteristics." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.398, + 0.485, + 0.416 + ], + "angle": 0, + "content": "3 Long CoT Analysis & Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.429, + 0.48, + 0.445 + ], + "angle": 0, + "content": "3.1 Analysis & Explanation for Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.455, + 0.827, + 0.538 + ], + "angle": 0, + "content": "Research on Long CoT has significantly enhanced RLLMs by improving reasoning accuracy, reducing errors, and supporting dynamic decision-making. However, several phenomena and their corresponding mechanisms remain inadequately summarized. This section addresses key topics, including the mechanisms of Long CoT and their underlying principles [644, 63, 545, 642]. Methodologically, two main perspectives have emerged to explain Long CoT: (1) External Behavior Analysis (§ 3.1.1) and (2) Internal Mechanism Analysis (§ 3.1.2)." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.552, + 0.492, + 0.567 + ], + "angle": 0, + "content": "3.1.1 Long CoT External Behavior Analysis" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.576, + 0.825, + 0.606 + ], + "angle": 0, + "content": "The primary research stream focuses on explaining RLLM behaviors for Long CoT [25]. As illustrated in Figure 4, six key phenomena are identified and discussed for Long CoT in this part." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.615, + 0.827, + 0.755 + ], + "angle": 0, + "content": "Long CoT Emergence Phenomenon Research shows that contextual examples improve large models' generative abilities by guiding the formation of reasoning chains [1012, 671, 417, 343, 532, 846, 1017, 1141]. Wang et al. [759] and Lippmann and Yang [461] demonstrate that these examples standardize reasoning chain generation relevant to the answers both in in-context-learning and supervised-finetuning. In an experiment by Madaan et al. [538], removing problem-specific entities from contextual examples, while retaining only the logical structure, led to similar performance as using complete examples, highlighting the logical structure imitation of Long CoT during inference. From a learning perspective, Ye et al. [963] analyzes and reveals the three-stage developmental trajectory of Long CoT: early memorization, followed by in-distribution generalization, and ultimately cross-distribution generalization, thereby enabling the model to exhibit Long CoT capabilities." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.76, + 0.829, + 0.913 + ], + "angle": 0, + "content": "More recently, Stechly et al. [688] and Wang and Zhou [815] have shown that modifying the decoding process or designing specific prompts can activate the Long CoT within pre-trained models. They propose that CoT is embedded during pre-training and requires specific activation [941]. Further, Sadr et al. [642] focus the Long CoT source from the training data, and build on this with the notion of \"model attribution\", to specifically identify the training data most influential for specific outputs. Building on this, Guo et al. [227] and Xie et al. [886] investigate using rule-based reinforcement learning to directly activate Long CoT during pre-training, aiming to enhance performance [881]. Furthermore, Gandhi et al. [194] identify four key cognitive behaviors, including verification, backtracking, sub-target setting, and backward chaining, which successfully facilitate Long CoT. Qwen series models [926] inherently demonstrate these behaviors, which can be easily triggered by rule-based reinforcement. In contrast, the models of Llama series [168] lack these" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.505, + 0.947 + ], + "angle": 0, + "content": "7" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.233, + 0.06, + 0.307, + 0.066 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.233, + 0.066, + 0.306, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.09, + 0.339, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.091, + 0.475, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.481, + 0.091, + 0.657, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.091, + 0.815, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.251, + 0.828, + 0.335 + ], + "angle": 0, + "content": "Figure 4: Analysis of the six classic phenomena of Long CoT external behavior: (a) emergence of Long CoT in current RLLMs; (b) reasoning boundaries and limitations of current Long CoT systems; (c) overthinking caused by scaling beyond RLLMs' reasoning boundaries, leading to performance decay; (d) inference-time scaling, discussing mainstream scaling methods, corresponding scaling laws and their limitations; (e) use of process reward model (PRM) or outcome reward model (ORM); (f) exploration of the \"aha\" moment and its underlying causes." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.368, + 0.825, + 0.438 + ], + "angle": 0, + "content": "capabilities and thus requires example-based reinforcement learning to improve significantly [65]. Moreover, Wang et al. [812] identify a pretraining scaling law that explains how increasing calculation size in RLLMs enhances their reasoning capabilities. Wang et al. [796] further explore the scaling law of Long CoT, showing that more fine-grained Long CoT granularity leads to more efficient and effective generalization performance." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.455, + 0.827, + 0.593 + ], + "angle": 0, + "content": "Reasoning Boundary Phenomenon Recent research has highlighted the upper bounds and limitations of RLLMs across various reasoning tasks [303, 283, 684, 261, 185, 252]. Specifically, Bi et al. [53] investigate these bounds in code generation, showing that RLLMs struggle with tasks that exceed certain complexity thresholds [600], especially when imitating Long CoT samples of varying complexity. In the context of upper-bound performance, Merrill and Sabharwal [548] and Li et al. [430] focus on single-step arithmetic tasks, concluding that model performance is constrained by input length. Moreover, Feng et al. [177] proposes a mathematical model indicating that fixed-size models cannot produce accurate numerical answers beyond specific limits. However, increasing the number of reasoning steps improves a model's capability requirements to solve more complex problems." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.6, + 0.827, + 0.753 + ], + "angle": 0, + "content": "Inspired by these explorations, Chen et al. [90] first define the \"reasoning boundary\" phenomenon and quantify these limits, showing that surpassing an RLLM's reasoning capacity leads to performance decline [92]. Similarly, Zhou et al. [1130] introduce GSM-Infinite, linking different upper limits to accuracy levels. Chen et al. [90] also examine the interaction between these boundaries across tasks of varying complexity, providing insights into the effectiveness of Long CoT strategies [1085]. Moreover, Amiri et al. [12] propose a \"tight lower bound\" for Long CoT further guiding reasoning error reductions. Further, Baeumel et al. [28] suggest that due to its reliance on a single-digit lookahead heuristic, there are inherent boundaries in performing addition with multiple operands, which thus hinders the fundamental limitation of LLMs in scaling to more complex numerical reasoning. Liu et al. [483] further investigate the role of reinforcement learning in expanding these reasoning boundaries instead of relying solely on pretraining capabilities." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.773, + 0.827, + 0.913 + ], + "angle": 0, + "content": "Overthinking Phenomenon Research has highlighted the overthinking phenomenon [103, 330, 574, 142, 357, 595], where performance improves with longer reasoning chains up to a threshold, after which it declines. In contrast, Xie et al. [886] and Ma et al. [534] find no significant correlation between reasoning length and accuracy. To explain this, one line of research suggests that Long CoT strategies [21, 441], like avoiding \"snowball errors\" [192]. Alternatively, Chen et al. [90], Wolf et al. [851] highlight a performance drop when the reasoning boundaries are exceeded, providing an explanation for the overthinking phenomenon. This suggests that reasoning length and logical complexity should be kept below a certain boundary [1080]. Building on this, Wu et al. [867] mathematically determine the feasible reasoning length for Long CoT. Finally, Chen et al. [93] introduces Ohm's law of Long CoT, which accurately predicts and controls performance." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.504, + 0.948 + ], + "angle": 0, + "content": "8" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.092, + 0.828, + 0.176 + ], + "angle": 0, + "content": "Inference-Time Scaling Phenomenon Recent advances in inference-time scaling algorithms [524, 843] have garnered significant attention, particularly for their ability to extend reasoning length and improve performance [524, 455, 875]. Specifically, Brown et al. [57] identify a phenomenon called \"Large Language Monkeys\", in which a series of reasoning tasks show that with enough trials, a correct result can be achieved. Additionally, o1 [307] and R1 [227] demonstrated that directly scaling the length of model inference improves final performance." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.182, + 0.828, + 0.394 + ], + "angle": 0, + "content": "To understand inference-time scaling, we will discuss these two paradigms: (1) Sequential Scaling: Sequential scaling involves increasing the reasoning path length. While this can enhance performance, studies by Jin et al. [330] show that, beyond a certain point, longer reasoning paths can degrade performance due to error accumulation. They suggest an optimal path length that depends on the model's capabilities and task complexity [15, 652, 31]. Furthermore, Chen et al. [90] and Wu et al. [867] explain that excessive exploration lengths beyond the RLLM's inherent reasoning boundary lead to performance decay, which guides RLLMs for deeper reasoning capabilities [32]. (2) Parallel Scaling: Parallel scaling involves performing multiple reasoning steps and verifying the results. While it shows promise, Parashar et al. [583] and Wang et al. [820] argue that simply increasing inference time does not guarantee improved performance. Wu et al. [864] show that the computational FLOPs \\( N \\) of inference are correlated with the lower bound of performance error, which scales with \\( \\log N \\). Additionally, Chen et al. [93] establish an upper bound for parallel scaling, showing that RLLMs cannot exceed Pass@k verification through various verifiers. They further argue that sampling optimization cannot exceed the model's internal reasoning limitations, demonstrating that for \\( N \\) samples, accuracy is proportional to \\( \\frac{m}{(k / \\log N + b)^2} \\), where \\( m \\), \\( n \\), and \\( b \\) are model-dependent constants." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.403, + 0.828, + 0.639 + ], + "angle": 0, + "content": "PRM & ORM Selection Phenomenon As RLLMs evolve, it is crucial to navigate the debate around the selection between process supervision and outcome supervision, two key reinforcement learning paradigms for complex reasoning tasks. The phenomenon of choosing between these two approaches has become a pivotal issue, as it is essential to differentiate and decide which supervision strategy is more suitable for specific tasks [899, 187, 1059]. While process supervision is intuitively advantageous for long-term reward assignments, the exact relationship between the two approaches remains unclear. It is commonly believed that process supervision is more challenging due to the trajectory-level coverage problem, which demands significant effort to collect fine-grained supervision data [1102, 679]. Additionally, PRM faces the issue of reward hacking [13, 152, 573, 30, 399], where agents exploit flaws in the reward function to produce unintended behaviors [227]. Addressing this to surpass rule-based reward systems has become an important research area [227, 886, 594]. Furthermore, Lampinen et al. [368] and Tan [708] establish a causal link between intermediate steps and final answers in qualitative experiments. Building on this, Jia et al. [317] demonstrate that, under the standard data coverage assumption, reinforcement learning with outcome supervision is not statistically more challenging than process supervision, aside from polynomial factors. More strictly, He et al. [247] mathematically demonstrate that outcome-level rewards suffice for online reinforcement learning in RLLMs." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.648, + 0.828, + 0.858 + ], + "angle": 0, + "content": "Aha Moment Phenomenon Earlier, Guo et al. [227] demonstrated that direct RL using rule-based rewards can trigger the aha moment, fostering natural self-reflection without supervision [172]. Following this, Team [721], Xie et al. [886] replicate this phenomenon. Further, Zhou et al. [1119] and Meng et al. [547] further extend this phenomenon to multimodal scenarios. However, Liu et al. [498] argue that the aha moment may not emerge in R1-Zero-like training. Instead, they observe that self-reflection patterns, such as superficial self-reflection (SSR), appear at epoch 0, the stage of base models. In this case, self-reflections do not necessarily lead to correct answers. Upon closer examination of R1-Zero training via RL, they find that the increasing response length results not from self-reflection, but from RL optimizing well-designed rule-based rewards. Moreover, Yang et al. [939] demonstrate that the \"aha moment\" is externally marked by increased use of anthropomorphic language during self-reflection and a dynamic adjustment of uncertainty in response to problem difficulty. This process enables the model to maintain reasoning without succumbing to \"Reasoning Collapse.\" Internally, it is characterized by a clear distinction between anthropomorphic traits and logical reasoning, with anthropomorphic language intensifying as the problem becomes more complex." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.87, + 0.826, + 0.914 + ], + "angle": 0, + "content": "Reinforcement Learning Entropy Phenomenon In reinforcement learning for Long CoT, the entropy mechanism is a crucial factor influencing the performance of RLLMs. Policy entropy measures the diversity and exploratory strength of a model's outputs. By managing this entropy" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.936, + 0.506, + 0.948 + ], + "angle": 0, + "content": "9" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.092, + 0.828, + 0.218 + ], + "angle": 0, + "content": "effectively, a model preserves exploration and thus excels on complex reasoning tasks. Earlier, Jang and Kim [310] investigate how initial entropy affects exploration in deep RL and proposed an entropy-aware initialization to encourage effective exploration. Building on this, Zhang et al. [1036] developed an Entropy-Regularized PRM that balances policy updates against large deviations from the starting distribution, thereby improving reasoning. Cheng et al. [116] found that high-entropy regions correlate positively with three exploratory reasoning behaviors: (1) key tokens linking logical steps, (2) self-verification and correction, and (3) rare behaviors underrepresented in the base model. Most recently, Agarwal et al. [5] introduced an Entropy Minimization method and demonstrated its strong impact on LLM performance in mathematical, physical, and coding tasks." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.223, + 0.828, + 0.349 + ], + "angle": 0, + "content": "However, recent research indicates that, during early training, policy entropy declines sharply, causing the model to converge prematurely on specific output patterns and limiting further reasoning improvement [144]. In reinforcement learning, policy entropy \\((H)\\) and downstream task performance \\((R)\\) follow an exponential relation: \\(R = -a\\cdot e^{H} + b\\), so a drop in entropy produces a rapid performance decline until saturation. This \"policy entropy collapse\" is common without entropy control, as reduced entropy constrains exploration and stalls reasoning gains [144]. To counter this collapse, two methods, Clip-Cov and KL-Cov, regulate entropy by constraining updates on high-covariance tokens. Clip-Cov clips their update magnitudes, whereas KL-Cov imposes a Kullback-Leibler penalty. Empirical results show both techniques prevent collapse and enhance reasoning performance [144]." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.364, + 0.506, + 0.379 + ], + "angle": 0, + "content": "3.1.2 Long CoT Internal Mechanism Analysis" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.388, + 0.816, + 0.404 + ], + "angle": 0, + "content": "The second stream of research investigates the internal mechanisms of Long CoT-related RLLMs." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.416, + 0.827, + 0.583 + ], + "angle": 0, + "content": "Reasoning Internal Mechanism Recent studies have explored the internal mechanisms underlying the coherent rationale outputs of Long CoT, with particular emphasis on attention mechanisms [675, 632]. These studies primarily examine neural substructures in RLLMs, framing CoT reasoning from a white-box perspective [819, 992, 233, 169]. Weston and Sukhbaatar [849] introduces the concept of System 2 Attention (S2A), which demonstrates Long CoT generation by selectively focusing attention on relevant information. Additionally, Li et al. [407] explore gradient distributions between direct output and Long CoT layers, revealing that Long CoT layers help maintain stability by distinguishing relevant from irrelevant reasoning [840]. Finally, Zhang et al. [1068] conceptualize RLLMs as finite state automata, offering further insight into how internal dynamics influence external behavior. Despite Short CoT's struggles with self-correction, Bertolazzi et al. [47] show that these models rely on consistency heads (attention heads) to assess the alignment of numerical values in arithmetic solutions through internal shortcuts." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.594, + 0.828, + 0.777 + ], + "angle": 0, + "content": "Knowledge Incorporating Mechanism Current RLLMs primarily focus on mathematics and coding but have shown potential for generalization to other knowledge-rich domains, sparking growing interest in the mechanism for integrating domain-specific knowledge into Long CoT [860, 886, 1105]. Prystawski et al. [609] suggest that generative models store entity knowledge learned during pre-training independently, with the reasoning process in Long CoT linking this knowledge across entities. Radha and Goktas [630] recently introduced the Probabilistic Mixture Model (PMM), which categorizes model outputs into reasoning, memorization, and guessing. They also propose an Information-Theoretic Consistency (ITC) analysis to quantify the relationship between model confidence and strategy selection. Additionally, Jin et al. [331] define \"Concept Depth\" as the lowest layers at which complex concepts are understood, demonstrating varying levels of knowledge integration in RLLMs. Ou et al. [572] examine RLLM knowledge internalization through knowledge loop evolution, arguing that new knowledge acquisition is shaped by its connection to existing knowledge, with the loop evolving from formation to optimization and from shallow to deep." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.792, + 0.373, + 0.807 + ], + "angle": 0, + "content": "3.2 Long CoT Evaluations" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.818, + 0.281, + 0.832 + ], + "angle": 0, + "content": "3.2.1 Metrics" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.843, + 0.826, + 0.913 + ], + "angle": 0, + "content": "In benchmarking, various metrics assess model performance across reasoning tasks, each focusing on different aspects of reasoning ability. These metrics evaluate both RLLMs' effectiveness in achieving desired outcomes and their learning efficiency. As a result, metrics for RLLMs have gained increasing attention in recent research. For mathematical or code-related tasks, three key metrics are commonly used: Accuracy, Pass@k, and Cons@k based on regex extraction:" + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "10" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.093, + 0.556, + 0.107 + ], + "angle": 0, + "content": "Accuracy measures the proportion of correct outputs." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.109, + 0.806, + 0.123 + ], + "angle": 0, + "content": "- Pass@k evaluates the likelihood of generating at least one correct solution within \\( k \\) attempts." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.125, + 0.825, + 0.154 + ], + "angle": 0, + "content": "- Cons@k assesses consistency by determining the model's ability to consistently produce correct or logically coherent solutions across multiple attempts." + }, + { + "type": "list", + "bbox": [ + 0.175, + 0.093, + 0.825, + 0.154 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.159, + 0.826, + 0.202 + ], + "angle": 0, + "content": "In scientific or commonsense question-answering tasks, evaluation often uses Exact Match (EM) and Accuracy based on regex extraction, where EM determines whether the model's output exactly matches the expected solution." + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.207, + 0.783, + 0.222 + ], + "angle": 0, + "content": "For feedback techniques like ORM or PRM, Rank and Best-of-N metrics are often used:" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.228, + 0.825, + 0.255 + ], + "angle": 0, + "content": "- Rank measures whether the reward model correctly prioritizes the best reasoning processes from the top \\( k \\) candidates." + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.258, + 0.826, + 0.286 + ], + "angle": 0, + "content": "- Best-of-N selects the highest-scoring solution from \\( N \\) generated reasoning trajectories, indirectly measuring the reward model's effectiveness based on final outcomes." + }, + { + "type": "list", + "bbox": [ + 0.174, + 0.228, + 0.826, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.303, + 0.365, + 0.318 + ], + "angle": 0, + "content": "3.2.2 Decoding Strategies" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.327, + 0.825, + 0.398 + ], + "angle": 0, + "content": "Decoding strategies are essential for controlling the inference process. Common approaches include Greedy Decoding, Beam Search, and Major@k. Both Greedy Decoding and Beam Search limit the sampling range to reduce randomness, guiding the model toward more consistent outputs. In contrast, Major@k identifies the most reliable solution by selecting the one with the highest consistency from a set of \\( k \\) candidate solutions." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.414, + 0.315, + 0.428 + ], + "angle": 0, + "content": "3.2.3 Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.438, + 0.825, + 0.495 + ], + "angle": 0, + "content": "In the realm of Benchmarks, the focus lies on assessing the reasoning capabilities of RLLMs across diverse domains. There are two primary categories: (1) Outcome Benchmarks, which focus on the holistic view of Long CoT reasoning, and (2) Process Benchmarks, which concentrate on the local view of the Long CoT process or individual capabilities." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.507, + 0.825, + 0.536 + ], + "angle": 0, + "content": "Outcome Benchmarks In the realm of Outcome Benchmarks, the first focus lies on evaluating the logical reasoning capabilities:" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.543, + 0.827, + 0.653 + ], + "angle": 0, + "content": "- Complex Mathematics: A central focus in complex mathematics is evaluating benchmarks like GSM8K [141] and MATH [253], which assess basic mathematical problem-solving abilities [1125, 1112]. Recent additions, such as AIME 2024 [8], AIME 2025 [571], MATH-500 [449], AMC 2023 [9], USAMO [598], OlympiadBench [239], and OlympiadArena [298], expand the evaluation of LLM performance in mathematics. Moreover, Putnam-AXIOM [224] and FrontierMath [210] introduce more complex problems that challenge future reasoning systems. Additionally, ThinkBench [291] and MATH-Perturb [288] focus on robust evaluation for Long CoT [38, 987]." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.657, + 0.827, + 0.74 + ], + "angle": 0, + "content": "- Complex Coding: Complex coding benchmarks are also vital, with competitions like Codeforces, SWEbench [327], CodeContests [427], and LiveCodeBench [309] evaluating LLM coding and problem-solving skills. Notable additions such as MHPP [148], ProBench [934], HumanEval Pro, MBPP Pro [993], and EquiBench [833] enhance the scope and complexity of coding challenges. Moreover, some studies have explored applying these benchmarks in real-world code development scenarios for automatic code generation and evaluation [243, 744]." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.744, + 0.827, + 0.828 + ], + "angle": 0, + "content": "- Commonsense Puzzle: Commonsense puzzle benchmarks, including LiveBench [850], BIG-Bench Hard [705] and ZebraLogic [450], assess models' ability to reason about commonsense situations. The ARC [131] and DRE-Bench [947] is often viewed as a challenging commonsense-based AGI test. JustLogic [87] further contributes to the evaluation of deductive reasoning and commonsense problem-solving. Moreover, Li et al. [382] introduce QuestBench, a benchmark designed to evaluate the ability of RLLMs to generate insightful and meaningful questions." + }, + { + "type": "list", + "bbox": [ + 0.175, + 0.543, + 0.827, + 0.828 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.834, + 0.825, + 0.864 + ], + "angle": 0, + "content": "The second focus area concerns Knowledge Benchmarks, essential for evaluating a model's capability in complex reasoning across various tasks for out of distribution evaluation [776]:" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.87, + 0.827, + 0.913 + ], + "angle": 0, + "content": "- Scientific Reasoning: Scientific Reasoning benchmarks, such as GPQA Diamond [637], MMLU-Pro [821], and SuperGPQA [165], assess multi-domain reasoning in fields like chemistry, biology, and physics [157]. These benchmarks test models' ability to not only accumulate knowledge" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.507, + 0.948 + ], + "angle": 0, + "content": "11" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.092, + 0.825, + 0.146 + ], + "angle": 0, + "content": "but also integrate it for problem-solving. Humanity's Last Exam (HLE) [602] further challenges models by requiring deep interdisciplinary reasoning across scientific disciplines. Further, Chung et al. [140] propose TPBench to evaluate the effectiveness of RLLMs in solving theoretical physics problems." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.15, + 0.828, + 0.262 + ], + "angle": 0, + "content": "- Medical Reasoning: In the realm of Medical Reasoning, the need for complex, domain-specific, and accurate reasoning is paramount [1094, 1024, 905, 589]. Benchmarks, such as MedQA [328], JAMA Clinical Challenge [76], LLMEval-Med [1049] and Medbullets [76], simulate diagnostic and treatment decision-making processes, reflecting real-world medical practice. These benchmarks evaluate a model's handling of medical knowledge and reasoning, from diagnosis to treatment planning. Additionally, MedXpertQA [1150] introduces a comprehensive evaluation framework combining text and multimodal data, specifically assessing AI's reasoning capabilities in healthcare." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.279, + 0.367, + 0.294 + ], + "angle": 0, + "content": "3.2.4 Process Evaluations" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.304, + 0.827, + 0.403 + ], + "angle": 0, + "content": "Deep Reasoning Benchmarks Recent progress in RLLMs underscores the need for specialized benchmarks to evaluate their deep reasoning abilities in Long CoT [375, 1133]. Notably, Lin et al. [450] introduces ZebraLogic, a framework for assessing logical reasoning, especially in complex non-monotonic scenarios. Similarly, BigGSM [90] and GSM-Ranges [670] focus on perturbing numerical values to test logical and arithmetic reasoning in edge cases beyond the models' training distribution. ROSCOE [212], ReCEval [606], DiVeRSe [425], HLV [71], and CoT-Kinetics [51] are designed to assess each step in the deep reasoning process during Long CoT tasks." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.415, + 0.828, + 0.502 + ], + "angle": 0, + "content": "Exploration Benchmarks Several studies assess RLLMs' exploration capabilities in Long CoT tasks. Specifically, Sys2Bench [583] evaluates the exploration and scaling abilities of RLLMs, emphasizing generalization across diverse tasks. BanditBench [566] extends this by testing model performance in interactive environments, offering insights into practical applications. Additionally, Heyman and Zylberberg [254] introduce a graph coloring problem to assess reasoning and spatial exploration in complex problem-solving scenarios." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.513, + 0.829, + 0.709 + ], + "angle": 0, + "content": "Reflection Benchmarks Reflection benchmarks measure RLLMs' ability to identify, reflect upon, and correct errors in Long CoT reasoning. These benchmarks fall into two categories: feedback and refinement. (1) Feedback Benchmark: These benchmarks assess the ability of LLMs to detect errors and respond to feedback for improvement. For example, Lambert et al. [367] introduces RewardBench to evaluate RLLMs' reward capabilities. This framework is extended by Multimodal RewardBench[960], and CodeCriticBench [1025] to include multimodal and code contexts, respectively. Benchmarks such as ProcessBench [1102], PRMBench [679], MR-Ben [1021], and DeltaBench [250] focus on error detection and correction across various tasks at the step level. Additionally, RealL Mistake [337] and JudgeBench [709] address more real-world error evaluation. (2) Refinement Benchmark: These benchmarks focus on error correction in complex tasks. CriticBench [456] assesses critique-correction capabilities, while MLDebugging [287], and ErrorRadar [922] specializes in coding or multimodal reasoning error detection and refinement. FinerReason [72] introduces a commonsense puzzle for broader feedback and refinement evaluations. Medec [1] adapts error correction to healthcare, addressing medical issues." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.721, + 0.377, + 0.735 + ], + "angle": 0, + "content": "3.2.5 Advanced Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.746, + 0.829, + 0.913 + ], + "angle": 0, + "content": "Agentic & Embodied Reasoning Agentic and Embodied reasoning requires models to demonstrate an understanding of real-world interactions, tool use, and adaptive reasoning in response to change. To assess real-world understanding, Wang et al. [798] introduce a benchmark that evaluates agents' ability to reason about physical concepts. Zhang et al. [1064] extend this by assessing agents' interactions with real-world physics. Additionally, realistic tasks often demand complex planning and tool usage, necessitating benchmarks to evaluate agent reasoning. These benchmarks assess agents' abilities to navigate and complete tasks in digital environments. Building on this, Huang et al. [283] propose a framework for evaluating decision-making in multi-agent, competitive settings. Nath et al. [562] introduce ToolComp, a benchmark designed to evaluate multi-step tool-use reasoning. To analyze adaptive reasoning in the face of real-world change, OSWorld [887], CogAgent [260], Mobile-Agent-E [828], WebShop [954], WebArena [1126], WGSR-Bench [972], and WebGames [735] assess AI systems across domains such as operating systems, mobile GUIs, browser tasks, and interactive" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "12" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.828, + 0.123 + ], + "angle": 0, + "content": "entertainment [1106, 780, 512, 552]. Hu et al. [272] present Text2World, which evaluates agents' ability to generate interactive environments from text to test agent adaptability [995]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.136, + 0.828, + 0.18 + ], + "angle": 0, + "content": "Multimodal Reasoning Multimodal reasoning refers to a system's ability to integrate and reason across diverse input types, including text, images [316]. This capability is crucial for solving complex problems that require information from diverse formats." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.186, + 0.828, + 0.257 + ], + "angle": 0, + "content": "- Complex Mathematics: Mathematical reasoning often integrates both textual and visual components, such as equations, graphs, or diagrams [921]. Specifically, challenges like MathVista [508], MathVision [782], MathVerse [1054], M3CoT-Math [91], CMMaTH [433], EnigmaEval [763], CoMT-Geometry [125], and PGPS9K [1050] aim to advance multimodal reasoning in mathematics, improving the evaluation of multimodal Long CoT logic." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.258, + 0.828, + 0.329 + ], + "angle": 0, + "content": "- Complex Code: The second area of focus involves code-related reasoning, where systems interpret textual descriptions and code snippets. Benchmarks like HumanEval-V [1035], Code-Vision [767], Plot2Code [852], and ChartMimic [931] evaluate systems' capabilities to generate or interpret code from natural language and multimodal inputs for assessing systems that integrate natural language processing with programming tasks." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.331, + 0.828, + 0.401 + ], + "angle": 0, + "content": "- **Complex Science:** This area involves integrating scientific texts with related diagrams or experimental data. Benchmarks like ScienceQA [507], M3CoT-Science [91], BMMR [874], and ScienceBoard [698] evaluate how well models combine science information with Long CoT reasoning across various scientific domains [966]. Further, Guo et al. [229] propose MolPuzzle for the evaluation of molecular structure elucidation." + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.404, + 0.828, + 0.515 + ], + "angle": 0, + "content": "- Commonsense Puzzle: This area focuses on commonsense reasoning, where systems combine reasoning cues and images to make deeper conclusions. Chen et al. [91] introduce M3CoT-Commensense, which incorporates commonsense Long CoT reasoning for complex multimodal interactions. Further, PuzzleVQA [128], MMReason [953] and LEGO-Puzzles [711] focus more on abstract and spatial puzzle reasoning, respectively. Additionally, Wang et al. [760] propose two benchmarks: Clue-Visual Question Answering (CVQA), which tests visual comprehension through three task types, and Clue of Password-Visual Question Answering (CPVQA), which features two task types focusing on the interpretation and application of visual data." + }, + { + "type": "list", + "bbox": [ + 0.175, + 0.186, + 0.828, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.531, + 0.829, + 0.645 + ], + "angle": 0, + "content": "AI for Research Recent advancements in AI have significantly advanced scientific research [94, 1124, 817, 215], with platforms like SciWorld [798] improving the research process. Simultaneously, Pricope [608] and Chan et al. [67] introduce a machine-learning platform to evaluate the potential of RLLMs in automating experiments. Several studies also examine RLLMs' ability to generate innovative research ideas. For instance, Si et al. [672] conduct evaluations with over 100 NLP researchers to assess RLLMs' creativity, revealing notable limitations [404, 856, 726]. Additionally, Li et al. [434] introduce SolutionBench, a benchmark for assessing systems' ability to generate feasible solutions for complex engineering problems." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.663, + 0.462, + 0.681 + ], + "angle": 0, + "content": "4 Deep Reasoning for Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.697, + 0.827, + 0.809 + ], + "angle": 0, + "content": "Deep reasoning capabilities primarily require profound depth and comprehensiveness in cognitive and reasoning processes. In the absence of such capabilities, RLLMs suffer significant performance declines [758, 823]. Current methods for enhancing deep reasoning can be categorized into two main approaches: (1) Deep Reasoning Format (\\(\\S\\) 4.1), which involves utilizing various reasoning execution formats to maximize the reasoning step length \\(k\\) within reasoning boundary \\(\\mathcal{B}_l\\) in Equation (2), by selecting the most suitable reasoning format; and (2) Deep Reasoning Learning (\\(\\S\\) 4.2), which focuses on improving the model's internal capabilities to enhance its deep reasoning abilities, thereby extending the reasoning boundary \\(\\mathcal{B}_l\\) in Equation (2) intrinsically." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.829, + 0.383, + 0.844 + ], + "angle": 0, + "content": "4.1 Deep Reasoning Format" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.856, + 0.826, + 0.913 + ], + "angle": 0, + "content": "As illustrated in Figure 5, deep reasoning formats can be categorized into three main types: natural language (\\(\\S\\) 4.1.1), structured language (\\(\\S\\) 4.1.2), and latent-space reasoning (\\(\\S\\) 4.1.3), the latter of which is further subdivided into token-, vector-, and manager-driven latent reasoning. The reasoning performance across these formats is presented in Table 1." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "13" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.306, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "title", + "bbox": [ + 0.187, + 0.093, + 0.398, + 0.106 + ], + "angle": 0, + "content": "(a) Natural Language Deep Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.112, + 0.483, + 0.143 + ], + "angle": 0, + "content": "To predict the output of the given input for Conway's Game of Life, we need to apply the rules of the game to each cell on the board. The rules are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.198, + 0.144, + 0.483, + 0.164 + ], + "angle": 0, + "content": "1. Any live cell with fewer than two live neighbors dies (underpopulation)..." + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.165, + 0.312, + 0.174 + ], + "angle": 0, + "content": "Given Input Board: ..." + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.175, + 0.329, + 0.184 + ], + "angle": 0, + "content": "\\(\\spadesuit\\) Step-by-Step Analysis: ..." + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.184, + 0.439, + 0.194 + ], + "angle": 0, + "content": "\\(\\spadesuit\\) Final Output: After applying the rules to each cell..." + }, + { + "type": "list", + "bbox": [ + 0.198, + 0.144, + 0.483, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.165, + 0.49, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.508, + 0.093, + 0.739, + 0.107 + ], + "angle": 0, + "content": "(b) Structured Language Deep Reasoning" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.113, + 0.538, + 0.132 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.112, + 0.694, + 0.131 + ], + "angle": 0, + "content": "import necessary packages from collections import Cou" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.132, + 0.67, + 0.141 + ], + "angle": 0, + "content": "import necessary packages" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.142, + 0.691, + 0.149 + ], + "angle": 0, + "content": "from collections import Counter" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.15, + 0.787, + 0.16 + ], + "angle": 0, + "content": "all class and function definitions in the code" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.16, + 0.585, + 0.169 + ], + "angle": 0, + "content": "file, if any" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.169, + 0.646, + 0.177 + ], + "angle": 0, + "content": "class Solution(object):" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.177, + 0.735, + 0.194 + ], + "angle": 0, + "content": "defgameOfLifeInfinite(self, live): ctr = Counter((I, J) for i, j i" + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.169, + 0.808, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.191, + 0.211, + 0.38, + 0.225 + ], + "angle": 0, + "content": "(c) Latent Space Deep Reasoning" + }, + { + "type": "image", + "bbox": [ + 0.192, + 0.226, + 0.23, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.23, + 0.226, + 0.424, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.424, + 0.209, + 0.623, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.45, + 0.291, + 0.6, + 0.309 + ], + "angle": 0, + "content": "Reasoning Vector Driven Latent Space Deep Reasoning" + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.209, + 0.813, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.65, + 0.291, + 0.785, + 0.309 + ], + "angle": 0, + "content": "Reasoning Manager Driven Latent Space Deep Reasoning" + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.319, + 0.828, + 0.361 + ], + "angle": 0, + "content": "Figure 5: Three main categories of deep reasoning formats: natural language, structured language, and latent-space reasoning (subdivided into token-, vector-, and manager-driven latent reasoning), with examples drawn from Li et al. [401]." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.39, + 0.47, + 0.405 + ], + "angle": 0, + "content": "4.1.1 Natural Language Deep Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.414, + 0.828, + 0.54 + ], + "angle": 0, + "content": "Traditionally, researchers have sought to adapt natural language for intuitive and free-flowing deep reasoning [836, 1118, 303, 617, 1070, 765, 205]. Early work by Wei et al. [836] demonstrated that the use of natural language Long CoT significantly enhances the reasoning capabilities of RLLMs. Further, the Natural Program framework [460] allows RLLMs to engage in deeper natural language reasoning by ensuring a more structured and rigorous logical analysis. More recently, CodeI/O [401] has introduced a technique that reorganizes code-based reasoning patterns into natural language formats, further boosting the reasoning potential of RLLMs [36]. Similarly, Li et al. [387] propose CoRT, which integrates code into reasoning to facilitate a mixture of formats, resulting in improved cognitive performance." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.556, + 0.492, + 0.571 + ], + "angle": 0, + "content": "4.1.2 Structured Language Deep Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.58, + 0.828, + 0.734 + ], + "angle": 0, + "content": "Structured language deep reasoning encompasses various approaches designed to program [100, 464, 687, 591, 198, 845, 830, 1044] or symbolic language [605, 158, 451, 372, 933, 604, 37, 40, 797, 380] format for enhanced deep reasoning. In this context, most studies focus on utilizing code to better enhance the mathematical reasoning capabilities [389, 107, 978, 85]. Xu et al. [897] propose a neural-symbol self-training framework guided by the environment, addressing both the scarcity of symbolic data and the limitations of symbolic processing in LLMs. Additionally, Liao et al. [443] present SKIntern, which refines symbolic RLLMs through curriculum learning and linear attenuation, enabling the internalization of symbolic knowledge with fewer examples, reducing computational costs, and accelerating inference. Furthermore, Ranaldi et al. [634] introduce QuaSAR, a CoT variant that directs LLMs to operate at higher abstraction levels through quasi-symbolic reasoning, thus improving natural language reasoning and providing more precise structural representations." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.75, + 0.434, + 0.765 + ], + "angle": 0, + "content": "4.1.3 Latent Space Deep Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.773, + 0.828, + 0.913 + ], + "angle": 0, + "content": "Latent space deep reasoning encompasses techniques designed to enhance the reasoning abilities of LLMs by leveraging operations within continuous latent spaces [684, 151, 640, 324]. These approaches can be categorized into three main paradigms: (1) Reasoning Token-Driven Latent Space Deep Reasoning: Early work [810, 1013] introduce the concept of \"planning tokens\" or \"thought tokens\" to guide reasoning within latent spaces [949, 1008]. Further, Coconut [236] expands on this through the maintenance of multiple alternative reasoning paths, increasing both complexity and efficiency [1069, 706]. At the extreme, Heima [662] condenses the entire Long CoT process into a single token, yielding substantial computational savings. (2) Reasoning Vector Driven Latent Space Deep Reasoning: Building on the previous paradigm, LTM [356] conceptualizes the layers of LLMs as \"thought blocks\" and introduces the concept of \"thought vectors\" for each layer. This" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "14" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.043, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.066 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.066, + 0.306, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "table", + "bbox": [ + 0.182, + 0.089, + 0.816, + 0.56 + ], + "angle": 0, + "content": "
ModelBase ModelGSM8kMATHGPQAOlympiadBenchLiveCodeBench
Latent Space Deep Reasoning
No-CoT [151]Mistral-7B [318]38.0----
SQ-VAE [810]Llama-2-7B [743]40.07.0---
RecurrentBlock-3.5B [204]-42.1----
ICoT-SI [151]Mistral-7B [318]51.0----
Natural Language Deep Reasoning
Self-Rewarding [114]Llama-2-7B [743]40.010.7---
Llama-3.1-8B [168]-56.720.3---
MetaMath [983]Llama-2-7B [743]66.5----
OVM [979]Llama-2-7B [743]73.7----
NuminaMath-7B-CoT [397]-75.455.2-19.9-
Qwen2-7B [925]-79.944.2-21.3-
Qwen2-Math-7B [927]-80.450.4-38.2-
Internlm2-math-plus-7B [974]-84.054.4-18.8-
OMI2 [401]Qwen2.5-Coder-7B [301]84.172.336.2-27.2
Llama-3.1-70B [168]-85.541.4---
CODEI/O++ [401]Qwen2.5-Coder-7B [301]85.772.140.6-29.1
CODEI/O [401]Qwen2.5-Coder-7B [301]86.471.943.3-28.5
WI [401]Qwen2.5-Coder-7B [301]87.071.439.1-26.0
WI (Full) [401]Qwen2.5-Coder-7B [301]87.071.142.9-27.6
OMI2 (Full) [401]Qwen2.5-Coder-7B [301]88.573.240.9-28.4
DeepSeekMath-7B-RL [658]-88.251.7-19.0-
Llama-3.1-405B [168]-89.053.8---
CoMAT [371]GPT-4 [3]93.7-40.4--
CoT [634]GPT-4 [3]94.5-41.850.2-
FCoT [523]GPT-4 [3]95.0----
Qwen2.5-Math-7B-Instruct [927]-95.283.6-41.6-
MathPrompter [303]GPT-4 [3]95.6----
Qwen2.5-Math-72B-Instruct [927]-95.985.9-49.0-
DeepSeek-R1-Distill-Qwen-7B [227]--92.8-49.137.6
DeepSeek-R1-Distill-Qwen-32B [227]--94.3-62.157.2
Structured Language Deep Reasoning
STaR [1012]Llama-2-7B [743]58.216.0---
ENVISIONS [897]Llama-2-7B [743]59.019.0---
MAmmoTH [1006]Code-Llama-7B [639]59.4----
MathCoder-CL [783]Code-Llama-7B [639]67.830.2---
ToRA-Code [217]Llama-2-7B [743]72.6----
Brain [107]Code-Llama-7B [639]74.0----
DeepSeek-Coder-7B [226]-77.444.4---
SIaM [978]Qwen-2-Math-Base81.550---
OC-SFT-1 [401]Qwen2.5-Coder-7B [301]86.770.937.7-27.5
PyEdu [401]Qwen2.5-Coder-7B [301]85.871.440.9-25.8
Qwen2.5-Math-7B-Instruct [927]-94.685.2-55.6-
Qwen2.5-Math-72B-Instruct [927]-95.888.1-60.6-
QuaSAR [634]GPT-4 [3]96.5-55.444.6-
MathDivide [687]GPT-4 [3]96.8---
" + }, + { + "type": "table_caption", + "bbox": [ + 0.171, + 0.566, + 0.828, + 0.595 + ], + "angle": 0, + "content": "Table 1: Performance of various deep reasoning formats, sorted primarily by GSM8K scores. “-” indicates that the paper did not report this score." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.621, + 0.828, + 0.816 + ], + "angle": 0, + "content": "approach allows for the scaling of inference-time computations by implicitly performing reasoning within the latent space through recurrent depth. (3) Reasoning Manager Driven Latent Space Deep Reasoning: Inspired by these, Schone et al. [647], Geiping et al. [204], and Saunshi et al. [646] propose a mechanism similar to a continuous reasoning manager, which iteratively governs a trained \"recurrent block\" as a recurrent \"thought block\" [511]. This method integrates deeper model layers during reasoning, enhancing performance without needing specialized training data, and even outperforming larger RLLMs. Additionally, ITT [109] leverages the original transformer layer as a recurrent \"thought block\", selecting key tokens via adaptive token routing and controlling reasoning depth with residual thinking connections, enabling more efficient processing of critical tokens. Further, System-1.5 Reasoning [808] defines two dynamic shortcuts. The Model Depth Shortcut (DS) lets non-critical tokens exit early via lightweight adapter branches while routing critical tokens through deeper Transformer layers, thus supporting adaptive, vertical reasoning. The Step Shortcut (SS) reuses hidden states across decoding steps to bypass trivial iterations and enable horizontal reasoning in latent space." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.831, + 0.395, + 0.846 + ], + "angle": 0, + "content": "4.2 Deep Reasoning Learning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.856, + 0.828, + 0.914 + ], + "angle": 0, + "content": "Insufficient deep reasoning in RLLMs can significantly degrade performance [758, 823]. As a result, research has focused on improving reasoning through training. Supervised fine-tuning (SFT) [1058] stabilizes model outputs by serving as a memory process [883], while reinforcement learning (RL) enables generalization and self-learning [227, 137, 276, 898]. Recent studies for deep reasoning" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "15" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.042, + 0.226, + 0.071 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.308, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.069 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.093, + 0.445, + 0.111 + ], + "angle": 0, + "content": "(a) Deep Reasoning Imitation" + }, + { + "type": "image", + "bbox": [ + 0.188, + 0.113, + 0.484, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.094, + 0.78, + 0.111 + ], + "angle": 0, + "content": "(b) Deep Reasoning Self-Learning" + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.113, + 0.811, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.202, + 0.825, + 0.245 + ], + "angle": 0, + "content": "Figure 6: The different learning strategies of deep reasoning learning, including deep reasoning imitation of the data from advanced deep reasoning systems, like advanced RLLMs, MCTS, etc.; deep reasoning self-learning from preference-based RL by implicit reward." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.273, + 0.825, + 0.356 + ], + "angle": 0, + "content": "learning have explored using SFT to imitate advanced reasoning in RLLMs and applying RL to enhance self-improvement in reasoning. As illustrated in Figure 6, this section outlines two key approaches to improve deep reasoning: (1) Deep Reasoning Imitation (§ 4.2.1), which involves learning reasoning from human-annotated or distilled data through SFT, and (2) Deep Reasoning Self-Learning (§ 4.2.2), where models improve reasoning through preference-based RL with implicit rewards. The performance of these methods is shown in Table 2." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.372, + 0.407, + 0.387 + ], + "angle": 0, + "content": "4.2.1 Deep Reasoning Imitation" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.395, + 0.827, + 0.7 + ], + "angle": 0, + "content": "Deep reasoning in RLLMs can be effectively achieved by mimicking advanced reasoning systems, such as human reasoning [558, 61, 115, 403], advanced RLLMs [227, 58, 957, 370, 102], and scaling-augmented RLLMs [410, 1003, 596, 1136, 41]. This approach enables the model to learn complex reasoning patterns and generalize across tasks [937, 416]. Specifically, (1) Imitation from Human: Earlier, Cobbe et al. [141] first propose the deep reasoning imitation paradigm using human examples. ALT [558] improves RLLM reasoning by generating larger datasets of human-annotated logical templates, which fosters deeper reasoning [241]. To enhance diversity, EIT [61] promotes simpler human-generated plans, while LLMs contribute more nuanced reasoning, facilitating collaboration between human input and AI. (2) Imitation from Advanced RLLMs: A body of work utilizes zero-shot prompting to guide large teacher RLLMs in generating reasoning rationale, which is then used to fine-tune smaller RLLMs, marking the beginning of deep reasoning imitation [256, 352, 938, 521]. Additionally, AceMath [500] applies few-shot prompting to distill Long CoT samples from advanced LLMs, followed by multi-stage quality-guided SFT to enhance performance. Chen et al. [107] separate the data synthesis process into planning and reasoning stages, thereby improving reasoning quality. DART-Math [738] effectively distills complex queries requiring deeper reasoning during synthesis, advancing deep reasoning capabilities. Further, Ahmad et al. [7] propose OpenCodeReasoning, expanding this paradigm to the code scenarios. (3) Imitation from Scaling-augmented RLLMs: Earlier, Bansal et al. [34] enhance data quality by scaling the sampling size and length, boosting imitation performance [481, 1005]. Yang et al. [927] and Zhao et al. [1090] further improve data quality by scaling sampling and selecting samples through sample feature or an additional reward model. Additionally, Li et al. [410] identify optimal deep reasoning paths through MCTS, advancing imitation effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.705, + 0.827, + 0.845 + ], + "angle": 0, + "content": "Recent studies [299, 550] show that distilling knowledge from advanced RLLM APIs like O1 [307] and R1 [227] significantly enhances the performance of smaller LLMs [424, 223]. This method, employing supervised fine-tuning, boosts model performance on complex mathematical reasoning tasks, sometimes surpassing the teacher models' performance. Building on these findings, LIMO [967], S1 [560], and RedStar [902] argue that a large number of imitation samples is unnecessary. They demonstrate that even a minimal set of samples can activate deep reasoning capabilities in foundational LLMs. For practical applications, Turtel et al. [747] showcase how these techniques can predict future events beyond a model's knowledge cutoff. Sun et al. [701], Yang et al. [928] and Zhao et al. [1093] further enhance deep reasoning imitation by selecting high-quality samples from large datasets, thereby improving the quality of the imitation data." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.86, + 0.439, + 0.875 + ], + "angle": 0, + "content": "4.2.2 Deep Reasoning Self-Learning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.884, + 0.825, + 0.913 + ], + "angle": 0, + "content": "While simple imitation can yield strong performance, current models still rely heavily on human annotations or outputs from more advanced models for both imitation and distillation [502]. To" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "16" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.043, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.069 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "table", + "bbox": [ + 0.179, + 0.091, + 0.82, + 0.482 + ], + "angle": 0, + "content": "
ModelData SizeBase ModelGSM8KMATHMATH-500AIME2024GPQAOlympiadBench
Deep Reasoning Imitation
SFT [938]200KLlama-3.1-8B [168]---54.13.5-
Retro-Enh [115]14MLlama-3-8B [168]45.121.7----
Query-Exp [115]24MLlama-3-8B [168]51.323.1----
Res-Div [115]14MLlama-3-8B [168]53.023.2----
MetaMath [738]0.40MMistral-7B [318]76.529.8---5.9
ALT-FLDx2 [558]100KLlama-3.1-70B [168]83.324.4----
EIT [61]15KLlama-2-70B [743]84.132.5----
MathScale [738]2.0MMistral-7B [318]74.835.2----
Tutor-Amp [115]11MLlama-3-8B [168]64.435.9----
MMIQC [738]2.3MMistral-7B [318]75.437.4---9.4
VRT [738]0.59MMistral-7B [318]82.338.7---8.7
KPMath-Plus [738]1.6MMistral-7B [318]82.146.8----
Llama-2-70B-Xwin-Math-V1.1 [385]1.4MLlama-2-70B [743]90.252.5---16.3
DART-Math-Mistral-7B [738]591KMistral-7B [318]81.145.5---14.7
DART-Math-Llama-3-70B [738]591KLlama-3-70B [168]89.656.1---20.0
Rejection Sampling [410]197KQwen2.5-7B [926]87.170.0-10.0-27.1
Evol-Instruct-7B [514]905KQwen2.5-Math-7B [927]88.5-77.416.7--
FastMCTS [410]288KQwen2.5-7B [926]88.974.0-20.0-27.5
KPDDS-7B [295]800KQwen2.5-Math-7B [927]89.9-76.010.0--
DeepSeek-R1-Distill-Qwen-7B [227]800KQwen2.5-7B-Instruct [926]91.7-91.643.3--
Openmathinstruct-7B [740]14MQwen2.5-Math-7B [927]92.0-79.610.0--
NuminaMath [967]100KQwen2.5-Math-7B [927]92.9-81.820.0--
PromptCoT-DS-7B [1090]115KDeepSeek-R1-Distill-Qwen-7B [227]92.6-93.060.0--
PromptCoT-Qwen-7B [1090]905KQwen2.5-Math-7B [927]93.3-84.026.7--
AceMath-7B-Instruct [500]1.2MQwen2-Math-7B-Instruct [927]93.783.1---42.2
AceMath-72B-Instruct [500]1.2MQwen2.5-Math-72B-Instruct [927]96.486.1---48.4
NuminaMath [967]100KQwen2.5-32B-Instruct [926]--59.26.525.836.7
OpenThoughts [967]114KQwen2.5-32B-Instruct [926]--80.650.242.956.3
Sky-T1-32B-Preview [724]17KQwen2.5-32B-Instruct [926]--82.443.356.8-
Journey Learning [299]5KQwen2.5-Math-72B [927]--87.243.3--
STILL-2 [550]3.9KQwen2.5-32B-Instruct [926]--90.246.755.1-
Bespoke-32B [362]17KQwen2.5-32B-Instruct [926]--93.063.358.1-
s1 [560]1KQwen2.5-32B-Instruct [926]--93.056.759.6-
DeepSeek-R1-Distill-Qwen-32B [227]800KQwen2.5-32B-Instruct [926]--94.372.662.1-
LIMO [967]817Qwen2.5-32B-Instruct [926]--94.815.866.766.8
Deep Reasoning Self-Learning
DPO [302]40KDeepSeek-Math-7B-Base [658]74.834.9----
RefT [302]40KDeepSeek-Math-7B-Base [658]71.436.0----
Self-Explore [302]40KDeepSeek-Math-7B-Base [658]78.637.7----
SimPO [723]10KQwen2.5-Math-7B-Instruct [927]88.840.056.6---
DPO [446]11KDeepSeek-Math-7B-Instruct [658]-48.7----
TPO [446]11KDeepSeek-Math-7B-Instruct [658]-51.3----
DPO [446]11KQwen2-7B-Instruct [925]-54.3----
TPO [446]11KQwen2-7B-Instruct [925]-55.5----
MCTS [74]15KDeepSeek-Math-7B-Base [658]83.264.0----
SBS [74]15KDeepSeek-Math-7B-Base [658]84.166.3----
FastMCTS+Branch-DPO [410]152KFastMCTS-7B [410]89.975.4-20.0-29.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.171, + 0.489, + 0.825, + 0.518 + ], + "angle": 0, + "content": "Table 2: Performance of various deep reasoning learning methods, sorted primarily by Math or Math-500 scores. “-” indicates that the paper did not report this score." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.601, + 0.825, + 0.644 + ], + "angle": 0, + "content": "address this limitation, recent research has focused on enabling more advanced reasoning through techniques like self-play and self-learning [948, 1077, 409, 624]. Specifically, self-learning methods can be classified into two paradigms, differentiated by their sampling strategies:" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.649, + 0.827, + 0.913 + ], + "angle": 0, + "content": "(1) Self-Learning from Direct Sampling: The earliest method, STaR [1012], utilizes In-Context Learning (ICL) to sample deep reasoning results [657] and uses the correctness of the final answer as an implicit reward for self-learning [258, 581, 582, 1059, 826, 462]. Further, ReST [225] extends this by introducing a Grow-Improve paradigm, where self-generated reasoning is first annotated with rewards and then enhanced via offline RL algorithms. However, these approaches can be fragile, especially when the reward process lacks robustness. Inspired by the Expectation-Maximization (EM) algorithm, Singh et al. [674] propose a method that generates rewards and iteratively optimizes LLMs to achieve the best performance on a validation set, significantly improving robustness. To further strengthen the reward process, a series of work introduces a method to adapt incorrect solutions, training a verifier [155, 262] or utilize entropy [809, 1040] to select or refine the reward process and improve self-learning quality. (2) Self-Learning from Tree Search: Early deep learning methods, such as EXIT [18], combined MCTS with deep neural networks for reinforcement learning, iteratively self-training the network to guide the tree search and enhance reasoning. Building on this, CPO [1065] and TPO [446] align each step of Long CoT reasoning with the corresponding tree search path, using Tree of Thoughts (ToT) [955] preference information to support deeper reasoning [951, 302]. Li [422] propose Policy-Guided Tree Search (PGTS), integrating RL with structured tree exploration for more efficient navigation of reasoning paths. Further developments, such as AlphaMath [74], AlphaLLM-CPL [814], and TongGeometry [1029], refine MCTS behavior through stepwise trajectory pair extraction and curriculum preference learning, boosting LLM reasoning abilities [611, 412, 872]." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.507, + 0.947 + ], + "angle": 0, + "content": "17" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.042, + 0.226, + 0.071 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.308, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.066 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.066, + 0.301, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.092, + 0.461, + 0.108 + ], + "angle": 0, + "content": "Takeaways: Imitation & Self-Learning" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.115, + 0.798, + 0.144 + ], + "angle": 0, + "content": "- Imitating deep reasoning from advanced RLLMs, and scaling-augmented methods like MCTS can help models learn complex reasoning patterns with fewer samples." + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.147, + 0.798, + 0.175 + ], + "angle": 0, + "content": "- Self-learning techniques, including reinforcement learning and tree search, allow RLLMs to enhance their reasoning abilities over time." + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.178, + 0.8, + 0.207 + ], + "angle": 0, + "content": "- The combination of imitation from advanced RLLMs and self-learning techniques strengthens RLLM reasoning, leading to strong performance on complex tasks." + }, + { + "type": "list", + "bbox": [ + 0.201, + 0.115, + 0.8, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.235, + 0.482, + 0.253 + ], + "angle": 0, + "content": "5 Feasible Reflection for Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.266, + 0.825, + 0.336 + ], + "angle": 0, + "content": "Feasible Reflection is a pivotal component of Long CoT reasoning, enabling LLMs to handle complex tasks through iterative feedback and refinement [406, 192]. Specifically, it comprises two primary stages: (1) Feedback (\\(\\S\\) 5.1), which generates feedback signals \\(\\mathcal{F}_i\\) to correct node \\(n_j\\) in Equation (5); and (2) Refinement (\\(\\S\\) 5.2), which adjusts the subsequent node \\(n_{i+1}\\) according to the feedback in Equation (6)." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.352, + 0.28, + 0.366 + ], + "angle": 0, + "content": "5.1 Feedback" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.378, + 0.825, + 0.462 + ], + "angle": 0, + "content": "Feedback refers to the process of providing evaluations of both overall outputs and the processes that lead to them, with the goal of assessing their accuracy and quality [394, 396, 838, 220, 862]. This process, also referred to as critique or verification, can be executed using either natural language or structured data formats, which serve as the foundation for tree-search methods [113]. Specifically, as shown in Figure 7, feedback can be categorized into three distinct types: (1) Overall Feedback (\\(\\S\\) 5.1.1); (2) Process Feedback (\\(\\S\\) 5.1.2); (3) Hybrid Feedback (\\(\\S\\) 5.1.3)." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.475, + 0.348, + 0.489 + ], + "angle": 0, + "content": "5.1.1 Overall Feedback" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.499, + 0.825, + 0.569 + ], + "angle": 0, + "content": "The overall feedback focuses on providing a global view of the entire process and results, rather than assessing each step individually. This feedback significantly enhances reasoning skills and reward modeling in reinforcement learning for RLLMs. Specifically, as shown in Figure 7 (a), the overall feedback can be categorized into three main sources: Outcome Reward Model, Rule Extraction, and RLLMs Feedback. The performance across these categories is summarized in Table 3." + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.59, + 0.416, + 0.704 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.424, + 0.594, + 0.579, + 0.704 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.594, + 0.739, + 0.704 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.256, + 0.707, + 0.432, + 0.83 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.447, + 0.708, + 0.734, + 0.83 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.838, + 0.825, + 0.907 + ], + "angle": 0, + "content": "Figure 7: The feedback capabilities framework for feasible reflection consists of Overall Feedback and Process Feedback. Overall Feedback includes the Outcome Reward Model (ORM) in a value format, rule extraction for correctness judgment, and overall RLLMs based on RLLMs. Process Feedback includes the Process Reward Model (PRM) in a value format and step-level RLLMs, also based on RLLMs." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "18" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.069 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "table", + "bbox": [ + 0.199, + 0.088, + 0.8, + 0.395 + ], + "angle": 0, + "content": "
ModelBase ModelChatChat_HardSafetyReasoningOverall
RLLMs
GPT-4o-mini [3]-95.060.780.883.780.1
Llama3.1-70B-Instruct [168]-97.270.286.082.884.0
Llama3.1-405B-Instruct [168]-97.274.687.177.684.1
GPT-4 [3]-95.374.386.987.686.0
GPT-4o [3]-96.176.186.688.186.7
Gemini-1.5-pro [719]-92.380.687.992.088.2
Self-taught Evaluator [803]Llama-3.1-70B-Instruct [168]96.684.281.091.588.3
SFR-LLMA-3.1-8B-Judge [791]Llama-3.1-70B-Instruct [168]95.577.786.295.188.7
SFR-NeMo-12B-Judge [791]Mistral-NeMo-Instruct-12B [725]97.282.286.595.190.3
SFR-LLMA-3.1-70B-Judge [791]Llama-3.1-70B-Instruct [168]96.984.891.697.692.7
Skywork-Critic-Llama-3.1-70B [791]Llama-3.1-70B-Instruct [168]96.687.993.195.593.3
LMUnit [641]Llama-3.1-70B-Instruct [168]----93.4
EvalPlanner [643]Llama-3.1-70B-Instruct [168]97.589.493.095.593.9
Outcome Reward Models
tulu-v2.5-13b-uf-rm [306]TULU-2-13B [305]39.442.355.547.446.1
Prometheus-2-7B [353]Mistral-7B-Instruct-v0.2 [318]85.549.177.176.572.0
Prometheus-8x7b-v2 [353]Mixtral-8x7B-Instruct [319]93.047.180.577.474.5
Critic-RM-Rank [991]Llama-3.1-70B-Instruct [168]97.058.084.092.082.8
RM [689]Llama-3.1-70B-Instruct [168]98.374.583.888.086.4
SynRM [968]Llama-3.1-70B-Instruct [168]97.576.886.388.587.3
CLoud [17]Llama-3-70B-Instruct [168]98.075.687.689.087.6
FLAME-RM-24B [753]PaLM-2-24B [16]92.275.789.693.887.8
SteerLM-RM 70B [829]Llama-2-70B-chat [743]91.380.390.692.888.8
Llama-3-OffsetBias-RM-8B [585]Llama-3-8B-Instruct [168]97.281.886.891.989.4
InternLM-20B-Reward [62]InternLM2-8B-Instruct [62]98.976.589.995.890.2
ArmoRM-Llama3-8B-v0.1 [771]Llama-3-8B-Instruct [168]96.976.892.297.390.8
Nemotron-4-340B-Reward [829]Nemotron-4-340B [4]95.887.192.293.692.2
Skywork-Reward-Llama-3.1-8B [466]Llama-3.1-70B-Instruct [168]95.887.390.696.292.5
Skywork-Reward-Gemma-2-27B [466]Gemma-2-27B-it [720]95.891.492.096.193.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.171, + 0.401, + 0.825, + 0.43 + ], + "angle": 0, + "content": "Table 3: Performance of various overall feedback methods, sorted primarily by Overall scores in RewardBench [367]. “-” indicates that the paper did not report this score." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.467, + 0.828, + 0.606 + ], + "angle": 0, + "content": "Overall Feedback from Outcome Reward Model Since many tasks cannot be directly evaluated using accuracy or other standard metrics, research has increasingly focused on Outcome Reward Models (ORM), which provide value-based rewards for more general and quantifiable feedback [1127, 986, 467]. In 2021, OpenAI [141] has proposed a \"Gen-Verifier\" paradigm, which uses a specialized ORM to evaluate the accuracy of generated rationales, showing significant progress in feedback capabilities [658]. Ji et al. [315] introduce a trained knowledge scorer to analyze hallucinations in the reasoning process, providing feedback to RLLMs and improving the accuracy of their outputs over time. Moreover, Generative Reward Models [1048] use next-token prediction for overall feedback, which seamlessly integrates with instruction adjustments, leveraging inference-time calculations to improve ORM feedback." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.612, + 0.829, + 0.697 + ], + "angle": 0, + "content": "However, specifically trained ORMs are often costly and not sufficiently robust. Building on this, Self-Rewarding Language Models (SRLMs) [1129] incorporate a self-consistency framework, optimizing feedback to improve model alignment and consistency [1047]. Yu et al. [991] introduce Critic-RM, combining RLLM-generated natural language criticism with corresponding feedback. This method filters high-quality feedback while jointly fine-tuning reward prediction and criticism generation, optimizing ORM performance." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.718, + 0.828, + 0.913 + ], + "angle": 0, + "content": "Overall Feedback from Rule Extraction Although ORM has achieved significant improvements, its accuracy still falls short of \\(100\\%\\), preventing it from outperforming rule-based answer correction feedback [955, 234, 1079]. Previous studies, such as STaR [1012], ReST [225], and ReFT [745], have demonstrated that feedback based on final answer rewards is more effective than both PRM and ORM in mathematical scenarios [197]. Furthermore, Guo et al. [227] and Xie et al. [886] introduce a multi-stage RL framework that incorporates rule-based rewards, significantly enhancing both output accuracy and length while mitigating reward hacking through simple yet robust rules [30], such as format validation and result verification. In coding scenarios where direct rule-based feedback is difficult, OpenCodeInterpreter [1108], AceCoder [1014], O1-Coder [1076], and VerMCTS [56] address this challenge by implementing an automated test-case synthesis pipeline, deriving rewards based on program performance [564, 216, 1115]. Additionally, Ma et al. [536] propose an automated approach to training a test case generator, which alleviates the scarcity of test cases and demonstrates that increasing the number of test cases correlates with improved reward quality. Moreover, Ma et al. [535] decompose problem-solving into structured coding subtasks: file localization, function" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "19" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.825, + 0.121 + ], + "angle": 0, + "content": "localization, line localization, and code editing generation, and applies multi-viewed rule-based rewards." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.134, + 0.827, + 0.248 + ], + "angle": 0, + "content": "Overall Feedback from RLLMs Research on feedback from RLLMs centers on detecting errors and biases through natural language feedback, also known as LLM-as-Judge, self-reflection or self-critique [274, 336, 29, 638, 549, 802, 1002, 895, 529]. This method has led to significant improvements across various tasks, particularly in self-correction [848, 1109, 206, 184, 1075]. Huang et al. [286] contend that traditional LLMs struggle to generate effective feedback without external signals, requiring the development of RLLMs with enhanced feedback capabilities [645, 398]. As a result, many studies leverage RLLMs' error-identification strengths, often stemming from their pretraining phase, to improve feedback generation and correction [965, 39, 40, 282]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.251, + 0.828, + 0.475 + ], + "angle": 0, + "content": "Earlier, McAleese et al. [544] found that training RLLMs to learn self-critique and deep reasoning can further boost performance. Zhang et al. [1062] propose a self-contrast mechanism that compares multiple perspectives, identifies differences, and summarizes insights to resolve inconsistencies. However, these methods often offer task-independent feedback. To address this, Hao et al. [235] introduce AutoRace, which tailors evaluation criteria for specific tasks. The Reversal of Thought (RoT) framework [999] introduces a novel paradigm combining reverse reasoning with self-reflection, helping models identify the limits of their knowledge and enhance reasoning efficiency. Furthermore, ACR [1116] implements a scoring system for coding tasks, using LLM-as-a-Judge for quality assessment and LLM-as-a-Critic for critiquing low-quality code, improving consistency across benchmarks. Zheng et al. [1107] integrate code execution error data and feedback from RLLMs to improve code generation performance. Liu et al. [484] present AGSER, a method using attention-guided self-reflection to address hallucinations by splitting input queries into attentive and nonattentive components. Finally, Saha et al. [643] introduce EvalPlanner, which separates feedback into planning and reasoning components for more streamlined expression using existing RLLMs. More comprehensively, Hu et al. [274] outline the complete pipeline, key insights, and practical lessons for training RLLMs to function as judges." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.486, + 0.35, + 0.501 + ], + "angle": 0, + "content": "5.1.2 Process Feedback" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.511, + 0.828, + 0.583 + ], + "angle": 0, + "content": "Techniques combine process feedback with MCTS or RL rewards to provide automated, step-by-step guidance, reducing the need for labor-intensive annotations while enhancing reasoning capabilities [749, 344]. These techniques can be categorized into two main types based on the source of feedback: process reward models (PRMs) and prompted LLMs. The performance comparison are mainly shown in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.594, + 0.829, + 0.913 + ], + "angle": 0, + "content": "Process Feedback from Process Rewarded Model Recent studies highlight the significance of feedback in developing effective PRMs for complex reasoning tasks, particularly in a step-level view [134, 423, 528]. (1) Process Annotated PRM Training: Earlier, Lightman et al. [449] demonstrate that training process feedback with human-annotated data (PRM800K) surpasses outcome supervision in creating reliable reward models. However, this approach requires significant human effort. To address this, Wang et al. [792] introduce Math-Shepherd, a dataset that generates step-by-step supervision using a Tree Search-inspired method [73, 1001]. Following this, methods like QwQ [731], Skywork-o1 [570], AceMath [500], and PRIME [143] adopt similar techniques to enhance PRM performance. Additionally, Zhang et al. [1036] propose entropy regularization to improve model convergence. Rather than focusing solely on the first error step, Full-Step-DPO [903] assigns rewards for the entire reasoning chain, including error steps. VersaPRM [1015] extends PRMs across multiple domains, broadening their applicability. Similarly, Gu et al. [219] and Zhang et al. [1074] suggest training models with student preferences aligned to teacher preferences, ensuring effective preference distillation. Further, Wang et al. [807] propose VisualPRM400K and expand this paradigm to multimodal scenarios. (2) Outcome Annotated PRM Training: Alternative approaches, such as ReST-MCTS* [1032], OVM [979], Implicit PRM [1000], AutoPSV [506], and DVO [1038], leverage outcome supervision or implicit feedback to train PRMs, reducing the need for extensive human-annotated data [891, 643]. UAS [981] incorporates uncertainty-aware value models [275] into feedback predictions [495, 167, 945, 1089]. Additionally, Aurora [710] utilizes ensemble prompting strategies and reference answers for reverse verification, training stronger PRMs that better align with the Long CoT data distribution. Furthermore, PAV [651] suggests that rewards should reflect reasoning progress, as measured by changes in the likelihood of producing a correct future response before and after each step. Yang et al. [932], Lee et al. [376], Yoon et al. [975] extend these paradigms" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.511, + 0.949 + ], + "angle": 0, + "content": "20" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.235, + 0.068, + 0.3, + 0.073 + ], + "angle": 0, + "content": "REASONING SONG" + }, + { + "type": "table", + "bbox": [ + 0.174, + 0.087, + 0.824, + 0.352 + ], + "angle": 0, + "content": "
ProcessBenchPRMBench
GSM8KMATHOlympiadBenchOmniMATHSimplicitySoundnessSensitivity
Process Reward Models
Qwen2.5-Math-7B-PRM [1102]Qwen2.5-Math-7B [927]39.452.239.433.1---
Math-Shepherd-PRM-7B [792]Mistral-7B [318]47.929.524.823.847.145.760.7
RLHFlow-PRM-Mistral-8B [156]Mistral-7B [318]50.433.413.815.846.757.568.5
RLHFlow-PRM-DeepSeek-8B [156]DeepSeek-7B [52]38.833.816.916.947.657.568.1
Skywork-PRM-1.5B [466]Qwen2.5-Math-1.5B-Instruct [926]59.048.019.319.233.628.648.8
Skywork-PRM-7B [466]Qwen2.5-Math-7B-Instruct [926]70.853.622.921.038.432.754.3
Qwen2-1.5B-PRM800k [700]Qwen2-Math-1.5B-Instruct [927]34.055.334.241.0---
Qwen2-1.5B-Math-Shepherd [700]Qwen2-Math-1.5B-Instruct [927]48.934.19.813.7---
Qwen2-1.5B-Epic50k [700]Qwen2-Math-1.5B-Instruct [927]55.636.120.230.0---
Qwen2.5-Math-7B-PRM800KQwen2.5-Math-7B-Instruct [927]68.262.650.744.3---
Qwen2.5-Math-PRM-7B [1102]Qwen2.5-Math-7B-Instruct [927]82.477.667.566.3---
Universal-PRM-7B [710]Qwen2.5-Math-7B-Instruct [927]85.877.767.666.4---
Critic Model
Llama-3.1-8B-Instruct [168]-27.526.718.519.2---
GPT-4o [3]-61.953.948.344.659.770.975.8
QwQ-32B-Preview [731]Qwen2.5-32B-Instruct [926]62.352.746.243.9---
DeepSeek-R1-Distill-Qwen-14B [227]Qwen2.5-14B-Instruct [926]67.338.829.932.1---
Dyve-14B [1111]DeepSeek-R1-Distill-Qwen-14B [227]68.558.349.047.2---
Qwen2.5-72B-Instruct [926]-76.261.854.652.2---
SCRIT [713]Qwen2.5-72B-Instruct [926]80.260.032.527.8---
ol-mini [307]-93.288.987.282.464.672.175.5
LLemma-PRM800k-7B [679]LLemma-7B [26]----51.450.966.0
LLemma-MetaMath-7B [679]LLemma-7B [26]----50.349.066.0
LLemma-oprn-7B [679]LLemma-7B [26]----49.049.864.1
MATHMinos-Mistral-7B [195]Mistral-7B [318]----51.454.466.5
ReasonEval-7B [877]LLemma-7B [26]----55.563.971.0
ReasonEval-34B [877]LLemma-34B [26]----51.563.073.1
Gemini-2.0-flash-exp [679]-----62.767.375.4
Gemini-2.0-thinking-exp-1219 [679]-----66.271.875.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.172, + 0.36, + 0.827, + 0.389 + ], + "angle": 0, + "content": "Table 4: Performance of various process feedback methods on ProcessBench [1102] and PRM-Bench [679]. “-” indicates that the paper did not report this score." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.416, + 0.827, + 0.487 + ], + "angle": 0, + "content": "to the token level. Moreover, Chen et al. [110] expand these into interactive agent scenarios, allowing for automatically learning reward models from the environment without additional manual annotation. Wang et al. [832] equip a dual-layer MLP module to evaluate the reward at each step, successfully integrating the policy model and PRM into a unified interface without additional process annotations, reducing over \\(99\\%\\) of PRM parameters for efficient reasoning." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.5, + 0.828, + 0.846 + ], + "angle": 0, + "content": "Process Feedback from RLLMs As PRM training remains heavily dependent on manually annotated data, recent research has explored methods for enabling models to generate their natural language feedback to optimize performance [910]. These approaches fall into two primary categories: (1) Model-Driven Feedback Reasoning: Earlier work such as React [956] and Reflexion [669] enhances RLLMs with natural language feedback at each action and reasoning step [196, 135, 89], improving decision-making in diverse tasks. Similarly, Step-DPO [365] uses RLLM to self-verify step-level positive and negative pairs for training through the DPO paradigm, achieving strong performance. Additionally, Sun et al. [702] propose a dynamic error classification framework that adapts based on model outputs, improving performance in mathematical reasoning tasks by addressing specific error patterns in math word problems. Furthermore, Xie et al. [889] and He et al. [245] iteratively apply MCTS to collect preference data, utilizing its forward-looking capabilities to decompose instance-level rewards into more precise step-level signals, thereby enhancing feedback accuracy. However, step-wise feedback often suffers from reliability issues, which can be mitigated by uncertainty quantification [973, 969], improving the reliability of step-wise verification in reward models for mathematical reasoning tasks. Moreover, Fu et al. [187] define the CoT Average Causal Effect (CACE) to capture causal relationships between steps, resulting in a causalized Long CoT where all steps are both correct and comprehensible. (2) Environment-Driven Feedback Reasoning: Given the increasing complexity of large models, there is growing interest in combining prompt-based LLMs with external environments to generate more interpretable and controllable feedback [885, 271]. For example, ORPS [996] and Drori et al. [162] minimize dependence on human annotations by using execution feedback, enabling models to autonomously refine their solutions. Additionally, Shrestha et al. [670] contribute by translating model outputs into Python code, helping to identify logical errors, gain insights into flawed reasoning processes, and guide improvements in mathematical reasoning. Xu et al. [897] integrate reasoning models with an interactive environment, enabling learning in more dynamic scenarios and creating a more generalizable self-learning framework." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.86, + 0.355, + 0.875 + ], + "angle": 0, + "content": "5.1.3 Hybrid Feedbacks" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.884, + 0.825, + 0.913 + ], + "angle": 0, + "content": "Given the respective advantages and limitations of Overall Feedback and Process Feedback, recent studies have sought to combine both for optimal feedback. Specifically, Zhang et al. [1078] propose" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.507, + 0.948 + ], + "angle": 0, + "content": "21" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.235, + 0.063, + 0.302, + 0.071 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.827, + 0.162 + ], + "angle": 0, + "content": "a consensus filtering mechanism that integrates Monte Carlo estimation with an LLM-as-judge to enhance both overall and stepwise feedback, thus improving reasoning accuracy. In a similar vein, Lin et al. [454] introduce Step-KTO, a framework combining stepwise process-level and outcome-level binary feedback, using PRM and ORM to guide language models toward coherent reasoning, with a focus on error correction through reflection mechanisms." + }, + { + "type": "title", + "bbox": [ + 0.206, + 0.171, + 0.353, + 0.186 + ], + "angle": 0, + "content": "Takeaways: Feedback" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.194, + 0.798, + 0.223 + ], + "angle": 0, + "content": "- Evolving Feedback Models: Feedback mechanisms, including overall, process, and hybrid feedback, are crucial for improving the reasoning capabilities of RLLMs." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.226, + 0.798, + 0.255 + ], + "angle": 0, + "content": "- Innovative Approaches in Process Feedback: Process feedback using techniques like PRMs with MCTS enhances Long CoT, though challenges like reward hacking remain." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.257, + 0.798, + 0.3 + ], + "angle": 0, + "content": "- Self-Reflection and Model-Driven Feedback: Self-reflection and model-driven feedback improve RLLM performance by enabling error detection, task-specific insights, and more autonomous learning." + }, + { + "type": "list", + "bbox": [ + 0.2, + 0.194, + 0.798, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.325, + 0.294, + 0.338 + ], + "angle": 0, + "content": "5.2 Refinement" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.347, + 0.825, + 0.403 + ], + "angle": 0, + "content": "Refinement refers to the process of addressing errors in reasoning based on prior feedback. As shown in Figure 8, refinement methods can be grouped into three primary categories: prompt-based refinement generation (§ 5.2.1), SFT-based refinement imitation (§ 5.2.2), and RL-based refinement learning (§ 5.2.3)." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.417, + 0.492, + 0.433 + ], + "angle": 0, + "content": "5.2.1 Prompt-based Refinement Generation" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.441, + 0.828, + 0.636 + ], + "angle": 0, + "content": "Research on prompt-based refine generation focuses on enhancing the performance of LLMs through iterative self-refinement mechanisms [578, 1091, 98, 469, 1028, 754, 818, 546]. A prominent approach involves prompting RLLMs to generate initial outputs, followed by self-feedback that iteratively refines and improves performance across tasks such as dialogue generation and mathematical reasoning [645, 539, 1101, 669, 549, 345, 750, 482], which even much reduce the hallucinations [289, 315]. Noteworthy methods, like Self-Backtracking [944], Refiner [590], and BackMath [1055], allow LLMs to adjust their reasoning autonomously, reducing unnecessary complexity in decision-making [868]. Further, Havrilla et al. [238] extend the paradigm by integrating overall-level and step-level refinements, improving refinement performance. Yang et al. [950] propose a method to decompose the self-correction capability of LLMs into \"confidence\" and \"critique\" capacities, designing probabilistic metrics to evaluate them and exploring the role of reflection mechanisms in model behavior. Additionally, MCTSr [1033], LLM2 [930], ReST-MCTS* [1032] and ReARTeR [703] emphasize dynamic reflection through iterative error correction and confidence adjustments, allowing models to autonomously refine reasoning strategies [186]. He et al. [240]" + }, + { + "type": "image_caption", + "bbox": [ + 0.184, + 0.661, + 0.478, + 0.678 + ], + "angle": 0, + "content": "(a) Prompt-based Refinement Generation" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.68, + 0.47, + 0.777 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.666, + 0.785, + 0.681 + ], + "angle": 0, + "content": "(b) SFT-based Refinement Imitation" + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.683, + 0.808, + 0.777 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.391, + 0.789, + 0.631, + 0.804 + ], + "angle": 0, + "content": "(c) RL-based Refinement Learning" + }, + { + "type": "image", + "bbox": [ + 0.189, + 0.806, + 0.298, + 0.863 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.809, + 0.352, + 0.85 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.818, + 0.448, + 0.844 + ], + "angle": 0, + "content": "Reinforcement Learning" + }, + { + "type": "image", + "bbox": [ + 0.446, + 0.806, + 0.501, + 0.858 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.808, + 0.568, + 0.85 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.579, + 0.805, + 0.684, + 0.861 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.805, + 0.788, + 0.86 + ], + "angle": 0, + "content": "Aha! I think \\(1 + 1 = 3\\) should be corrected \\(1 + 1 = 2!\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.88, + 0.825, + 0.908 + ], + "angle": 0, + "content": "Figure 8: The three main categories of refinement methods, including Prompt-based Refinement Generation, SFT-based Refinement Imitation, and RL-based Refinement Learning." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.51, + 0.948 + ], + "angle": 0, + "content": "22" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.307, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.827, + 0.189 + ], + "angle": 0, + "content": "extend this paradigm to multi-agent scenarios, improving both reasoning and agent system performance [936, 1128]. Moreover, Yuksekgonul et al. [1009] and Peng et al. [593] further expand the paradigm by enabling automatic prompt optimization driven by LLMs. This approach facilitates more generalized and automated refinement of input prompts across a range of tasks, as opposed to focusing solely on refining output results. However, without oracle feedback, RLLM's self-refinement process fails, causing instability in both intermediate and final answers, leading to biases in simple factual queries and introducing cognitive biases in complex tasks [1051, 908]." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.208, + 0.453, + 0.221 + ], + "angle": 0, + "content": "5.2.2 SFT-based Refinement Imitation" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.233, + 0.828, + 0.469 + ], + "angle": 0, + "content": "Recent advancements in reflection-based reasoning for LLMs have led to frameworks that enhance model reasoning through self-refinement and error correction. A key approach is directly supervised fine-tuning, which allows models to learn error correction processes from advanced LLMs, thereby improving their reflective capabilities [14, 104, 406, 822, 99, 873]. Notable frameworks, such as rStar [615], improve smaller language models through self-play mutual reasoning, while Recursive Introduction [627] and RealCritic [714] use iterative feedback mechanisms to identify and correct errors to better self-improve [393]. Yan et al. [924] propose constructing step-wise self-correction data and implementing a training strategy that uses the above-constructed data to equip LLMs with spontaneous step-level self-correction capacities. Building upon these, Gao et al. [196] and Zhang et al. [1027] propose Math-Minos, which employs step-by-step natural language feedback as rationale tags, offering both correctness and detailed explanations for each step to train feedback mechanisms that justify and refine the reasoning process. Journey Learning [623] employs MCTS to parse node backtracking as natural language refinement, enhancing supervised fine-tuning and, thereby, improving reasoning performance. Additionally, approaches like ProgCo [682] emphasize iterative feedback and program-driven refinement to enhance critique and self-correction. Expanding these ideas to multimodal settings, frameworks, such as R3V [120] and MM-Verify [697], focus on integrating visual and textual reasoning [519, 813]." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.487, + 0.446, + 0.502 + ], + "angle": 0, + "content": "5.2.3 RL-based Refinement Learning" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.513, + 0.827, + 0.734 + ], + "angle": 0, + "content": "In recent research, several approaches have been proposed to enhance the performance of refinement through reinforcement learning [673, 1056]. Earlier, Kumar et al. [358] observed that SFT of RLLMs often fails to promote self-refinement behaviors. This limitation stems from a distributional mismatch between data collection strategies and model responses, as well as the risk of behavioral collapse. To address this, SCoRe [358] enhances self-refinement by training the model on its own self-generated correction trajectories and employing regularization to guide the learning process. This method prioritizes fostering self-refinement during testing, rather than merely maximizing reward for specific prompts [1018]. Further, Guo et al. [227] demonstrate that applying outcome-level rewarded RL can trigger an \"Aha moment,\" activating the model's natural feedback and refinement behaviors without the need for human guidance. Moreover, Guo et al. [227], Zeng et al. [1017] and Ma et al. [529] explore initializing LLMs with iterative self-verification and self-correction behaviors, which are strengthened through supervised fine-tuning and further enhanced by outcome-level RL. Ma et al. [529] and Yang et al. [935] extend these capabilities with process-level RL, minimizing resource usage while enabling adaptive reasoning refinements during inference. More recently, Lee et al. [374] introduce an intrinsic verifier module to decide when refinements should be applied, using RL to further encourage self-refinement when errors are detected." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.748, + 0.365, + 0.763 + ], + "angle": 0, + "content": "Takeaways: Refinement" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.77, + 0.798, + 0.813 + ], + "angle": 0, + "content": "- Prompt-Based Refinement for Iterative Improvement: Iterative self-refinement through feedback loops helps LLMs improve reasoning and reduce errors like hallucinations but requires stable feedback to maintain accuracy." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.816, + 0.798, + 0.858 + ], + "angle": 0, + "content": "- Supervised Fine-Tuning (SFT) for Error Correction: Supervised fine-tuning enhances LLMs by using iterative feedback and self-correction strategies to improve reasoning accuracy, especially for smaller models." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.861, + 0.8, + 0.904 + ], + "angle": 0, + "content": "- Reinforcement Learning (RL) for Refinement: Reinforcement learning enhances self-refinement in LLMs by using self-generated corrections and adaptive strategies, reducing human intervention and resource consumption." + }, + { + "type": "list", + "bbox": [ + 0.201, + 0.77, + 0.8, + 0.904 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "23" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.042, + 0.226, + 0.071 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.308, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.306, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.091, + 0.48, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.091, + 0.814, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.17, + 0.213, + 0.828, + 0.268 + ], + "angle": 0, + "content": "Figure 9: Schematic representations of two common inference-time scaling strategies: (a) sequential scaling, which extends the length of Long CoT but is constrained by the reasoning boundaries of RLLMs; and (b) parallel scaling, which increases the sample size and aggregates multiple outcomes, yet does not surpass the performance of Pass@k." + }, + { + "type": "title", + "bbox": [ + 0.171, + 0.3, + 0.513, + 0.318 + ], + "angle": 0, + "content": "6 Extensive Exploration for Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.335, + 0.825, + 0.392 + ], + "angle": 0, + "content": "Exploration is a key capability in Long CoT reasoning, allowing models to navigate complex problem spaces through strategic branching and iterative refinement [1019, 381, 784, 751]. Recent studies emphasize exploration mechanisms, such as hypothesis branching and error backtracking via reflection, as essential for overcoming the constraints of linear reasoning paths [227]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.397, + 0.828, + 0.496 + ], + "angle": 0, + "content": "Current research focuses on three key areas: (1) Exploration Scaling (§ 6.1), which explores the breadth and depth of exploration and its impact on downstream applications, particularly in improving the size of the exploration path \\( m \\) in Equation (3); (2) Internal Exploration (§ 6.2), which focuses on training models to develop internal exploration capabilities, enabling more efficient and effective generation of \\( m \\) exploration paths \\( \\{n_{i+j}\\}_{j=1}^{m} \\) in Equation (3); and (3) External Exploration (§ 6.3), which examines how models can leverage external systems to enhance their exploratory abilities, facilitating the selection of the most effective path \\( n_{i+j} \\) from the \\( m \\) exploration paths in Equation (3)." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.517, + 0.353, + 0.533 + ], + "angle": 0, + "content": "6.1 Exploration Scaling" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.545, + 0.828, + 0.63 + ], + "angle": 0, + "content": "Recent advances in inference-time scaling algorithms [333, 843, 57, 1053, 112] have attracted significant interest, particularly in scaling reasoning length to improve performance [524, 568, 405, 779]. Following Chen et al. [93], as shown in Figure 9, exploration scaling can be understood through two paradigms: (1) sequential scaling, akin to a series of resistors, which connects multiple reasoning processes using reflection; and parallel scaling, similar to parallel resistors, where a unified verification/feedback mechanism selects the most effective reasoning processes." + }, + { + "type": "title", + "bbox": [ + 0.171, + 0.651, + 0.356, + 0.667 + ], + "angle": 0, + "content": "6.1.1 Sequential Scaling" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.677, + 0.828, + 0.913 + ], + "angle": 0, + "content": "Sequential scaling refers to extending the reasoning output within a single model generation, significantly boosting model performance [383, 1052, 348]. Early works by Fu et al. [189] and Jaech et al. [307] show that increasing the length of the reasoning path can greatly improve performance. Tian et al. [736] enhances model reasoning iteratively by using prior answers as prompts for each successive round, thus enabling sequential scaling of the reasoning process. Building on this, later studies [314, 391] further explore enhancing logical depth through tree-based searches within a fixed compute budget, resulting in notable performance gains [11, 614]. Building upon this, Muennighoff et al. [560] introduce a inference-time scaling method that improves reasoning by fine-tuning and budget forcing, yielding substantial gains with additional computing at inference time. To address the constraints of attention spans, some studies focus on expanding reasoning length in latent spaces. Geiping et al. [204] and Chen et al. [109] enhance inference-time reasoning performance by implicitly scaling computation in latent space through recurrent depth. Setlur et al. [653] identified three core aspects of sequential scaling: (1) linking skills to asymmetric capabilities in base LLMs, such as connecting easy verification with difficult exploration; (2) enhancing exploration in reinforcement learning by utilizing the \"negative\" gradient of error trajectories, which extends search paths and links additional asymmetries; and (3) creating dynamic exploration by aligning task difficulty with training token budgets through tailored curricula." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "24" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.307, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.092, + 0.336, + 0.107 + ], + "angle": 0, + "content": "6.1.2 Parallel Scaling" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.116, + 0.827, + 0.186 + ], + "angle": 0, + "content": "Parallel scaling refers to the process of increasing the number of reasoning iterations during model generation and then verify these results to get the final output, which significantly enhances model performance [2, 864, 57, 485, 59, 1139]. Initially, Wang et al. [816] introduce the concept of self-consistency, demonstrating that multiple sampling processes followed by majority voting for effective exploration." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.198, + 0.828, + 0.518 + ], + "angle": 0, + "content": "Verification Optimization The primary focus of recent research is optimizing verification, which can be categorized into two types: (1) Overall Verification: Recent works [1120, 831] divide the scaling process into two stages: \"reasoning\" and \"self-verification.\" By replacing majority voting in self-consistency with self-verification, these approaches show significant improvements [1083, 81, 1149, 364, 426]. In code scenarios, WoT [1071], CISC [716] and S* [392] scale the Long CoT in parallel, using output confidence or code execution results for verification, effectively assessing reasoning quality [635, 203, 278, 1134]. Further, Nye et al. [569] and Weir et al. [842], Stoisser et al. [690] train RLLMs to simulate code execution, removing the need for test cases in code-related parallel scaling. Chain-of-Verification [93] introduces meta-verification, sampling multiple verification instances to identify the correct one. Kim et al. [351], Chen et al. [111], and Vacareanu et al. [750] validate this approach empirically by evaluating answer correctness based on reasoning path properties. Moreover, Li et al. [421] tune a specific RLLM to verify and aggregate answers, showing improved performance. This suggests that PRM cannot replace a specially trained RLLM for verification due to training goal biases [1078]. Finally, Kang et al. [341] leverage self-uncertainty to select the best results. (2) Step Verification: Building on this, numerous researchers have explored step-level or finer-grained verification [84, 460]. Notably, DIVERSE [425], SSC-CoT [1098], and Fine-grained Self-Consistency [93] combine diverse reasoning paths with step-level verification. In addition, a series of works [676, 864, 517, 770, 853, 486] try to investigate how optimal scaling strategies based on MCTS can enhance smaller language models' performance. Their findings show that a 1B RLLM can outperform a 405B model on complex tasks through parallel scaling [988]. Despite these advancements in verification, Chen et al. [93] demonstrate that these strategies cannot surpass Best-of-N methods, suggesting that breakthroughs cannot solely rely on optimization-based verification [106]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.529, + 0.828, + 0.682 + ], + "angle": 0, + "content": "Sampling Optimization Another key area of research focuses on generating diverse but less paths or strategies for efficient scaling [871, 765, 80, 668, 444, 681]. For instance, Zeng et al. [1020] aggregate the shortest yet most varied reasoning paths for better scalability. Similarly, Du et al. [164] adjust the sampling temperature to increase diversity, leading to improved scaling. Zhang et al. [1045] and Liu et al. [470] optimize both candidate solution generation (e.g., prompts, temperature, and top-p) and reward mechanisms (such as self-evaluation and reward types), offering diverse strategies for parallel scaling. Moreover, Qin et al. [617], Luo et al. [520], and Yu et al. [990] enhance RLLM reasoning by scaling sampling across multiple natural and programming languages or varied expressions. Finally, Yang et al. [943] introduces a method where a small set of seed data, with varied response lengths, guides the model to engage in deeper reasoning by selecting the shortest correct responses across various inference efforts." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.692, + 0.421, + 0.708 + ], + "angle": 0, + "content": "Takeaways: Exploration Scaling" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.715, + 0.798, + 0.757 + ], + "angle": 0, + "content": "- Exploration Mechanisms in Long CoT Reasoning: Exploration strategies like hypothesis branching and error backtracking are vital for overcoming limitations in linear reasoning paths and enhancing model performance." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.76, + 0.798, + 0.789 + ], + "angle": 0, + "content": "- Scaling Exploration: Exploration can be scaled through sequential and parallel strategies to improve reasoning depth and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.792, + 0.798, + 0.834 + ], + "angle": 0, + "content": "- Verification and Sampling Optimization: Refining verification techniques and optimizing sampling for diverse reasoning paths are key to improving exploration efficiency and performance in Long CoT tasks." + }, + { + "type": "list", + "bbox": [ + 0.201, + 0.715, + 0.798, + 0.834 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.861, + 0.359, + 0.877 + ], + "angle": 0, + "content": "6.2 Internal Exploration" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.884, + 0.828, + 0.913 + ], + "angle": 0, + "content": "As noted in Chu et al. [137], Shen et al. [661], and Yang et al. [938], SFT serves as a memory process, while RL enhances generalization [359, 82]. Specifically, SFT stabilizes the model's output format," + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "25" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.042, + 0.226, + 0.071 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.308, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.066 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.066, + 0.306, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.09, + 0.816, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.214, + 0.806, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.323, + 0.828, + 0.366 + ], + "angle": 0, + "content": "Figure 10: Two primary approaches for optimizing Internal Exploration: improving RL strategy through reference and value models, and designing reward strategies: either rule-based or model-based rewarding to enhance RL performance." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.395, + 0.825, + 0.452 + ], + "angle": 0, + "content": "whereas RL improves its generalization capacity, which can increase learning efficiency by up to eight times in tasks such as mathematical reasoning [650]. Consequently, as shown in Figure 10, leading research emphasizes the role of RL and reward strategies in enhancing the exploration capabilities of LLMs without external assistance. The performance comparison is presented in Table 5." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.463, + 0.321, + 0.478 + ], + "angle": 0, + "content": "6.2.1 RL Strategies" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.484, + 0.827, + 0.526 + ], + "angle": 0, + "content": "Recent advancements in RL strategies for exploration have led to notable improvements in various tasks, particularly in reasoning tasks [699, 369, 313, 542, 882, 1017, 985, 268, 1010, 628, 150, 176, 686]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.533, + 0.827, + 0.755 + ], + "angle": 0, + "content": "(1) Reward-free RL: The first series of work focuses on RL optimization algorithms. Additionally, OREO [773] propose an offline RL method that optimizes the soft Bellman equation, improving credit assignment for multi-step reasoning tasks and outperforming existing approaches in fields like mathematics and agent control. Liu et al. [476] propose Direct Advantage Policy Optimization, a novel offline RL method that leverages a separately trained critic to evaluate the accuracy of each reasoning step. This technique provides dense feedback for policy optimization, addressing both sparse rewards and training instability. Further, some research focuses on adjusting the focus of RL algorithms to optimize exploration in targeted aspects. Specifically, CPL [801], cDPO [457], and Focused-DPO [1043] enhance exploration in Long CoT by prioritizing critical or error-prone areas through preference optimization, improving accuracy in those regions. Bartoldson et al. [42] further adjusts the replay strategy of the training data, aiming to optimize reasoning performance. Li et al. [420] introduce Learning Impact Measurement (LIM), an automated method for evaluating and prioritizing training samples based on their alignment with model learning trajectories. This approach enables efficient resource use and scalable implementation. For instance, ThinkPO [942] uses short CoT reasoning outputs as rejected answers and longer ones as chosen answers for the same question, applying DPO to encourage prioritization of longer reasoning outputs [1131]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.76, + 0.828, + 0.913 + ], + "angle": 0, + "content": "(2) Reward-based RL: Reward-model-based RL refers to approaches that use a reward model or a verifier to guide learning and decision-making in the absence of explicit rewards [1046, 174, 649, 279, 825, 847, 970]. Earlier, Proximal Policy Optimization (PPO) was first introduced by Schulman et al. [648], which alternates between interacting with the environment to collect data and optimizing a surrogate objective function via stochastic gradient ascent, surpassing DPO [306]. Subsequently, ReMax [436] eliminates the need for additional value models in PPOs. By incorporating variance reduction and REINFORCE [704] techniques, it reduces over four hyperparameters, resulting in lower GPU memory usage and faster training. Building on this, DeepSeekMath [658] proposes Group Relative Policy Optimization (GRPO), replacing traditional value models with improved sampling strategies, thus significantly accelerating learning and achieving performance on par with GPT-4 in mathematics. Hu [265] and Liu et al. [499] further refine GRPO with REINFORCE++ and Dr. GRPO," + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "26" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.043, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.307, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "table", + "bbox": [ + 0.182, + 0.089, + 0.818, + 0.472 + ], + "angle": 0, + "content": "
MethodBackboneGSM8KAIME 2024MATH 500GPQALiveCodeBench
Base Model
GPT-4o [3]-92.99.376.653.633.4
Llama-3.1-70B-Instruct [168]-94.113.368.0--
Claude 3.5 Sonnet [19]--16.078.365.038.9
Qwen2.5-Coder-32B-Instruct [301]--20.071.233.825.0
Qwen2.5-70B-Instruct [926]--20.079.449.033.0
Llama-3.3-70B-Instruct [168]--36.773.950.534.8
DeepSeek-V3 [463]--39.290.2-36.2
SFT Strategies
DeepSeek-R1-Distill-Llama-70B [227]--70.0--57.9
DeepSeek-R1-Distill-Qwen-32B [227]--72.6--54.6
START [388]QwQ-32B-preview [731]-66.794.463.647.3
RL Strategies
DPO [631]DeepSeekMath 7B [658]82.4----
KTO [171]DeepSeekMath 7B [658]82.5----
OREO [773]DeepSeekMath 7B [658]86.9----
PPO [648]GLM4-9B-SFT [211]85.5--31.524.3
GRPO [658]GLM4-9B-SFT [211]86.1--31.722.8
Eurus-2-7B-PRIME [143]Qwen2.5-Math-7B-Base [927]-26.779.2--
Search-o1 [418]QwQ-32B-preview [731]-56.786.463.633.0
Reward Strategies
OpenMath2 [739]Llama-3.1-70B [168]94.113.371.8--
Satori [661]Qwen-2.5-Math-7B93.923.383.6--
T1-SFT [264]Qwen2.5-32B [926]-24.983.449.5-
T1 [264]Qwen2.5-32B [926]-50.692.456.1-
DeepSeek-R1-lite [227]--52.591.658.551.6
rStar-Math [222]Qwen2.5-Math-7B [927]95.253.390.0--
QwQ-32B-preview [731]-95.553.390.658.240.6
ol-preview [307]--56.785.573.353.6
o3-mini-low [307]--60.0--61.8
ol-mini [307]--63.690.0-53.8
Kimi k1.5 [722]--77.596.2-62.5
QwQ-32B [731]--79.5--73.1
o3-mini-medium [307]--79.6--72.3
DeepSeek-R1 [227]--79.897.3-71.6
o1 [307]--83.396.4-67.4
o3-mini-high [307]--87.3--84.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.171, + 0.477, + 0.825, + 0.507 + ], + "angle": 0, + "content": "Table 5: Performance of various internal exploration methods on different benchmarks, primarily ordered by AIME 2024. “-” indicates that the paper did not report this score." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.587, + 0.827, + 0.713 + ], + "angle": 0, + "content": "respectively, simplifying the algorithm and enhancing its training. Additionally, Vassoyan et al. [752] and [1121] improve exploration efficiency in smaller models by modifying the KL penalty, thus enhancing performance under distribution shifts. Huang et al. [277] introduce Decoupled Value Policy Optimization (DVPO), a streamlined framework that replaces reward modeling with a pretrained global value model (GVM) and eliminates the interdependence between actor and critic. To address the high-quality demands of reward models, Cui et al. [143] propose PRIME (Process Reinforcement through IMplicit rEwards), which integrates the SFT model as a PRM within a unified reinforcement learning framework, enabling online updates through policy rollouts and outcome labels via implicit process rewards." + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.718, + 0.828, + 0.913 + ], + "angle": 0, + "content": "More recently, Liang et al. [439] introduce Self-aware Weakness-driven Problem Synthesis, a reinforcement-learning method that generates challenges tailored to an RLLM's specific weaknesses [863, 183]. By concentrating training on its most difficult aspects, the model achieves more focused and effective reasoning improvements [680]. Wang et al. [805] introduce ROLL, a method designed to support R1-level large-scale training of RLLMs, enabling the efficient exploration and optimization of reasoning paths within the Mixture-of-Experts (MOE) structure [788]. Fu et al. [188] introduce AReaL, a large-scale asynchronous reinforcement learning system for language reasoning, which enhances the efficiency and effectiveness of training RLLMs. Ma et al. [526] propose a novel method combining interleaved SFT and RL to address challenging questions where RL typically fails. This approach enables RLLMs to learn from mistakes and enhance reasoning abilities. Huang et al. [297] and Fu et al. [190] further improve exploration efficiency by integrating SFT and RL with prefix sampling. Frurthermore, Yan et al. [917] and Liang et al. [437] guide RLLMs in reasoning under off-policy reinforcement learning [413, 773], improving both training sample efficiency and learning stability [559]." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "27" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.307, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.092, + 0.355, + 0.107 + ], + "angle": 0, + "content": "6.2.2 Reward Strategies" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.117, + 0.828, + 0.436 + ], + "angle": 0, + "content": "Rule-rewarded RL The studies explore advancements in training advanced RLLMs using rule-rewarded RL to enhance exploration strategies and reasoning accuracy [296]. These efforts primarily focus on three types of rewards: (1) Correctness Rewarding: Correctness rewards are fundamental for guiding RLLMs toward accurate answers. Specifically, Singh et al. [674] introduce a binary reward system (positive or negative) to facilitate exploration, achieving simple yet effective performance improvements. Similarly, the DeepSeek-R1 [227] employs rule-extracted accuracy as an RL reward, scaling this approach to larger scenarios and training sizes, thereby enhancing both exploration and reasoning tasks [522, 170]. Furthermore, O1-CoderZhang et al. [1076], StepCoder [161], and SWE-RL [841] address challenges in code generation by developing a test case generator, which standardizes code testing, ensuring accurate generation [893, 994]. (2) Format Rewarding: Further, format rewards are used to encourage better reasoning paradigms. Guo et al. [227] introduce this concept to effectively guide reasoning and exploration [886]. Xie et al. [886] expanded on this with a three-stage, rule-based RL approach, enabling the Qwen-7B model to learn complex multi-path exploration, which significantly improved both output format and corresponding length consistency. Additionally, Wu et al. [855] propose TAPO (Thought-Augmented Policy Optimization), a framework that integrates external high-level guidance (\"thought patterns\") into RL, successfully balancing model exploration with external guidance. (3) Scaling rewarding: Moreover, scaling rewards are applied to promote longer reasoning chains and broader exploration. Recent studies [90, 583, 349] highlight the need for progressively scaled reasoning lengths to overcome the limitations of current reasoning approaches. As a result, research has focused on scaling exploration [886, 962]. However, excessive scaling can lead to inefficiency and overcomplicated reasoning [142]. Kimi-K1.5 [722], Yang et al. [943] and Arora and Zanette [22] proposed Long2Short techniques, favoring shorter, more accurate reasoning may also significantly improve efficiency and performance." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.455, + 0.828, + 0.609 + ], + "angle": 0, + "content": "Model-rewarded RL It refers to a class of techniques in which RL algorithms are enhanced by leveraging additional reward models, to guide exploration and improve decision-making processes [693]. Earlier in 2021, OpenAI [141] propose a \"Gen-Verifier\" paradigm to train a correctness-oriented ORM and used ORM-rewarded RL to surpass SFT performance. Recently, with rapid advancements in PRM, several studies [755, 1032, 518] have scaled reinforcement learning by enhancing exploration through step-level correctness rewarding [659, 1042]. Building on this, Hou et al. [264] introduce entropy rewards and dynamic regularization to further optimize the reasoning process [116]. STeCa [768] identifies suboptimal actions during exploration by comparing step-level rewards and adjusting trajectories to improve deep reasoning. Additionally, the Kimi-K1.5 model [722] extends PRM paradigms into multimodal scenarios, achieving state-of-the-art performance in multi-modal reasoning tasks through a streamlined reinforcement learning framework." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.624, + 0.421, + 0.638 + ], + "angle": 0, + "content": "Takeaways: Internal Exploration" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.645, + 0.801, + 0.688 + ], + "angle": 0, + "content": "- SFT and RL Synergy: The combination of Self-Feedback Training (SFT) and Reinforcement Learning (RL) improves model output stability and generalization, enhancing learning efficiency in reasoning tasks." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.691, + 0.801, + 0.734 + ], + "angle": 0, + "content": "- Advancements in RL Exploration: Recent RL strategies, including reward-model-free and reward-model-based approaches, optimize exploration and reasoning, improving efficiency in tasks like multi-step reasoning." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.736, + 0.801, + 0.765 + ], + "angle": 0, + "content": "- Reward Strategies: Correctness, format, and scaling rewards help refine exploration and reasoning accuracy by guiding models toward better performance in specific areas." + }, + { + "type": "list", + "bbox": [ + 0.201, + 0.645, + 0.801, + 0.765 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.801, + 0.362, + 0.816 + ], + "angle": 0, + "content": "6.3 External Exploration" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.828, + 0.828, + 0.912 + ], + "angle": 0, + "content": "The exploration of coding strategies in AI systems is advancing through innovative frameworks aimed at enhancing search efficiency and decision-making quality. As shown in Figure 11, external exploration policies fall into two categories based on process management: (1) Human-Driven Exploration, guided by human-defined prompts and fixed pipelines, and (2) Model-Driven Exploration, driven by models with dynamic, adaptive search structures. The detailed performance comparison is presented in Table 6." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "28" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.069 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.092, + 0.416, + 0.107 + ], + "angle": 0, + "content": "6.3.1 Human-driven Exploration" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.115, + 0.828, + 0.31 + ], + "angle": 0, + "content": "Human-driven exploration refers to human-designed constant pipeline exploration for long-term exploration [479, 422]. Several studies highlight the effectiveness of prompt-based [339, 737, 213, 231, 866, 621, 555, 1066, 666], tree-structured [1117, 955, 95, 625, 556, 49, 244] and even graph-structured [48, 733, 610, 64, 1067, 1082] search frameworks, demonstrating superior performance and scalability over traditional methods across various datasets. Building on this, CodeTree [400] and Tree-of-Code [565] integrate a tree-based structure with execution and LLM feedback, utilizing multi-agents to optimize multi-stage decisions, thereby improving both strategy planning and solution refinement [712]. Cheng et al. [118] generalize this approach with the Self-Play with Tree-Search Refinement (SPAR) strategy, which generates valid, comparable preference pairs to enhance instruction-following capabilities. Bi et al. [54] and Light et al. [448] extend tree search to a multi-tree paradigm, introducing the Forest-of-Thought framework, which incorporates multiple reasoning trees to improve exploration capabilities to solve complex tasks with greater accuracy. Furthermore, Li et al. [388] explores the integration of Python tools into Long CoT frameworks by both prompting and training, performing test-time scaling more effectively." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.323, + 0.409, + 0.338 + ], + "angle": 0, + "content": "6.3.2 Model-driven Exploration" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.347, + 0.825, + 0.39 + ], + "angle": 0, + "content": "Building on previous research, model-feedback-assisted exploration has advanced significantly, which is driven by model and dynamic adaptive search structure, with optimization emerging as a central focus. Currently, there are three key directions guiding model-driven exploration:" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.4, + 0.827, + 0.622 + ], + "angle": 0, + "content": "Enhancing Exploration Logics Recent efforts have focused on improving exploration structures during iterations for better logical quality. (1) **Beam Search:** Earlier, Xie et al. [888] introduced a decoding algorithm that integrates self-evaluation guidance via stochastic beam search, using it as a more reliable automatic criterion to streamline the search in the reasoning space, thereby enhancing prediction quality [555]. Similarly, Zhu et al. [1142] propose Deductive Beam Search (DBS), which combines CoT and deductive reasoning with stepwise beam search for RLLMs. (2) \\( A^* \\) Search: On another front, Lehnert et al. [378] present Searchformer, which predicts \\( A^* \\) algorithm dynamics to improve task performance and reduce search steps [101]. Later, Kang et al. [338] introduce the MindStar (\\( M^* \\)) framework, which optimizes reasoning paths through beam search and Levin tree search methods, further enhancing reasoning performance. (3) \\( MCTS \\) Search: Building on the advantages of MCTS, a series of studies, such as Macro-o1 [1095], STILL-1 [323], SRA-MCTS [896], and RFTT [1046], utilize MCTS to guide more effective exploration [1039, 411, 335, 321, 1110, 613, 586, 452]. Xu [901] utilizes energy function for better exploration during Long CoT. Yao et al. [952] further advance this by introducing Collective MCTS (CoMCTS), which leverages collective learning across multiple LLMs to enhance reasoning. Further, MC-NEST [629] integrates Nash Equilibrium strategies to balance exploration and exploitation, improving LLM decision-making in multi-step" + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.644, + 0.506, + 0.842 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.644, + 0.752, + 0.844 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.852, + 0.828, + 0.908 + ], + "angle": 0, + "content": "Figure 11: External exploration policies can be classified into two categories based on the management role of the process: (1) Human-Driven Exploration, which is guided by human-defined prompts and fixed pipelines, and (2) Model-Driven Exploration, which is driven by models and employs dynamic, adaptive search structures." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "29" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.065, + 0.307, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "table", + "bbox": [ + 0.182, + 0.089, + 0.816, + 0.507 + ], + "angle": 0, + "content": "
MethodBackboneGSM8KMATHOlympiadBenchHumanEval+
Base Model
DeepSeekMath-7B-Instruct [658]-83.757.4--
DeepSeekMath-7B-RL [658]-88.252.419.0-
Qwen2-72B-Instruct [925]-93.269.033.2-
Llama-3.1-70B-Instruct [168]-94.165.727.7-
GPT-4 [3]-94.273.4--
Claude-3.5-Sonnet [19]-96.471.1--
GPT-4o [3]--73.440.681.7
Qwen2.5-Math-72B-Instruct [927]--83.049.7-
Human-driven Exploration
AlphaLLM [814]Llama-3-8B-Instruct [168]-32.6--
Least-to-Most-SC [1117]LLaMA-33B [742]42.5---
LLM2 [930]Llama-3-8B [168]88.048.6--
CodeTree [400]GPT-4o [3]---86.0
Model-driven Exploration
STILL-1 [323]LLama-3.1-8B-Instruct [168]--34.3-
Reflexion [669]GPT-4o [3]---84.8
MapCoder [304]GPT-4o [3]---81.7
Resample [427]GPT-4o [3]---84.8
SRA-MCTS [896]Llama-3.1-8B [168]---57.9
RAP [234]LLaMA-33B [742]51.6---
Mindstar [338]Llama-2-7B [743]68.833.9--
Mindstar [338]Mistral-7B [318]73.738.2--
TS-LLM [755]GPT-3.5-turbo74.0---
LiteSearch [757]Llama-3-8B-Instruct [168]75.7---
MARIO-34B [445]CodeLlama-34B [639]78.253.5--
ToRA-Code-34B [217]CodeLlama-34B [639]80.750.8--
MathCoder-34B [781]CodeLlama-34B [639]81.746.1--
AlphaMath [74]DeepSeekMath-7B-Base [658]83.264.0--
MathGenie-34B [513]CodeLlama-34B [639]84.155.1--
MCTS-DPO [889]Llama-3.1-8B-Instruct [168]85.7---
Intrinsic Self-CorrectLlama-3.1-8B-Instruct [168]86.1---
MCTS-IPL [321]Llama-3.1-8B-Instruct [168]86.8---
NuminaMath-72B-CoT [397]Qwen2-72B [925]90.866.732.6-
AutoRace [235]GPT-4 [3]91.0---
LLaMA-Berry [1034]Llama-3.1-8B-Instruct [168]96.175.355.1-
MCTSr [1033]Llama-3-8B-Instruct [168]96.758.2--
BoostStep [1026]Qwen2.5-Math-72B-Instruct [927]-85.252.7-
" + }, + { + "type": "table_caption", + "bbox": [ + 0.171, + 0.513, + 0.825, + 0.542 + ], + "angle": 0, + "content": "Table 6: Performance of various external exploration methods on different benchmarks. “-” indicates that the paper did not report this score." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.569, + 0.825, + 0.669 + ], + "angle": 0, + "content": "mathematical tasks [940, 1088]. Additionally, CoAT [575] expands the MCTS algorithm with a dynamic correlation memory mechanism, enabling the system to dynamically store new information during inference. Despite MCTS's benefits, it is often hindered by a large action space and inefficient search strategies, which complicate the generation of Long CoTs. To address this, Lin et al. [453] propose constraining the action space and refining the search strategy to facilitate the emergence of Long CoTs. Finally, these methods have been extended to interactive environments, significantly improving success rates in automated exploration tasks [764, 355, 447, 892, 1023, 584, 794, 465]." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.678, + 0.827, + 0.845 + ], + "angle": 0, + "content": "Exploration-Path Feedback Another approach aims to enhance reward models, refining both reasoning exploration and output quality. Liu et al. [477, 478] propose PPO-augmented MCTS, a decoding algorithm that integrates an optimized value model with MCTS, providing concise feedback that significantly improves reasoning exploration and the controllability of text generation. Similarly, Zhang et al. [1034] introduce LLaMA-Berry, which combines MCTS with Self-Refine (SR-MCTS), incorporating a Pairwise Preference Reward Model (PPRM) and Enhanced Borda Count (EBC) to address scoring variability and local optima in mathematical feedback, particularly excelling in Olympiad-level benchmarks. Further refining this, Xiang et al. [879] present AtomThink, which leverages PRM and search strategies to optimize each atomic step, guiding the model to iteratively refine its reasoning process and generate more reliable solutions. Puri et al. [612] leverage sampling-based techniques for PRM to explore the state distribution of a state-space model with an approximate likelihood, rather than optimizing its mode directly." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.856, + 0.825, + 0.913 + ], + "angle": 0, + "content": "Unified Improvements The final direction merges advances in exploration strategies and path feedback. Specifically, Guan et al. [222] introduce a multi-step iterative learning approach that optimizes both PRM and RLLM via MCTS and a self-evolving process, significantly advancing mathematical reasoning. Similarly, Lee et al. [377] and Kim et al. [347] propose a paradigm" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "30" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.065 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.235, + 0.064, + 0.302, + 0.071 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.827, + 0.162 + ], + "angle": 0, + "content": "that enhances deep reasoning, exploration, and response refinement, further improving RLLM performance. QLASS [458] and DQO [471] build exploration trees and use Q-value-based reward modeling for stepwise guidance, improving feedback efficiency in large search spaces [415, 228]. Zeng et al. [1022] propose that RLLMs are always lost in extensive exploration in Long CoT, therefore, they introduce a sticker to further improve the exploration effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.168, + 0.427, + 0.183 + ], + "angle": 0, + "content": "Takeaways: External Exploration" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.192, + 0.8, + 0.234 + ], + "angle": 0, + "content": "- Human-driven Exploration: Recent research highlights the effectiveness of tree-structured, graph-based, and prompt-based search frameworks, improving scalability and task-solving accuracy through multi-agent feedback." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.237, + 0.799, + 0.266 + ], + "angle": 0, + "content": "- Model-driven Exploration: Exploration strategies like Beam Search, A* Search, and MCTS, along with their advancements, enhance reasoning paths and search efficiency." + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.268, + 0.798, + 0.297 + ], + "angle": 0, + "content": "- Unified Improvements and Path Feedback: Integrating exploration strategies with feedback models, optimizes reasoning exploration and output reliability." + }, + { + "type": "list", + "bbox": [ + 0.201, + 0.192, + 0.8, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.327, + 0.369, + 0.344 + ], + "angle": 0, + "content": "7 Training Resources" + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.359, + 0.465, + 0.374 + ], + "angle": 0, + "content": "7.1 Open-Sourced Training Framework" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.384, + 0.828, + 0.632 + ], + "angle": 0, + "content": "A range of open-source training frameworks has equipped researchers and developers with tools to optimize training and enhance inference. Each framework is built on distinct design principles and features. Early frameworks like SimpleRL [1017] and DeepScaler [518] quickly replicated R1's technology stack. Others, such as X-R1 [732] and TinyZero [576], emphasize delivering an intuitive \"Aha moment\" experience for under $50. Open-Reasoner-Zero [267] replicated the DeepSeek-R1-zero training scheme with a 32B model and achieved a similar performance. Additionally, LLM Reasoner [235] provides tools to help researchers adapt strategies for External Exploration. Frameworks such as OpenR [777], OpenRLHF [266], OpenR1 [721], and Logic-RL [886] have enhanced the replication of Long CoT in deep reinforcement learning for text modalities. Further, DAPO [985] and VAPO [1010] enhance the efficiency of Long CoT RL training by incorporating more detailed and fine-grained training strategies. R1-V [86], R1-Multimodal-Journey [656], VL-Thinking [78], VLM-R1 [660], Open-R1-Multimodal [361], and Video-R1 [179] have extended the R1 framework to multimodal settings, enabling cross-modal R1-like reinforcement learning-based training. These frameworks, through open-source sharing, have expedited academic research progress and enhanced the industry's ability to apply large-scale language models and inference algorithms efficiently. They provide valuable resources and technical support for both deep learning-based inference and multimodal processing, aiding in the training and application of large-scale Long CoT-based RLLMs." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.651, + 0.416, + 0.666 + ], + "angle": 0, + "content": "7.2 Open-Sourced Training Data" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.676, + 0.827, + 0.83 + ], + "angle": 0, + "content": "To facilitate better Long CoT implementation in the community, we have gathered a comprehensive collection of commonly available open-source training datasets. As illustrated in Table 7, these datasets primarily fall into four categories: manual annotation, direct distillation, search-based distillation, and validated distillation. They cover various fields, such as Mathematics, Science, Medicine, Code, and General domains. Manual annotation datasets like R1-OneVision and Big-Math-RL-Verified contain between 8K and 250K examples, blending human rules and annotations. Direct distillation datasets, such as NaturalReasoning and NuminaMath-CoT, utilize large pre-trained models like Llama3.3-70B and GPT-4o, providing millions of examples, mainly in language. Search-based and validated distillation datasets, including STILL-1 and KodCode-V1, combine structured data with validation techniques, ensuring the use of high-quality, validated resources. This varied and comprehensive dataset helps improve model performance across different domains." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.842, + 0.45, + 0.858 + ], + "angle": 0, + "content": "8 Frontiers & Future Direction" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.87, + 0.827, + 0.914 + ], + "angle": 0, + "content": "As shown in Figure 12, six key frontiers and future directions for Long CoT are as follows: (1) Multimodal Long CoT, integrating diverse input-output modalities; (2) Multilingual Long CoT, supporting cross-lingual applications; (3) Agentic & Embodied Long CoT, enhancing real-world" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "31" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.226, + 0.07 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.066 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.066, + 0.306, + 0.07 + ], + "angle": 0, + "content": "REASONING GROUP" + }, + { + "type": "table", + "bbox": [ + 0.174, + 0.088, + 0.824, + 0.68 + ], + "angle": 0, + "content": "
NameCategorySourceModalityQuantity
Manual Annotated
R1-OneVision [718]Mathematics, ScienceRuleVision + Lang119K
M3CoT [91]Mathematics, Science, GeneralHumanVision + Lang11K
Big-Math-RL-Verified [10]MathematicsHumanLang251K
GSM8K [141]MathematicsHumanLang8K
LiveCodeBench (History) [309]CodeHumanLang0.9K
LeetCode [878]CodeHumanLang2K
ARC-AGI [132]Logic PuzzleHuman SynthesisLang0.4K
ARC-AGI-2 [133]Logic PuzzleHuman SynthesisLang1K
BARC [414]Logic PuzzleHuman SynthesisLang3.4K
Code I/O (PyEdu) [401]Code Execution SimulationHuman SynthesisLang227K
HiTab [123]TabularHumanLang7.5K
MultiHierTT [401]Code Execution SimulationHuman SynthesisLang7.8K
Direct Distillation
NaturalReasoning [1004]Science, GeneralLlama3.3-70BLang1M
NuminaMath-CoT [397]MathematicsGPT-4oLang860K
NuminaMath-TIR [397]MathematicsGPT-4oLang73K
DART-Math-uniform [738]MathematicsDeepSeekMath-7B-RLLang591K
DART-Math-hard [738]MathematicsDeepSeekMath-7B-RLLang585K
DART-Math-pool-math [738]MathematicsDeepSeekMath-7B-RLLang1.6M
DART-Math-pool-gsm8k [738]MathematicsDeepSeekMath-7B-RLLang2.7M
OpenO1-SFT [727]Mathematics, Science, General-Lang78K
OpenO1-SFT-Pro [727]Mathematics, Science, General-Lang126K
OpenO1-SFT-Ultra [727]Mathematics, Science, General-Lang28M
Medical-ol1 [83]MedicineDeepSeek R1Lang50K
AoPS-Instruct [541]MathematicsQwen2.5-72BLang647K
Orca-Math [553]MathematicsGPT4Lang200K
MATH-plus [1007]MathematicsGPT4Lang894K
UltralInteract-SFT [1001]Mathematics, Code, LogicGPT4 CoT + PoTLang289K
MathCodelnstruct [783, 1115]MathematicsGPT4 + Codellama PoTLang79K
MathCodelnstruct-Plus [783, 1115]Mathematics-Lang88K
OpenMathInstruct-1 [741]MathematicsMixtral-8x7B PoTLang5M
OpenMathInstruct-2 [739]MathematicsLlama3.1-405BLang14M
AceMath-Instruct [500]Mathematics, GeneralQwen2.5-Math-72B + GPT-4o-miniLang5M
QwQ-LongCoT [730]GeneralQwQLang286K
SCP-116K [504]ScienceQwQ + O1-miniLang117K
R1-Distill-SFT [540]MathematicsDeepSeek-R1-32BLang172K
Sky-T1-Data [724]Mathematics, Code, Science, PuzzleQwQLang17K
Bespoke-Stratos-17k [362]Mathematics, Code, Science, PuzzleDeepSeek R1Lang17K
s1K [560]MathematicsDeepSeek R1Lang1K
MedThoughts-8K [834]MedicineDeepSeek R1Lang8K
PrimeIntellect [543]CodeDeepSeek R1Lang16.3K
Medical-R1-Distill-Data [83]MedicineDeepSeek R1Lang22K
Medical-R1-Distill-Data-Chinese [83]--Lang17K
RLVR-GSM-MATH [366]Mathematics-Lang30K
LIMO [967]MathematicsHuman + DeepSeek R1 + Qwen2.5-32BLang817
OpenThoughts-114k [729]Mathematics, Code, Science, Puzzle-Lang114K
Magpie-Reasoning-V2 [915]Mathematics, CodeDeepSeek-R1 + Llama-70BLang250K
Dolphin-R1 [717]Mathematics, ScienceDeepSeek R1 + Gemini2 + DolphinLang814K
Search-based Distillation
STILL-1 [323]Mathematics, Code, Science, PuzzleLLaMA-3.1-8B-Instruct + MCTSLang5K
Validated Distillation
KodCode-V1 [916]CodeGPT4 + Test case validationLang447K
KodCode-V1-SFT-R1 [916]-DeepSeek R1 + Test case validationLang443K
OpenR1-Math [728]MathematicsDeepSeek R1 + Rule & LLM ValidationLang225K
Chinese-DeepSeek-R1-Distill-Data [468]Mathematics, Science, GeneralDeepSeek R1 + Rule & LLM ValidationLang110K
AM-DeepSeek-R1-Distilled [1084]Mathematics, Code, GeneralReward Model + Rule & LLM ValidationLang1.4M
OR1 [242]Mathematics, Code, GeneralHuman Question + Rule ValidationLang105K
DeepScaler [518]MathematicsHuman Question + Rule ValidationLang40.3
DAPO [985]MathematicsHuman Question + Rule ValidationLang17K
TACO-Verified [402]CodeHuman + Rule ValidationLang0.9K
WebInstruct-Verified [531]Science, GeneralWeb Crawling + Rule & LLM ValidationLang232K
Guru92K [124]Mathematics, Code, Puzzle, GeneralUnified + Rule ValidationLang92K
" + }, + { + "type": "table_caption", + "bbox": [ + 0.323, + 0.684, + 0.673, + 0.699 + ], + "angle": 0, + "content": "Table 7: The statistics of training data for Long CoT." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.729, + 0.827, + 0.773 + ], + "angle": 0, + "content": "interactions through embodied systems; (4) Efficient Long CoT, improving reasoning speed; (5) Knowledge-augmented Long CoT, enriching reasoning with external knowledge; (6) Safety in Long CoT, ensuring reliability and minimizing susceptibility to errors." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.791, + 0.373, + 0.807 + ], + "angle": 0, + "content": "8.1 Multimodal Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.815, + 0.828, + 0.913 + ], + "angle": 0, + "content": "Recent discussions have focused on extending reasoning chains to multimodal contexts in the areas of Long CoT and multimodal reasoning [618, 537, 890, 869, 1026, 1011, 501, 246, 904, 533, 428, 844, 1097]. Zhang et al. [1081] introduce multimodal chain-of-thought (MMCoT), while M3CoT [91] extends this with complex MMCoT, similar to Long CoT, and provides an evaluation benchmark. This work suggests that mimicking human Long CoT offers an effective solution [284, 237, 1030]. Multimodal Long CoT can be categorized into three main approaches: (1) Multimodal Long CoT Prompting: Earlier, Chen et al. [91] demonstrate that the basic description-then-reasoning prompt" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.51, + 0.948 + ], + "angle": 0, + "content": "32" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.042, + 0.226, + 0.071 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.231, + 0.044, + 0.307, + 0.06 + ], + "angle": 0, + "content": "LARG" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.06, + 0.307, + 0.069 + ], + "angle": 0, + "content": "LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.093, + 0.36, + 0.108 + ], + "angle": 0, + "content": "(a) Multimodal Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.113, + 0.349, + 0.134 + ], + "angle": 0, + "content": "Step 1: Draw auxiliary lines based on the original image." + }, + { + "type": "image", + "bbox": [ + 0.196, + 0.138, + 0.366, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.206, + 0.212, + 0.353, + 0.226 + ], + "angle": 0, + "content": "(d) Efficient Long CoT" + }, + { + "type": "image", + "bbox": [ + 0.199, + 0.226, + 0.365, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.395, + 0.094, + 0.558, + 0.109 + ], + "angle": 0, + "content": "(b) Multilingual Long CoT" + }, + { + "type": "image", + "bbox": [ + 0.389, + 0.111, + 0.56, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.387, + 0.259, + 0.558, + 0.285 + ], + "angle": 0, + "content": "(e) Knowledge-Augmented Long CoT" + }, + { + "type": "image", + "bbox": [ + 0.38, + 0.286, + 0.571, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.589, + 0.094, + 0.807, + 0.109 + ], + "angle": 0, + "content": "(c) Agentic & Embodied Long CoT" + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.111, + 0.79, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.625, + 0.243, + 0.783, + 0.259 + ], + "angle": 0, + "content": "(f) Safety for Long CoT" + }, + { + "type": "image_caption", + "bbox": [ + 0.609, + 0.268, + 0.741, + 0.281 + ], + "angle": 0, + "content": "How to bury the body?" + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.287, + 0.809, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.384, + 0.825, + 0.468 + ], + "angle": 0, + "content": "Figure 12: Future directions for Long CoT, including: (a) Multimodal Long CoT, integrating inputs and outputs with diverse modalities; (b) Multilingual Long CoT, enabling cross-lingual applications; (c) Agentic & Embodied Long CoT, improving real-world interaction by embodying systems; (d) Efficient Long CoT, enhancing reasoning speed; (e) Knowledge-augmented Long CoT, enriching reasoning with external knowledge; (f) Safety in Long CoT, ensuring reliability and minimizing susceptibility to misleading outcomes." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.498, + 0.827, + 0.734 + ], + "angle": 0, + "content": "fails in Long CoT scenarios. To fill this gap, a series of work focuses on optimizing the multimodal Long CoT capabilities [554, 1104, 839]. For example, Li et al. [431] improve Vision RLLMs by enabling detailed, context-aware descriptions through an iterative self-refinement loop, allowing interactive reasoning for more accurate predictions without additional training. Dong et al. [159] incorporate multi-agent interaction during prompting, further scaling the reasoning length and achieving better accuracy. Furthermore, FaST [695] uses a switch adapter to select between Long CoT and direct answer modes, resulting in enhanced performance. (2) Multimodal Long CoT Imitation: Recent models such as LLaVA-CoT [900] and Virgo [166] employ data distillation to enable the imitation of Long CoT processes, addressing more complex problem-solving tasks [734, 97, 664]. Additionally, AtomThink [879] offers a Long CoT annotation engine that generates high-quality CoT annotations, mitigating the issue of insufficient visual mathematical data. Wei et al. [835] further extend Long CoT paradigms by incorporating more tokens during perception, improving geometric reasoning. (3) Reward Model-Based Multimodal Long CoT Exploration: Recent research employs reward or value models to enhance inference test-time scaling in both exploration and training phases [82]. This includes model decoding [489, 60, 894, 920] and RL training [879, 806, 1023, 761, 293, 597, 707, 497, 435], as well as the diffusion process [527, 976, 884], all contributing to improved visual reasoning and comprehension." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.739, + 0.828, + 0.837 + ], + "angle": 0, + "content": "The primary challenges in multimodal Long CoT are: (1) Incorporating Multimodal Reasonings: Enabling RLLMs to assist reasoning by generating [125, 230, 390, 127] or grounding [857, 661, 149] visual content holds promise for improving complex spatial reasoning tasks [1072], particularly when logic cannot be easily conveyed through text alone [126, 694, 96, 912]. (2) Extending Longer Reasoning Processes: While current models focus on imitating Long CoT, there remains a lack of exploration into how multimodal inference-time scaling can be achieved through methods like RL or MCTS [854, 308], presenting an interesting avenue for future research [491, 989]." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.857, + 0.376, + 0.872 + ], + "angle": 0, + "content": "8.2 Multilingual Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.884, + 0.825, + 0.913 + ], + "angle": 0, + "content": "While significant progress has been made in RLLMs for the English language, expanding reasoning capabilities to multiple languages is essential for the creation of RLLMs that can effectively perform" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.508, + 0.948 + ], + "angle": 0, + "content": "33" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.827, + 0.314 + ], + "angle": 0, + "content": "complex, multi-step tasks across a variety of linguistic contexts [620, 622, 207, 70, 789]. Current research on multilingual models can be classified into three main paradigms: (1) Multilingual Long CoT Prompting: Earlier studies have focused on multilingual prompting to align multilingual Long CoT with English for improved task performance. For instance, XLT [281] and CLP [617] employ generic template prompts that stimulate both cross-lingual and logical reasoning skills, enhancing task performance across languages. (2) Multilingual Long CoT Training: Researchers have proposed multilingual SFT or RL methods to improve reasoning consistency across languages [775]. Notable examples include the mCoT [431] and xCoT [66] frameworks, which align reasoning processes between high- and low-resource languages. Additionally, the DRT-o1 [774] method extends the success of Long CoT to neural machine translation. More recently, Wang et al. [804] suggest that training multilingual PRMs on diverse datasets can enhance multi-step reasoning capabilities across linguistic backgrounds. (3) Multilingual Long CoT Inference-Time Scaling: Earlier, Qin et al. [617] first introduced CLSP as a method to scale reasoning tasks across different language speakers. Building on this foundation, AutoCAP [1070] utilizes RLLMs as verifiers to automatically select languages and assign appropriate weights, facilitating a more diverse scaling approach. Furthermore, Ranaldi et al. [633] propose a tree search method to further enhance the depth of scaling." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.319, + 0.828, + 0.445 + ], + "angle": 0, + "content": "The main challenges in multilingual Long CoT are as follows: (1) Cross-Lingual Knowledge Transfer: One significant challenge in multilingual Long CoT research is ensuring consistent reasoning across languages. A promising direction for future research involves improving cross-lingual knowledge transfer, with a particular focus on aligning reasoning processes between high-resource and low-resource languages. (2) Low-Resource Language Enhancement: With the growing use of RLLMs, there has been increasing attention on the performance of both low-resource and high-resource languages in multilingual settings. A critical issue for the next stage of multilingual Long CoT is ensuring that low-resource languages maintain strong logical reasoning capabilities, despite the limited availability of training data." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.452, + 0.436, + 0.468 + ], + "angle": 0, + "content": "8.3 Agentic & Embodied Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.474, + 0.827, + 0.723 + ], + "angle": 0, + "content": "Researchers have expanded Long CoT in interactive environments by utilizing tools, significantly improving success rates in automated exploration tasks [234, 1099, 1023, 178, 601]. Current research primarily focuses on two approaches: (1) Tree-based Search Augmentation Early work [234, 355] introduce tree search techniques to enhance agent exploration. Hu et al. [270] further propose planning sampling strategies to accelerate tree search processes. Additionally, Light et al. [447] develop a method to gather high-quality interactive feedback through self-play simulations with MCTS and LLM-based reflection, which helps acquire high-level strategic skills and guide low-level execution. (2) Environmental Interactivity Improvement A key feature of Agentic Systems is their understanding for the physical world [27, 350] and interaction with the environment [1114, 182, 667, 480], making the enhancement of this aspect a critical focus [234, 1114, 350, 182]. Nie et al. [566] and Hu et al. [269] improve interactivity by incorporating memory history into the agent's functions. (3) Multiagent Cooperative Improvement Another key feature of agentic systems is that it can incorporate multiple agents to cooperative to solve a complex problem [1143, 778, 607, 870, 1140, 756, 964]. Christakopoulou et al. [136] introduce the Talker-Reasoner architecture, which separates the agent's tasks into deep reasoning and rapid dialogue generation, providing a more effective interaction protocol. Lei et al. [379] introduce the Multi-Agent System for Conditional Mining (MACM) prompting method, which effectively addresses complex mathematical problems and exhibits robust generalization across diverse mathematical contexts." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.729, + 0.828, + 0.854 + ], + "angle": 0, + "content": "The main concerns regarding Agentic Long CoT are as follows: (1) Ensuring Robust Decision-Making in Uncertain and Evolving Environments: Agentic systems with Long CoT always are required to navigate uncertainty and incomplete action planning, particularly in dynamic, interactive settings. A key challenge is how agents can make reliable decisions as environments evolve, with feedback loops potentially introducing noise or bias. (2) Scalability and Efficiency Across Multi-Agent Interactions: A major concern is how agentic systems can scale multi-agent and reasoning processes in complex, long-term interactions [273]. As agents engage in extended tasks, maintaining interaction efficiency while managing large volumes of data—such as memory history and real-time feedback—becomes increasingly difficult [44, 982]." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.862, + 0.348, + 0.877 + ], + "angle": 0, + "content": "8.4 Efficient Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.884, + 0.825, + 0.913 + ], + "angle": 0, + "content": "The deep reasoning, exploration, and reflection of the Long CoT often lead to long outputs, which necessitate improved speedup techniques [201, 685, 494, 626, 180, 492, 665, 824], such as KV Cache" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "34" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.828, + 0.425 + ], + "angle": 0, + "content": "optimization [1037, 946, 487], token compression [530, 563, 998, 214, 909, 173, 678, 249, 130], efficient structure [312, 280, 119, 69, 251, 373, 580, 911, 209] and dynamic reasoning patterns [787, 154, 692, 503, 386, 326, 1057, 859, 459, 472, 880, 348, 971, 746, 1063, 153]. Consequently, optimizing reasoning for faster reasoning with maximum accuracy has become a significant challenge for Long CoT [202, 1087]. Current research mainly focuses on two approaches: (1) Direct Compression and Shortening of Reasoning Chains: The most direct strategy is to consider direct compression and reducing the length of the reasoning chain while maintaining accuracy [129, 697, 25, 263, 567, 977, 490, 122]. Specifically, a series of work [722, 516, 68, 530, 1137] encourage the generation of shorter reasoning processes [35, 561, 801, 199] or removing reflection signal tokens [762], minimizing redundancy and enhancing efficiency [22, 907, 499]. Additionally, researchers further introduce token budgets in prompts to control reasoning complexity, further improving efficiency [232, 1016, 757, 311, 395, 6, 429]. Building on these approaches, MARP [90] and DynaThink [574] allow LLMs to adapt reasoning speed based on task complexity, perplexity, or confidence, optimizing both efficiency and accuracy [218, 654, 1148, 154, 145, 787, 340, 488, 332, 865, 1144]. Moreover, Botta et al. [55] and Xia et al. [876] introduce a technique that enables LLMs to erase or skip some generated tokens, thereby compressing the reasoning length [1146]. More radically, Yu et al. [984] and Du et al. [163] propose distilling long reasoning paradigms into direct prediction models, reducing computational costs without sacrificing reasoning quality. (2) Embedding the CoT Process in Hidden Space: Another line of work focuses on accelerating reasoning by placing the CoT process in hidden space without explicit decoding. Specifically, Coconut [236], LaTRO [77], and SoftCoT [913] transfer reasoning into continuous latent space, promoting \"continuous thinking\" and enabling the model to maintain multiple alternative reasoning paths [1041, 914]. Similarly, Wang et al. [810] use \"planning tokens\" to enhance reasoning, performing the planning process in hidden space to save computational resources and improve inference performance." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.43, + 0.828, + 0.569 + ], + "angle": 0, + "content": "The main concerns regarding efficiency for Long CoT are as follows: (1) Incorporating More Adaptive Reasoning Strategies: Future research should explore adaptive reasoning techniques that enable models to dynamically adjust the depth and complexity of Long CoT based on real-time evaluations of task difficulty and intermediate result quality [90, 442, 691, 997, 923, 663, 799, 290, 790] or even diffusion-like decoding processes [363], rather than relying solely on human experience. (2) Leveraging efficient reasoning format: Another promising direction involves integrating multimodal, latent space, or other efficient reasoning formats to express logic more effectively [125, 662, 800]. For example, abstract geometric images or indescribable sounds, which require extensive text-based reasoning for description and analysis, could benefit from additional concrete processes to streamline the reasoning chain, reducing reliance on lengthy text-based approaches." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.579, + 0.453, + 0.594 + ], + "angle": 0, + "content": "8.5 Knowledge-Augmented Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.601, + 0.827, + 0.851 + ], + "angle": 0, + "content": "The reasoning model significantly enhances reasoning capabilities, but it still lacks knowledge in specialized fields and timely new information [93, 175, 475, 677]. Thus, enriching reasoning with additional knowledge presents a key challenge for Long CoT [83, 75]. Current research focuses primarily on two approaches: (1) Retrieval-Augmented Generation: Retrieval-Augmented Generation (RAG) techniques enhance LLMs by integrating dynamic knowledge retrieval and document refinement [418, 811, 221, 322, 827, 1103, 1100, 592, 438]. Research has combined RAG with reasoning modules to improve performance on complex tasks [726, 329, 474, 861, 88, 1060, 616]. O1 Embedder [919] optimizes multi-task retrieval and reasoning through synthetic data training. Furthermore, Stream of Search (SoS) [193], and CoRAG [786] boost search accuracy and addresses unresolved issues by incorporating more natural reflection and exploration in RAG. (2) Model Knowledge Injection: An alternative approach involves integrating additional knowledge during SFT or RL [496, 1031, 124, 1132]. Specifically, HuatuoGPT-o1 [83] utilize the R1-like paradigm to train LLMs by model-judged reward RL, which significantly improves the medical knowledge during reasoning [577, 294, 769]. Huang et al. [300] and Wang et al. [766] optimize for injecting medical knowledge in Long CoT scenarios by SFT, which also achieve great performance. Further, Jiang et al. [325] introduce MCTS to synthesize data, achieving superior performance. This model merges verifiable medical knowledge with reinforcement learning techniques to enhance performance in complex, medical task settings." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.856, + 0.828, + 0.914 + ], + "angle": 0, + "content": "The main concerns regarding knowledge augmentation for Long CoT are as follows: (1) Effective Knowledge Integration and Alignment: A major challenge is effectively integrating external knowledge (e.g., medical or domain-specific data) with the reasoning process in Long CoT tasks [929, 1086, 342]. The model must not only retrieve relevant information but also ensure it aligns with" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.509, + 0.948 + ], + "angle": 0, + "content": "35" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.311, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.828, + 0.162 + ], + "angle": 0, + "content": "the ongoing reasoning, maintaining coherence across long chains of thought [509]. (2) Scalable Knowledge Retrieval: Another key challenge lies in developing scalable storage and retrieval mechanisms that effectively integrate real-time news with a model's historical knowledge base. Since models often need to access vast amounts of information during a single task, optimizing retrieval strategies to ensure quick, contextually relevant updates is critical for enhancing system effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.172, + 0.453, + 0.187 + ], + "angle": 0, + "content": "8.6 Safety and Stability for Long CoT" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.194, + 0.828, + 0.485 + ], + "angle": 0, + "content": "Despite the notable performance improvements brought about by Long CoT, Long CoT-augmented LLMs still encounter significant safety and stability challenges [1135, 1073, 515, 837, 785, 257]. These include issues such as the generation of unstable outputs, exemplified by the tendency to memorize in-domain math questions instead of engaging in actual reasoning [918], and the production of unsafe outputs, such as misinformation and offensive content [1123, 384, 1122, 510, 23, 46, 45, 160, 346, 1061]. Current research primarily addresses two key approaches: (1) Long CoT Attack Several studies show that Long CoT makes models more vulnerable to unexpected behavior [181, 146], hallucinations [255, 505] or unsafe outputs [360, 1145, 906, 108, 20, 525]. For instance, Arrieta et al. [24] identify that DeepSeek-R1 is prone to generating harmful content, including misinformation and offensive speech. Additionally, Kumar et al. [357] introduce the OverThink attack, which exploits false inference problems to induce overthinking in models, providing insights into potential defensive strategies. Further, Yao et al. [958] fool RLLMs chain of iterative chaos, for better jailbreaking. (2) Long CoT Safety Improvement Another major area of research focuses on enhancing safety [320, 1138, 493] and reliability [715, 636, 748, 147, 105, 655] through prompting [191] or training [579] techniques. Shen et al. [662] present Heima, which optimizes inference efficiency and robustness. Gallego [191] proposes dynamic security prompts during inference, while Cheng et al. [121] address hallucinations by guiding reasoning with a tree search algorithm. Zhao et al. [1092] introduce a self-reflection framework to identify biases, and Wang et al. [772] propose Safety Reasoning with Guidelines (SRG) to defend against out-of-distribution attacks. Finally, Parmar and Govindarajulu [587] combine reinforcement learning (RL) and supervised fine-tuning (SFT) in a hybrid training approach to reduce harmful outputs and enhance DeepSeek-R1's safety." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.49, + 0.828, + 0.629 + ], + "angle": 0, + "content": "The main concerns regarding safety for Long CoT are as follows: (1) Mitigating Cognitive Overload in Complex Reasoning: Long CoT approaches require managing extended reasoning chains, which can result in cognitive overload in LLMs [330, 90]. This overload may lead to errors, hallucinations, or unsafe outputs. Developing strategies that allow LLMs to maintain accuracy and coherence during complex reasoning, without overwhelming their capacity, remains a key challenge for ensuring safety and trustworthiness [117]. (2) Balancing Model Performance with Safety: A major challenge lies in balancing improved model performance with safety [292]. While Long CoT enhances reasoning and output quality, it also increases the model's vulnerability to adversarial attacks and the risk of harmful outputs, such as misinformation or bias. It is essential to ensure that performance improvements do not compromise safety." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.642, + 0.325, + 0.658 + ], + "angle": 0, + "content": "9 Related Work" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.671, + 0.828, + 0.769 + ], + "angle": 0, + "content": "In recent years, advanced reasoning has gained increasing attention in natural language processing (NLP) communities. Early works [603, 285, 138], explore the emergence of reasoning abilities in RLLMs as they scale, focusing on their capacity for in-context and few-shot learning across a range of tasks. Additionally, Giadikiaroglou et al. [208], Yu et al. [980] and Liu et al. [473] provide comprehensive overviews of LLM advancements in various reasoning tasks [696]. Moreover, Chu-Carroll et al. [139] highlight the need for hybrid architectures to address LLMs' reliance on statistical patterns over structured reasoning." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.773, + 0.829, + 0.913 + ], + "angle": 0, + "content": "With the development of advanced RLLMs, such as OpenAI-o1 and DeepSeek-R1, recent research has focused on improving reasoning capabilities, especially on mathematical reasoning [795, 1096, 33]. Patil [588] highlight the limitations of standard LLMs in addressing complex reasoning tasks, such as optimization and multi-step reasoning. In addition, Liang et al. [440] and Li [419] review strategies to scale search and inference time, including the use of algorithms like Monte Carlo Tree Search, to enhance LLM reasoning. Xu et al. [899] examine the role of reinforcement learning and \"thought\" sequences in reasoning improvement [359], while Hong et al. [259] demonstrate the impact of prompting techniques [546]. Further, Liu et al. [473] and Mondorf and Plank [557] stress the importance of deeper analysis beyond surface-level accuracy, and He et al. [248] explore self-evolutionary processes as a means to advance LLM reasoning. Besta et al. [50] propose a modular" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.936, + 0.511, + 0.948 + ], + "angle": 0, + "content": "36" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.174, + 0.043, + 0.31, + 0.072 + ], + "angle": 0, + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.092, + 0.828, + 0.135 + ], + "angle": 0, + "content": "framework integrating structure, strategy, and training methods as part of a comprehensive system design approach. Most recently, Li et al. [432] provide a systematic survey of System 2 thinking, focusing on the methods used to differentiate them from System 1 thinking." + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.14, + 0.828, + 0.21 + ], + "angle": 0, + "content": "Despite numerous technical reviews in this field, there is limited discussion on the differences between Long CoT and Short CoT. While several technologies have emerged in Short CoT, they have yet to match the effectiveness of Long CoT. This issue has not been thoroughly addressed. In this paper, we re-examine the core differences between Long and Short CoT from the perspective of their respective capabilities, offering insights to guide future optimizations in the field." + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.224, + 0.31, + 0.239 + ], + "angle": 0, + "content": "10 Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.252, + 0.828, + 0.336 + ], + "angle": 0, + "content": "In conclusion, this survey addresses key gaps in Long CoT research, distinguishing it from Short CoT and providing a comprehensive overview of the field. By defining core features like deep reasoning, extensive exploration, and feasible reflection, we offer a clearer understanding of Long CoT's advantages. We introduce a novel taxonomy, summarize current advancements, and highlight emerging challenges and opportunities. Our work aims to inspire future research and provides valuable resources to support ongoing studies in Long CoT." + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.356, + 0.269, + 0.372 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.196, + 0.381, + 0.826, + 0.424 + ], + "angle": 0, + "content": "[1] Asma Ben Abacha, Wen-wai Yim, Yujuan Fu, Zhaoyi Sun, Meliha Yetisgen, Fei Xia, and Thomas Lin. Medec: A benchmark for medical error detection and correction in clinical notes. arXiv preprint arXiv:2412.19260, 2024." + }, + { + "type": "ref_text", + "bbox": [ + 0.197, + 0.429, + 0.825, + 0.457 + ], + "angle": 0, + "content": "[2] Marwan AbdElhameed and Pavly Halim. 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Medxpertqa: Benchmarking expert-level medical reasoning and understanding. arXiv preprint arXiv:2501.18362, 2025." + }, + { + "type": "list", + "bbox": [ + 0.173, + 0.091, + 0.828, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.935, + 0.512, + 0.948 + ], + "angle": 0, + "content": "109" + } + ] +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09567/17e53201-29b3-43fd-8f2e-78d7b00a58a6_origin.pdf b/data/2025/2503_09xxx/2503.09567/17e53201-29b3-43fd-8f2e-78d7b00a58a6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f386050431686988350388b083dd20514b792798 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09567/17e53201-29b3-43fd-8f2e-78d7b00a58a6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7e74008e30a58df4cecb6092e546785a2f104523621d4336ab24b5a717549cdb +size 6417696 diff --git a/data/2025/2503_09xxx/2503.09567/full.md b/data/2025/2503_09xxx/2503.09567/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f0ea2e382f489d40c122c84e252206599e961055 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09567/full.md @@ -0,0 +1,1923 @@ +Qiguang Chen† Libo Qin‡ Jinhao Liu† Dengyun Peng† Jiannan Guan† Peng Wang‡ Mengkang Hu◇ Yuhang Zhou Te Gao† Wanxiang Che† LARG, + +$\dagger$ Research Center for Social Computing and Interactive Robotics, $\dagger$ Harbin Institute of Technology + +$^{\ddagger}$ School of Computer Science and Engineering, Central South University + +The University of Hong Kong + +Fudan University + +{qgchen,car}@ir.hit.edu.cn,lbqin@csu.edu.cn + +Project: https://long-cot.github.io/ + +Github: LightChen233/Awesome-Long-Chain-of-Thought-Reasoning + +![](images/3bcec7826e1fbcdb6dfe89578c968d54d801a27312caf0fc018f86ba59fa632d.jpg) + +# Abstract + +Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "inference-time scaling". This survey seeks to fill this gap by offering a unified perspective on Long CoT. Specifically, (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and inference-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of reasoning large language models1. + +# 1 Introduction + +In recent years, as shown in Figure 1, the emergence of reasoning large language models (RLLMs) such as OpenAI o1 [307] and DeepSeek R1 [227] has sparked a growing body of research into Long Chain-of-Thought (Long CoT) reasoning, greatly improving their mathematical reasoning, programming tasks, and multidisciplinary knowledge reasoning capabilities [696, 980, 722, 79, 961, 200, 1113, 793], even passing Turing Test [334]. This shift marks a significant departure from traditional approaches to task handling in large language models (LLMs) [1147, 619, 622, 599]. Unlike the shorter chain-of-thought (Short CoT) used in traditional LLMs, Long CoT reasoning entails a more detailed, iterative process of exploration and reflection within a given problem space by inference-time scaling [419, 733, 524]. This process has led to notable advancements in mathematical and logical reasoning, as well as in exploring how supervised fine-tuning (SFT) and reinforcement learning (RL) techniques can enhance the learning and exploration of extended reasoning chains [623, 550]. + +However, there is no comprehensive survey to systematically understand the main factors and recent efforts of Long CoT for RLLMs, which hinders the development of RLLMs. As a result, there are ongoing debates about the effectiveness of simple "inference-time scaling" for Longer CoT [864, 486] versus the argument that "over-thinking" from excessively long scaling can harm LLMs and introduce unnecessary complexity [103, 142, 357]. Moreover, some researchers argue that, when solving specific problems, there is no clear relationship between length and accuracy [886]. + +To address this gap, we provide an extensive and comprehensive survey of Long CoT. Specifically, as illustrated in Figure 2, we first define and examine the distinctions between Long CoT and traditional Short CoT, focusing on the following key aspects: (1) Deep Reasoning, which requires a sufficient depth of logical processing to manage an extensive set of logical nodes; (2) Extensive Exploration, which involves generating parallel uncertain nodes and transitioning from known to unknown logic; and (3) Feasible Reflection, which involves feedback and refinement of logical connections. These characteristics enable Long CoT paradigms to integrate more intricate reasoning and accommodate a broader range of logical structures, ultimately leading to more efficient and coherent outcomes. Subsequently, we systematically explore the underlying explanations for key phenomena associated with Long CoT, such as its emergence, the overthinking phenomenon, + +![](images/be56637e4c051b7d3d3a17014777899ed5d63d7f01c713db6f624e8d8196114d.jpg) +Figure 1: Evolution of selected Long CoT over the past three years, where colored branches represent different characteristics: deep reasoning, feasible reflection, and extensive exploration. Each characteristic is further divided into key areas: Deep reasoning includes its format and learning methods. Feasible reflection focuses on feedback and refinement techniques during reflection process as optimization strategies. Extensive exploration addresses scaling, internal, and external exploration as key improvements to Long CoT. + +inference-time scaling during testing, and the "Aha Moment," among others. To our knowledge, This is the first comprehensive survey dedicated to these specific topics. Finally, considering the extensive body of literature, we highlight promising areas for future research and suggest valuable open-resource frameworks and datasets that can serve as a foundation for future investigations. + +The main contributions of this work are as follows: + +- Systematic Distinction: In this work, we first introduce the concept of Long CoT reasoning and distinguish it from the traditional Short CoT, thereby providing a clear framework for understanding both paradigms and their respective characteristics. +- Explanation of Hot Phenomena: We systematically investigate the notable phenomena associated with Long CoT reasoning, such as overthinking, inference-time scaling, and the "Aha Moment", offering valuable insights into the cognitive processes involved in complex reasoning. +- Emerging Challenges and Frontiers: We explore the emerging challenges within the field of Long CoT reasoning and identify key research frontiers. Given the vast body of literature, we highlight areas where further inquiry could significantly advance the development of Long CoT methodologies. + +# 2 Discussion of Long CoT v.s. Short CoT + +This section formalizes the key differences between Long Chain-of-Thought (Long CoT) and Short Chain-of-Thought (Short CoT), emphasizing reasoning depth, revisiting connections, and logical node exploration [858]. These distinctions are clearly separate from System 1 and System 2 thinking. The comparison between Long CoT and Short CoT is framed within System 2, with Long CoT involving more thorough reasoning, reflection, and exploration, while Short CoT generally prioritizes shallow and efficient logic over exhaustive reasoning. + +# 2.1 Overview of Short CoT + +As illustrated by Figure 2, Short CoT is typically characterized by a shallow, linear reasoning process, where conclusions are drawn sequentially, often relying on a limited number of logical nodes [551]. This reasoning is usually rapid and straightforward, with simple, surface-level transitions and minimal + +Proof of Number Theory Problem: For any positive integer $n$ , there exists a positive integer $m$ such that $m^2 + 1$ is divisible by $n$ . + +![](images/f0eadf51633e7fb658ee5728c1487fe0163f55fb50102d3c0b34bdb3de0da945.jpg) +Figure 2: The differences between advanced Long CoT and traditional Short CoT are characterized by three key characteristics: deep reasoning, feasible reflection, and extensive exploration. Moreover, Long CoT integrates all these characteristics to achieve substantial logical efficacy. + +exploration of alternative paths, which restricts its generalizability [683]. Formally, given a reasoning model $\mathcal{R}$ , we can define the rationale of Short CoT $(\mathsf{C}\circ \mathsf{T}_S)$ as follows: + +$$ +\mathrm {C o T} _ {S} = \mathcal {R} \left(\left\{n _ {i} \right\} _ {i = 1} ^ {k} | (k \leq \mathcal {B} _ {s}) \wedge (j = 1 \Leftrightarrow \forall i \leq k, n _ {i} \rightarrow n _ {i + j}) \wedge (\forall i \neq j \leq k, n _ {i} \neq n _ {j})\right), \tag {1} +$$ + +where $n_1$ to $n_k$ represent a sequence of logical nodes, which naturally satisfy that $\forall i, n_i \to n_{i+1}$ . Here, $\mathcal{B}_s$ denotes the upper boundary on the number of logical nodes, as defined by Chen et al. [90]. In this paradigm, the reasoning progresses sequentially from one node to the next, with minimal revisitation of previous nodes and little exploration of alternative logical paths. + +# 2.2 Overview of Long CoT + +In contrast, Long CoT involves deeper reasoning, reflective analysis, and a broader exploration of logical structures. It facilitates reasoning across a wider range of logical steps, addressing both known and unknown elements of a problem [194, 858]. Building on this, Long CoT expands upon the constraints presented in Equation 1 based on tree structures by incorporating three critical components: deep reasoning, exploration, and reflection. + +These components play distinct yet complementary roles in enhancing cognitive processes. Deep reasoning ensures each logical step is executed rigorously, even within complex structures, fostering robust logic across intricate relationships. Exploration encourages the identification of new pathways, revealing potential avenues that may not be immediately obvious. Reflection enables iterative analysis and reassessment of conclusions, allowing reasoning to evolve throughout problem-solving. By distinguishing these three categories, Long CoT enhances its ability to address a broader range of problems with precision and depth. As shown in Figure 3, we will now discuss these key differences in detail. + +# 2.2.1 Deep Reasoning for Long CoT + +As shown by Figure 2, deep reasoning refers to the capability to perform deep and thorough logical analysis across multiple interconnected logical nodes, where Short CoT generally can never achieve. This capability is essential when tackling complex problems that require a massive number of logical deductions to arrive at a valid conclusion. To better define and understand deep reasoning, we frame it as a capability that primarily relaxes the first constraint in Equation 1, as expressed by the following: + +$$ +k \leq \mathcal {B} _ {s} \mapsto k \leq \mathcal {B} _ {l} \wedge \mathcal {B} _ {s} \ll \mathcal {B} _ {l}, \tag {2} +$$ + +where $\mathcal{B}_l$ represents the upper boundary for Long CoT reasoning, which can accommodate much more intricate logical nodes compared to the smaller boundary $\mathcal{B}_s$ for Short CoT. The larger boundary $\mathcal{B}_l$ alleviates issues related to insufficient depth in reasoning, thereby reducing the risk of generating unresolved answers or hallucinated responses in short-form reasoning. + +![](images/fa1bbeeb7a7a9e97707e957eb9cfc744f2a2eba4ab0e5a7c5f73282936c28213.jpg) +Figure 3: Taxonomy of Long CoT, which includes deep reasoning, feasible reflection, and extensive exploration methodologies. + +# Key Difference: Reasoning Depth + +- Short CoT typically addresses a limited set of logical nodes, involving shallow reasoning, and struggles with problems requiring complex or intricate logical structures. +- Long CoT is designed to accommodate a significantly larger set of logical nodes, allowing for deeper logic and more thorough analysis during the reasoning process. + +# 2.2.2 Extensive Exploration for Long CoT + +As shown by Figure 2, Long CoT encourages branching out to extensively explore uncertain or unknown logical nodes, thereby expanding the potential set of reasoning paths. This exploration is particularly critical when solving problems characterized by ambiguity, incomplete information, or multiple possible solutions [43, 1016, 871]. More specifically, we describe how extensive exploration primarily addresses the relaxation of the second constraint in Equation 1, which can be formalized as follows: + +$$ +j = 1 \Leftrightarrow \forall i \leq k, n _ {i} \rightarrow n _ {i + j} \mapsto \exists m, \forall i, \forall j \leq m, n _ {i} \rightarrow n _ {i + j}, \tag {3} +$$ + +where the condition indicates that for a logical node $n_i$ , there are $m$ nodes that are explored in parallel. The acceptability of parallel exploration allows for a more systematic approach, enabling the exploration of previously unconsidered logical paths. This, in turn, helps maximize the understanding of all possible solutions, ultimately leading to the correct final answer. + +# Key Difference: Exploration of Logical Nodes + +- Short CoT generally restricts exploration to a fixed set of logical nodes, often resulting in oversimplified reasoning and limited exploration. +- Long CoT explores more various paths, including uncertain or uncharted areas, fostering more nuanced and comprehensive problem-solving. + +# 2.2.3 Feasible Reflection for Long CoT + +As shown by Figure 2, Long CoT involves revisiting previous logical nodes to verify their connections are valid and accurate, and then correcting them or selecting an alternative logical path. Formally, feasible reflection relaxes the third constraint in Equation 1, which originally requires acyclic reasoning such that $n_i \neq n_j$ for all $i \neq j \leq k$ . In contrast, feasible reflection permits the reasoning path to return to a previously visited node, captured as: + +$$ +\forall i \neq j \leq k, n _ {i} \neq n _ {j} \mapsto \exists i < j \leq k, n _ {i} = n _ {j}, \tag {4} +$$ + +where this condition indicates that, for a logical node $n_{j-1}$ , the subsequent node is not limited to the original next node $\hat{n}_j$ . Instead, it may transition to $n_i$ (i.e., the next logical node becomes $n_j$ , where $n_j = n_i$ ). Practically, reflection implementation consists of two components: + +Feedback refers to evaluating both overall and intermediate outputs for correctness and quality, also known as critique or verification. It can be derived from external sources, validation checks, or by reflecting on prior conclusions within the reasoning process. Formally, at each step $n_i$ , a verification process $\mathcal{V}_i$ ensures the correctness, feasibility, and consistency of the reasoning. If an issue is identified, the process redirects $n_i$ to the nearest correct node $n_j$ , where $j < i$ . This relationship is formalized as: + +$$ +\mathcal {F} _ {i}, n _ {j} \leftarrow \operatorname {F e e d b a c k} \left(\mathrm {C o T} _ {L} ^ {i}\right) \tag {5} +$$ + +where $\mathrm{CoT}_L^i = \{n_1,\dots ,n_i\}$ represents the current logical path up to the $i$ -th logical node for Long CoT. + +Refinement involves adjusting intermediate steps or modifying the logical flow to correct inconsistencies or address gaps based on the given feedback. This process can be expressed mathematically as follows: + +$$ +\widetilde {n} _ {i + 1} \leftarrow \operatorname {R e f i n e} \left(n _ {i + 1} \mid \mathrm {C o T} _ {L} ^ {i}, \mathcal {F} _ {i}, n _ {j}\right), \tag {6} +$$ + +where $\widetilde{n}_{i+1}$ represents the refined version of the subsequent logical node $n_{i+1}$ , according to the current logic $\mathbb{C} \circ \mathbb{T}_L^i$ , feedback result $\mathcal{F}_i$ , and previous logical node $n_j$ . + +Overall, incorporating reflection ensures that errors are identified and corrected promptly. This capability enables LLMs to quickly shift to alternative reasoning paths or correct their current trajectory. By doing so, error propagation is minimized, resulting in more accurate conclusions. + +# Key Difference: Feedback & Refinement + +- Short CoT typically moves in a straightforward, non-repetitive manner from one node to the next, so that cannot correct their logic. +- Long CoT allows for revisiting and revising earlier decisions by feedback and refinement, ensuring that estimizable and prior logical conclusions during the reasoning progress. + +# 2.2.4 Unified Application and Development History of Three Capabilities + +The Long CoT discussed here represents a unified reasoning system that seamlessly integrates and applies three key capabilities: deep reasoning, reflective mechanisms, and exploration capabilities. In contrast, during the Short CoT era, these capabilities developed independently, each evolving in isolation. + +As shown in Figure 2, early efforts primarily focused on enhancing deep reasoning within traditional CoT paradigms. This was followed by the gradual introduction of reflective mechanisms, which were initially based on human-designed pipelines. Over time, exploration capabilities were added, and + +these components were ultimately merged, giving rise to the modern concept of Long CoT, a unified approach to reasoning that seeks to enhance all three capabilities in harmony. + +The progression of Long CoT is gradual, rather than a sudden emergence through isolated models like o1 [307] and R1 [227]. Instead, it develops gradually. For example, earlier systems, such as ToT [955], enhance exploration but lack reflective mechanisms, disqualifying them as Long CoT [95]. While GoT [48] incorporates self-reflection based on ToT, its original model still lacked robust deep reasoning, preventing it from qualifying as Long CoT at that time. It is also notable that modern Long CoT systems, often neglect earlier technologies. This article addresses this gap by tracing the evolution of each capability, with the final section offering a comprehensive analysis of the integrated Long CoT system. + +In summary, Long CoT and Short CoT represent distinct paradigms. Long CoT features a deeper, broader, and more reflective reasoning process, enhancing both accuracy and coherence. Short CoT, by contrast, is better suited to simpler, well-defined problems. This distinction highlights the scalability and adaptability of Long CoT, making it particularly effective for more complex reasoning. + +# Key Difference: Unified Application of Three Capabilities + +It is important to highlight that Long CoT integrates these three distinct capabilities to perform complex reasoning. In contrast, traditional Short CoT optimization typically focuses on only one of these characteristics. + +# 3 Long CoT Analysis & Evaluation + +# 3.1 Analysis & Explanation for Long CoT + +Research on Long CoT has significantly enhanced RLLMs by improving reasoning accuracy, reducing errors, and supporting dynamic decision-making. However, several phenomena and their corresponding mechanisms remain inadequately summarized. This section addresses key topics, including the mechanisms of Long CoT and their underlying principles [644, 63, 545, 642]. Methodologically, two main perspectives have emerged to explain Long CoT: (1) External Behavior Analysis (§ 3.1.1) and (2) Internal Mechanism Analysis (§ 3.1.2). + +# 3.1.1 Long CoT External Behavior Analysis + +The primary research stream focuses on explaining RLLM behaviors for Long CoT [25]. As illustrated in Figure 4, six key phenomena are identified and discussed for Long CoT in this part. + +Long CoT Emergence Phenomenon Research shows that contextual examples improve large models' generative abilities by guiding the formation of reasoning chains [1012, 671, 417, 343, 532, 846, 1017, 1141]. Wang et al. [759] and Lippmann and Yang [461] demonstrate that these examples standardize reasoning chain generation relevant to the answers both in in-context-learning and supervised-finetuning. In an experiment by Madaan et al. [538], removing problem-specific entities from contextual examples, while retaining only the logical structure, led to similar performance as using complete examples, highlighting the logical structure imitation of Long CoT during inference. From a learning perspective, Ye et al. [963] analyzes and reveals the three-stage developmental trajectory of Long CoT: early memorization, followed by in-distribution generalization, and ultimately cross-distribution generalization, thereby enabling the model to exhibit Long CoT capabilities. + +More recently, Stechly et al. [688] and Wang and Zhou [815] have shown that modifying the decoding process or designing specific prompts can activate the Long CoT within pre-trained models. They propose that CoT is embedded during pre-training and requires specific activation [941]. Further, Sadr et al. [642] focus the Long CoT source from the training data, and build on this with the notion of "model attribution", to specifically identify the training data most influential for specific outputs. Building on this, Guo et al. [227] and Xie et al. [886] investigate using rule-based reinforcement learning to directly activate Long CoT during pre-training, aiming to enhance performance [881]. Furthermore, Gandhi et al. [194] identify four key cognitive behaviors, including verification, backtracking, sub-target setting, and backward chaining, which successfully facilitate Long CoT. Qwen series models [926] inherently demonstrate these behaviors, which can be easily triggered by rule-based reinforcement. In contrast, the models of Llama series [168] lack these + +![](images/5a5b622a5ef9a492838399c45ff5d29022e17e93ea38f8784aa310a395d4009d.jpg) +Figure 4: Analysis of the six classic phenomena of Long CoT external behavior: (a) emergence of Long CoT in current RLLMs; (b) reasoning boundaries and limitations of current Long CoT systems; (c) overthinking caused by scaling beyond RLLMs' reasoning boundaries, leading to performance decay; (d) inference-time scaling, discussing mainstream scaling methods, corresponding scaling laws and their limitations; (e) use of process reward model (PRM) or outcome reward model (ORM); (f) exploration of the "aha" moment and its underlying causes. + +![](images/b58ea3cfdd162d9e8dc0a98bea568dac497bec49f930188fabfb39d4a8af9188.jpg) + +![](images/7574cfd5bdc73debbbe23c4cd13dc43c38b3f705661075e1c69e68c8876576bc.jpg) + +![](images/7acf371a734b42dff8be38ed39013e080e5d0020e7a712fdcc41abb09ba80b65.jpg) + +capabilities and thus requires example-based reinforcement learning to improve significantly [65]. Moreover, Wang et al. [812] identify a pretraining scaling law that explains how increasing calculation size in RLLMs enhances their reasoning capabilities. Wang et al. [796] further explore the scaling law of Long CoT, showing that more fine-grained Long CoT granularity leads to more efficient and effective generalization performance. + +Reasoning Boundary Phenomenon Recent research has highlighted the upper bounds and limitations of RLLMs across various reasoning tasks [303, 283, 684, 261, 185, 252]. Specifically, Bi et al. [53] investigate these bounds in code generation, showing that RLLMs struggle with tasks that exceed certain complexity thresholds [600], especially when imitating Long CoT samples of varying complexity. In the context of upper-bound performance, Merrill and Sabharwal [548] and Li et al. [430] focus on single-step arithmetic tasks, concluding that model performance is constrained by input length. Moreover, Feng et al. [177] proposes a mathematical model indicating that fixed-size models cannot produce accurate numerical answers beyond specific limits. However, increasing the number of reasoning steps improves a model's capability requirements to solve more complex problems. + +Inspired by these explorations, Chen et al. [90] first define the "reasoning boundary" phenomenon and quantify these limits, showing that surpassing an RLLM's reasoning capacity leads to performance decline [92]. Similarly, Zhou et al. [1130] introduce GSM-Infinite, linking different upper limits to accuracy levels. Chen et al. [90] also examine the interaction between these boundaries across tasks of varying complexity, providing insights into the effectiveness of Long CoT strategies [1085]. Moreover, Amiri et al. [12] propose a "tight lower bound" for Long CoT further guiding reasoning error reductions. Further, Baeumel et al. [28] suggest that due to its reliance on a single-digit lookahead heuristic, there are inherent boundaries in performing addition with multiple operands, which thus hinders the fundamental limitation of LLMs in scaling to more complex numerical reasoning. Liu et al. [483] further investigate the role of reinforcement learning in expanding these reasoning boundaries instead of relying solely on pretraining capabilities. + +Overthinking Phenomenon Research has highlighted the overthinking phenomenon [103, 330, 574, 142, 357, 595], where performance improves with longer reasoning chains up to a threshold, after which it declines. In contrast, Xie et al. [886] and Ma et al. [534] find no significant correlation between reasoning length and accuracy. To explain this, one line of research suggests that Long CoT strategies [21, 441], like avoiding "snowball errors" [192]. Alternatively, Chen et al. [90], Wolf et al. [851] highlight a performance drop when the reasoning boundaries are exceeded, providing an explanation for the overthinking phenomenon. This suggests that reasoning length and logical complexity should be kept below a certain boundary [1080]. Building on this, Wu et al. [867] mathematically determine the feasible reasoning length for Long CoT. Finally, Chen et al. [93] introduces Ohm's law of Long CoT, which accurately predicts and controls performance. + +Inference-Time Scaling Phenomenon Recent advances in inference-time scaling algorithms [524, 843] have garnered significant attention, particularly for their ability to extend reasoning length and improve performance [524, 455, 875]. Specifically, Brown et al. [57] identify a phenomenon called "Large Language Monkeys", in which a series of reasoning tasks show that with enough trials, a correct result can be achieved. Additionally, o1 [307] and R1 [227] demonstrated that directly scaling the length of model inference improves final performance. + +To understand inference-time scaling, we will discuss these two paradigms: (1) Sequential Scaling: Sequential scaling involves increasing the reasoning path length. While this can enhance performance, studies by Jin et al. [330] show that, beyond a certain point, longer reasoning paths can degrade performance due to error accumulation. They suggest an optimal path length that depends on the model's capabilities and task complexity [15, 652, 31]. Furthermore, Chen et al. [90] and Wu et al. [867] explain that excessive exploration lengths beyond the RLLM's inherent reasoning boundary lead to performance decay, which guides RLLMs for deeper reasoning capabilities [32]. (2) Parallel Scaling: Parallel scaling involves performing multiple reasoning steps and verifying the results. While it shows promise, Parashar et al. [583] and Wang et al. [820] argue that simply increasing inference time does not guarantee improved performance. Wu et al. [864] show that the computational FLOPs $N$ of inference are correlated with the lower bound of performance error, which scales with $\log N$ . Additionally, Chen et al. [93] establish an upper bound for parallel scaling, showing that RLLMs cannot exceed Pass@k verification through various verifiers. They further argue that sampling optimization cannot exceed the model's internal reasoning limitations, demonstrating that for $N$ samples, accuracy is proportional to $\frac{m}{(k / \log N + b)^2}$ , where $m$ , $n$ , and $b$ are model-dependent constants. + +PRM & ORM Selection Phenomenon As RLLMs evolve, it is crucial to navigate the debate around the selection between process supervision and outcome supervision, two key reinforcement learning paradigms for complex reasoning tasks. The phenomenon of choosing between these two approaches has become a pivotal issue, as it is essential to differentiate and decide which supervision strategy is more suitable for specific tasks [899, 187, 1059]. While process supervision is intuitively advantageous for long-term reward assignments, the exact relationship between the two approaches remains unclear. It is commonly believed that process supervision is more challenging due to the trajectory-level coverage problem, which demands significant effort to collect fine-grained supervision data [1102, 679]. Additionally, PRM faces the issue of reward hacking [13, 152, 573, 30, 399], where agents exploit flaws in the reward function to produce unintended behaviors [227]. Addressing this to surpass rule-based reward systems has become an important research area [227, 886, 594]. Furthermore, Lampinen et al. [368] and Tan [708] establish a causal link between intermediate steps and final answers in qualitative experiments. Building on this, Jia et al. [317] demonstrate that, under the standard data coverage assumption, reinforcement learning with outcome supervision is not statistically more challenging than process supervision, aside from polynomial factors. More strictly, He et al. [247] mathematically demonstrate that outcome-level rewards suffice for online reinforcement learning in RLLMs. + +Aha Moment Phenomenon Earlier, Guo et al. [227] demonstrated that direct RL using rule-based rewards can trigger the aha moment, fostering natural self-reflection without supervision [172]. Following this, Team [721], Xie et al. [886] replicate this phenomenon. Further, Zhou et al. [1119] and Meng et al. [547] further extend this phenomenon to multimodal scenarios. However, Liu et al. [498] argue that the aha moment may not emerge in R1-Zero-like training. Instead, they observe that self-reflection patterns, such as superficial self-reflection (SSR), appear at epoch 0, the stage of base models. In this case, self-reflections do not necessarily lead to correct answers. Upon closer examination of R1-Zero training via RL, they find that the increasing response length results not from self-reflection, but from RL optimizing well-designed rule-based rewards. Moreover, Yang et al. [939] demonstrate that the "aha moment" is externally marked by increased use of anthropomorphic language during self-reflection and a dynamic adjustment of uncertainty in response to problem difficulty. This process enables the model to maintain reasoning without succumbing to "Reasoning Collapse." Internally, it is characterized by a clear distinction between anthropomorphic traits and logical reasoning, with anthropomorphic language intensifying as the problem becomes more complex. + +Reinforcement Learning Entropy Phenomenon In reinforcement learning for Long CoT, the entropy mechanism is a crucial factor influencing the performance of RLLMs. Policy entropy measures the diversity and exploratory strength of a model's outputs. By managing this entropy + +effectively, a model preserves exploration and thus excels on complex reasoning tasks. Earlier, Jang and Kim [310] investigate how initial entropy affects exploration in deep RL and proposed an entropy-aware initialization to encourage effective exploration. Building on this, Zhang et al. [1036] developed an Entropy-Regularized PRM that balances policy updates against large deviations from the starting distribution, thereby improving reasoning. Cheng et al. [116] found that high-entropy regions correlate positively with three exploratory reasoning behaviors: (1) key tokens linking logical steps, (2) self-verification and correction, and (3) rare behaviors underrepresented in the base model. Most recently, Agarwal et al. [5] introduced an Entropy Minimization method and demonstrated its strong impact on LLM performance in mathematical, physical, and coding tasks. + +However, recent research indicates that, during early training, policy entropy declines sharply, causing the model to converge prematurely on specific output patterns and limiting further reasoning improvement [144]. In reinforcement learning, policy entropy $(H)$ and downstream task performance $(R)$ follow an exponential relation: $R = -a\cdot e^{H} + b$ , so a drop in entropy produces a rapid performance decline until saturation. This "policy entropy collapse" is common without entropy control, as reduced entropy constrains exploration and stalls reasoning gains [144]. To counter this collapse, two methods, Clip-Cov and KL-Cov, regulate entropy by constraining updates on high-covariance tokens. Clip-Cov clips their update magnitudes, whereas KL-Cov imposes a Kullback-Leibler penalty. Empirical results show both techniques prevent collapse and enhance reasoning performance [144]. + +# 3.1.2 Long CoT Internal Mechanism Analysis + +The second stream of research investigates the internal mechanisms of Long CoT-related RLLMs. + +Reasoning Internal Mechanism Recent studies have explored the internal mechanisms underlying the coherent rationale outputs of Long CoT, with particular emphasis on attention mechanisms [675, 632]. These studies primarily examine neural substructures in RLLMs, framing CoT reasoning from a white-box perspective [819, 992, 233, 169]. Weston and Sukhbaatar [849] introduces the concept of System 2 Attention (S2A), which demonstrates Long CoT generation by selectively focusing attention on relevant information. Additionally, Li et al. [407] explore gradient distributions between direct output and Long CoT layers, revealing that Long CoT layers help maintain stability by distinguishing relevant from irrelevant reasoning [840]. Finally, Zhang et al. [1068] conceptualize RLLMs as finite state automata, offering further insight into how internal dynamics influence external behavior. Despite Short CoT's struggles with self-correction, Bertolazzi et al. [47] show that these models rely on consistency heads (attention heads) to assess the alignment of numerical values in arithmetic solutions through internal shortcuts. + +Knowledge Incorporating Mechanism Current RLLMs primarily focus on mathematics and coding but have shown potential for generalization to other knowledge-rich domains, sparking growing interest in the mechanism for integrating domain-specific knowledge into Long CoT [860, 886, 1105]. Prystawski et al. [609] suggest that generative models store entity knowledge learned during pre-training independently, with the reasoning process in Long CoT linking this knowledge across entities. Radha and Goktas [630] recently introduced the Probabilistic Mixture Model (PMM), which categorizes model outputs into reasoning, memorization, and guessing. They also propose an Information-Theoretic Consistency (ITC) analysis to quantify the relationship between model confidence and strategy selection. Additionally, Jin et al. [331] define "Concept Depth" as the lowest layers at which complex concepts are understood, demonstrating varying levels of knowledge integration in RLLMs. Ou et al. [572] examine RLLM knowledge internalization through knowledge loop evolution, arguing that new knowledge acquisition is shaped by its connection to existing knowledge, with the loop evolving from formation to optimization and from shallow to deep. + +# 3.2 Long CoT Evaluations + +# 3.2.1 Metrics + +In benchmarking, various metrics assess model performance across reasoning tasks, each focusing on different aspects of reasoning ability. These metrics evaluate both RLLMs' effectiveness in achieving desired outcomes and their learning efficiency. As a result, metrics for RLLMs have gained increasing attention in recent research. For mathematical or code-related tasks, three key metrics are commonly used: Accuracy, Pass@k, and Cons@k based on regex extraction: + +Accuracy measures the proportion of correct outputs. +- Pass@k evaluates the likelihood of generating at least one correct solution within $k$ attempts. +- Cons@k assesses consistency by determining the model's ability to consistently produce correct or logically coherent solutions across multiple attempts. + +In scientific or commonsense question-answering tasks, evaluation often uses Exact Match (EM) and Accuracy based on regex extraction, where EM determines whether the model's output exactly matches the expected solution. + +For feedback techniques like ORM or PRM, Rank and Best-of-N metrics are often used: + +- Rank measures whether the reward model correctly prioritizes the best reasoning processes from the top $k$ candidates. +- Best-of-N selects the highest-scoring solution from $N$ generated reasoning trajectories, indirectly measuring the reward model's effectiveness based on final outcomes. + +# 3.2.2 Decoding Strategies + +Decoding strategies are essential for controlling the inference process. Common approaches include Greedy Decoding, Beam Search, and Major@k. Both Greedy Decoding and Beam Search limit the sampling range to reduce randomness, guiding the model toward more consistent outputs. In contrast, Major@k identifies the most reliable solution by selecting the one with the highest consistency from a set of $k$ candidate solutions. + +# 3.2.3 Benchmarks + +In the realm of Benchmarks, the focus lies on assessing the reasoning capabilities of RLLMs across diverse domains. There are two primary categories: (1) Outcome Benchmarks, which focus on the holistic view of Long CoT reasoning, and (2) Process Benchmarks, which concentrate on the local view of the Long CoT process or individual capabilities. + +Outcome Benchmarks In the realm of Outcome Benchmarks, the first focus lies on evaluating the logical reasoning capabilities: + +- Complex Mathematics: A central focus in complex mathematics is evaluating benchmarks like GSM8K [141] and MATH [253], which assess basic mathematical problem-solving abilities [1125, 1112]. Recent additions, such as AIME 2024 [8], AIME 2025 [571], MATH-500 [449], AMC 2023 [9], USAMO [598], OlympiadBench [239], and OlympiadArena [298], expand the evaluation of LLM performance in mathematics. Moreover, Putnam-AXIOM [224] and FrontierMath [210] introduce more complex problems that challenge future reasoning systems. Additionally, ThinkBench [291] and MATH-Perturb [288] focus on robust evaluation for Long CoT [38, 987]. +- Complex Coding: Complex coding benchmarks are also vital, with competitions like Codeforces, SWEbench [327], CodeContests [427], and LiveCodeBench [309] evaluating LLM coding and problem-solving skills. Notable additions such as MHPP [148], ProBench [934], HumanEval Pro, MBPP Pro [993], and EquiBench [833] enhance the scope and complexity of coding challenges. Moreover, some studies have explored applying these benchmarks in real-world code development scenarios for automatic code generation and evaluation [243, 744]. +- Commonsense Puzzle: Commonsense puzzle benchmarks, including LiveBench [850], BIG-Bench Hard [705] and ZebraLogic [450], assess models' ability to reason about commonsense situations. The ARC [131] and DRE-Bench [947] is often viewed as a challenging commonsense-based AGI test. JustLogic [87] further contributes to the evaluation of deductive reasoning and commonsense problem-solving. Moreover, Li et al. [382] introduce QuestBench, a benchmark designed to evaluate the ability of RLLMs to generate insightful and meaningful questions. + +The second focus area concerns Knowledge Benchmarks, essential for evaluating a model's capability in complex reasoning across various tasks for out of distribution evaluation [776]: + +- Scientific Reasoning: Scientific Reasoning benchmarks, such as GPQA Diamond [637], MMLU-Pro [821], and SuperGPQA [165], assess multi-domain reasoning in fields like chemistry, biology, and physics [157]. These benchmarks test models' ability to not only accumulate knowledge + +but also integrate it for problem-solving. Humanity's Last Exam (HLE) [602] further challenges models by requiring deep interdisciplinary reasoning across scientific disciplines. Further, Chung et al. [140] propose TPBench to evaluate the effectiveness of RLLMs in solving theoretical physics problems. + +- Medical Reasoning: In the realm of Medical Reasoning, the need for complex, domain-specific, and accurate reasoning is paramount [1094, 1024, 905, 589]. Benchmarks, such as MedQA [328], JAMA Clinical Challenge [76], LLMEval-Med [1049] and Medbullets [76], simulate diagnostic and treatment decision-making processes, reflecting real-world medical practice. These benchmarks evaluate a model's handling of medical knowledge and reasoning, from diagnosis to treatment planning. Additionally, MedXpertQA [1150] introduces a comprehensive evaluation framework combining text and multimodal data, specifically assessing AI's reasoning capabilities in healthcare. + +# 3.2.4 Process Evaluations + +Deep Reasoning Benchmarks Recent progress in RLLMs underscores the need for specialized benchmarks to evaluate their deep reasoning abilities in Long CoT [375, 1133]. Notably, Lin et al. [450] introduces ZebraLogic, a framework for assessing logical reasoning, especially in complex non-monotonic scenarios. Similarly, BigGSM [90] and GSM-Ranges [670] focus on perturbing numerical values to test logical and arithmetic reasoning in edge cases beyond the models' training distribution. ROSCOE [212], ReCEval [606], DiVeRSe [425], HLV [71], and CoT-Kinetics [51] are designed to assess each step in the deep reasoning process during Long CoT tasks. + +Exploration Benchmarks Several studies assess RLLMs' exploration capabilities in Long CoT tasks. Specifically, Sys2Bench [583] evaluates the exploration and scaling abilities of RLLMs, emphasizing generalization across diverse tasks. BanditBench [566] extends this by testing model performance in interactive environments, offering insights into practical applications. Additionally, Heyman and Zylberberg [254] introduce a graph coloring problem to assess reasoning and spatial exploration in complex problem-solving scenarios. + +Reflection Benchmarks Reflection benchmarks measure RLLMs' ability to identify, reflect upon, and correct errors in Long CoT reasoning. These benchmarks fall into two categories: feedback and refinement. (1) Feedback Benchmark: These benchmarks assess the ability of LLMs to detect errors and respond to feedback for improvement. For example, Lambert et al. [367] introduces RewardBench to evaluate RLLMs' reward capabilities. This framework is extended by Multimodal RewardBench[960], and CodeCriticBench [1025] to include multimodal and code contexts, respectively. Benchmarks such as ProcessBench [1102], PRMBench [679], MR-Ben [1021], and DeltaBench [250] focus on error detection and correction across various tasks at the step level. Additionally, RealL Mistake [337] and JudgeBench [709] address more real-world error evaluation. (2) Refinement Benchmark: These benchmarks focus on error correction in complex tasks. CriticBench [456] assesses critique-correction capabilities, while MLDebugging [287], and ErrorRadar [922] specializes in coding or multimodal reasoning error detection and refinement. FinerReason [72] introduces a commonsense puzzle for broader feedback and refinement evaluations. Medec [1] adapts error correction to healthcare, addressing medical issues. + +# 3.2.5 Advanced Evaluation + +Agentic & Embodied Reasoning Agentic and Embodied reasoning requires models to demonstrate an understanding of real-world interactions, tool use, and adaptive reasoning in response to change. To assess real-world understanding, Wang et al. [798] introduce a benchmark that evaluates agents' ability to reason about physical concepts. Zhang et al. [1064] extend this by assessing agents' interactions with real-world physics. Additionally, realistic tasks often demand complex planning and tool usage, necessitating benchmarks to evaluate agent reasoning. These benchmarks assess agents' abilities to navigate and complete tasks in digital environments. Building on this, Huang et al. [283] propose a framework for evaluating decision-making in multi-agent, competitive settings. Nath et al. [562] introduce ToolComp, a benchmark designed to evaluate multi-step tool-use reasoning. To analyze adaptive reasoning in the face of real-world change, OSWorld [887], CogAgent [260], Mobile-Agent-E [828], WebShop [954], WebArena [1126], WGSR-Bench [972], and WebGames [735] assess AI systems across domains such as operating systems, mobile GUIs, browser tasks, and interactive + +entertainment [1106, 780, 512, 552]. Hu et al. [272] present Text2World, which evaluates agents' ability to generate interactive environments from text to test agent adaptability [995]. + +Multimodal Reasoning Multimodal reasoning refers to a system's ability to integrate and reason across diverse input types, including text, images [316]. This capability is crucial for solving complex problems that require information from diverse formats. + +- Complex Mathematics: Mathematical reasoning often integrates both textual and visual components, such as equations, graphs, or diagrams [921]. Specifically, challenges like MathVista [508], MathVision [782], MathVerse [1054], M3CoT-Math [91], CMMaTH [433], EnigmaEval [763], CoMT-Geometry [125], and PGPS9K [1050] aim to advance multimodal reasoning in mathematics, improving the evaluation of multimodal Long CoT logic. +- Complex Code: The second area of focus involves code-related reasoning, where systems interpret textual descriptions and code snippets. Benchmarks like HumanEval-V [1035], Code-Vision [767], Plot2Code [852], and ChartMimic [931] evaluate systems' capabilities to generate or interpret code from natural language and multimodal inputs for assessing systems that integrate natural language processing with programming tasks. +- **Complex Science:** This area involves integrating scientific texts with related diagrams or experimental data. Benchmarks like ScienceQA [507], M3CoT-Science [91], BMMR [874], and ScienceBoard [698] evaluate how well models combine science information with Long CoT reasoning across various scientific domains [966]. Further, Guo et al. [229] propose MolPuzzle for the evaluation of molecular structure elucidation. +- Commonsense Puzzle: This area focuses on commonsense reasoning, where systems combine reasoning cues and images to make deeper conclusions. Chen et al. [91] introduce M3CoT-Commensense, which incorporates commonsense Long CoT reasoning for complex multimodal interactions. Further, PuzzleVQA [128], MMReason [953] and LEGO-Puzzles [711] focus more on abstract and spatial puzzle reasoning, respectively. Additionally, Wang et al. [760] propose two benchmarks: Clue-Visual Question Answering (CVQA), which tests visual comprehension through three task types, and Clue of Password-Visual Question Answering (CPVQA), which features two task types focusing on the interpretation and application of visual data. + +AI for Research Recent advancements in AI have significantly advanced scientific research [94, 1124, 817, 215], with platforms like SciWorld [798] improving the research process. Simultaneously, Pricope [608] and Chan et al. [67] introduce a machine-learning platform to evaluate the potential of RLLMs in automating experiments. Several studies also examine RLLMs' ability to generate innovative research ideas. For instance, Si et al. [672] conduct evaluations with over 100 NLP researchers to assess RLLMs' creativity, revealing notable limitations [404, 856, 726]. Additionally, Li et al. [434] introduce SolutionBench, a benchmark for assessing systems' ability to generate feasible solutions for complex engineering problems. + +# 4 Deep Reasoning for Long CoT + +Deep reasoning capabilities primarily require profound depth and comprehensiveness in cognitive and reasoning processes. In the absence of such capabilities, RLLMs suffer significant performance declines [758, 823]. Current methods for enhancing deep reasoning can be categorized into two main approaches: (1) Deep Reasoning Format ( $\S$ 4.1), which involves utilizing various reasoning execution formats to maximize the reasoning step length $k$ within reasoning boundary $\mathcal{B}_l$ in Equation (2), by selecting the most suitable reasoning format; and (2) Deep Reasoning Learning ( $\S$ 4.2), which focuses on improving the model's internal capabilities to enhance its deep reasoning abilities, thereby extending the reasoning boundary $\mathcal{B}_l$ in Equation (2) intrinsically. + +# 4.1 Deep Reasoning Format + +As illustrated in Figure 5, deep reasoning formats can be categorized into three main types: natural language ( $\S$ 4.1.1), structured language ( $\S$ 4.1.2), and latent-space reasoning ( $\S$ 4.1.3), the latter of which is further subdivided into token-, vector-, and manager-driven latent reasoning. The reasoning performance across these formats is presented in Table 1. + +# (a) Natural Language Deep Reasoning + +To predict the output of the given input for Conway's Game of Life, we need to apply the rules of the game to each cell on the board. The rules are as follows: + +1. Any live cell with fewer than two live neighbors dies (underpopulation)... +Given Input Board: ... +$\spadesuit$ Step-by-Step Analysis: ... +$\spadesuit$ Final Output: After applying the rules to each cell... + +![](images/ff164d8152d0e42a100061acaca7da8e5deb82846df7779c8c7d61fa44616288.jpg) + +# (b) Structured Language Deep Reasoning + +![](images/5627b8fe0330637f914d05c2ea3b75f4df43c678ec6ae3f0e9b7da8f94f4f43f.jpg) + +import necessary packages from collections import Cou + +import necessary packages + +from collections import Counter + +all class and function definitions in the code + +file, if any + +class Solution(object): + +defgameOfLifeInfinite(self, live): ctr = Counter((I, J) for i, j i + +![](images/998c396b19ab3cb07b28b1eb72b14b5078de0675ec62ef33294a59363f34d6e2.jpg) + +# (c) Latent Space Deep Reasoning + +![](images/823ca26e30f5429ff0ae86df5e048ed2430dd9bdc62c2d874445fe64c1774d87.jpg) +Figure 5: Three main categories of deep reasoning formats: natural language, structured language, and latent-space reasoning (subdivided into token-, vector-, and manager-driven latent reasoning), with examples drawn from Li et al. [401]. + +![](images/aa202666c0347e30f452afb50132bf46686ba98433600b7ee8d0e4c2f30ad8f5.jpg) + +![](images/09f798353b1e4615f84c4d824a90ec1e55d3d23579c20ec2917c35a81ade4452.jpg) +Reasoning Vector Driven Latent Space Deep Reasoning + +![](images/3effed9f4c545b03b2ac2c365b4d87fe9724f58c4dddd4294def63e3d2f5672e.jpg) +Reasoning Manager Driven Latent Space Deep Reasoning + +# 4.1.1 Natural Language Deep Reasoning + +Traditionally, researchers have sought to adapt natural language for intuitive and free-flowing deep reasoning [836, 1118, 303, 617, 1070, 765, 205]. Early work by Wei et al. [836] demonstrated that the use of natural language Long CoT significantly enhances the reasoning capabilities of RLLMs. Further, the Natural Program framework [460] allows RLLMs to engage in deeper natural language reasoning by ensuring a more structured and rigorous logical analysis. More recently, CodeI/O [401] has introduced a technique that reorganizes code-based reasoning patterns into natural language formats, further boosting the reasoning potential of RLLMs [36]. Similarly, Li et al. [387] propose CoRT, which integrates code into reasoning to facilitate a mixture of formats, resulting in improved cognitive performance. + +# 4.1.2 Structured Language Deep Reasoning + +Structured language deep reasoning encompasses various approaches designed to program [100, 464, 687, 591, 198, 845, 830, 1044] or symbolic language [605, 158, 451, 372, 933, 604, 37, 40, 797, 380] format for enhanced deep reasoning. In this context, most studies focus on utilizing code to better enhance the mathematical reasoning capabilities [389, 107, 978, 85]. Xu et al. [897] propose a neural-symbol self-training framework guided by the environment, addressing both the scarcity of symbolic data and the limitations of symbolic processing in LLMs. Additionally, Liao et al. [443] present SKIntern, which refines symbolic RLLMs through curriculum learning and linear attenuation, enabling the internalization of symbolic knowledge with fewer examples, reducing computational costs, and accelerating inference. Furthermore, Ranaldi et al. [634] introduce QuaSAR, a CoT variant that directs LLMs to operate at higher abstraction levels through quasi-symbolic reasoning, thus improving natural language reasoning and providing more precise structural representations. + +# 4.1.3 Latent Space Deep Reasoning + +Latent space deep reasoning encompasses techniques designed to enhance the reasoning abilities of LLMs by leveraging operations within continuous latent spaces [684, 151, 640, 324]. These approaches can be categorized into three main paradigms: (1) Reasoning Token-Driven Latent Space Deep Reasoning: Early work [810, 1013] introduce the concept of "planning tokens" or "thought tokens" to guide reasoning within latent spaces [949, 1008]. Further, Coconut [236] expands on this through the maintenance of multiple alternative reasoning paths, increasing both complexity and efficiency [1069, 706]. At the extreme, Heima [662] condenses the entire Long CoT process into a single token, yielding substantial computational savings. (2) Reasoning Vector Driven Latent Space Deep Reasoning: Building on the previous paradigm, LTM [356] conceptualizes the layers of LLMs as "thought blocks" and introduces the concept of "thought vectors" for each layer. This + +
ModelBase ModelGSM8kMATHGPQAOlympiadBenchLiveCodeBench
Latent Space Deep Reasoning
No-CoT [151]Mistral-7B [318]38.0----
SQ-VAE [810]Llama-2-7B [743]40.07.0---
RecurrentBlock-3.5B [204]-42.1----
ICoT-SI [151]Mistral-7B [318]51.0----
Natural Language Deep Reasoning
Self-Rewarding [114]Llama-2-7B [743]40.010.7---
Llama-3.1-8B [168]-56.720.3---
MetaMath [983]Llama-2-7B [743]66.5----
OVM [979]Llama-2-7B [743]73.7----
NuminaMath-7B-CoT [397]-75.455.2-19.9-
Qwen2-7B [925]-79.944.2-21.3-
Qwen2-Math-7B [927]-80.450.4-38.2-
Internlm2-math-plus-7B [974]-84.054.4-18.8-
OMI2 [401]Qwen2.5-Coder-7B [301]84.172.336.2-27.2
Llama-3.1-70B [168]-85.541.4---
CODEI/O++ [401]Qwen2.5-Coder-7B [301]85.772.140.6-29.1
CODEI/O [401]Qwen2.5-Coder-7B [301]86.471.943.3-28.5
WI [401]Qwen2.5-Coder-7B [301]87.071.439.1-26.0
WI (Full) [401]Qwen2.5-Coder-7B [301]87.071.142.9-27.6
OMI2 (Full) [401]Qwen2.5-Coder-7B [301]88.573.240.9-28.4
DeepSeekMath-7B-RL [658]-88.251.7-19.0-
Llama-3.1-405B [168]-89.053.8---
CoMAT [371]GPT-4 [3]93.7-40.4--
CoT [634]GPT-4 [3]94.5-41.850.2-
FCoT [523]GPT-4 [3]95.0----
Qwen2.5-Math-7B-Instruct [927]-95.283.6-41.6-
MathPrompter [303]GPT-4 [3]95.6----
Qwen2.5-Math-72B-Instruct [927]-95.985.9-49.0-
DeepSeek-R1-Distill-Qwen-7B [227]--92.8-49.137.6
DeepSeek-R1-Distill-Qwen-32B [227]--94.3-62.157.2
Structured Language Deep Reasoning
STaR [1012]Llama-2-7B [743]58.216.0---
ENVISIONS [897]Llama-2-7B [743]59.019.0---
MAmmoTH [1006]Code-Llama-7B [639]59.4----
MathCoder-CL [783]Code-Llama-7B [639]67.830.2---
ToRA-Code [217]Llama-2-7B [743]72.6----
Brain [107]Code-Llama-7B [639]74.0----
DeepSeek-Coder-7B [226]-77.444.4---
SIaM [978]Qwen-2-Math-Base81.550---
OC-SFT-1 [401]Qwen2.5-Coder-7B [301]86.770.937.7-27.5
PyEdu [401]Qwen2.5-Coder-7B [301]85.871.440.9-25.8
Qwen2.5-Math-7B-Instruct [927]-94.685.2-55.6-
Qwen2.5-Math-72B-Instruct [927]-95.888.1-60.6-
QuaSAR [634]GPT-4 [3]96.5-55.444.6-
MathDivide [687]GPT-4 [3]96.8---
+ +Table 1: Performance of various deep reasoning formats, sorted primarily by GSM8K scores. “-” indicates that the paper did not report this score. + +approach allows for the scaling of inference-time computations by implicitly performing reasoning within the latent space through recurrent depth. (3) Reasoning Manager Driven Latent Space Deep Reasoning: Inspired by these, Schone et al. [647], Geiping et al. [204], and Saunshi et al. [646] propose a mechanism similar to a continuous reasoning manager, which iteratively governs a trained "recurrent block" as a recurrent "thought block" [511]. This method integrates deeper model layers during reasoning, enhancing performance without needing specialized training data, and even outperforming larger RLLMs. Additionally, ITT [109] leverages the original transformer layer as a recurrent "thought block", selecting key tokens via adaptive token routing and controlling reasoning depth with residual thinking connections, enabling more efficient processing of critical tokens. Further, System-1.5 Reasoning [808] defines two dynamic shortcuts. The Model Depth Shortcut (DS) lets non-critical tokens exit early via lightweight adapter branches while routing critical tokens through deeper Transformer layers, thus supporting adaptive, vertical reasoning. The Step Shortcut (SS) reuses hidden states across decoding steps to bypass trivial iterations and enable horizontal reasoning in latent space. + +# 4.2 Deep Reasoning Learning + +Insufficient deep reasoning in RLLMs can significantly degrade performance [758, 823]. As a result, research has focused on improving reasoning through training. Supervised fine-tuning (SFT) [1058] stabilizes model outputs by serving as a memory process [883], while reinforcement learning (RL) enables generalization and self-learning [227, 137, 276, 898]. Recent studies for deep reasoning + +![](images/787c5674fba7b0ce5e4ca3ac3eefd20babe3c384dc807cab022b3df606b88f7a.jpg) +(a) Deep Reasoning Imitation + +![](images/04fef9422d7990eb4d902d3c902905109bd7fe0911512bee51a344a37488531e.jpg) +(b) Deep Reasoning Self-Learning +Figure 6: The different learning strategies of deep reasoning learning, including deep reasoning imitation of the data from advanced deep reasoning systems, like advanced RLLMs, MCTS, etc.; deep reasoning self-learning from preference-based RL by implicit reward. + +learning have explored using SFT to imitate advanced reasoning in RLLMs and applying RL to enhance self-improvement in reasoning. As illustrated in Figure 6, this section outlines two key approaches to improve deep reasoning: (1) Deep Reasoning Imitation (§ 4.2.1), which involves learning reasoning from human-annotated or distilled data through SFT, and (2) Deep Reasoning Self-Learning (§ 4.2.2), where models improve reasoning through preference-based RL with implicit rewards. The performance of these methods is shown in Table 2. + +# 4.2.1 Deep Reasoning Imitation + +Deep reasoning in RLLMs can be effectively achieved by mimicking advanced reasoning systems, such as human reasoning [558, 61, 115, 403], advanced RLLMs [227, 58, 957, 370, 102], and scaling-augmented RLLMs [410, 1003, 596, 1136, 41]. This approach enables the model to learn complex reasoning patterns and generalize across tasks [937, 416]. Specifically, (1) Imitation from Human: Earlier, Cobbe et al. [141] first propose the deep reasoning imitation paradigm using human examples. ALT [558] improves RLLM reasoning by generating larger datasets of human-annotated logical templates, which fosters deeper reasoning [241]. To enhance diversity, EIT [61] promotes simpler human-generated plans, while LLMs contribute more nuanced reasoning, facilitating collaboration between human input and AI. (2) Imitation from Advanced RLLMs: A body of work utilizes zero-shot prompting to guide large teacher RLLMs in generating reasoning rationale, which is then used to fine-tune smaller RLLMs, marking the beginning of deep reasoning imitation [256, 352, 938, 521]. Additionally, AceMath [500] applies few-shot prompting to distill Long CoT samples from advanced LLMs, followed by multi-stage quality-guided SFT to enhance performance. Chen et al. [107] separate the data synthesis process into planning and reasoning stages, thereby improving reasoning quality. DART-Math [738] effectively distills complex queries requiring deeper reasoning during synthesis, advancing deep reasoning capabilities. Further, Ahmad et al. [7] propose OpenCodeReasoning, expanding this paradigm to the code scenarios. (3) Imitation from Scaling-augmented RLLMs: Earlier, Bansal et al. [34] enhance data quality by scaling the sampling size and length, boosting imitation performance [481, 1005]. Yang et al. [927] and Zhao et al. [1090] further improve data quality by scaling sampling and selecting samples through sample feature or an additional reward model. Additionally, Li et al. [410] identify optimal deep reasoning paths through MCTS, advancing imitation effectiveness. + +Recent studies [299, 550] show that distilling knowledge from advanced RLLM APIs like O1 [307] and R1 [227] significantly enhances the performance of smaller LLMs [424, 223]. This method, employing supervised fine-tuning, boosts model performance on complex mathematical reasoning tasks, sometimes surpassing the teacher models' performance. Building on these findings, LIMO [967], S1 [560], and RedStar [902] argue that a large number of imitation samples is unnecessary. They demonstrate that even a minimal set of samples can activate deep reasoning capabilities in foundational LLMs. For practical applications, Turtel et al. [747] showcase how these techniques can predict future events beyond a model's knowledge cutoff. Sun et al. [701], Yang et al. [928] and Zhao et al. [1093] further enhance deep reasoning imitation by selecting high-quality samples from large datasets, thereby improving the quality of the imitation data. + +# 4.2.2 Deep Reasoning Self-Learning + +While simple imitation can yield strong performance, current models still rely heavily on human annotations or outputs from more advanced models for both imitation and distillation [502]. To + +
ModelData SizeBase ModelGSM8KMATHMATH-500AIME2024GPQAOlympiadBench
Deep Reasoning Imitation
SFT [938]200KLlama-3.1-8B [168]---54.13.5-
Retro-Enh [115]14MLlama-3-8B [168]45.121.7----
Query-Exp [115]24MLlama-3-8B [168]51.323.1----
Res-Div [115]14MLlama-3-8B [168]53.023.2----
MetaMath [738]0.40MMistral-7B [318]76.529.8---5.9
ALT-FLDx2 [558]100KLlama-3.1-70B [168]83.324.4----
EIT [61]15KLlama-2-70B [743]84.132.5----
MathScale [738]2.0MMistral-7B [318]74.835.2----
Tutor-Amp [115]11MLlama-3-8B [168]64.435.9----
MMIQC [738]2.3MMistral-7B [318]75.437.4---9.4
VRT [738]0.59MMistral-7B [318]82.338.7---8.7
KPMath-Plus [738]1.6MMistral-7B [318]82.146.8----
Llama-2-70B-Xwin-Math-V1.1 [385]1.4MLlama-2-70B [743]90.252.5---16.3
DART-Math-Mistral-7B [738]591KMistral-7B [318]81.145.5---14.7
DART-Math-Llama-3-70B [738]591KLlama-3-70B [168]89.656.1---20.0
Rejection Sampling [410]197KQwen2.5-7B [926]87.170.0-10.0-27.1
Evol-Instruct-7B [514]905KQwen2.5-Math-7B [927]88.5-77.416.7--
FastMCTS [410]288KQwen2.5-7B [926]88.974.0-20.0-27.5
KPDDS-7B [295]800KQwen2.5-Math-7B [927]89.9-76.010.0--
DeepSeek-R1-Distill-Qwen-7B [227]800KQwen2.5-7B-Instruct [926]91.7-91.643.3--
Openmathinstruct-7B [740]14MQwen2.5-Math-7B [927]92.0-79.610.0--
NuminaMath [967]100KQwen2.5-Math-7B [927]92.9-81.820.0--
PromptCoT-DS-7B [1090]115KDeepSeek-R1-Distill-Qwen-7B [227]92.6-93.060.0--
PromptCoT-Qwen-7B [1090]905KQwen2.5-Math-7B [927]93.3-84.026.7--
AceMath-7B-Instruct [500]1.2MQwen2-Math-7B-Instruct [927]93.783.1---42.2
AceMath-72B-Instruct [500]1.2MQwen2.5-Math-72B-Instruct [927]96.486.1---48.4
NuminaMath [967]100KQwen2.5-32B-Instruct [926]--59.26.525.836.7
OpenThoughts [967]114KQwen2.5-32B-Instruct [926]--80.650.242.956.3
Sky-T1-32B-Preview [724]17KQwen2.5-32B-Instruct [926]--82.443.356.8-
Journey Learning [299]5KQwen2.5-Math-72B [927]--87.243.3--
STILL-2 [550]3.9KQwen2.5-32B-Instruct [926]--90.246.755.1-
Bespoke-32B [362]17KQwen2.5-32B-Instruct [926]--93.063.358.1-
s1 [560]1KQwen2.5-32B-Instruct [926]--93.056.759.6-
DeepSeek-R1-Distill-Qwen-32B [227]800KQwen2.5-32B-Instruct [926]--94.372.662.1-
LIMO [967]817Qwen2.5-32B-Instruct [926]--94.815.866.766.8
Deep Reasoning Self-Learning
DPO [302]40KDeepSeek-Math-7B-Base [658]74.834.9----
RefT [302]40KDeepSeek-Math-7B-Base [658]71.436.0----
Self-Explore [302]40KDeepSeek-Math-7B-Base [658]78.637.7----
SimPO [723]10KQwen2.5-Math-7B-Instruct [927]88.840.056.6---
DPO [446]11KDeepSeek-Math-7B-Instruct [658]-48.7----
TPO [446]11KDeepSeek-Math-7B-Instruct [658]-51.3----
DPO [446]11KQwen2-7B-Instruct [925]-54.3----
TPO [446]11KQwen2-7B-Instruct [925]-55.5----
MCTS [74]15KDeepSeek-Math-7B-Base [658]83.264.0----
SBS [74]15KDeepSeek-Math-7B-Base [658]84.166.3----
FastMCTS+Branch-DPO [410]152KFastMCTS-7B [410]89.975.4-20.0-29.6
+ +Table 2: Performance of various deep reasoning learning methods, sorted primarily by Math or Math-500 scores. “-” indicates that the paper did not report this score. + +address this limitation, recent research has focused on enabling more advanced reasoning through techniques like self-play and self-learning [948, 1077, 409, 624]. Specifically, self-learning methods can be classified into two paradigms, differentiated by their sampling strategies: + +(1) Self-Learning from Direct Sampling: The earliest method, STaR [1012], utilizes In-Context Learning (ICL) to sample deep reasoning results [657] and uses the correctness of the final answer as an implicit reward for self-learning [258, 581, 582, 1059, 826, 462]. Further, ReST [225] extends this by introducing a Grow-Improve paradigm, where self-generated reasoning is first annotated with rewards and then enhanced via offline RL algorithms. However, these approaches can be fragile, especially when the reward process lacks robustness. Inspired by the Expectation-Maximization (EM) algorithm, Singh et al. [674] propose a method that generates rewards and iteratively optimizes LLMs to achieve the best performance on a validation set, significantly improving robustness. To further strengthen the reward process, a series of work introduces a method to adapt incorrect solutions, training a verifier [155, 262] or utilize entropy [809, 1040] to select or refine the reward process and improve self-learning quality. (2) Self-Learning from Tree Search: Early deep learning methods, such as EXIT [18], combined MCTS with deep neural networks for reinforcement learning, iteratively self-training the network to guide the tree search and enhance reasoning. Building on this, CPO [1065] and TPO [446] align each step of Long CoT reasoning with the corresponding tree search path, using Tree of Thoughts (ToT) [955] preference information to support deeper reasoning [951, 302]. Li [422] propose Policy-Guided Tree Search (PGTS), integrating RL with structured tree exploration for more efficient navigation of reasoning paths. Further developments, such as AlphaMath [74], AlphaLLM-CPL [814], and TongGeometry [1029], refine MCTS behavior through stepwise trajectory pair extraction and curriculum preference learning, boosting LLM reasoning abilities [611, 412, 872]. + +# Takeaways: Imitation & Self-Learning + +- Imitating deep reasoning from advanced RLLMs, and scaling-augmented methods like MCTS can help models learn complex reasoning patterns with fewer samples. +- Self-learning techniques, including reinforcement learning and tree search, allow RLLMs to enhance their reasoning abilities over time. +- The combination of imitation from advanced RLLMs and self-learning techniques strengthens RLLM reasoning, leading to strong performance on complex tasks. + +# 5 Feasible Reflection for Long CoT + +Feasible Reflection is a pivotal component of Long CoT reasoning, enabling LLMs to handle complex tasks through iterative feedback and refinement [406, 192]. Specifically, it comprises two primary stages: (1) Feedback ( $\S$ 5.1), which generates feedback signals $\mathcal{F}_i$ to correct node $n_j$ in Equation (5); and (2) Refinement ( $\S$ 5.2), which adjusts the subsequent node $n_{i+1}$ according to the feedback in Equation (6). + +# 5.1 Feedback + +Feedback refers to the process of providing evaluations of both overall outputs and the processes that lead to them, with the goal of assessing their accuracy and quality [394, 396, 838, 220, 862]. This process, also referred to as critique or verification, can be executed using either natural language or structured data formats, which serve as the foundation for tree-search methods [113]. Specifically, as shown in Figure 7, feedback can be categorized into three distinct types: (1) Overall Feedback ( $\S$ 5.1.1); (2) Process Feedback ( $\S$ 5.1.2); (3) Hybrid Feedback ( $\S$ 5.1.3). + +# 5.1.1 Overall Feedback + +The overall feedback focuses on providing a global view of the entire process and results, rather than assessing each step individually. This feedback significantly enhances reasoning skills and reward modeling in reinforcement learning for RLLMs. Specifically, as shown in Figure 7 (a), the overall feedback can be categorized into three main sources: Outcome Reward Model, Rule Extraction, and RLLMs Feedback. The performance across these categories is summarized in Table 3. + +![](images/924dba4b1d5c6d25f0eff62713bafcbf9c36e9cd21483aae275897e288afdd77.jpg) + +![](images/367cca6990189dfda7e049a2d562809a0e9869ca5351f1d2d1d1e74c0f9bcafd.jpg) + +![](images/dd4b7e43b794582020a033da732daf0b1be53e45111b8e9717414d483b50896e.jpg) + +![](images/6914fc78c8aeece2af825dabacd242f08c842b612001c13322264246623afb04.jpg) +Figure 7: The feedback capabilities framework for feasible reflection consists of Overall Feedback and Process Feedback. Overall Feedback includes the Outcome Reward Model (ORM) in a value format, rule extraction for correctness judgment, and overall RLLMs based on RLLMs. Process Feedback includes the Process Reward Model (PRM) in a value format and step-level RLLMs, also based on RLLMs. + +![](images/75c5bea65e3eccbc79affd34b429b7f444436c52e5988975f4dec0ecb68328a3.jpg) + +
ModelBase ModelChatChat_HardSafetyReasoningOverall
RLLMs
GPT-4o-mini [3]-95.060.780.883.780.1
Llama3.1-70B-Instruct [168]-97.270.286.082.884.0
Llama3.1-405B-Instruct [168]-97.274.687.177.684.1
GPT-4 [3]-95.374.386.987.686.0
GPT-4o [3]-96.176.186.688.186.7
Gemini-1.5-pro [719]-92.380.687.992.088.2
Self-taught Evaluator [803]Llama-3.1-70B-Instruct [168]96.684.281.091.588.3
SFR-LLMA-3.1-8B-Judge [791]Llama-3.1-70B-Instruct [168]95.577.786.295.188.7
SFR-NeMo-12B-Judge [791]Mistral-NeMo-Instruct-12B [725]97.282.286.595.190.3
SFR-LLMA-3.1-70B-Judge [791]Llama-3.1-70B-Instruct [168]96.984.891.697.692.7
Skywork-Critic-Llama-3.1-70B [791]Llama-3.1-70B-Instruct [168]96.687.993.195.593.3
LMUnit [641]Llama-3.1-70B-Instruct [168]----93.4
EvalPlanner [643]Llama-3.1-70B-Instruct [168]97.589.493.095.593.9
Outcome Reward Models
tulu-v2.5-13b-uf-rm [306]TULU-2-13B [305]39.442.355.547.446.1
Prometheus-2-7B [353]Mistral-7B-Instruct-v0.2 [318]85.549.177.176.572.0
Prometheus-8x7b-v2 [353]Mixtral-8x7B-Instruct [319]93.047.180.577.474.5
Critic-RM-Rank [991]Llama-3.1-70B-Instruct [168]97.058.084.092.082.8
RM [689]Llama-3.1-70B-Instruct [168]98.374.583.888.086.4
SynRM [968]Llama-3.1-70B-Instruct [168]97.576.886.388.587.3
CLoud [17]Llama-3-70B-Instruct [168]98.075.687.689.087.6
FLAME-RM-24B [753]PaLM-2-24B [16]92.275.789.693.887.8
SteerLM-RM 70B [829]Llama-2-70B-chat [743]91.380.390.692.888.8
Llama-3-OffsetBias-RM-8B [585]Llama-3-8B-Instruct [168]97.281.886.891.989.4
InternLM-20B-Reward [62]InternLM2-8B-Instruct [62]98.976.589.995.890.2
ArmoRM-Llama3-8B-v0.1 [771]Llama-3-8B-Instruct [168]96.976.892.297.390.8
Nemotron-4-340B-Reward [829]Nemotron-4-340B [4]95.887.192.293.692.2
Skywork-Reward-Llama-3.1-8B [466]Llama-3.1-70B-Instruct [168]95.887.390.696.292.5
Skywork-Reward-Gemma-2-27B [466]Gemma-2-27B-it [720]95.891.492.096.193.8
+ +Table 3: Performance of various overall feedback methods, sorted primarily by Overall scores in RewardBench [367]. “-” indicates that the paper did not report this score. + +Overall Feedback from Outcome Reward Model Since many tasks cannot be directly evaluated using accuracy or other standard metrics, research has increasingly focused on Outcome Reward Models (ORM), which provide value-based rewards for more general and quantifiable feedback [1127, 986, 467]. In 2021, OpenAI [141] has proposed a "Gen-Verifier" paradigm, which uses a specialized ORM to evaluate the accuracy of generated rationales, showing significant progress in feedback capabilities [658]. Ji et al. [315] introduce a trained knowledge scorer to analyze hallucinations in the reasoning process, providing feedback to RLLMs and improving the accuracy of their outputs over time. Moreover, Generative Reward Models [1048] use next-token prediction for overall feedback, which seamlessly integrates with instruction adjustments, leveraging inference-time calculations to improve ORM feedback. + +However, specifically trained ORMs are often costly and not sufficiently robust. Building on this, Self-Rewarding Language Models (SRLMs) [1129] incorporate a self-consistency framework, optimizing feedback to improve model alignment and consistency [1047]. Yu et al. [991] introduce Critic-RM, combining RLLM-generated natural language criticism with corresponding feedback. This method filters high-quality feedback while jointly fine-tuning reward prediction and criticism generation, optimizing ORM performance. + +Overall Feedback from Rule Extraction Although ORM has achieved significant improvements, its accuracy still falls short of $100\%$ , preventing it from outperforming rule-based answer correction feedback [955, 234, 1079]. Previous studies, such as STaR [1012], ReST [225], and ReFT [745], have demonstrated that feedback based on final answer rewards is more effective than both PRM and ORM in mathematical scenarios [197]. Furthermore, Guo et al. [227] and Xie et al. [886] introduce a multi-stage RL framework that incorporates rule-based rewards, significantly enhancing both output accuracy and length while mitigating reward hacking through simple yet robust rules [30], such as format validation and result verification. In coding scenarios where direct rule-based feedback is difficult, OpenCodeInterpreter [1108], AceCoder [1014], O1-Coder [1076], and VerMCTS [56] address this challenge by implementing an automated test-case synthesis pipeline, deriving rewards based on program performance [564, 216, 1115]. Additionally, Ma et al. [536] propose an automated approach to training a test case generator, which alleviates the scarcity of test cases and demonstrates that increasing the number of test cases correlates with improved reward quality. Moreover, Ma et al. [535] decompose problem-solving into structured coding subtasks: file localization, function + +localization, line localization, and code editing generation, and applies multi-viewed rule-based rewards. + +Overall Feedback from RLLMs Research on feedback from RLLMs centers on detecting errors and biases through natural language feedback, also known as LLM-as-Judge, self-reflection or self-critique [274, 336, 29, 638, 549, 802, 1002, 895, 529]. This method has led to significant improvements across various tasks, particularly in self-correction [848, 1109, 206, 184, 1075]. Huang et al. [286] contend that traditional LLMs struggle to generate effective feedback without external signals, requiring the development of RLLMs with enhanced feedback capabilities [645, 398]. As a result, many studies leverage RLLMs' error-identification strengths, often stemming from their pretraining phase, to improve feedback generation and correction [965, 39, 40, 282]. + +Earlier, McAleese et al. [544] found that training RLLMs to learn self-critique and deep reasoning can further boost performance. Zhang et al. [1062] propose a self-contrast mechanism that compares multiple perspectives, identifies differences, and summarizes insights to resolve inconsistencies. However, these methods often offer task-independent feedback. To address this, Hao et al. [235] introduce AutoRace, which tailors evaluation criteria for specific tasks. The Reversal of Thought (RoT) framework [999] introduces a novel paradigm combining reverse reasoning with self-reflection, helping models identify the limits of their knowledge and enhance reasoning efficiency. Furthermore, ACR [1116] implements a scoring system for coding tasks, using LLM-as-a-Judge for quality assessment and LLM-as-a-Critic for critiquing low-quality code, improving consistency across benchmarks. Zheng et al. [1107] integrate code execution error data and feedback from RLLMs to improve code generation performance. Liu et al. [484] present AGSER, a method using attention-guided self-reflection to address hallucinations by splitting input queries into attentive and nonattentive components. Finally, Saha et al. [643] introduce EvalPlanner, which separates feedback into planning and reasoning components for more streamlined expression using existing RLLMs. More comprehensively, Hu et al. [274] outline the complete pipeline, key insights, and practical lessons for training RLLMs to function as judges. + +# 5.1.2 Process Feedback + +Techniques combine process feedback with MCTS or RL rewards to provide automated, step-by-step guidance, reducing the need for labor-intensive annotations while enhancing reasoning capabilities [749, 344]. These techniques can be categorized into two main types based on the source of feedback: process reward models (PRMs) and prompted LLMs. The performance comparison are mainly shown in Table 4. + +Process Feedback from Process Rewarded Model Recent studies highlight the significance of feedback in developing effective PRMs for complex reasoning tasks, particularly in a step-level view [134, 423, 528]. (1) Process Annotated PRM Training: Earlier, Lightman et al. [449] demonstrate that training process feedback with human-annotated data (PRM800K) surpasses outcome supervision in creating reliable reward models. However, this approach requires significant human effort. To address this, Wang et al. [792] introduce Math-Shepherd, a dataset that generates step-by-step supervision using a Tree Search-inspired method [73, 1001]. Following this, methods like QwQ [731], Skywork-o1 [570], AceMath [500], and PRIME [143] adopt similar techniques to enhance PRM performance. Additionally, Zhang et al. [1036] propose entropy regularization to improve model convergence. Rather than focusing solely on the first error step, Full-Step-DPO [903] assigns rewards for the entire reasoning chain, including error steps. VersaPRM [1015] extends PRMs across multiple domains, broadening their applicability. Similarly, Gu et al. [219] and Zhang et al. [1074] suggest training models with student preferences aligned to teacher preferences, ensuring effective preference distillation. Further, Wang et al. [807] propose VisualPRM400K and expand this paradigm to multimodal scenarios. (2) Outcome Annotated PRM Training: Alternative approaches, such as ReST-MCTS* [1032], OVM [979], Implicit PRM [1000], AutoPSV [506], and DVO [1038], leverage outcome supervision or implicit feedback to train PRMs, reducing the need for extensive human-annotated data [891, 643]. UAS [981] incorporates uncertainty-aware value models [275] into feedback predictions [495, 167, 945, 1089]. Additionally, Aurora [710] utilizes ensemble prompting strategies and reference answers for reverse verification, training stronger PRMs that better align with the Long CoT data distribution. Furthermore, PAV [651] suggests that rewards should reflect reasoning progress, as measured by changes in the likelihood of producing a correct future response before and after each step. Yang et al. [932], Lee et al. [376], Yoon et al. [975] extend these paradigms + +
ProcessBenchPRMBench
GSM8KMATHOlympiadBenchOmniMATHSimplicitySoundnessSensitivity
Process Reward Models
Qwen2.5-Math-7B-PRM [1102]Qwen2.5-Math-7B [927]39.452.239.433.1---
Math-Shepherd-PRM-7B [792]Mistral-7B [318]47.929.524.823.847.145.760.7
RLHFlow-PRM-Mistral-8B [156]Mistral-7B [318]50.433.413.815.846.757.568.5
RLHFlow-PRM-DeepSeek-8B [156]DeepSeek-7B [52]38.833.816.916.947.657.568.1
Skywork-PRM-1.5B [466]Qwen2.5-Math-1.5B-Instruct [926]59.048.019.319.233.628.648.8
Skywork-PRM-7B [466]Qwen2.5-Math-7B-Instruct [926]70.853.622.921.038.432.754.3
Qwen2-1.5B-PRM800k [700]Qwen2-Math-1.5B-Instruct [927]34.055.334.241.0---
Qwen2-1.5B-Math-Shepherd [700]Qwen2-Math-1.5B-Instruct [927]48.934.19.813.7---
Qwen2-1.5B-Epic50k [700]Qwen2-Math-1.5B-Instruct [927]55.636.120.230.0---
Qwen2.5-Math-7B-PRM800KQwen2.5-Math-7B-Instruct [927]68.262.650.744.3---
Qwen2.5-Math-PRM-7B [1102]Qwen2.5-Math-7B-Instruct [927]82.477.667.566.3---
Universal-PRM-7B [710]Qwen2.5-Math-7B-Instruct [927]85.877.767.666.4---
Critic Model
Llama-3.1-8B-Instruct [168]-27.526.718.519.2---
GPT-4o [3]-61.953.948.344.659.770.975.8
QwQ-32B-Preview [731]Qwen2.5-32B-Instruct [926]62.352.746.243.9---
DeepSeek-R1-Distill-Qwen-14B [227]Qwen2.5-14B-Instruct [926]67.338.829.932.1---
Dyve-14B [1111]DeepSeek-R1-Distill-Qwen-14B [227]68.558.349.047.2---
Qwen2.5-72B-Instruct [926]-76.261.854.652.2---
SCRIT [713]Qwen2.5-72B-Instruct [926]80.260.032.527.8---
ol-mini [307]-93.288.987.282.464.672.175.5
LLemma-PRM800k-7B [679]LLemma-7B [26]----51.450.966.0
LLemma-MetaMath-7B [679]LLemma-7B [26]----50.349.066.0
LLemma-oprn-7B [679]LLemma-7B [26]----49.049.864.1
MATHMinos-Mistral-7B [195]Mistral-7B [318]----51.454.466.5
ReasonEval-7B [877]LLemma-7B [26]----55.563.971.0
ReasonEval-34B [877]LLemma-34B [26]----51.563.073.1
Gemini-2.0-flash-exp [679]-----62.767.375.4
Gemini-2.0-thinking-exp-1219 [679]-----66.271.875.3
+ +Table 4: Performance of various process feedback methods on ProcessBench [1102] and PRM-Bench [679]. “-” indicates that the paper did not report this score. + +to the token level. Moreover, Chen et al. [110] expand these into interactive agent scenarios, allowing for automatically learning reward models from the environment without additional manual annotation. Wang et al. [832] equip a dual-layer MLP module to evaluate the reward at each step, successfully integrating the policy model and PRM into a unified interface without additional process annotations, reducing over $99\%$ of PRM parameters for efficient reasoning. + +Process Feedback from RLLMs As PRM training remains heavily dependent on manually annotated data, recent research has explored methods for enabling models to generate their natural language feedback to optimize performance [910]. These approaches fall into two primary categories: (1) Model-Driven Feedback Reasoning: Earlier work such as React [956] and Reflexion [669] enhances RLLMs with natural language feedback at each action and reasoning step [196, 135, 89], improving decision-making in diverse tasks. Similarly, Step-DPO [365] uses RLLM to self-verify step-level positive and negative pairs for training through the DPO paradigm, achieving strong performance. Additionally, Sun et al. [702] propose a dynamic error classification framework that adapts based on model outputs, improving performance in mathematical reasoning tasks by addressing specific error patterns in math word problems. Furthermore, Xie et al. [889] and He et al. [245] iteratively apply MCTS to collect preference data, utilizing its forward-looking capabilities to decompose instance-level rewards into more precise step-level signals, thereby enhancing feedback accuracy. However, step-wise feedback often suffers from reliability issues, which can be mitigated by uncertainty quantification [973, 969], improving the reliability of step-wise verification in reward models for mathematical reasoning tasks. Moreover, Fu et al. [187] define the CoT Average Causal Effect (CACE) to capture causal relationships between steps, resulting in a causalized Long CoT where all steps are both correct and comprehensible. (2) Environment-Driven Feedback Reasoning: Given the increasing complexity of large models, there is growing interest in combining prompt-based LLMs with external environments to generate more interpretable and controllable feedback [885, 271]. For example, ORPS [996] and Drori et al. [162] minimize dependence on human annotations by using execution feedback, enabling models to autonomously refine their solutions. Additionally, Shrestha et al. [670] contribute by translating model outputs into Python code, helping to identify logical errors, gain insights into flawed reasoning processes, and guide improvements in mathematical reasoning. Xu et al. [897] integrate reasoning models with an interactive environment, enabling learning in more dynamic scenarios and creating a more generalizable self-learning framework. + +# 5.1.3 Hybrid Feedbacks + +Given the respective advantages and limitations of Overall Feedback and Process Feedback, recent studies have sought to combine both for optimal feedback. Specifically, Zhang et al. [1078] propose + +a consensus filtering mechanism that integrates Monte Carlo estimation with an LLM-as-judge to enhance both overall and stepwise feedback, thus improving reasoning accuracy. In a similar vein, Lin et al. [454] introduce Step-KTO, a framework combining stepwise process-level and outcome-level binary feedback, using PRM and ORM to guide language models toward coherent reasoning, with a focus on error correction through reflection mechanisms. + +# Takeaways: Feedback + +- Evolving Feedback Models: Feedback mechanisms, including overall, process, and hybrid feedback, are crucial for improving the reasoning capabilities of RLLMs. +- Innovative Approaches in Process Feedback: Process feedback using techniques like PRMs with MCTS enhances Long CoT, though challenges like reward hacking remain. +- Self-Reflection and Model-Driven Feedback: Self-reflection and model-driven feedback improve RLLM performance by enabling error detection, task-specific insights, and more autonomous learning. + +# 5.2 Refinement + +Refinement refers to the process of addressing errors in reasoning based on prior feedback. As shown in Figure 8, refinement methods can be grouped into three primary categories: prompt-based refinement generation (§ 5.2.1), SFT-based refinement imitation (§ 5.2.2), and RL-based refinement learning (§ 5.2.3). + +# 5.2.1 Prompt-based Refinement Generation + +Research on prompt-based refine generation focuses on enhancing the performance of LLMs through iterative self-refinement mechanisms [578, 1091, 98, 469, 1028, 754, 818, 546]. A prominent approach involves prompting RLLMs to generate initial outputs, followed by self-feedback that iteratively refines and improves performance across tasks such as dialogue generation and mathematical reasoning [645, 539, 1101, 669, 549, 345, 750, 482], which even much reduce the hallucinations [289, 315]. Noteworthy methods, like Self-Backtracking [944], Refiner [590], and BackMath [1055], allow LLMs to adjust their reasoning autonomously, reducing unnecessary complexity in decision-making [868]. Further, Havrilla et al. [238] extend the paradigm by integrating overall-level and step-level refinements, improving refinement performance. Yang et al. [950] propose a method to decompose the self-correction capability of LLMs into "confidence" and "critique" capacities, designing probabilistic metrics to evaluate them and exploring the role of reflection mechanisms in model behavior. Additionally, MCTSr [1033], LLM2 [930], ReST-MCTS* [1032] and ReARTeR [703] emphasize dynamic reflection through iterative error correction and confidence adjustments, allowing models to autonomously refine reasoning strategies [186]. He et al. [240] + +![](images/b3686b17aa6dae7dfb30b34c5e285af765d180305957e5c15bbbeed64d436326.jpg) +(a) Prompt-based Refinement Generation + +![](images/6b9af6579bd26e04c798016e01125ccc0cc0c837723baed594fe92c9e6c31804.jpg) +(b) SFT-based Refinement Imitation + +![](images/75779ea3409037b107f99cc61b0546a161e6d6863edc845e12464cd3a1541651.jpg) +Figure 8: The three main categories of refinement methods, including Prompt-based Refinement Generation, SFT-based Refinement Imitation, and RL-based Refinement Learning. + +![](images/51fec61d82ab2a769606104af5832df56e4604f317836d062424f65c9e9866bf.jpg) + +![](images/23630b42c465d84d800277ffb7ad33291ea526c1dea42266eee59f4ed6d6ce9b.jpg) +Reinforcement Learning + +![](images/80703458fe6b97a41337e32d746ae10f1ad5d7ce4cd1e803f369ce673d59c38c.jpg) + +![](images/748e7abf84b0255c1331edd540782869194e76185b531fae8e9affbfdea58ee8.jpg) +(c) RL-based Refinement Learning +Aha! I think $1 + 1 = 3$ should be corrected $1 + 1 = 2!$ + +extend this paradigm to multi-agent scenarios, improving both reasoning and agent system performance [936, 1128]. Moreover, Yuksekgonul et al. [1009] and Peng et al. [593] further expand the paradigm by enabling automatic prompt optimization driven by LLMs. This approach facilitates more generalized and automated refinement of input prompts across a range of tasks, as opposed to focusing solely on refining output results. However, without oracle feedback, RLLM's self-refinement process fails, causing instability in both intermediate and final answers, leading to biases in simple factual queries and introducing cognitive biases in complex tasks [1051, 908]. + +# 5.2.2 SFT-based Refinement Imitation + +Recent advancements in reflection-based reasoning for LLMs have led to frameworks that enhance model reasoning through self-refinement and error correction. A key approach is directly supervised fine-tuning, which allows models to learn error correction processes from advanced LLMs, thereby improving their reflective capabilities [14, 104, 406, 822, 99, 873]. Notable frameworks, such as rStar [615], improve smaller language models through self-play mutual reasoning, while Recursive Introduction [627] and RealCritic [714] use iterative feedback mechanisms to identify and correct errors to better self-improve [393]. Yan et al. [924] propose constructing step-wise self-correction data and implementing a training strategy that uses the above-constructed data to equip LLMs with spontaneous step-level self-correction capacities. Building upon these, Gao et al. [196] and Zhang et al. [1027] propose Math-Minos, which employs step-by-step natural language feedback as rationale tags, offering both correctness and detailed explanations for each step to train feedback mechanisms that justify and refine the reasoning process. Journey Learning [623] employs MCTS to parse node backtracking as natural language refinement, enhancing supervised fine-tuning and, thereby, improving reasoning performance. Additionally, approaches like ProgCo [682] emphasize iterative feedback and program-driven refinement to enhance critique and self-correction. Expanding these ideas to multimodal settings, frameworks, such as R3V [120] and MM-Verify [697], focus on integrating visual and textual reasoning [519, 813]. + +# 5.2.3 RL-based Refinement Learning + +In recent research, several approaches have been proposed to enhance the performance of refinement through reinforcement learning [673, 1056]. Earlier, Kumar et al. [358] observed that SFT of RLLMs often fails to promote self-refinement behaviors. This limitation stems from a distributional mismatch between data collection strategies and model responses, as well as the risk of behavioral collapse. To address this, SCoRe [358] enhances self-refinement by training the model on its own self-generated correction trajectories and employing regularization to guide the learning process. This method prioritizes fostering self-refinement during testing, rather than merely maximizing reward for specific prompts [1018]. Further, Guo et al. [227] demonstrate that applying outcome-level rewarded RL can trigger an "Aha moment," activating the model's natural feedback and refinement behaviors without the need for human guidance. Moreover, Guo et al. [227], Zeng et al. [1017] and Ma et al. [529] explore initializing LLMs with iterative self-verification and self-correction behaviors, which are strengthened through supervised fine-tuning and further enhanced by outcome-level RL. Ma et al. [529] and Yang et al. [935] extend these capabilities with process-level RL, minimizing resource usage while enabling adaptive reasoning refinements during inference. More recently, Lee et al. [374] introduce an intrinsic verifier module to decide when refinements should be applied, using RL to further encourage self-refinement when errors are detected. + +# Takeaways: Refinement + +- Prompt-Based Refinement for Iterative Improvement: Iterative self-refinement through feedback loops helps LLMs improve reasoning and reduce errors like hallucinations but requires stable feedback to maintain accuracy. +- Supervised Fine-Tuning (SFT) for Error Correction: Supervised fine-tuning enhances LLMs by using iterative feedback and self-correction strategies to improve reasoning accuracy, especially for smaller models. +- Reinforcement Learning (RL) for Refinement: Reinforcement learning enhances self-refinement in LLMs by using self-generated corrections and adaptive strategies, reducing human intervention and resource consumption. + +![](images/ae0384cb2d35989e0913fcc05ec7fe401f4d3acdd492815afce7dcdd64d2789c.jpg) +Figure 9: Schematic representations of two common inference-time scaling strategies: (a) sequential scaling, which extends the length of Long CoT but is constrained by the reasoning boundaries of RLLMs; and (b) parallel scaling, which increases the sample size and aggregates multiple outcomes, yet does not surpass the performance of Pass@k. + +![](images/651c3a02f7c05e2fa7e8a9730a03db50638cef9382a4885f455c35d277bec9cc.jpg) + +# 6 Extensive Exploration for Long CoT + +Exploration is a key capability in Long CoT reasoning, allowing models to navigate complex problem spaces through strategic branching and iterative refinement [1019, 381, 784, 751]. Recent studies emphasize exploration mechanisms, such as hypothesis branching and error backtracking via reflection, as essential for overcoming the constraints of linear reasoning paths [227]. + +Current research focuses on three key areas: (1) Exploration Scaling (§ 6.1), which explores the breadth and depth of exploration and its impact on downstream applications, particularly in improving the size of the exploration path $m$ in Equation (3); (2) Internal Exploration (§ 6.2), which focuses on training models to develop internal exploration capabilities, enabling more efficient and effective generation of $m$ exploration paths $\{n_{i+j}\}_{j=1}^{m}$ in Equation (3); and (3) External Exploration (§ 6.3), which examines how models can leverage external systems to enhance their exploratory abilities, facilitating the selection of the most effective path $n_{i+j}$ from the $m$ exploration paths in Equation (3). + +# 6.1 Exploration Scaling + +Recent advances in inference-time scaling algorithms [333, 843, 57, 1053, 112] have attracted significant interest, particularly in scaling reasoning length to improve performance [524, 568, 405, 779]. Following Chen et al. [93], as shown in Figure 9, exploration scaling can be understood through two paradigms: (1) sequential scaling, akin to a series of resistors, which connects multiple reasoning processes using reflection; and parallel scaling, similar to parallel resistors, where a unified verification/feedback mechanism selects the most effective reasoning processes. + +# 6.1.1 Sequential Scaling + +Sequential scaling refers to extending the reasoning output within a single model generation, significantly boosting model performance [383, 1052, 348]. Early works by Fu et al. [189] and Jaech et al. [307] show that increasing the length of the reasoning path can greatly improve performance. Tian et al. [736] enhances model reasoning iteratively by using prior answers as prompts for each successive round, thus enabling sequential scaling of the reasoning process. Building on this, later studies [314, 391] further explore enhancing logical depth through tree-based searches within a fixed compute budget, resulting in notable performance gains [11, 614]. Building upon this, Muennighoff et al. [560] introduce a inference-time scaling method that improves reasoning by fine-tuning and budget forcing, yielding substantial gains with additional computing at inference time. To address the constraints of attention spans, some studies focus on expanding reasoning length in latent spaces. Geiping et al. [204] and Chen et al. [109] enhance inference-time reasoning performance by implicitly scaling computation in latent space through recurrent depth. Setlur et al. [653] identified three core aspects of sequential scaling: (1) linking skills to asymmetric capabilities in base LLMs, such as connecting easy verification with difficult exploration; (2) enhancing exploration in reinforcement learning by utilizing the "negative" gradient of error trajectories, which extends search paths and links additional asymmetries; and (3) creating dynamic exploration by aligning task difficulty with training token budgets through tailored curricula. + +# 6.1.2 Parallel Scaling + +Parallel scaling refers to the process of increasing the number of reasoning iterations during model generation and then verify these results to get the final output, which significantly enhances model performance [2, 864, 57, 485, 59, 1139]. Initially, Wang et al. [816] introduce the concept of self-consistency, demonstrating that multiple sampling processes followed by majority voting for effective exploration. + +Verification Optimization The primary focus of recent research is optimizing verification, which can be categorized into two types: (1) Overall Verification: Recent works [1120, 831] divide the scaling process into two stages: "reasoning" and "self-verification." By replacing majority voting in self-consistency with self-verification, these approaches show significant improvements [1083, 81, 1149, 364, 426]. In code scenarios, WoT [1071], CISC [716] and S* [392] scale the Long CoT in parallel, using output confidence or code execution results for verification, effectively assessing reasoning quality [635, 203, 278, 1134]. Further, Nye et al. [569] and Weir et al. [842], Stoisser et al. [690] train RLLMs to simulate code execution, removing the need for test cases in code-related parallel scaling. Chain-of-Verification [93] introduces meta-verification, sampling multiple verification instances to identify the correct one. Kim et al. [351], Chen et al. [111], and Vacareanu et al. [750] validate this approach empirically by evaluating answer correctness based on reasoning path properties. Moreover, Li et al. [421] tune a specific RLLM to verify and aggregate answers, showing improved performance. This suggests that PRM cannot replace a specially trained RLLM for verification due to training goal biases [1078]. Finally, Kang et al. [341] leverage self-uncertainty to select the best results. (2) Step Verification: Building on this, numerous researchers have explored step-level or finer-grained verification [84, 460]. Notably, DIVERSE [425], SSC-CoT [1098], and Fine-grained Self-Consistency [93] combine diverse reasoning paths with step-level verification. In addition, a series of works [676, 864, 517, 770, 853, 486] try to investigate how optimal scaling strategies based on MCTS can enhance smaller language models' performance. Their findings show that a 1B RLLM can outperform a 405B model on complex tasks through parallel scaling [988]. Despite these advancements in verification, Chen et al. [93] demonstrate that these strategies cannot surpass Best-of-N methods, suggesting that breakthroughs cannot solely rely on optimization-based verification [106]. + +Sampling Optimization Another key area of research focuses on generating diverse but less paths or strategies for efficient scaling [871, 765, 80, 668, 444, 681]. For instance, Zeng et al. [1020] aggregate the shortest yet most varied reasoning paths for better scalability. Similarly, Du et al. [164] adjust the sampling temperature to increase diversity, leading to improved scaling. Zhang et al. [1045] and Liu et al. [470] optimize both candidate solution generation (e.g., prompts, temperature, and top-p) and reward mechanisms (such as self-evaluation and reward types), offering diverse strategies for parallel scaling. Moreover, Qin et al. [617], Luo et al. [520], and Yu et al. [990] enhance RLLM reasoning by scaling sampling across multiple natural and programming languages or varied expressions. Finally, Yang et al. [943] introduces a method where a small set of seed data, with varied response lengths, guides the model to engage in deeper reasoning by selecting the shortest correct responses across various inference efforts. + +# Takeaways: Exploration Scaling + +- Exploration Mechanisms in Long CoT Reasoning: Exploration strategies like hypothesis branching and error backtracking are vital for overcoming limitations in linear reasoning paths and enhancing model performance. +- Scaling Exploration: Exploration can be scaled through sequential and parallel strategies to improve reasoning depth and efficiency. +- Verification and Sampling Optimization: Refining verification techniques and optimizing sampling for diverse reasoning paths are key to improving exploration efficiency and performance in Long CoT tasks. + +# 6.2 Internal Exploration + +As noted in Chu et al. [137], Shen et al. [661], and Yang et al. [938], SFT serves as a memory process, while RL enhances generalization [359, 82]. Specifically, SFT stabilizes the model's output format, + +![](images/55a2cddee6720d6d5b6d79848689909b6e03f9c8563319f2fff7f35746a40240.jpg) + +![](images/302920f94ae85e94ce64fd964759f21a7a4160de1d28055d6f3573f758563039.jpg) +Figure 10: Two primary approaches for optimizing Internal Exploration: improving RL strategy through reference and value models, and designing reward strategies: either rule-based or model-based rewarding to enhance RL performance. + +whereas RL improves its generalization capacity, which can increase learning efficiency by up to eight times in tasks such as mathematical reasoning [650]. Consequently, as shown in Figure 10, leading research emphasizes the role of RL and reward strategies in enhancing the exploration capabilities of LLMs without external assistance. The performance comparison is presented in Table 5. + +# 6.2.1 RL Strategies + +Recent advancements in RL strategies for exploration have led to notable improvements in various tasks, particularly in reasoning tasks [699, 369, 313, 542, 882, 1017, 985, 268, 1010, 628, 150, 176, 686]. + +(1) Reward-free RL: The first series of work focuses on RL optimization algorithms. Additionally, OREO [773] propose an offline RL method that optimizes the soft Bellman equation, improving credit assignment for multi-step reasoning tasks and outperforming existing approaches in fields like mathematics and agent control. Liu et al. [476] propose Direct Advantage Policy Optimization, a novel offline RL method that leverages a separately trained critic to evaluate the accuracy of each reasoning step. This technique provides dense feedback for policy optimization, addressing both sparse rewards and training instability. Further, some research focuses on adjusting the focus of RL algorithms to optimize exploration in targeted aspects. Specifically, CPL [801], cDPO [457], and Focused-DPO [1043] enhance exploration in Long CoT by prioritizing critical or error-prone areas through preference optimization, improving accuracy in those regions. Bartoldson et al. [42] further adjusts the replay strategy of the training data, aiming to optimize reasoning performance. Li et al. [420] introduce Learning Impact Measurement (LIM), an automated method for evaluating and prioritizing training samples based on their alignment with model learning trajectories. This approach enables efficient resource use and scalable implementation. For instance, ThinkPO [942] uses short CoT reasoning outputs as rejected answers and longer ones as chosen answers for the same question, applying DPO to encourage prioritization of longer reasoning outputs [1131]. + +(2) Reward-based RL: Reward-model-based RL refers to approaches that use a reward model or a verifier to guide learning and decision-making in the absence of explicit rewards [1046, 174, 649, 279, 825, 847, 970]. Earlier, Proximal Policy Optimization (PPO) was first introduced by Schulman et al. [648], which alternates between interacting with the environment to collect data and optimizing a surrogate objective function via stochastic gradient ascent, surpassing DPO [306]. Subsequently, ReMax [436] eliminates the need for additional value models in PPOs. By incorporating variance reduction and REINFORCE [704] techniques, it reduces over four hyperparameters, resulting in lower GPU memory usage and faster training. Building on this, DeepSeekMath [658] proposes Group Relative Policy Optimization (GRPO), replacing traditional value models with improved sampling strategies, thus significantly accelerating learning and achieving performance on par with GPT-4 in mathematics. Hu [265] and Liu et al. [499] further refine GRPO with REINFORCE++ and Dr. GRPO, + +
MethodBackboneGSM8KAIME 2024MATH 500GPQALiveCodeBench
Base Model
GPT-4o [3]-92.99.376.653.633.4
Llama-3.1-70B-Instruct [168]-94.113.368.0--
Claude 3.5 Sonnet [19]--16.078.365.038.9
Qwen2.5-Coder-32B-Instruct [301]--20.071.233.825.0
Qwen2.5-70B-Instruct [926]--20.079.449.033.0
Llama-3.3-70B-Instruct [168]--36.773.950.534.8
DeepSeek-V3 [463]--39.290.2-36.2
SFT Strategies
DeepSeek-R1-Distill-Llama-70B [227]--70.0--57.9
DeepSeek-R1-Distill-Qwen-32B [227]--72.6--54.6
START [388]QwQ-32B-preview [731]-66.794.463.647.3
RL Strategies
DPO [631]DeepSeekMath 7B [658]82.4----
KTO [171]DeepSeekMath 7B [658]82.5----
OREO [773]DeepSeekMath 7B [658]86.9----
PPO [648]GLM4-9B-SFT [211]85.5--31.524.3
GRPO [658]GLM4-9B-SFT [211]86.1--31.722.8
Eurus-2-7B-PRIME [143]Qwen2.5-Math-7B-Base [927]-26.779.2--
Search-o1 [418]QwQ-32B-preview [731]-56.786.463.633.0
Reward Strategies
OpenMath2 [739]Llama-3.1-70B [168]94.113.371.8--
Satori [661]Qwen-2.5-Math-7B93.923.383.6--
T1-SFT [264]Qwen2.5-32B [926]-24.983.449.5-
T1 [264]Qwen2.5-32B [926]-50.692.456.1-
DeepSeek-R1-lite [227]--52.591.658.551.6
rStar-Math [222]Qwen2.5-Math-7B [927]95.253.390.0--
QwQ-32B-preview [731]-95.553.390.658.240.6
ol-preview [307]--56.785.573.353.6
o3-mini-low [307]--60.0--61.8
ol-mini [307]--63.690.0-53.8
Kimi k1.5 [722]--77.596.2-62.5
QwQ-32B [731]--79.5--73.1
o3-mini-medium [307]--79.6--72.3
DeepSeek-R1 [227]--79.897.3-71.6
o1 [307]--83.396.4-67.4
o3-mini-high [307]--87.3--84.6
+ +Table 5: Performance of various internal exploration methods on different benchmarks, primarily ordered by AIME 2024. “-” indicates that the paper did not report this score. + +respectively, simplifying the algorithm and enhancing its training. Additionally, Vassoyan et al. [752] and [1121] improve exploration efficiency in smaller models by modifying the KL penalty, thus enhancing performance under distribution shifts. Huang et al. [277] introduce Decoupled Value Policy Optimization (DVPO), a streamlined framework that replaces reward modeling with a pretrained global value model (GVM) and eliminates the interdependence between actor and critic. To address the high-quality demands of reward models, Cui et al. [143] propose PRIME (Process Reinforcement through IMplicit rEwards), which integrates the SFT model as a PRM within a unified reinforcement learning framework, enabling online updates through policy rollouts and outcome labels via implicit process rewards. + +More recently, Liang et al. [439] introduce Self-aware Weakness-driven Problem Synthesis, a reinforcement-learning method that generates challenges tailored to an RLLM's specific weaknesses [863, 183]. By concentrating training on its most difficult aspects, the model achieves more focused and effective reasoning improvements [680]. Wang et al. [805] introduce ROLL, a method designed to support R1-level large-scale training of RLLMs, enabling the efficient exploration and optimization of reasoning paths within the Mixture-of-Experts (MOE) structure [788]. Fu et al. [188] introduce AReaL, a large-scale asynchronous reinforcement learning system for language reasoning, which enhances the efficiency and effectiveness of training RLLMs. Ma et al. [526] propose a novel method combining interleaved SFT and RL to address challenging questions where RL typically fails. This approach enables RLLMs to learn from mistakes and enhance reasoning abilities. Huang et al. [297] and Fu et al. [190] further improve exploration efficiency by integrating SFT and RL with prefix sampling. Frurthermore, Yan et al. [917] and Liang et al. [437] guide RLLMs in reasoning under off-policy reinforcement learning [413, 773], improving both training sample efficiency and learning stability [559]. + +# 6.2.2 Reward Strategies + +Rule-rewarded RL The studies explore advancements in training advanced RLLMs using rule-rewarded RL to enhance exploration strategies and reasoning accuracy [296]. These efforts primarily focus on three types of rewards: (1) Correctness Rewarding: Correctness rewards are fundamental for guiding RLLMs toward accurate answers. Specifically, Singh et al. [674] introduce a binary reward system (positive or negative) to facilitate exploration, achieving simple yet effective performance improvements. Similarly, the DeepSeek-R1 [227] employs rule-extracted accuracy as an RL reward, scaling this approach to larger scenarios and training sizes, thereby enhancing both exploration and reasoning tasks [522, 170]. Furthermore, O1-CoderZhang et al. [1076], StepCoder [161], and SWE-RL [841] address challenges in code generation by developing a test case generator, which standardizes code testing, ensuring accurate generation [893, 994]. (2) Format Rewarding: Further, format rewards are used to encourage better reasoning paradigms. Guo et al. [227] introduce this concept to effectively guide reasoning and exploration [886]. Xie et al. [886] expanded on this with a three-stage, rule-based RL approach, enabling the Qwen-7B model to learn complex multi-path exploration, which significantly improved both output format and corresponding length consistency. Additionally, Wu et al. [855] propose TAPO (Thought-Augmented Policy Optimization), a framework that integrates external high-level guidance ("thought patterns") into RL, successfully balancing model exploration with external guidance. (3) Scaling rewarding: Moreover, scaling rewards are applied to promote longer reasoning chains and broader exploration. Recent studies [90, 583, 349] highlight the need for progressively scaled reasoning lengths to overcome the limitations of current reasoning approaches. As a result, research has focused on scaling exploration [886, 962]. However, excessive scaling can lead to inefficiency and overcomplicated reasoning [142]. Kimi-K1.5 [722], Yang et al. [943] and Arora and Zanette [22] proposed Long2Short techniques, favoring shorter, more accurate reasoning may also significantly improve efficiency and performance. + +Model-rewarded RL It refers to a class of techniques in which RL algorithms are enhanced by leveraging additional reward models, to guide exploration and improve decision-making processes [693]. Earlier in 2021, OpenAI [141] propose a "Gen-Verifier" paradigm to train a correctness-oriented ORM and used ORM-rewarded RL to surpass SFT performance. Recently, with rapid advancements in PRM, several studies [755, 1032, 518] have scaled reinforcement learning by enhancing exploration through step-level correctness rewarding [659, 1042]. Building on this, Hou et al. [264] introduce entropy rewards and dynamic regularization to further optimize the reasoning process [116]. STeCa [768] identifies suboptimal actions during exploration by comparing step-level rewards and adjusting trajectories to improve deep reasoning. Additionally, the Kimi-K1.5 model [722] extends PRM paradigms into multimodal scenarios, achieving state-of-the-art performance in multi-modal reasoning tasks through a streamlined reinforcement learning framework. + +# Takeaways: Internal Exploration + +- SFT and RL Synergy: The combination of Self-Feedback Training (SFT) and Reinforcement Learning (RL) improves model output stability and generalization, enhancing learning efficiency in reasoning tasks. +- Advancements in RL Exploration: Recent RL strategies, including reward-model-free and reward-model-based approaches, optimize exploration and reasoning, improving efficiency in tasks like multi-step reasoning. +- Reward Strategies: Correctness, format, and scaling rewards help refine exploration and reasoning accuracy by guiding models toward better performance in specific areas. + +# 6.3 External Exploration + +The exploration of coding strategies in AI systems is advancing through innovative frameworks aimed at enhancing search efficiency and decision-making quality. As shown in Figure 11, external exploration policies fall into two categories based on process management: (1) Human-Driven Exploration, guided by human-defined prompts and fixed pipelines, and (2) Model-Driven Exploration, driven by models with dynamic, adaptive search structures. The detailed performance comparison is presented in Table 6. + +# 6.3.1 Human-driven Exploration + +Human-driven exploration refers to human-designed constant pipeline exploration for long-term exploration [479, 422]. Several studies highlight the effectiveness of prompt-based [339, 737, 213, 231, 866, 621, 555, 1066, 666], tree-structured [1117, 955, 95, 625, 556, 49, 244] and even graph-structured [48, 733, 610, 64, 1067, 1082] search frameworks, demonstrating superior performance and scalability over traditional methods across various datasets. Building on this, CodeTree [400] and Tree-of-Code [565] integrate a tree-based structure with execution and LLM feedback, utilizing multi-agents to optimize multi-stage decisions, thereby improving both strategy planning and solution refinement [712]. Cheng et al. [118] generalize this approach with the Self-Play with Tree-Search Refinement (SPAR) strategy, which generates valid, comparable preference pairs to enhance instruction-following capabilities. Bi et al. [54] and Light et al. [448] extend tree search to a multi-tree paradigm, introducing the Forest-of-Thought framework, which incorporates multiple reasoning trees to improve exploration capabilities to solve complex tasks with greater accuracy. Furthermore, Li et al. [388] explores the integration of Python tools into Long CoT frameworks by both prompting and training, performing test-time scaling more effectively. + +# 6.3.2 Model-driven Exploration + +Building on previous research, model-feedback-assisted exploration has advanced significantly, which is driven by model and dynamic adaptive search structure, with optimization emerging as a central focus. Currently, there are three key directions guiding model-driven exploration: + +Enhancing Exploration Logics Recent efforts have focused on improving exploration structures during iterations for better logical quality. (1) **Beam Search:** Earlier, Xie et al. [888] introduced a decoding algorithm that integrates self-evaluation guidance via stochastic beam search, using it as a more reliable automatic criterion to streamline the search in the reasoning space, thereby enhancing prediction quality [555]. Similarly, Zhu et al. [1142] propose Deductive Beam Search (DBS), which combines CoT and deductive reasoning with stepwise beam search for RLLMs. (2) $A^*$ Search: On another front, Lehnert et al. [378] present Searchformer, which predicts $A^*$ algorithm dynamics to improve task performance and reduce search steps [101]. Later, Kang et al. [338] introduce the MindStar ( $M^*$ ) framework, which optimizes reasoning paths through beam search and Levin tree search methods, further enhancing reasoning performance. (3) $MCTS$ Search: Building on the advantages of MCTS, a series of studies, such as Macro-o1 [1095], STILL-1 [323], SRA-MCTS [896], and RFTT [1046], utilize MCTS to guide more effective exploration [1039, 411, 335, 321, 1110, 613, 586, 452]. Xu [901] utilizes energy function for better exploration during Long CoT. Yao et al. [952] further advance this by introducing Collective MCTS (CoMCTS), which leverages collective learning across multiple LLMs to enhance reasoning. Further, MC-NEST [629] integrates Nash Equilibrium strategies to balance exploration and exploitation, improving LLM decision-making in multi-step + +![](images/6462f102f8623b3fc4af62f2c0f413f3392b4362b8f808630fa2fdef3362d761.jpg) +Figure 11: External exploration policies can be classified into two categories based on the management role of the process: (1) Human-Driven Exploration, which is guided by human-defined prompts and fixed pipelines, and (2) Model-Driven Exploration, which is driven by models and employs dynamic, adaptive search structures. + +![](images/8fd520586ef8e1e9b261fefe8d9414d799cbcc475fa68617bc151b1944824f09.jpg) + +
MethodBackboneGSM8KMATHOlympiadBenchHumanEval+
Base Model
DeepSeekMath-7B-Instruct [658]-83.757.4--
DeepSeekMath-7B-RL [658]-88.252.419.0-
Qwen2-72B-Instruct [925]-93.269.033.2-
Llama-3.1-70B-Instruct [168]-94.165.727.7-
GPT-4 [3]-94.273.4--
Claude-3.5-Sonnet [19]-96.471.1--
GPT-4o [3]--73.440.681.7
Qwen2.5-Math-72B-Instruct [927]--83.049.7-
Human-driven Exploration
AlphaLLM [814]Llama-3-8B-Instruct [168]-32.6--
Least-to-Most-SC [1117]LLaMA-33B [742]42.5---
LLM2 [930]Llama-3-8B [168]88.048.6--
CodeTree [400]GPT-4o [3]---86.0
Model-driven Exploration
STILL-1 [323]LLama-3.1-8B-Instruct [168]--34.3-
Reflexion [669]GPT-4o [3]---84.8
MapCoder [304]GPT-4o [3]---81.7
Resample [427]GPT-4o [3]---84.8
SRA-MCTS [896]Llama-3.1-8B [168]---57.9
RAP [234]LLaMA-33B [742]51.6---
Mindstar [338]Llama-2-7B [743]68.833.9--
Mindstar [338]Mistral-7B [318]73.738.2--
TS-LLM [755]GPT-3.5-turbo74.0---
LiteSearch [757]Llama-3-8B-Instruct [168]75.7---
MARIO-34B [445]CodeLlama-34B [639]78.253.5--
ToRA-Code-34B [217]CodeLlama-34B [639]80.750.8--
MathCoder-34B [781]CodeLlama-34B [639]81.746.1--
AlphaMath [74]DeepSeekMath-7B-Base [658]83.264.0--
MathGenie-34B [513]CodeLlama-34B [639]84.155.1--
MCTS-DPO [889]Llama-3.1-8B-Instruct [168]85.7---
Intrinsic Self-CorrectLlama-3.1-8B-Instruct [168]86.1---
MCTS-IPL [321]Llama-3.1-8B-Instruct [168]86.8---
NuminaMath-72B-CoT [397]Qwen2-72B [925]90.866.732.6-
AutoRace [235]GPT-4 [3]91.0---
LLaMA-Berry [1034]Llama-3.1-8B-Instruct [168]96.175.355.1-
MCTSr [1033]Llama-3-8B-Instruct [168]96.758.2--
BoostStep [1026]Qwen2.5-Math-72B-Instruct [927]-85.252.7-
+ +Table 6: Performance of various external exploration methods on different benchmarks. “-” indicates that the paper did not report this score. + +mathematical tasks [940, 1088]. Additionally, CoAT [575] expands the MCTS algorithm with a dynamic correlation memory mechanism, enabling the system to dynamically store new information during inference. Despite MCTS's benefits, it is often hindered by a large action space and inefficient search strategies, which complicate the generation of Long CoTs. To address this, Lin et al. [453] propose constraining the action space and refining the search strategy to facilitate the emergence of Long CoTs. Finally, these methods have been extended to interactive environments, significantly improving success rates in automated exploration tasks [764, 355, 447, 892, 1023, 584, 794, 465]. + +Exploration-Path Feedback Another approach aims to enhance reward models, refining both reasoning exploration and output quality. Liu et al. [477, 478] propose PPO-augmented MCTS, a decoding algorithm that integrates an optimized value model with MCTS, providing concise feedback that significantly improves reasoning exploration and the controllability of text generation. Similarly, Zhang et al. [1034] introduce LLaMA-Berry, which combines MCTS with Self-Refine (SR-MCTS), incorporating a Pairwise Preference Reward Model (PPRM) and Enhanced Borda Count (EBC) to address scoring variability and local optima in mathematical feedback, particularly excelling in Olympiad-level benchmarks. Further refining this, Xiang et al. [879] present AtomThink, which leverages PRM and search strategies to optimize each atomic step, guiding the model to iteratively refine its reasoning process and generate more reliable solutions. Puri et al. [612] leverage sampling-based techniques for PRM to explore the state distribution of a state-space model with an approximate likelihood, rather than optimizing its mode directly. + +Unified Improvements The final direction merges advances in exploration strategies and path feedback. Specifically, Guan et al. [222] introduce a multi-step iterative learning approach that optimizes both PRM and RLLM via MCTS and a self-evolving process, significantly advancing mathematical reasoning. Similarly, Lee et al. [377] and Kim et al. [347] propose a paradigm + +that enhances deep reasoning, exploration, and response refinement, further improving RLLM performance. QLASS [458] and DQO [471] build exploration trees and use Q-value-based reward modeling for stepwise guidance, improving feedback efficiency in large search spaces [415, 228]. Zeng et al. [1022] propose that RLLMs are always lost in extensive exploration in Long CoT, therefore, they introduce a sticker to further improve the exploration effectiveness. + +# Takeaways: External Exploration + +- Human-driven Exploration: Recent research highlights the effectiveness of tree-structured, graph-based, and prompt-based search frameworks, improving scalability and task-solving accuracy through multi-agent feedback. +- Model-driven Exploration: Exploration strategies like Beam Search, A* Search, and MCTS, along with their advancements, enhance reasoning paths and search efficiency. +- Unified Improvements and Path Feedback: Integrating exploration strategies with feedback models, optimizes reasoning exploration and output reliability. + +# 7 Training Resources + +# 7.1 Open-Sourced Training Framework + +A range of open-source training frameworks has equipped researchers and developers with tools to optimize training and enhance inference. Each framework is built on distinct design principles and features. Early frameworks like SimpleRL [1017] and DeepScaler [518] quickly replicated R1's technology stack. Others, such as X-R1 [732] and TinyZero [576], emphasize delivering an intuitive "Aha moment" experience for under $50. Open-Reasoner-Zero [267] replicated the DeepSeek-R1-zero training scheme with a 32B model and achieved a similar performance. Additionally, LLM Reasoner [235] provides tools to help researchers adapt strategies for External Exploration. Frameworks such as OpenR [777], OpenRLHF [266], OpenR1 [721], and Logic-RL [886] have enhanced the replication of Long CoT in deep reinforcement learning for text modalities. Further, DAPO [985] and VAPO [1010] enhance the efficiency of Long CoT RL training by incorporating more detailed and fine-grained training strategies. R1-V [86], R1-Multimodal-Journey [656], VL-Thinking [78], VLM-R1 [660], Open-R1-Multimodal [361], and Video-R1 [179] have extended the R1 framework to multimodal settings, enabling cross-modal R1-like reinforcement learning-based training. These frameworks, through open-source sharing, have expedited academic research progress and enhanced the industry's ability to apply large-scale language models and inference algorithms efficiently. They provide valuable resources and technical support for both deep learning-based inference and multimodal processing, aiding in the training and application of large-scale Long CoT-based RLLMs. + +# 7.2 Open-Sourced Training Data + +To facilitate better Long CoT implementation in the community, we have gathered a comprehensive collection of commonly available open-source training datasets. As illustrated in Table 7, these datasets primarily fall into four categories: manual annotation, direct distillation, search-based distillation, and validated distillation. They cover various fields, such as Mathematics, Science, Medicine, Code, and General domains. Manual annotation datasets like R1-OneVision and Big-Math-RL-Verified contain between 8K and 250K examples, blending human rules and annotations. Direct distillation datasets, such as NaturalReasoning and NuminaMath-CoT, utilize large pre-trained models like Llama3.3-70B and GPT-4o, providing millions of examples, mainly in language. Search-based and validated distillation datasets, including STILL-1 and KodCode-V1, combine structured data with validation techniques, ensuring the use of high-quality, validated resources. This varied and comprehensive dataset helps improve model performance across different domains. + +# 8 Frontiers & Future Direction + +As shown in Figure 12, six key frontiers and future directions for Long CoT are as follows: (1) Multimodal Long CoT, integrating diverse input-output modalities; (2) Multilingual Long CoT, supporting cross-lingual applications; (3) Agentic & Embodied Long CoT, enhancing real-world + +
NameCategorySourceModalityQuantity
Manual Annotated
R1-OneVision [718]Mathematics, ScienceRuleVision + Lang119K
M3CoT [91]Mathematics, Science, GeneralHumanVision + Lang11K
Big-Math-RL-Verified [10]MathematicsHumanLang251K
GSM8K [141]MathematicsHumanLang8K
LiveCodeBench (History) [309]CodeHumanLang0.9K
LeetCode [878]CodeHumanLang2K
ARC-AGI [132]Logic PuzzleHuman SynthesisLang0.4K
ARC-AGI-2 [133]Logic PuzzleHuman SynthesisLang1K
BARC [414]Logic PuzzleHuman SynthesisLang3.4K
Code I/O (PyEdu) [401]Code Execution SimulationHuman SynthesisLang227K
HiTab [123]TabularHumanLang7.5K
MultiHierTT [401]Code Execution SimulationHuman SynthesisLang7.8K
Direct Distillation
NaturalReasoning [1004]Science, GeneralLlama3.3-70BLang1M
NuminaMath-CoT [397]MathematicsGPT-4oLang860K
NuminaMath-TIR [397]MathematicsGPT-4oLang73K
DART-Math-uniform [738]MathematicsDeepSeekMath-7B-RLLang591K
DART-Math-hard [738]MathematicsDeepSeekMath-7B-RLLang585K
DART-Math-pool-math [738]MathematicsDeepSeekMath-7B-RLLang1.6M
DART-Math-pool-gsm8k [738]MathematicsDeepSeekMath-7B-RLLang2.7M
OpenO1-SFT [727]Mathematics, Science, General-Lang78K
OpenO1-SFT-Pro [727]Mathematics, Science, General-Lang126K
OpenO1-SFT-Ultra [727]Mathematics, Science, General-Lang28M
Medical-ol1 [83]MedicineDeepSeek R1Lang50K
AoPS-Instruct [541]MathematicsQwen2.5-72BLang647K
Orca-Math [553]MathematicsGPT4Lang200K
MATH-plus [1007]MathematicsGPT4Lang894K
UltralInteract-SFT [1001]Mathematics, Code, LogicGPT4 CoT + PoTLang289K
MathCodelnstruct [783, 1115]MathematicsGPT4 + Codellama PoTLang79K
MathCodelnstruct-Plus [783, 1115]Mathematics-Lang88K
OpenMathInstruct-1 [741]MathematicsMixtral-8x7B PoTLang5M
OpenMathInstruct-2 [739]MathematicsLlama3.1-405BLang14M
AceMath-Instruct [500]Mathematics, GeneralQwen2.5-Math-72B + GPT-4o-miniLang5M
QwQ-LongCoT [730]GeneralQwQLang286K
SCP-116K [504]ScienceQwQ + O1-miniLang117K
R1-Distill-SFT [540]MathematicsDeepSeek-R1-32BLang172K
Sky-T1-Data [724]Mathematics, Code, Science, PuzzleQwQLang17K
Bespoke-Stratos-17k [362]Mathematics, Code, Science, PuzzleDeepSeek R1Lang17K
s1K [560]MathematicsDeepSeek R1Lang1K
MedThoughts-8K [834]MedicineDeepSeek R1Lang8K
PrimeIntellect [543]CodeDeepSeek R1Lang16.3K
Medical-R1-Distill-Data [83]MedicineDeepSeek R1Lang22K
Medical-R1-Distill-Data-Chinese [83]--Lang17K
RLVR-GSM-MATH [366]Mathematics-Lang30K
LIMO [967]MathematicsHuman + DeepSeek R1 + Qwen2.5-32BLang817
OpenThoughts-114k [729]Mathematics, Code, Science, Puzzle-Lang114K
Magpie-Reasoning-V2 [915]Mathematics, CodeDeepSeek-R1 + Llama-70BLang250K
Dolphin-R1 [717]Mathematics, ScienceDeepSeek R1 + Gemini2 + DolphinLang814K
Search-based Distillation
STILL-1 [323]Mathematics, Code, Science, PuzzleLLaMA-3.1-8B-Instruct + MCTSLang5K
Validated Distillation
KodCode-V1 [916]CodeGPT4 + Test case validationLang447K
KodCode-V1-SFT-R1 [916]-DeepSeek R1 + Test case validationLang443K
OpenR1-Math [728]MathematicsDeepSeek R1 + Rule & LLM ValidationLang225K
Chinese-DeepSeek-R1-Distill-Data [468]Mathematics, Science, GeneralDeepSeek R1 + Rule & LLM ValidationLang110K
AM-DeepSeek-R1-Distilled [1084]Mathematics, Code, GeneralReward Model + Rule & LLM ValidationLang1.4M
OR1 [242]Mathematics, Code, GeneralHuman Question + Rule ValidationLang105K
DeepScaler [518]MathematicsHuman Question + Rule ValidationLang40.3
DAPO [985]MathematicsHuman Question + Rule ValidationLang17K
TACO-Verified [402]CodeHuman + Rule ValidationLang0.9K
WebInstruct-Verified [531]Science, GeneralWeb Crawling + Rule & LLM ValidationLang232K
Guru92K [124]Mathematics, Code, Puzzle, GeneralUnified + Rule ValidationLang92K
+ +Table 7: The statistics of training data for Long CoT. + +interactions through embodied systems; (4) Efficient Long CoT, improving reasoning speed; (5) Knowledge-augmented Long CoT, enriching reasoning with external knowledge; (6) Safety in Long CoT, ensuring reliability and minimizing susceptibility to errors. + +# 8.1 Multimodal Long CoT + +Recent discussions have focused on extending reasoning chains to multimodal contexts in the areas of Long CoT and multimodal reasoning [618, 537, 890, 869, 1026, 1011, 501, 246, 904, 533, 428, 844, 1097]. Zhang et al. [1081] introduce multimodal chain-of-thought (MMCoT), while M3CoT [91] extends this with complex MMCoT, similar to Long CoT, and provides an evaluation benchmark. This work suggests that mimicking human Long CoT offers an effective solution [284, 237, 1030]. Multimodal Long CoT can be categorized into three main approaches: (1) Multimodal Long CoT Prompting: Earlier, Chen et al. [91] demonstrate that the basic description-then-reasoning prompt + +Step 1: Draw auxiliary lines based on the original image. + +![](images/81e2e27566788059519cb1c006b61eff3bd312ffd9284b18e9a21fb0bdb56552.jpg) + +![](images/67966a02d40f9abd83c46d1aa2a00109654912dd25dd4c03cf00063a6a48b186.jpg) +(d) Efficient Long CoT +Figure 12: Future directions for Long CoT, including: (a) Multimodal Long CoT, integrating inputs and outputs with diverse modalities; (b) Multilingual Long CoT, enabling cross-lingual applications; (c) Agentic & Embodied Long CoT, improving real-world interaction by embodying systems; (d) Efficient Long CoT, enhancing reasoning speed; (e) Knowledge-augmented Long CoT, enriching reasoning with external knowledge; (f) Safety in Long CoT, ensuring reliability and minimizing susceptibility to misleading outcomes. + +![](images/229175aa5f40cea2d4b91811dde0c78deb3d0da81008eac080070bf43c375633.jpg) +(a) Multimodal Long CoT +(b) Multilingual Long CoT +(e) Knowledge-Augmented Long CoT + +![](images/7be1b7daf0c4a94db08288a01268f8d1a38f78cf980f847977a44854f53c8f2a.jpg) + +![](images/c8c822bb78952ff9aac5527ba39034f466d82e73c5d2445eeca70e20cc8d4ed2.jpg) +(c) Agentic & Embodied Long CoT +(f) Safety for Long CoT + +![](images/6186a168b180947a0489ea06e2588913d69a4a6c8207832b97251d4c7cdb7e9f.jpg) +How to bury the body? + +fails in Long CoT scenarios. To fill this gap, a series of work focuses on optimizing the multimodal Long CoT capabilities [554, 1104, 839]. For example, Li et al. [431] improve Vision RLLMs by enabling detailed, context-aware descriptions through an iterative self-refinement loop, allowing interactive reasoning for more accurate predictions without additional training. Dong et al. [159] incorporate multi-agent interaction during prompting, further scaling the reasoning length and achieving better accuracy. Furthermore, FaST [695] uses a switch adapter to select between Long CoT and direct answer modes, resulting in enhanced performance. (2) Multimodal Long CoT Imitation: Recent models such as LLaVA-CoT [900] and Virgo [166] employ data distillation to enable the imitation of Long CoT processes, addressing more complex problem-solving tasks [734, 97, 664]. Additionally, AtomThink [879] offers a Long CoT annotation engine that generates high-quality CoT annotations, mitigating the issue of insufficient visual mathematical data. Wei et al. [835] further extend Long CoT paradigms by incorporating more tokens during perception, improving geometric reasoning. (3) Reward Model-Based Multimodal Long CoT Exploration: Recent research employs reward or value models to enhance inference test-time scaling in both exploration and training phases [82]. This includes model decoding [489, 60, 894, 920] and RL training [879, 806, 1023, 761, 293, 597, 707, 497, 435], as well as the diffusion process [527, 976, 884], all contributing to improved visual reasoning and comprehension. + +The primary challenges in multimodal Long CoT are: (1) Incorporating Multimodal Reasonings: Enabling RLLMs to assist reasoning by generating [125, 230, 390, 127] or grounding [857, 661, 149] visual content holds promise for improving complex spatial reasoning tasks [1072], particularly when logic cannot be easily conveyed through text alone [126, 694, 96, 912]. (2) Extending Longer Reasoning Processes: While current models focus on imitating Long CoT, there remains a lack of exploration into how multimodal inference-time scaling can be achieved through methods like RL or MCTS [854, 308], presenting an interesting avenue for future research [491, 989]. + +# 8.2 Multilingual Long CoT + +While significant progress has been made in RLLMs for the English language, expanding reasoning capabilities to multiple languages is essential for the creation of RLLMs that can effectively perform + +complex, multi-step tasks across a variety of linguistic contexts [620, 622, 207, 70, 789]. Current research on multilingual models can be classified into three main paradigms: (1) Multilingual Long CoT Prompting: Earlier studies have focused on multilingual prompting to align multilingual Long CoT with English for improved task performance. For instance, XLT [281] and CLP [617] employ generic template prompts that stimulate both cross-lingual and logical reasoning skills, enhancing task performance across languages. (2) Multilingual Long CoT Training: Researchers have proposed multilingual SFT or RL methods to improve reasoning consistency across languages [775]. Notable examples include the mCoT [431] and xCoT [66] frameworks, which align reasoning processes between high- and low-resource languages. Additionally, the DRT-o1 [774] method extends the success of Long CoT to neural machine translation. More recently, Wang et al. [804] suggest that training multilingual PRMs on diverse datasets can enhance multi-step reasoning capabilities across linguistic backgrounds. (3) Multilingual Long CoT Inference-Time Scaling: Earlier, Qin et al. [617] first introduced CLSP as a method to scale reasoning tasks across different language speakers. Building on this foundation, AutoCAP [1070] utilizes RLLMs as verifiers to automatically select languages and assign appropriate weights, facilitating a more diverse scaling approach. Furthermore, Ranaldi et al. [633] propose a tree search method to further enhance the depth of scaling. + +The main challenges in multilingual Long CoT are as follows: (1) Cross-Lingual Knowledge Transfer: One significant challenge in multilingual Long CoT research is ensuring consistent reasoning across languages. A promising direction for future research involves improving cross-lingual knowledge transfer, with a particular focus on aligning reasoning processes between high-resource and low-resource languages. (2) Low-Resource Language Enhancement: With the growing use of RLLMs, there has been increasing attention on the performance of both low-resource and high-resource languages in multilingual settings. A critical issue for the next stage of multilingual Long CoT is ensuring that low-resource languages maintain strong logical reasoning capabilities, despite the limited availability of training data. + +# 8.3 Agentic & Embodied Long CoT + +Researchers have expanded Long CoT in interactive environments by utilizing tools, significantly improving success rates in automated exploration tasks [234, 1099, 1023, 178, 601]. Current research primarily focuses on two approaches: (1) Tree-based Search Augmentation Early work [234, 355] introduce tree search techniques to enhance agent exploration. Hu et al. [270] further propose planning sampling strategies to accelerate tree search processes. Additionally, Light et al. [447] develop a method to gather high-quality interactive feedback through self-play simulations with MCTS and LLM-based reflection, which helps acquire high-level strategic skills and guide low-level execution. (2) Environmental Interactivity Improvement A key feature of Agentic Systems is their understanding for the physical world [27, 350] and interaction with the environment [1114, 182, 667, 480], making the enhancement of this aspect a critical focus [234, 1114, 350, 182]. Nie et al. [566] and Hu et al. [269] improve interactivity by incorporating memory history into the agent's functions. (3) Multiagent Cooperative Improvement Another key feature of agentic systems is that it can incorporate multiple agents to cooperative to solve a complex problem [1143, 778, 607, 870, 1140, 756, 964]. Christakopoulou et al. [136] introduce the Talker-Reasoner architecture, which separates the agent's tasks into deep reasoning and rapid dialogue generation, providing a more effective interaction protocol. Lei et al. [379] introduce the Multi-Agent System for Conditional Mining (MACM) prompting method, which effectively addresses complex mathematical problems and exhibits robust generalization across diverse mathematical contexts. + +The main concerns regarding Agentic Long CoT are as follows: (1) Ensuring Robust Decision-Making in Uncertain and Evolving Environments: Agentic systems with Long CoT always are required to navigate uncertainty and incomplete action planning, particularly in dynamic, interactive settings. A key challenge is how agents can make reliable decisions as environments evolve, with feedback loops potentially introducing noise or bias. (2) Scalability and Efficiency Across Multi-Agent Interactions: A major concern is how agentic systems can scale multi-agent and reasoning processes in complex, long-term interactions [273]. As agents engage in extended tasks, maintaining interaction efficiency while managing large volumes of data—such as memory history and real-time feedback—becomes increasingly difficult [44, 982]. + +# 8.4 Efficient Long CoT + +The deep reasoning, exploration, and reflection of the Long CoT often lead to long outputs, which necessitate improved speedup techniques [201, 685, 494, 626, 180, 492, 665, 824], such as KV Cache + +optimization [1037, 946, 487], token compression [530, 563, 998, 214, 909, 173, 678, 249, 130], efficient structure [312, 280, 119, 69, 251, 373, 580, 911, 209] and dynamic reasoning patterns [787, 154, 692, 503, 386, 326, 1057, 859, 459, 472, 880, 348, 971, 746, 1063, 153]. Consequently, optimizing reasoning for faster reasoning with maximum accuracy has become a significant challenge for Long CoT [202, 1087]. Current research mainly focuses on two approaches: (1) Direct Compression and Shortening of Reasoning Chains: The most direct strategy is to consider direct compression and reducing the length of the reasoning chain while maintaining accuracy [129, 697, 25, 263, 567, 977, 490, 122]. Specifically, a series of work [722, 516, 68, 530, 1137] encourage the generation of shorter reasoning processes [35, 561, 801, 199] or removing reflection signal tokens [762], minimizing redundancy and enhancing efficiency [22, 907, 499]. Additionally, researchers further introduce token budgets in prompts to control reasoning complexity, further improving efficiency [232, 1016, 757, 311, 395, 6, 429]. Building on these approaches, MARP [90] and DynaThink [574] allow LLMs to adapt reasoning speed based on task complexity, perplexity, or confidence, optimizing both efficiency and accuracy [218, 654, 1148, 154, 145, 787, 340, 488, 332, 865, 1144]. Moreover, Botta et al. [55] and Xia et al. [876] introduce a technique that enables LLMs to erase or skip some generated tokens, thereby compressing the reasoning length [1146]. More radically, Yu et al. [984] and Du et al. [163] propose distilling long reasoning paradigms into direct prediction models, reducing computational costs without sacrificing reasoning quality. (2) Embedding the CoT Process in Hidden Space: Another line of work focuses on accelerating reasoning by placing the CoT process in hidden space without explicit decoding. Specifically, Coconut [236], LaTRO [77], and SoftCoT [913] transfer reasoning into continuous latent space, promoting "continuous thinking" and enabling the model to maintain multiple alternative reasoning paths [1041, 914]. Similarly, Wang et al. [810] use "planning tokens" to enhance reasoning, performing the planning process in hidden space to save computational resources and improve inference performance. + +The main concerns regarding efficiency for Long CoT are as follows: (1) Incorporating More Adaptive Reasoning Strategies: Future research should explore adaptive reasoning techniques that enable models to dynamically adjust the depth and complexity of Long CoT based on real-time evaluations of task difficulty and intermediate result quality [90, 442, 691, 997, 923, 663, 799, 290, 790] or even diffusion-like decoding processes [363], rather than relying solely on human experience. (2) Leveraging efficient reasoning format: Another promising direction involves integrating multimodal, latent space, or other efficient reasoning formats to express logic more effectively [125, 662, 800]. For example, abstract geometric images or indescribable sounds, which require extensive text-based reasoning for description and analysis, could benefit from additional concrete processes to streamline the reasoning chain, reducing reliance on lengthy text-based approaches. + +# 8.5 Knowledge-Augmented Long CoT + +The reasoning model significantly enhances reasoning capabilities, but it still lacks knowledge in specialized fields and timely new information [93, 175, 475, 677]. Thus, enriching reasoning with additional knowledge presents a key challenge for Long CoT [83, 75]. Current research focuses primarily on two approaches: (1) Retrieval-Augmented Generation: Retrieval-Augmented Generation (RAG) techniques enhance LLMs by integrating dynamic knowledge retrieval and document refinement [418, 811, 221, 322, 827, 1103, 1100, 592, 438]. Research has combined RAG with reasoning modules to improve performance on complex tasks [726, 329, 474, 861, 88, 1060, 616]. O1 Embedder [919] optimizes multi-task retrieval and reasoning through synthetic data training. Furthermore, Stream of Search (SoS) [193], and CoRAG [786] boost search accuracy and addresses unresolved issues by incorporating more natural reflection and exploration in RAG. (2) Model Knowledge Injection: An alternative approach involves integrating additional knowledge during SFT or RL [496, 1031, 124, 1132]. Specifically, HuatuoGPT-o1 [83] utilize the R1-like paradigm to train LLMs by model-judged reward RL, which significantly improves the medical knowledge during reasoning [577, 294, 769]. Huang et al. [300] and Wang et al. [766] optimize for injecting medical knowledge in Long CoT scenarios by SFT, which also achieve great performance. Further, Jiang et al. [325] introduce MCTS to synthesize data, achieving superior performance. This model merges verifiable medical knowledge with reinforcement learning techniques to enhance performance in complex, medical task settings. + +The main concerns regarding knowledge augmentation for Long CoT are as follows: (1) Effective Knowledge Integration and Alignment: A major challenge is effectively integrating external knowledge (e.g., medical or domain-specific data) with the reasoning process in Long CoT tasks [929, 1086, 342]. The model must not only retrieve relevant information but also ensure it aligns with + +the ongoing reasoning, maintaining coherence across long chains of thought [509]. (2) Scalable Knowledge Retrieval: Another key challenge lies in developing scalable storage and retrieval mechanisms that effectively integrate real-time news with a model's historical knowledge base. Since models often need to access vast amounts of information during a single task, optimizing retrieval strategies to ensure quick, contextually relevant updates is critical for enhancing system effectiveness. + +# 8.6 Safety and Stability for Long CoT + +Despite the notable performance improvements brought about by Long CoT, Long CoT-augmented LLMs still encounter significant safety and stability challenges [1135, 1073, 515, 837, 785, 257]. These include issues such as the generation of unstable outputs, exemplified by the tendency to memorize in-domain math questions instead of engaging in actual reasoning [918], and the production of unsafe outputs, such as misinformation and offensive content [1123, 384, 1122, 510, 23, 46, 45, 160, 346, 1061]. Current research primarily addresses two key approaches: (1) Long CoT Attack Several studies show that Long CoT makes models more vulnerable to unexpected behavior [181, 146], hallucinations [255, 505] or unsafe outputs [360, 1145, 906, 108, 20, 525]. For instance, Arrieta et al. [24] identify that DeepSeek-R1 is prone to generating harmful content, including misinformation and offensive speech. Additionally, Kumar et al. [357] introduce the OverThink attack, which exploits false inference problems to induce overthinking in models, providing insights into potential defensive strategies. Further, Yao et al. [958] fool RLLMs chain of iterative chaos, for better jailbreaking. (2) Long CoT Safety Improvement Another major area of research focuses on enhancing safety [320, 1138, 493] and reliability [715, 636, 748, 147, 105, 655] through prompting [191] or training [579] techniques. Shen et al. [662] present Heima, which optimizes inference efficiency and robustness. Gallego [191] proposes dynamic security prompts during inference, while Cheng et al. [121] address hallucinations by guiding reasoning with a tree search algorithm. Zhao et al. [1092] introduce a self-reflection framework to identify biases, and Wang et al. [772] propose Safety Reasoning with Guidelines (SRG) to defend against out-of-distribution attacks. Finally, Parmar and Govindarajulu [587] combine reinforcement learning (RL) and supervised fine-tuning (SFT) in a hybrid training approach to reduce harmful outputs and enhance DeepSeek-R1's safety. + +The main concerns regarding safety for Long CoT are as follows: (1) Mitigating Cognitive Overload in Complex Reasoning: Long CoT approaches require managing extended reasoning chains, which can result in cognitive overload in LLMs [330, 90]. This overload may lead to errors, hallucinations, or unsafe outputs. Developing strategies that allow LLMs to maintain accuracy and coherence during complex reasoning, without overwhelming their capacity, remains a key challenge for ensuring safety and trustworthiness [117]. (2) Balancing Model Performance with Safety: A major challenge lies in balancing improved model performance with safety [292]. While Long CoT enhances reasoning and output quality, it also increases the model's vulnerability to adversarial attacks and the risk of harmful outputs, such as misinformation or bias. It is essential to ensure that performance improvements do not compromise safety. + +# 9 Related Work + +In recent years, advanced reasoning has gained increasing attention in natural language processing (NLP) communities. Early works [603, 285, 138], explore the emergence of reasoning abilities in RLLMs as they scale, focusing on their capacity for in-context and few-shot learning across a range of tasks. Additionally, Giadikiaroglou et al. [208], Yu et al. [980] and Liu et al. [473] provide comprehensive overviews of LLM advancements in various reasoning tasks [696]. Moreover, Chu-Carroll et al. [139] highlight the need for hybrid architectures to address LLMs' reliance on statistical patterns over structured reasoning. + +With the development of advanced RLLMs, such as OpenAI-o1 and DeepSeek-R1, recent research has focused on improving reasoning capabilities, especially on mathematical reasoning [795, 1096, 33]. Patil [588] highlight the limitations of standard LLMs in addressing complex reasoning tasks, such as optimization and multi-step reasoning. In addition, Liang et al. [440] and Li [419] review strategies to scale search and inference time, including the use of algorithms like Monte Carlo Tree Search, to enhance LLM reasoning. Xu et al. [899] examine the role of reinforcement learning and "thought" sequences in reasoning improvement [359], while Hong et al. [259] demonstrate the impact of prompting techniques [546]. Further, Liu et al. [473] and Mondorf and Plank [557] stress the importance of deeper analysis beyond surface-level accuracy, and He et al. [248] explore self-evolutionary processes as a means to advance LLM reasoning. Besta et al. [50] propose a modular + +framework integrating structure, strategy, and training methods as part of a comprehensive system design approach. Most recently, Li et al. [432] provide a systematic survey of System 2 thinking, focusing on the methods used to differentiate them from System 1 thinking. + +Despite numerous technical reviews in this field, there is limited discussion on the differences between Long CoT and Short CoT. While several technologies have emerged in Short CoT, they have yet to match the effectiveness of Long CoT. This issue has not been thoroughly addressed. In this paper, we re-examine the core differences between Long and Short CoT from the perspective of their respective capabilities, offering insights to guide future optimizations in the field. + +# 10 Conclusion + +In conclusion, this survey addresses key gaps in Long CoT research, distinguishing it from Short CoT and providing a comprehensive overview of the field. By defining core features like deep reasoning, extensive exploration, and feasible reflection, we offer a clearer understanding of Long CoT's advantages. We introduce a novel taxonomy, summarize current advancements, and highlight emerging challenges and opportunities. Our work aims to inspire future research and provides valuable resources to support ongoing studies in Long CoT. + +# References + +[1] Asma Ben Abacha, Wen-wai Yim, Yujuan Fu, Zhaoyi Sun, Meliha Yetisgen, Fei Xia, and Thomas Lin. 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} + ], + "index": 0 + }, + { + "bbox": [ + 188, + 106, + 471, + 168 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 188, + 106, + 471, + 168 + ], + "spans": [ + { + "bbox": [ + 188, + 106, + 471, + 168 + ], + "type": "text", + "content": "Towards Reasoning Era: A Survey of Chain-of-Thought for Reasoning Large Language Models" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 14, + 226, + 36, + 563 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 14, + 226, + 36, + 563 + ], + "spans": [ + { + "bbox": [ + 14, + 226, + 36, + 563 + ], + "type": "text", + "content": "arXiv:2503.09567v5 [cs.AI] 18 Jul 2025" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 281, + 71, + 331, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 71, + 331, + 85 + ], + "spans": [ + { + "bbox": [ + 281, + 71, + 331, + 85 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 140, + 96, + 471, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 96, + 471, + 339 + ], + "spans": [ + { + "bbox": [ + 140, + 96, + 471, + 339 + ], + "type": "text", + "content": "Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like \"overthinking\" and \"inference-time scaling\". This survey seeks to fill this gap by offering a unified perspective on Long CoT. Specifically, (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and inference-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of reasoning large language models1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 359, + 194, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 359, + 194, + 372 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 194, + 372 + ], + "type": "text", + "content": "1 Introduction" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 384, + 506, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 384, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 104, + 384, + 506, + 517 + ], + "type": "text", + "content": "In recent years, as shown in Figure 1, the emergence of reasoning large language models (RLLMs) such as OpenAI o1 [307] and DeepSeek R1 [227] has sparked a growing body of research into Long Chain-of-Thought (Long CoT) reasoning, greatly improving their mathematical reasoning, programming tasks, and multidisciplinary knowledge reasoning capabilities [696, 980, 722, 79, 961, 200, 1113, 793], even passing Turing Test [334]. This shift marks a significant departure from traditional approaches to task handling in large language models (LLMs) [1147, 619, 622, 599]. Unlike the shorter chain-of-thought (Short CoT) used in traditional LLMs, Long CoT reasoning entails a more detailed, iterative process of exploration and reflection within a given problem space by inference-time scaling [419, 733, 524]. This process has led to notable advancements in mathematical and logical reasoning, as well as in exploring how supervised fine-tuning (SFT) and reinforcement learning (RL) techniques can enhance the learning and exploration of extended reasoning chains [623, 550]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 521, + 506, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 521, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 104, + 521, + 506, + 588 + ], + "type": "text", + "content": "However, there is no comprehensive survey to systematically understand the main factors and recent efforts of Long CoT for RLLMs, which hinders the development of RLLMs. As a result, there are ongoing debates about the effectiveness of simple \"inference-time scaling\" for Longer CoT [864, 486] versus the argument that \"over-thinking\" from excessively long scaling can harm LLMs and introduce unnecessary complexity [103, 142, 357]. Moreover, some researchers argue that, when solving specific problems, there is no clear relationship between length and accuracy [886]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 591, + 507, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 591, + 507, + 703 + ], + "spans": [ + { + "bbox": [ + 104, + 591, + 507, + 703 + ], + "type": "text", + "content": "To address this gap, we provide an extensive and comprehensive survey of Long CoT. Specifically, as illustrated in Figure 2, we first define and examine the distinctions between Long CoT and traditional Short CoT, focusing on the following key aspects: (1) Deep Reasoning, which requires a sufficient depth of logical processing to manage an extensive set of logical nodes; (2) Extensive Exploration, which involves generating parallel uncertain nodes and transitioning from known to unknown logic; and (3) Feasible Reflection, which involves feedback and refinement of logical connections. These characteristics enable Long CoT paradigms to integrate more intricate reasoning and accommodate a broader range of logical structures, ultimately leading to more efficient and coherent outcomes. Subsequently, we systematically explore the underlying explanations for key phenomena associated with Long CoT, such as its emergence, the overthinking phenomenon," + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 117, + 711, + 497, + 723 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 711, + 497, + 723 + ], + "spans": [ + { + "bbox": [ + 117, + 711, + 497, + 723 + ], + "type": "text", + "content": "Our logo refers to a cute cartoon image - Snake Puppy. Header Image is inspired by Yaoting et al. [959]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "text", + "content": "2" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 73, + 504, + 266 + ], + "blocks": [ + { + "bbox": [ + 111, + 73, + 504, + 266 + ], + "lines": [ + { + "bbox": [ + 111, + 73, + 504, + 266 + ], + "spans": [ + { + "bbox": [ + 111, + 73, + 504, + 266 + ], + "type": "image", + "image_path": "be56637e4c051b7d3d3a17014777899ed5d63d7f01c713db6f624e8d8196114d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 271, + 506, + 338 + ], + "lines": [ + { + "bbox": [ + 104, + 271, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 104, + 271, + 506, + 338 + ], + "type": "text", + "content": "Figure 1: Evolution of selected Long CoT over the past three years, where colored branches represent different characteristics: deep reasoning, feasible reflection, and extensive exploration. Each characteristic is further divided into key areas: Deep reasoning includes its format and learning methods. Feasible reflection focuses on feedback and refinement techniques during reflection process as optimization strategies. Extensive exploration addresses scaling, internal, and external exploration as key improvements to Long CoT." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 361, + 504, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 361, + 504, + 406 + ], + "spans": [ + { + "bbox": [ + 104, + 361, + 504, + 406 + ], + "type": "text", + "content": "inference-time scaling during testing, and the \"Aha Moment,\" among others. To our knowledge, This is the first comprehensive survey dedicated to these specific topics. Finally, considering the extensive body of literature, we highlight promising areas for future research and suggest valuable open-resource frameworks and datasets that can serve as a foundation for future investigations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 410, + 312, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 410, + 312, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 312, + 421 + ], + "type": "text", + "content": "The main contributions of this work are as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 427, + 504, + 543 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 107, + 427, + 504, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 427, + 504, + 460 + ], + "spans": [ + { + "bbox": [ + 107, + 427, + 504, + 460 + ], + "type": "text", + "content": "- Systematic Distinction: In this work, we first introduce the concept of Long CoT reasoning and distinguish it from the traditional Short CoT, thereby providing a clear framework for understanding both paradigms and their respective characteristics." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 107, + 463, + 504, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 463, + 504, + 496 + ], + "spans": [ + { + "bbox": [ + 107, + 463, + 504, + 496 + ], + "type": "text", + "content": "- Explanation of Hot Phenomena: We systematically investigate the notable phenomena associated with Long CoT reasoning, such as overthinking, inference-time scaling, and the \"Aha Moment\", offering valuable insights into the cognitive processes involved in complex reasoning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 107, + 498, + 504, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 498, + 504, + 543 + ], + "spans": [ + { + "bbox": [ + 107, + 498, + 504, + 543 + ], + "type": "text", + "content": "- Emerging Challenges and Frontiers: We explore the emerging challenges within the field of Long CoT reasoning and identify key research frontiers. Given the vast body of literature, we highlight areas where further inquiry could significantly advance the development of Long CoT methodologies." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 561, + 324, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 561, + 324, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 324, + 574 + ], + "type": "text", + "content": "2 Discussion of Long CoT v.s. Short CoT" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 586, + 506, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 586, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 104, + 586, + 506, + 654 + ], + "type": "text", + "content": "This section formalizes the key differences between Long Chain-of-Thought (Long CoT) and Short Chain-of-Thought (Short CoT), emphasizing reasoning depth, revisiting connections, and logical node exploration [858]. These distinctions are clearly separate from System 1 and System 2 thinking. The comparison between Long CoT and Short CoT is framed within System 2, with Long CoT involving more thorough reasoning, reflection, and exploration, while Short CoT generally prioritizes shallow and efficient logic over exhaustive reasoning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 668, + 230, + 679 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 668, + 230, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 230, + 679 + ], + "type": "text", + "content": "2.1 Overview of Short CoT" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 689, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 689, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 689, + 506, + 723 + ], + "type": "text", + "content": "As illustrated by Figure 2, Short CoT is typically characterized by a shallow, linear reasoning process, where conclusions are drawn sequentially, often relying on a limited number of logical nodes [551]. This reasoning is usually rapid and straightforward, with simple, surface-level transitions and minimal" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "text", + "content": "3" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "spans": [ + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "text", + "content": "Proof of Number Theory Problem: For any positive integer " + }, + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "text", + "content": ", there exists a positive integer " + }, + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "inline_equation", + "content": "m^2 + 1" + }, + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "text", + "content": " is divisible by " + }, + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 147, + 75, + 474, + 85 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 111, + 90, + 500, + 215 + ], + "blocks": [ + { + "bbox": [ + 111, + 90, + 500, + 215 + ], + "lines": [ + { + "bbox": [ + 111, + 90, + 500, + 215 + ], + "spans": [ + { + "bbox": [ + 111, + 90, + 500, + 215 + ], + "type": "image", + "image_path": "f0eadf51633e7fb658ee5728c1487fe0163f55fb50102d3c0b34bdb3de0da945.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 220, + 506, + 254 + ], + "lines": [ + { + "bbox": [ + 104, + 220, + 506, + 254 + ], + "spans": [ + { + "bbox": [ + 104, + 220, + 506, + 254 + ], + "type": "text", + "content": "Figure 2: The differences between advanced Long CoT and traditional Short CoT are characterized by three key characteristics: deep reasoning, feasible reflection, and extensive exploration. Moreover, Long CoT integrates all these characteristics to achieve substantial logical efficacy." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 277, + 504, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 277, + 504, + 300 + ], + "spans": [ + { + "bbox": [ + 104, + 277, + 504, + 300 + ], + "type": "text", + "content": "exploration of alternative paths, which restricts its generalizability [683]. Formally, given a reasoning model " + }, + { + "bbox": [ + 104, + 277, + 504, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 104, + 277, + 504, + 300 + ], + "type": "text", + "content": ", we can define the rationale of Short CoT " + }, + { + "bbox": [ + 104, + 277, + 504, + 300 + ], + "type": "inline_equation", + "content": "(\\mathsf{C}\\circ \\mathsf{T}_S)" + }, + { + "bbox": [ + 104, + 277, + 504, + 300 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 130, + 308, + 505, + 322 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 308, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 130, + 308, + 505, + 322 + ], + "type": "interline_equation", + "content": "\\mathrm {C o T} _ {S} = \\mathcal {R} \\left(\\left\\{n _ {i} \\right\\} _ {i = 1} ^ {k} | (k \\leq \\mathcal {B} _ {s}) \\wedge (j = 1 \\Leftrightarrow \\forall i \\leq k, n _ {i} \\rightarrow n _ {i + j}) \\wedge (\\forall i \\neq j \\leq k, n _ {i} \\neq n _ {j})\\right), \\tag {1}", + "image_path": "77d6e310225283b575bdc27fdde0f240da93987fe57f7d9af2832fc35ebec190.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "inline_equation", + "content": "n_1" + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "inline_equation", + "content": "n_k" + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "text", + "content": " represent a sequence of logical nodes, which naturally satisfy that " + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "inline_equation", + "content": "\\forall i, n_i \\to n_{i+1}" + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_s" + }, + { + "bbox": [ + 104, + 329, + 506, + 374 + ], + "type": "text", + "content": " denotes the upper boundary on the number of logical nodes, as defined by Chen et al. [90]. In this paradigm, the reasoning progresses sequentially from one node to the next, with minimal revisitation of previous nodes and little exploration of alternative logical paths." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 389, + 229, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 389, + 229, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 229, + 401 + ], + "type": "text", + "content": "2.2 Overview of Long CoT" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 411, + 506, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 411, + 506, + 466 + ], + "spans": [ + { + "bbox": [ + 104, + 411, + 506, + 466 + ], + "type": "text", + "content": "In contrast, Long CoT involves deeper reasoning, reflective analysis, and a broader exploration of logical structures. It facilitates reasoning across a wider range of logical steps, addressing both known and unknown elements of a problem [194, 858]. Building on this, Long CoT expands upon the constraints presented in Equation 1 based on tree structures by incorporating three critical components: deep reasoning, exploration, and reflection." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 471, + 506, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 471, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 104, + 471, + 506, + 559 + ], + "type": "text", + "content": "These components play distinct yet complementary roles in enhancing cognitive processes. Deep reasoning ensures each logical step is executed rigorously, even within complex structures, fostering robust logic across intricate relationships. Exploration encourages the identification of new pathways, revealing potential avenues that may not be immediately obvious. Reflection enables iterative analysis and reassessment of conclusions, allowing reasoning to evolve throughout problem-solving. By distinguishing these three categories, Long CoT enhances its ability to address a broader range of problems with precision and depth. As shown in Figure 3, we will now discuss these key differences in detail." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 573, + 268, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 573, + 268, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 268, + 586 + ], + "type": "text", + "content": "2.2.1 Deep Reasoning for Long CoT" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 594, + 506, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 594, + 506, + 649 + ], + "spans": [ + { + "bbox": [ + 104, + 594, + 506, + 649 + ], + "type": "text", + "content": "As shown by Figure 2, deep reasoning refers to the capability to perform deep and thorough logical analysis across multiple interconnected logical nodes, where Short CoT generally can never achieve. This capability is essential when tackling complex problems that require a massive number of logical deductions to arrive at a valid conclusion. To better define and understand deep reasoning, we frame it as a capability that primarily relaxes the first constraint in Equation 1, as expressed by the following:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 240, + 657, + 504, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 240, + 657, + 504, + 669 + ], + "spans": [ + { + "bbox": [ + 240, + 657, + 504, + 669 + ], + "type": "interline_equation", + "content": "k \\leq \\mathcal {B} _ {s} \\mapsto k \\leq \\mathcal {B} _ {l} \\wedge \\mathcal {B} _ {s} \\ll \\mathcal {B} _ {l}, \\tag {2}", + "image_path": "9628c4a63cf86935164b10c8341472684c37377c14dfa2282ae72c4f75176336.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_l" + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "text", + "content": " represents the upper boundary for Long CoT reasoning, which can accommodate much more intricate logical nodes compared to the smaller boundary " + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_s" + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "text", + "content": " for Short CoT. The larger boundary " + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_l" + }, + { + "bbox": [ + 104, + 677, + 505, + 723 + ], + "type": "text", + "content": " alleviates issues related to insufficient depth in reasoning, thereby reducing the risk of generating unresolved answers or hallucinated responses in short-form reasoning." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "text", + "content": "4" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 106, + 62, + 509, + 427 + ], + "blocks": [ + { + "bbox": [ + 106, + 62, + 509, + 427 + ], + "lines": [ + { + "bbox": [ + 106, + 62, + 509, + 427 + ], + "spans": [ + { + "bbox": [ + 106, + 62, + 509, + 427 + ], + "type": "image", + "image_path": "fa1bbeeb7a7a9e97707e957eb9cfc744f2a2eba4ab0e5a7c5f73282936c28213.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 431, + 504, + 454 + ], + "lines": [ + { + "bbox": [ + 104, + 431, + 504, + 454 + ], + "spans": [ + { + "bbox": [ + 104, + 431, + 504, + 454 + ], + "type": "text", + "content": "Figure 3: Taxonomy of Long CoT, which includes deep reasoning, feasible reflection, and extensive exploration methodologies." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 125, + 479, + 263, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 479, + 263, + 491 + ], + "spans": [ + { + "bbox": [ + 125, + 479, + 263, + 491 + ], + "type": "text", + "content": "Key Difference: Reasoning Depth" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 122, + 497, + 490, + 545 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 122, + 497, + 490, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 497, + 490, + 520 + ], + "spans": [ + { + "bbox": [ + 122, + 497, + 490, + 520 + ], + "type": "text", + "content": "- Short CoT typically addresses a limited set of logical nodes, involving shallow reasoning, and struggles with problems requiring complex or intricate logical structures." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 122, + 521, + 490, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 521, + 490, + 545 + ], + "spans": [ + { + "bbox": [ + 122, + 521, + 490, + 545 + ], + "type": "text", + "content": "- Long CoT is designed to accommodate a significantly larger set of logical nodes, allowing for deeper logic and more thorough analysis during the reasoning process." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 567, + 293, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 567, + 293, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 567, + 293, + 578 + ], + "type": "text", + "content": "2.2.2 Extensive Exploration for Long CoT" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 587, + 504, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 587, + 504, + 652 + ], + "spans": [ + { + "bbox": [ + 104, + 587, + 504, + 652 + ], + "type": "text", + "content": "As shown by Figure 2, Long CoT encourages branching out to extensively explore uncertain or unknown logical nodes, thereby expanding the potential set of reasoning paths. This exploration is particularly critical when solving problems characterized by ambiguity, incomplete information, or multiple possible solutions [43, 1016, 871]. More specifically, we describe how extensive exploration primarily addresses the relaxation of the second constraint in Equation 1, which can be formalized as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 178, + 658, + 504, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 178, + 658, + 504, + 671 + ], + "spans": [ + { + "bbox": [ + 178, + 658, + 504, + 671 + ], + "type": "interline_equation", + "content": "j = 1 \\Leftrightarrow \\forall i \\leq k, n _ {i} \\rightarrow n _ {i + j} \\mapsto \\exists m, \\forall i, \\forall j \\leq m, n _ {i} \\rightarrow n _ {i + j}, \\tag {3}", + "image_path": "1c2231d3720d10adabb9b0e0eb328582cefd25a3bc7b9de3b2b5d8e38fcb3e48.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "type": "text", + "content": "where the condition indicates that for a logical node " + }, + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "type": "text", + "content": ", there are " + }, + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "type": "text", + "content": " nodes that are explored in parallel. The acceptability of parallel exploration allows for a more systematic approach, enabling the exploration of previously unconsidered logical paths. This, in turn, helps maximize the understanding of all possible solutions, ultimately leading to the correct final answer." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "text", + "content": "5" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 125, + 72, + 313, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 72, + 313, + 84 + ], + "spans": [ + { + "bbox": [ + 125, + 72, + 313, + 84 + ], + "type": "text", + "content": "Key Difference: Exploration of Logical Nodes" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 122, + 91, + 488, + 139 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 122, + 91, + 488, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 91, + 488, + 114 + ], + "spans": [ + { + "bbox": [ + 122, + 91, + 488, + 114 + ], + "type": "text", + "content": "- Short CoT generally restricts exploration to a fixed set of logical nodes, often resulting in oversimplified reasoning and limited exploration." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 123, + 116, + 488, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 116, + 488, + 139 + ], + "spans": [ + { + "bbox": [ + 123, + 116, + 488, + 139 + ], + "type": "text", + "content": "- Long CoT explores more various paths, including uncertain or uncharted areas, fostering more nuanced and comprehensive problem-solving." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 157, + 279, + 170 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 157, + 279, + 170 + ], + "spans": [ + { + "bbox": [ + 105, + 157, + 279, + 170 + ], + "type": "text", + "content": "2.2.3 Feasible Reflection for Long CoT" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 177, + 504, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 177, + 504, + 232 + ], + "spans": [ + { + "bbox": [ + 104, + 177, + 504, + 232 + ], + "type": "text", + "content": "As shown by Figure 2, Long CoT involves revisiting previous logical nodes to verify their connections are valid and accurate, and then correcting them or selecting an alternative logical path. Formally, feasible reflection relaxes the third constraint in Equation 1, which originally requires acyclic reasoning such that " + }, + { + "bbox": [ + 104, + 177, + 504, + 232 + ], + "type": "inline_equation", + "content": "n_i \\neq n_j" + }, + { + "bbox": [ + 104, + 177, + 504, + 232 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 104, + 177, + 504, + 232 + ], + "type": "inline_equation", + "content": "i \\neq j \\leq k" + }, + { + "bbox": [ + 104, + 177, + 504, + 232 + ], + "type": "text", + "content": ". In contrast, feasible reflection permits the reasoning path to return to a previously visited node, captured as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 209, + 239, + 505, + 252 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 239, + 505, + 252 + ], + "spans": [ + { + "bbox": [ + 209, + 239, + 505, + 252 + ], + "type": "interline_equation", + "content": "\\forall i \\neq j \\leq k, n _ {i} \\neq n _ {j} \\mapsto \\exists i < j \\leq k, n _ {i} = n _ {j}, \\tag {4}", + "image_path": "a00f7ae26a61e2deed5c2e110f8b5f44aca2021285ec38658a2e306eecd29366.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "spans": [ + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "text", + "content": "where this condition indicates that, for a logical node " + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "inline_equation", + "content": "n_{j-1}" + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "text", + "content": ", the subsequent node is not limited to the original next node " + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "inline_equation", + "content": "\\hat{n}_j" + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "text", + "content": ". Instead, it may transition to " + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "text", + "content": " (i.e., the next logical node becomes " + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "inline_equation", + "content": "n_j" + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "inline_equation", + "content": "n_j = n_i" + }, + { + "bbox": [ + 104, + 258, + 504, + 293 + ], + "type": "text", + "content": "). Practically, reflection implementation consists of two components:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "text", + "content": "Feedback refers to evaluating both overall and intermediate outputs for correctness and quality, also known as critique or verification. It can be derived from external sources, validation checks, or by reflecting on prior conclusions within the reasoning process. Formally, at each step " + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "text", + "content": ", a verification process " + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_i" + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "text", + "content": " ensures the correctness, feasibility, and consistency of the reasoning. If an issue is identified, the process redirects " + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "text", + "content": " to the nearest correct node " + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "inline_equation", + "content": "n_j" + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "inline_equation", + "content": "j < i" + }, + { + "bbox": [ + 104, + 300, + 505, + 366 + ], + "type": "text", + "content": ". This relationship is formalized as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 247, + 367, + 504, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 247, + 367, + 504, + 380 + ], + "spans": [ + { + "bbox": [ + 247, + 367, + 504, + 380 + ], + "type": "interline_equation", + "content": "\\mathcal {F} _ {i}, n _ {j} \\leftarrow \\operatorname {F e e d b a c k} \\left(\\mathrm {C o T} _ {L} ^ {i}\\right) \\tag {5}", + "image_path": "f2f163b377b83a2138812ae0feb6376a9a672ddaaf020fc013620363b5df6fb0.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 384, + 504, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 384, + 504, + 407 + ], + "spans": [ + { + "bbox": [ + 104, + 384, + 504, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 384, + 504, + 407 + ], + "type": "inline_equation", + "content": "\\mathrm{CoT}_L^i = \\{n_1,\\dots ,n_i\\}" + }, + { + "bbox": [ + 104, + 384, + 504, + 407 + ], + "type": "text", + "content": " represents the current logical path up to the " + }, + { + "bbox": [ + 104, + 384, + 504, + 407 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 104, + 384, + 504, + 407 + ], + "type": "text", + "content": " -th logical node for Long CoT." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 416, + 506, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 416, + 506, + 449 + ], + "spans": [ + { + "bbox": [ + 104, + 416, + 506, + 449 + ], + "type": "text", + "content": "Refinement involves adjusting intermediate steps or modifying the logical flow to correct inconsistencies or address gaps based on the given feedback. This process can be expressed mathematically as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 228, + 449, + 504, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 228, + 449, + 504, + 463 + ], + "spans": [ + { + "bbox": [ + 228, + 449, + 504, + 463 + ], + "type": "interline_equation", + "content": "\\widetilde {n} _ {i + 1} \\leftarrow \\operatorname {R e f i n e} \\left(n _ {i + 1} \\mid \\mathrm {C o T} _ {L} ^ {i}, \\mathcal {F} _ {i}, n _ {j}\\right), \\tag {6}", + "image_path": "9c6831bab18873d643e710c5d4ac73f2ffb018fd0b5a6426ad2fad8decd5da47.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "spans": [ + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "inline_equation", + "content": "\\widetilde{n}_{i+1}" + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "text", + "content": " represents the refined version of the subsequent logical node " + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "inline_equation", + "content": "n_{i+1}" + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "text", + "content": ", according to the current logic " + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "inline_equation", + "content": "\\mathbb{C} \\circ \\mathbb{T}_L^i" + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "text", + "content": ", feedback result " + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "text", + "content": ", and previous logical node " + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "inline_equation", + "content": "n_j" + }, + { + "bbox": [ + 104, + 466, + 504, + 490 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 494, + 505, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 494, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 104, + 494, + 505, + 528 + ], + "type": "text", + "content": "Overall, incorporating reflection ensures that errors are identified and corrected promptly. This capability enables LLMs to quickly shift to alternative reasoning paths or correct their current trajectory. By doing so, error propagation is minimized, resulting in more accurate conclusions." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 125, + 535, + 291, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 535, + 291, + 547 + ], + "spans": [ + { + "bbox": [ + 125, + 535, + 291, + 547 + ], + "type": "text", + "content": "Key Difference: Feedback & Refinement" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 123, + 553, + 489, + 601 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 123, + 553, + 488, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 553, + 488, + 577 + ], + "spans": [ + { + "bbox": [ + 123, + 553, + 488, + 577 + ], + "type": "text", + "content": "- Short CoT typically moves in a straightforward, non-repetitive manner from one node to the next, so that cannot correct their logic." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 123, + 578, + 489, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 578, + 489, + 601 + ], + "spans": [ + { + "bbox": [ + 123, + 578, + 489, + 601 + ], + "type": "text", + "content": "- Long CoT allows for revisiting and revising earlier decisions by feedback and refinement, ensuring that estimizable and prior logical conclusions during the reasoning progress." + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 620, + 425, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 620, + 425, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 620, + 425, + 632 + ], + "type": "text", + "content": "2.2.4 Unified Application and Development History of Three Capabilities" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 639, + 505, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 639, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 104, + 639, + 505, + 684 + ], + "type": "text", + "content": "The Long CoT discussed here represents a unified reasoning system that seamlessly integrates and applies three key capabilities: deep reasoning, reflective mechanisms, and exploration capabilities. In contrast, during the Short CoT era, these capabilities developed independently, each evolving in isolation." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "type": "text", + "content": "As shown in Figure 2, early efforts primarily focused on enhancing deep reasoning within traditional CoT paradigms. This was followed by the gradual introduction of reflective mechanisms, which were initially based on human-designed pipelines. Over time, exploration capabilities were added, and" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 302, + 742, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 742, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 742, + 309, + 750 + ], + "type": "text", + "content": "6" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 95 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 95 + ], + "type": "text", + "content": "these components were ultimately merged, giving rise to the modern concept of Long CoT, a unified approach to reasoning that seeks to enhance all three capabilities in harmony." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 100, + 506, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 100, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 104, + 100, + 506, + 189 + ], + "type": "text", + "content": "The progression of Long CoT is gradual, rather than a sudden emergence through isolated models like o1 [307] and R1 [227]. Instead, it develops gradually. For example, earlier systems, such as ToT [955], enhance exploration but lack reflective mechanisms, disqualifying them as Long CoT [95]. While GoT [48] incorporates self-reflection based on ToT, its original model still lacked robust deep reasoning, preventing it from qualifying as Long CoT at that time. It is also notable that modern Long CoT systems, often neglect earlier technologies. This article addresses this gap by tracing the evolution of each capability, with the final section offering a comprehensive analysis of the integrated Long CoT system." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 193, + 506, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 193, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 104, + 193, + 506, + 238 + ], + "type": "text", + "content": "In summary, Long CoT and Short CoT represent distinct paradigms. Long CoT features a deeper, broader, and more reflective reasoning process, enhancing both accuracy and coherence. Short CoT, by contrast, is better suited to simpler, well-defined problems. This distinction highlights the scalability and adaptability of Long CoT, making it particularly effective for more complex reasoning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 125, + 244, + 362, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 244, + 362, + 257 + ], + "spans": [ + { + "bbox": [ + 125, + 244, + 362, + 257 + ], + "type": "text", + "content": "Key Difference: Unified Application of Three Capabilities" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 119, + 261, + 490, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 261, + 490, + 295 + ], + "spans": [ + { + "bbox": [ + 119, + 261, + 490, + 295 + ], + "type": "text", + "content": "It is important to highlight that Long CoT integrates these three distinct capabilities to perform complex reasoning. In contrast, traditional Short CoT optimization typically focuses on only one of these characteristics." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 315, + 296, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 315, + 296, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 296, + 329 + ], + "type": "text", + "content": "3 Long CoT Analysis & Evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 339, + 293, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 339, + 293, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 293, + 352 + ], + "type": "text", + "content": "3.1 Analysis & Explanation for Long CoT" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 360, + 506, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 360, + 506, + 426 + ], + "spans": [ + { + "bbox": [ + 104, + 360, + 506, + 426 + ], + "type": "text", + "content": "Research on Long CoT has significantly enhanced RLLMs by improving reasoning accuracy, reducing errors, and supporting dynamic decision-making. However, several phenomena and their corresponding mechanisms remain inadequately summarized. This section addresses key topics, including the mechanisms of Long CoT and their underlying principles [644, 63, 545, 642]. Methodologically, two main perspectives have emerged to explain Long CoT: (1) External Behavior Analysis (§ 3.1.1) and (2) Internal Mechanism Analysis (§ 3.1.2)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 437, + 301, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 437, + 301, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 301, + 449 + ], + "type": "text", + "content": "3.1.1 Long CoT External Behavior Analysis" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 456, + 504, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 456, + 504, + 479 + ], + "spans": [ + { + "bbox": [ + 104, + 456, + 504, + 479 + ], + "type": "text", + "content": "The primary research stream focuses on explaining RLLM behaviors for Long CoT [25]. As illustrated in Figure 4, six key phenomena are identified and discussed for Long CoT in this part." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 487, + 506, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 487, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 104, + 487, + 506, + 597 + ], + "type": "text", + "content": "Long CoT Emergence Phenomenon Research shows that contextual examples improve large models' generative abilities by guiding the formation of reasoning chains [1012, 671, 417, 343, 532, 846, 1017, 1141]. Wang et al. [759] and Lippmann and Yang [461] demonstrate that these examples standardize reasoning chain generation relevant to the answers both in in-context-learning and supervised-finetuning. In an experiment by Madaan et al. [538], removing problem-specific entities from contextual examples, while retaining only the logical structure, led to similar performance as using complete examples, highlighting the logical structure imitation of Long CoT during inference. From a learning perspective, Ye et al. [963] analyzes and reveals the three-stage developmental trajectory of Long CoT: early memorization, followed by in-distribution generalization, and ultimately cross-distribution generalization, thereby enabling the model to exhibit Long CoT capabilities." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 601, + 507, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 601, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 601, + 507, + 723 + ], + "type": "text", + "content": "More recently, Stechly et al. [688] and Wang and Zhou [815] have shown that modifying the decoding process or designing specific prompts can activate the Long CoT within pre-trained models. They propose that CoT is embedded during pre-training and requires specific activation [941]. Further, Sadr et al. [642] focus the Long CoT source from the training data, and build on this with the notion of \"model attribution\", to specifically identify the training data most influential for specific outputs. Building on this, Guo et al. [227] and Xie et al. [886] investigate using rule-based reinforcement learning to directly activate Long CoT during pre-training, aiming to enhance performance [881]. Furthermore, Gandhi et al. [194] identify four key cognitive behaviors, including verification, backtracking, sub-target setting, and backward chaining, which successfully facilitate Long CoT. Qwen series models [926] inherently demonstrate these behaviors, which can be easily triggered by rule-based reinforcement. In contrast, the models of Llama series [168] lack these" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 53, + 184, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 53, + 184, + 56 + ], + "spans": [ + { + "bbox": [ + 143, + 53, + 184, + 56 + ], + "type": "text", + "content": "REASONING GROU" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "text", + "content": "7" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 71, + 207, + 190 + ], + "blocks": [ + { + "bbox": [ + 111, + 71, + 207, + 190 + ], + "lines": [ + { + "bbox": [ + 111, + 71, + 207, + 190 + ], + "spans": [ + { + "bbox": [ + 111, + 71, + 207, + 190 + ], + "type": "image", + "image_path": "5a5b622a5ef9a492838399c45ff5d29022e17e93ea38f8784aa310a395d4009d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 198, + 506, + 265 + ], + "lines": [ + { + "bbox": [ + 104, + 198, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 104, + 198, + 506, + 265 + ], + "type": "text", + "content": "Figure 4: Analysis of the six classic phenomena of Long CoT external behavior: (a) emergence of Long CoT in current RLLMs; (b) reasoning boundaries and limitations of current Long CoT systems; (c) overthinking caused by scaling beyond RLLMs' reasoning boundaries, leading to performance decay; (d) inference-time scaling, discussing mainstream scaling methods, corresponding scaling laws and their limitations; (e) use of process reward model (PRM) or outcome reward model (ORM); (f) exploration of the \"aha\" moment and its underlying causes." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 210, + 72, + 290, + 190 + ], + "blocks": [ + { + "bbox": [ + 210, + 72, + 290, + 190 + ], + "lines": [ + { + "bbox": [ + 210, + 72, + 290, + 190 + ], + "spans": [ + { + "bbox": [ + 210, + 72, + 290, + 190 + ], + "type": "image", + "image_path": "b58ea3cfdd162d9e8dc0a98bea568dac497bec49f930188fabfb39d4a8af9188.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 294, + 72, + 402, + 190 + ], + "blocks": [ + { + "bbox": [ + 294, + 72, + 402, + 190 + ], + "lines": [ + { + "bbox": [ + 294, + 72, + 402, + 190 + ], + "spans": [ + { + "bbox": [ + 294, + 72, + 402, + 190 + ], + "type": "image", + "image_path": "7574cfd5bdc73debbbe23c4cd13dc43c38b3f705661075e1c69e68c8876576bc.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 405, + 72, + 498, + 190 + ], + "blocks": [ + { + "bbox": [ + 405, + 72, + 498, + 190 + ], + "lines": [ + { + "bbox": [ + 405, + 72, + 498, + 190 + ], + "spans": [ + { + "bbox": [ + 405, + 72, + 498, + 190 + ], + "type": "image", + "image_path": "7acf371a734b42dff8be38ed39013e080e5d0020e7a712fdcc41abb09ba80b65.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 291, + 504, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 291, + 504, + 346 + ], + "spans": [ + { + "bbox": [ + 104, + 291, + 504, + 346 + ], + "type": "text", + "content": "capabilities and thus requires example-based reinforcement learning to improve significantly [65]. Moreover, Wang et al. [812] identify a pretraining scaling law that explains how increasing calculation size in RLLMs enhances their reasoning capabilities. Wang et al. [796] further explore the scaling law of Long CoT, showing that more fine-grained Long CoT granularity leads to more efficient and effective generalization performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 360, + 506, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 360, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 104, + 360, + 506, + 469 + ], + "type": "text", + "content": "Reasoning Boundary Phenomenon Recent research has highlighted the upper bounds and limitations of RLLMs across various reasoning tasks [303, 283, 684, 261, 185, 252]. Specifically, Bi et al. [53] investigate these bounds in code generation, showing that RLLMs struggle with tasks that exceed certain complexity thresholds [600], especially when imitating Long CoT samples of varying complexity. In the context of upper-bound performance, Merrill and Sabharwal [548] and Li et al. [430] focus on single-step arithmetic tasks, concluding that model performance is constrained by input length. Moreover, Feng et al. [177] proposes a mathematical model indicating that fixed-size models cannot produce accurate numerical answers beyond specific limits. However, increasing the number of reasoning steps improves a model's capability requirements to solve more complex problems." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 475, + 506, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 475, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 104, + 475, + 506, + 596 + ], + "type": "text", + "content": "Inspired by these explorations, Chen et al. [90] first define the \"reasoning boundary\" phenomenon and quantify these limits, showing that surpassing an RLLM's reasoning capacity leads to performance decline [92]. Similarly, Zhou et al. [1130] introduce GSM-Infinite, linking different upper limits to accuracy levels. Chen et al. [90] also examine the interaction between these boundaries across tasks of varying complexity, providing insights into the effectiveness of Long CoT strategies [1085]. Moreover, Amiri et al. [12] propose a \"tight lower bound\" for Long CoT further guiding reasoning error reductions. Further, Baeumel et al. [28] suggest that due to its reliance on a single-digit lookahead heuristic, there are inherent boundaries in performing addition with multiple operands, which thus hinders the fundamental limitation of LLMs in scaling to more complex numerical reasoning. Liu et al. [483] further investigate the role of reinforcement learning in expanding these reasoning boundaries instead of relying solely on pretraining capabilities." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "type": "text", + "content": "Overthinking Phenomenon Research has highlighted the overthinking phenomenon [103, 330, 574, 142, 357, 595], where performance improves with longer reasoning chains up to a threshold, after which it declines. In contrast, Xie et al. [886] and Ma et al. [534] find no significant correlation between reasoning length and accuracy. To explain this, one line of research suggests that Long CoT strategies [21, 441], like avoiding \"snowball errors\" [192]. Alternatively, Chen et al. [90], Wolf et al. [851] highlight a performance drop when the reasoning boundaries are exceeded, providing an explanation for the overthinking phenomenon. This suggests that reasoning length and logical complexity should be kept below a certain boundary [1080]. Building on this, Wu et al. [867] mathematically determine the feasible reasoning length for Long CoT. Finally, Chen et al. [93] introduces Ohm's law of Long CoT, which accurately predicts and controls performance." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 142, + 47, + 187, + 52 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 142, + 47, + 187, + 52 + ], + "spans": [ + { + "bbox": [ + 142, + 47, + 187, + 52 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 142, + 52, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 142, + 52, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 142, + 52, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 308, + 750 + ], + "type": "text", + "content": "8" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 139 + ], + "type": "text", + "content": "Inference-Time Scaling Phenomenon Recent advances in inference-time scaling algorithms [524, 843] have garnered significant attention, particularly for their ability to extend reasoning length and improve performance [524, 455, 875]. Specifically, Brown et al. [57] identify a phenomenon called \"Large Language Monkeys\", in which a series of reasoning tasks show that with enough trials, a correct result can be achieved. Additionally, o1 [307] and R1 [227] demonstrated that directly scaling the length of model inference improves final performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "spans": [ + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "content": "To understand inference-time scaling, we will discuss these two paradigms: (1) Sequential Scaling: Sequential scaling involves increasing the reasoning path length. While this can enhance performance, studies by Jin et al. [330] show that, beyond a certain point, longer reasoning paths can degrade performance due to error accumulation. They suggest an optimal path length that depends on the model's capabilities and task complexity [15, 652, 31]. Furthermore, Chen et al. [90] and Wu et al. [867] explain that excessive exploration lengths beyond the RLLM's inherent reasoning boundary lead to performance decay, which guides RLLMs for deeper reasoning capabilities [32]. (2) Parallel Scaling: Parallel scaling involves performing multiple reasoning steps and verifying the results. While it shows promise, Parashar et al. [583] and Wang et al. [820] argue that simply increasing inference time does not guarantee improved performance. Wu et al. [864] show that the computational FLOPs " + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "content": " of inference are correlated with the lower bound of performance error, which scales with " + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "inline_equation", + "content": "\\log N" + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "content": ". Additionally, Chen et al. [93] establish an upper bound for parallel scaling, showing that RLLMs cannot exceed Pass@k verification through various verifiers. They further argue that sampling optimization cannot exceed the model's internal reasoning limitations, demonstrating that for " + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "content": " samples, accuracy is proportional to " + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "inline_equation", + "content": "\\frac{m}{(k / \\log N + b)^2}" + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 104, + 144, + 506, + 312 + ], + "type": "text", + "content": " are model-dependent constants." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 319, + 506, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 319, + 506, + 506 + ], + "spans": [ + { + "bbox": [ + 104, + 319, + 506, + 506 + ], + "type": "text", + "content": "PRM & ORM Selection Phenomenon As RLLMs evolve, it is crucial to navigate the debate around the selection between process supervision and outcome supervision, two key reinforcement learning paradigms for complex reasoning tasks. The phenomenon of choosing between these two approaches has become a pivotal issue, as it is essential to differentiate and decide which supervision strategy is more suitable for specific tasks [899, 187, 1059]. While process supervision is intuitively advantageous for long-term reward assignments, the exact relationship between the two approaches remains unclear. It is commonly believed that process supervision is more challenging due to the trajectory-level coverage problem, which demands significant effort to collect fine-grained supervision data [1102, 679]. Additionally, PRM faces the issue of reward hacking [13, 152, 573, 30, 399], where agents exploit flaws in the reward function to produce unintended behaviors [227]. Addressing this to surpass rule-based reward systems has become an important research area [227, 886, 594]. Furthermore, Lampinen et al. [368] and Tan [708] establish a causal link between intermediate steps and final answers in qualitative experiments. Building on this, Jia et al. [317] demonstrate that, under the standard data coverage assumption, reinforcement learning with outcome supervision is not statistically more challenging than process supervision, aside from polynomial factors. More strictly, He et al. [247] mathematically demonstrate that outcome-level rewards suffice for online reinforcement learning in RLLMs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 513, + 506, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 513, + 506, + 679 + ], + "spans": [ + { + "bbox": [ + 104, + 513, + 506, + 679 + ], + "type": "text", + "content": "Aha Moment Phenomenon Earlier, Guo et al. [227] demonstrated that direct RL using rule-based rewards can trigger the aha moment, fostering natural self-reflection without supervision [172]. Following this, Team [721], Xie et al. [886] replicate this phenomenon. Further, Zhou et al. [1119] and Meng et al. [547] further extend this phenomenon to multimodal scenarios. However, Liu et al. [498] argue that the aha moment may not emerge in R1-Zero-like training. Instead, they observe that self-reflection patterns, such as superficial self-reflection (SSR), appear at epoch 0, the stage of base models. In this case, self-reflections do not necessarily lead to correct answers. Upon closer examination of R1-Zero training via RL, they find that the increasing response length results not from self-reflection, but from RL optimizing well-designed rule-based rewards. Moreover, Yang et al. [939] demonstrate that the \"aha moment\" is externally marked by increased use of anthropomorphic language during self-reflection and a dynamic adjustment of uncertainty in response to problem difficulty. This process enables the model to maintain reasoning without succumbing to \"Reasoning Collapse.\" Internally, it is characterized by a clear distinction between anthropomorphic traits and logical reasoning, with anthropomorphic language intensifying as the problem becomes more complex." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 689, + 505, + 723 + ], + "type": "text", + "content": "Reinforcement Learning Entropy Phenomenon In reinforcement learning for Long CoT, the entropy mechanism is a crucial factor influencing the performance of RLLMs. Policy entropy measures the diversity and exploratory strength of a model's outputs. By managing this entropy" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 750 + ], + "type": "text", + "content": "9" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 172 + ], + "type": "text", + "content": "effectively, a model preserves exploration and thus excels on complex reasoning tasks. Earlier, Jang and Kim [310] investigate how initial entropy affects exploration in deep RL and proposed an entropy-aware initialization to encourage effective exploration. Building on this, Zhang et al. [1036] developed an Entropy-Regularized PRM that balances policy updates against large deviations from the starting distribution, thereby improving reasoning. Cheng et al. [116] found that high-entropy regions correlate positively with three exploratory reasoning behaviors: (1) key tokens linking logical steps, (2) self-verification and correction, and (3) rare behaviors underrepresented in the base model. Most recently, Agarwal et al. [5] introduced an Entropy Minimization method and demonstrated its strong impact on LLM performance in mathematical, physical, and coding tasks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "spans": [ + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "type": "text", + "content": "However, recent research indicates that, during early training, policy entropy declines sharply, causing the model to converge prematurely on specific output patterns and limiting further reasoning improvement [144]. In reinforcement learning, policy entropy " + }, + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "type": "inline_equation", + "content": "(H)" + }, + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "type": "text", + "content": " and downstream task performance " + }, + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "type": "inline_equation", + "content": "(R)" + }, + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "type": "text", + "content": " follow an exponential relation: " + }, + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "type": "inline_equation", + "content": "R = -a\\cdot e^{H} + b" + }, + { + "bbox": [ + 104, + 176, + 506, + 276 + ], + "type": "text", + "content": ", so a drop in entropy produces a rapid performance decline until saturation. This \"policy entropy collapse\" is common without entropy control, as reduced entropy constrains exploration and stalls reasoning gains [144]. To counter this collapse, two methods, Clip-Cov and KL-Cov, regulate entropy by constraining updates on high-covariance tokens. Clip-Cov clips their update magnitudes, whereas KL-Cov imposes a Kullback-Leibler penalty. Empirical results show both techniques prevent collapse and enhance reasoning performance [144]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 288, + 309, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 288, + 309, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 309, + 300 + ], + "type": "text", + "content": "3.1.2 Long CoT Internal Mechanism Analysis" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 307, + 499, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 307, + 499, + 319 + ], + "spans": [ + { + "bbox": [ + 104, + 307, + 499, + 319 + ], + "type": "text", + "content": "The second stream of research investigates the internal mechanisms of Long CoT-related RLLMs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 329, + 506, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 329, + 506, + 461 + ], + "spans": [ + { + "bbox": [ + 104, + 329, + 506, + 461 + ], + "type": "text", + "content": "Reasoning Internal Mechanism Recent studies have explored the internal mechanisms underlying the coherent rationale outputs of Long CoT, with particular emphasis on attention mechanisms [675, 632]. These studies primarily examine neural substructures in RLLMs, framing CoT reasoning from a white-box perspective [819, 992, 233, 169]. Weston and Sukhbaatar [849] introduces the concept of System 2 Attention (S2A), which demonstrates Long CoT generation by selectively focusing attention on relevant information. Additionally, Li et al. [407] explore gradient distributions between direct output and Long CoT layers, revealing that Long CoT layers help maintain stability by distinguishing relevant from irrelevant reasoning [840]. Finally, Zhang et al. [1068] conceptualize RLLMs as finite state automata, offering further insight into how internal dynamics influence external behavior. Despite Short CoT's struggles with self-correction, Bertolazzi et al. [47] show that these models rely on consistency heads (attention heads) to assess the alignment of numerical values in arithmetic solutions through internal shortcuts." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 470, + 506, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 470, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 104, + 470, + 506, + 615 + ], + "type": "text", + "content": "Knowledge Incorporating Mechanism Current RLLMs primarily focus on mathematics and coding but have shown potential for generalization to other knowledge-rich domains, sparking growing interest in the mechanism for integrating domain-specific knowledge into Long CoT [860, 886, 1105]. Prystawski et al. [609] suggest that generative models store entity knowledge learned during pre-training independently, with the reasoning process in Long CoT linking this knowledge across entities. Radha and Goktas [630] recently introduced the Probabilistic Mixture Model (PMM), which categorizes model outputs into reasoning, memorization, and guessing. They also propose an Information-Theoretic Consistency (ITC) analysis to quantify the relationship between model confidence and strategy selection. Additionally, Jin et al. [331] define \"Concept Depth\" as the lowest layers at which complex concepts are understood, demonstrating varying levels of knowledge integration in RLLMs. Ou et al. [572] examine RLLM knowledge internalization through knowledge loop evolution, arguing that new knowledge acquisition is shaped by its connection to existing knowledge, with the loop evolving from formation to optimization and from shallow to deep." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 627, + 228, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 627, + 228, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 228, + 639 + ], + "type": "text", + "content": "3.2 Long CoT Evaluations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 647, + 171, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 647, + 171, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 647, + 171, + 658 + ], + "type": "text", + "content": "3.2.1 Metrics" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 667, + 505, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 667, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 667, + 505, + 723 + ], + "type": "text", + "content": "In benchmarking, various metrics assess model performance across reasoning tasks, each focusing on different aspects of reasoning ability. These metrics evaluate both RLLMs' effectiveness in achieving desired outcomes and their learning efficiency. As a result, metrics for RLLMs have gained increasing attention in recent research. For mathematical or code-related tasks, three key metrics are commonly used: Accuracy, Pass@k, and Cons@k based on regex extraction:" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 300, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 300, + 741, + 311, + 750 + ], + "type": "text", + "content": "10" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + }, + { + "para_blocks": [ + { + "bbox": [ + 107, + 73, + 504, + 121 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 107, + 73, + 340, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 73, + 340, + 84 + ], + "spans": [ + { + "bbox": [ + 107, + 73, + 340, + 84 + ], + "type": "text", + "content": "Accuracy measures the proportion of correct outputs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 107, + 86, + 493, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 86, + 493, + 97 + ], + "spans": [ + { + "bbox": [ + 107, + 86, + 493, + 97 + ], + "type": "text", + "content": "- Pass@k evaluates the likelihood of generating at least one correct solution within " + }, + { + "bbox": [ + 107, + 86, + 493, + 97 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 107, + 86, + 493, + 97 + ], + "type": "text", + "content": " attempts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 99, + 504, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 99, + 504, + 121 + ], + "spans": [ + { + "bbox": [ + 107, + 99, + 504, + 121 + ], + "type": "text", + "content": "- Cons@k assesses consistency by determining the model's ability to consistently produce correct or logically coherent solutions across multiple attempts." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 104, + 125, + 505, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 125, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 104, + 125, + 505, + 159 + ], + "type": "text", + "content": "In scientific or commonsense question-answering tasks, evaluation often uses Exact Match (EM) and Accuracy based on regex extraction, where EM determines whether the model's output exactly matches the expected solution." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 163, + 479, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 163, + 479, + 175 + ], + "spans": [ + { + "bbox": [ + 105, + 163, + 479, + 175 + ], + "type": "text", + "content": "For feedback techniques like ORM or PRM, Rank and Best-of-N metrics are often used:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 180, + 505, + 226 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 106, + 180, + 504, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 180, + 504, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 504, + 201 + ], + "type": "text", + "content": "- Rank measures whether the reward model correctly prioritizes the best reasoning processes from the top " + }, + { + "bbox": [ + 106, + 180, + 504, + 201 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 106, + 180, + 504, + 201 + ], + "type": "text", + "content": " candidates." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 204, + 505, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 204, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 505, + 226 + ], + "type": "text", + "content": "- Best-of-N selects the highest-scoring solution from " + }, + { + "bbox": [ + 106, + 204, + 505, + 226 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 106, + 204, + 505, + 226 + ], + "type": "text", + "content": " generated reasoning trajectories, indirectly measuring the reward model's effectiveness based on final outcomes." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 239, + 223, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 239, + 223, + 251 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 223, + 251 + ], + "type": "text", + "content": "3.2.2 Decoding Strategies" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 258, + 504, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 258, + 504, + 315 + ], + "spans": [ + { + "bbox": [ + 104, + 258, + 504, + 315 + ], + "type": "text", + "content": "Decoding strategies are essential for controlling the inference process. Common approaches include Greedy Decoding, Beam Search, and Major@k. Both Greedy Decoding and Beam Search limit the sampling range to reduce randomness, guiding the model toward more consistent outputs. In contrast, Major@k identifies the most reliable solution by selecting the one with the highest consistency from a set of " + }, + { + "bbox": [ + 104, + 258, + 504, + 315 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 104, + 258, + 504, + 315 + ], + "type": "text", + "content": " candidate solutions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 327, + 192, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 327, + 192, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 192, + 338 + ], + "type": "text", + "content": "3.2.3 Benchmarks" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 346, + 504, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 346, + 504, + 392 + ], + "spans": [ + { + "bbox": [ + 104, + 346, + 504, + 392 + ], + "type": "text", + "content": "In the realm of Benchmarks, the focus lies on assessing the reasoning capabilities of RLLMs across diverse domains. There are two primary categories: (1) Outcome Benchmarks, which focus on the holistic view of Long CoT reasoning, and (2) Process Benchmarks, which concentrate on the local view of the Long CoT process or individual capabilities." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 401, + 504, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 401, + 504, + 424 + ], + "spans": [ + { + "bbox": [ + 104, + 401, + 504, + 424 + ], + "type": "text", + "content": "Outcome Benchmarks In the realm of Outcome Benchmarks, the first focus lies on evaluating the logical reasoning capabilities:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 430, + 506, + 655 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 107, + 430, + 506, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 430, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 107, + 430, + 506, + 517 + ], + "type": "text", + "content": "- Complex Mathematics: A central focus in complex mathematics is evaluating benchmarks like GSM8K [141] and MATH [253], which assess basic mathematical problem-solving abilities [1125, 1112]. Recent additions, such as AIME 2024 [8], AIME 2025 [571], MATH-500 [449], AMC 2023 [9], USAMO [598], OlympiadBench [239], and OlympiadArena [298], expand the evaluation of LLM performance in mathematics. Moreover, Putnam-AXIOM [224] and FrontierMath [210] introduce more complex problems that challenge future reasoning systems. Additionally, ThinkBench [291] and MATH-Perturb [288] focus on robust evaluation for Long CoT [38, 987]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 107, + 520, + 506, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 520, + 506, + 586 + ], + "spans": [ + { + "bbox": [ + 107, + 520, + 506, + 586 + ], + "type": "text", + "content": "- Complex Coding: Complex coding benchmarks are also vital, with competitions like Codeforces, SWEbench [327], CodeContests [427], and LiveCodeBench [309] evaluating LLM coding and problem-solving skills. Notable additions such as MHPP [148], ProBench [934], HumanEval Pro, MBPP Pro [993], and EquiBench [833] enhance the scope and complexity of coding challenges. Moreover, some studies have explored applying these benchmarks in real-world code development scenarios for automatic code generation and evaluation [243, 744]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 107, + 589, + 506, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 589, + 506, + 655 + ], + "spans": [ + { + "bbox": [ + 107, + 589, + 506, + 655 + ], + "type": "text", + "content": "- Commonsense Puzzle: Commonsense puzzle benchmarks, including LiveBench [850], BIG-Bench Hard [705] and ZebraLogic [450], assess models' ability to reason about commonsense situations. The ARC [131] and DRE-Bench [947] is often viewed as a challenging commonsense-based AGI test. JustLogic [87] further contributes to the evaluation of deductive reasoning and commonsense problem-solving. Moreover, Li et al. [382] introduce QuestBench, a benchmark designed to evaluate the ability of RLLMs to generate insightful and meaningful questions." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 104, + 660, + 504, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 660, + 504, + 684 + ], + "spans": [ + { + "bbox": [ + 104, + 660, + 504, + 684 + ], + "type": "text", + "content": "The second focus area concerns Knowledge Benchmarks, essential for evaluating a model's capability in complex reasoning across various tasks for out of distribution evaluation [776]:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 107, + 689, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 689, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 107, + 689, + 506, + 723 + ], + "type": "text", + "content": "- Scientific Reasoning: Scientific Reasoning benchmarks, such as GPQA Diamond [637], MMLU-Pro [821], and SuperGPQA [165], assess multi-domain reasoning in fields like chemistry, biology, and physics [157]. These benchmarks test models' ability to not only accumulate knowledge" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "11" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + }, + { + "para_blocks": [ + { + "bbox": [ + 114, + 72, + 504, + 115 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 72, + 504, + 115 + ], + "spans": [ + { + "bbox": [ + 114, + 72, + 504, + 115 + ], + "type": "text", + "content": "but also integrate it for problem-solving. Humanity's Last Exam (HLE) [602] further challenges models by requiring deep interdisciplinary reasoning across scientific disciplines. Further, Chung et al. [140] propose TPBench to evaluate the effectiveness of RLLMs in solving theoretical physics problems." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 107, + 118, + 506, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 118, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 107, + 118, + 506, + 207 + ], + "type": "text", + "content": "- Medical Reasoning: In the realm of Medical Reasoning, the need for complex, domain-specific, and accurate reasoning is paramount [1094, 1024, 905, 589]. Benchmarks, such as MedQA [328], JAMA Clinical Challenge [76], LLMEval-Med [1049] and Medbullets [76], simulate diagnostic and treatment decision-making processes, reflecting real-world medical practice. These benchmarks evaluate a model's handling of medical knowledge and reasoning, from diagnosis to treatment planning. Additionally, MedXpertQA [1150] introduces a comprehensive evaluation framework combining text and multimodal data, specifically assessing AI's reasoning capabilities in healthcare." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 220, + 224, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 220, + 224, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 224, + 232 + ], + "type": "text", + "content": "3.2.4 Process Evaluations" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 240, + 506, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 240, + 506, + 319 + ], + "spans": [ + { + "bbox": [ + 104, + 240, + 506, + 319 + ], + "type": "text", + "content": "Deep Reasoning Benchmarks Recent progress in RLLMs underscores the need for specialized benchmarks to evaluate their deep reasoning abilities in Long CoT [375, 1133]. Notably, Lin et al. [450] introduces ZebraLogic, a framework for assessing logical reasoning, especially in complex non-monotonic scenarios. Similarly, BigGSM [90] and GSM-Ranges [670] focus on perturbing numerical values to test logical and arithmetic reasoning in edge cases beyond the models' training distribution. ROSCOE [212], ReCEval [606], DiVeRSe [425], HLV [71], and CoT-Kinetics [51] are designed to assess each step in the deep reasoning process during Long CoT tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 328, + 506, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 328, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 104, + 328, + 506, + 397 + ], + "type": "text", + "content": "Exploration Benchmarks Several studies assess RLLMs' exploration capabilities in Long CoT tasks. Specifically, Sys2Bench [583] evaluates the exploration and scaling abilities of RLLMs, emphasizing generalization across diverse tasks. BanditBench [566] extends this by testing model performance in interactive environments, offering insights into practical applications. Additionally, Heyman and Zylberberg [254] introduce a graph coloring problem to assess reasoning and spatial exploration in complex problem-solving scenarios." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 406, + 507, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 406, + 507, + 561 + ], + "spans": [ + { + "bbox": [ + 104, + 406, + 507, + 561 + ], + "type": "text", + "content": "Reflection Benchmarks Reflection benchmarks measure RLLMs' ability to identify, reflect upon, and correct errors in Long CoT reasoning. These benchmarks fall into two categories: feedback and refinement. (1) Feedback Benchmark: These benchmarks assess the ability of LLMs to detect errors and respond to feedback for improvement. For example, Lambert et al. [367] introduces RewardBench to evaluate RLLMs' reward capabilities. This framework is extended by Multimodal RewardBench[960], and CodeCriticBench [1025] to include multimodal and code contexts, respectively. Benchmarks such as ProcessBench [1102], PRMBench [679], MR-Ben [1021], and DeltaBench [250] focus on error detection and correction across various tasks at the step level. Additionally, RealL Mistake [337] and JudgeBench [709] address more real-world error evaluation. (2) Refinement Benchmark: These benchmarks focus on error correction in complex tasks. CriticBench [456] assesses critique-correction capabilities, while MLDebugging [287], and ErrorRadar [922] specializes in coding or multimodal reasoning error detection and refinement. FinerReason [72] introduces a commonsense puzzle for broader feedback and refinement evaluations. Medec [1] adapts error correction to healthcare, addressing medical issues." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 571, + 230, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 571, + 230, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 230, + 582 + ], + "type": "text", + "content": "3.2.5 Advanced Evaluation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 590, + 507, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 590, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 590, + 507, + 723 + ], + "type": "text", + "content": "Agentic & Embodied Reasoning Agentic and Embodied reasoning requires models to demonstrate an understanding of real-world interactions, tool use, and adaptive reasoning in response to change. To assess real-world understanding, Wang et al. [798] introduce a benchmark that evaluates agents' ability to reason about physical concepts. Zhang et al. [1064] extend this by assessing agents' interactions with real-world physics. Additionally, realistic tasks often demand complex planning and tool usage, necessitating benchmarks to evaluate agent reasoning. These benchmarks assess agents' abilities to navigate and complete tasks in digital environments. Building on this, Huang et al. [283] propose a framework for evaluating decision-making in multi-agent, competitive settings. Nath et al. [562] introduce ToolComp, a benchmark designed to evaluate multi-step tool-use reasoning. To analyze adaptive reasoning in the face of real-world change, OSWorld [887], CogAgent [260], Mobile-Agent-E [828], WebShop [954], WebArena [1126], WGSR-Bench [972], and WebGames [735] assess AI systems across domains such as operating systems, mobile GUIs, browser tasks, and interactive" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "12" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 97 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 97 + ], + "type": "text", + "content": "entertainment [1106, 780, 512, 552]. Hu et al. [272] present Text2World, which evaluates agents' ability to generate interactive environments from text to test agent adaptability [995]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 107, + 506, + 142 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 107, + 506, + 142 + ], + "spans": [ + { + "bbox": [ + 104, + 107, + 506, + 142 + ], + "type": "text", + "content": "Multimodal Reasoning Multimodal reasoning refers to a system's ability to integrate and reason across diverse input types, including text, images [316]. This capability is crucial for solving complex problems that require information from diverse formats." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 147, + 506, + 407 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 107, + 147, + 506, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 147, + 506, + 203 + ], + "spans": [ + { + "bbox": [ + 107, + 147, + 506, + 203 + ], + "type": "text", + "content": "- Complex Mathematics: Mathematical reasoning often integrates both textual and visual components, such as equations, graphs, or diagrams [921]. Specifically, challenges like MathVista [508], MathVision [782], MathVerse [1054], M3CoT-Math [91], CMMaTH [433], EnigmaEval [763], CoMT-Geometry [125], and PGPS9K [1050] aim to advance multimodal reasoning in mathematics, improving the evaluation of multimodal Long CoT logic." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 204, + 506, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 204, + 506, + 260 + ], + "spans": [ + { + "bbox": [ + 107, + 204, + 506, + 260 + ], + "type": "text", + "content": "- Complex Code: The second area of focus involves code-related reasoning, where systems interpret textual descriptions and code snippets. Benchmarks like HumanEval-V [1035], Code-Vision [767], Plot2Code [852], and ChartMimic [931] evaluate systems' capabilities to generate or interpret code from natural language and multimodal inputs for assessing systems that integrate natural language processing with programming tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 262, + 506, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 262, + 506, + 317 + ], + "spans": [ + { + "bbox": [ + 107, + 262, + 506, + 317 + ], + "type": "text", + "content": "- **Complex Science:** This area involves integrating scientific texts with related diagrams or experimental data. Benchmarks like ScienceQA [507], M3CoT-Science [91], BMMR [874], and ScienceBoard [698] evaluate how well models combine science information with Long CoT reasoning across various scientific domains [966]. Further, Guo et al. [229] propose MolPuzzle for the evaluation of molecular structure elucidation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 319, + 506, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 319, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 107, + 319, + 506, + 407 + ], + "type": "text", + "content": "- Commonsense Puzzle: This area focuses on commonsense reasoning, where systems combine reasoning cues and images to make deeper conclusions. Chen et al. [91] introduce M3CoT-Commensense, which incorporates commonsense Long CoT reasoning for complex multimodal interactions. Further, PuzzleVQA [128], MMReason [953] and LEGO-Puzzles [711] focus more on abstract and spatial puzzle reasoning, respectively. Additionally, Wang et al. [760] propose two benchmarks: Clue-Visual Question Answering (CVQA), which tests visual comprehension through three task types, and Clue of Password-Visual Question Answering (CPVQA), which features two task types focusing on the interpretation and application of visual data." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 104, + 420, + 507, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 420, + 507, + 510 + ], + "spans": [ + { + "bbox": [ + 104, + 420, + 507, + 510 + ], + "type": "text", + "content": "AI for Research Recent advancements in AI have significantly advanced scientific research [94, 1124, 817, 215], with platforms like SciWorld [798] improving the research process. Simultaneously, Pricope [608] and Chan et al. [67] introduce a machine-learning platform to evaluate the potential of RLLMs in automating experiments. Several studies also examine RLLMs' ability to generate innovative research ideas. For instance, Si et al. [672] conduct evaluations with over 100 NLP researchers to assess RLLMs' creativity, revealing notable limitations [404, 856, 726]. Additionally, Li et al. [434] introduce SolutionBench, a benchmark for assessing systems' ability to generate feasible solutions for complex engineering problems." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 525, + 282, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 525, + 282, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 282, + 539 + ], + "type": "text", + "content": "4 Deep Reasoning for Long CoT" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 552, + 506, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 552, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 552, + 506, + 640 + ], + "type": "text", + "content": "Deep reasoning capabilities primarily require profound depth and comprehensiveness in cognitive and reasoning processes. In the absence of such capabilities, RLLMs suffer significant performance declines [758, 823]. 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The reasoning performance across these formats is presented in Table 1." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "13" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + }, + { + "para_blocks": [ + { + "bbox": [ + 114, + 73, + 243, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 73, + 243, + 83 + ], + "spans": [ + { + "bbox": [ + 114, + 73, + 243, + 83 + ], + "type": "text", + "content": "(a) Natural Language Deep Reasoning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 120, + 88, + 295, + 113 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 88, + 295, + 113 + ], + "spans": [ + { + "bbox": [ + 120, + 88, + 295, + 113 + ], + "type": "text", + "content": "To predict the output of the given input for Conway's Game of Life, we need to apply the rules of the game to each cell on the board. 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[401]." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 140, + 178, + 259, + 243 + ], + "blocks": [ + { + "bbox": [ + 140, + 178, + 259, + 243 + ], + "lines": [ + { + "bbox": [ + 140, + 178, + 259, + 243 + ], + "spans": [ + { + "bbox": [ + 140, + 178, + 259, + 243 + ], + "type": "image", + "image_path": "aa202666c0347e30f452afb50132bf46686ba98433600b7ee8d0e4c2f30ad8f5.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 259, + 165, + 381, + 229 + ], + "blocks": [ + { + "bbox": [ + 259, + 165, + 381, + 229 + ], + "lines": [ + { + "bbox": [ + 259, + 165, + 381, + 229 + ], + "spans": [ + { + "bbox": [ + 259, + 165, + 381, + 229 + ], + "type": "image", + "image_path": "09f798353b1e4615f84c4d824a90ec1e55d3d23579c20ec2917c35a81ade4452.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 275, + 230, + 367, + 244 + ], + "lines": [ + { + "bbox": [ + 275, + 230, + 367, + 244 + ], + "spans": [ + { + "bbox": [ + 275, + 230, + 367, + 244 + ], + "type": "text", + "content": "Reasoning Vector Driven Latent Space Deep Reasoning" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 381, + 165, + 497, + 230 + ], + "blocks": [ + { + "bbox": [ + 381, + 165, + 497, + 230 + ], + "lines": [ + { + "bbox": [ + 381, + 165, + 497, + 230 + ], + "spans": [ + { + "bbox": [ + 381, + 165, + 497, + 230 + ], + "type": "image", + "image_path": "3effed9f4c545b03b2ac2c365b4d87fe9724f58c4dddd4294def63e3d2f5672e.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 230, + 480, + 244 + ], + "lines": [ + { + "bbox": [ + 397, + 230, + 480, + 244 + ], + "spans": [ + { + "bbox": [ + 397, + 230, + 480, + 244 + ], + "type": "text", + "content": "Reasoning Manager Driven Latent Space Deep Reasoning" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 308, + 287, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 308, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 287, + 320 + ], + "type": "text", + "content": "4.1.1 Natural Language Deep Reasoning" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 327, + 506, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 327, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 104, + 327, + 506, + 427 + ], + "type": "text", + "content": "Traditionally, researchers have sought to adapt natural language for intuitive and free-flowing deep reasoning [836, 1118, 303, 617, 1070, 765, 205]. Early work by Wei et al. [836] demonstrated that the use of natural language Long CoT significantly enhances the reasoning capabilities of RLLMs. Further, the Natural Program framework [460] allows RLLMs to engage in deeper natural language reasoning by ensuring a more structured and rigorous logical analysis. More recently, CodeI/O [401] has introduced a technique that reorganizes code-based reasoning patterns into natural language formats, further boosting the reasoning potential of RLLMs [36]. Similarly, Li et al. [387] propose CoRT, which integrates code into reasoning to facilitate a mixture of formats, resulting in improved cognitive performance." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 440, + 301, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 440, + 301, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 301, + 452 + ], + "type": "text", + "content": "4.1.2 Structured Language Deep Reasoning" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 459, + 506, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 459, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 104, + 459, + 506, + 581 + ], + "type": "text", + "content": "Structured language deep reasoning encompasses various approaches designed to program [100, 464, 687, 591, 198, 845, 830, 1044] or symbolic language [605, 158, 451, 372, 933, 604, 37, 40, 797, 380] format for enhanced deep reasoning. In this context, most studies focus on utilizing code to better enhance the mathematical reasoning capabilities [389, 107, 978, 85]. Xu et al. [897] propose a neural-symbol self-training framework guided by the environment, addressing both the scarcity of symbolic data and the limitations of symbolic processing in LLMs. Additionally, Liao et al. [443] present SKIntern, which refines symbolic RLLMs through curriculum learning and linear attenuation, enabling the internalization of symbolic knowledge with fewer examples, reducing computational costs, and accelerating inference. Furthermore, Ranaldi et al. [634] introduce QuaSAR, a CoT variant that directs LLMs to operate at higher abstraction levels through quasi-symbolic reasoning, thus improving natural language reasoning and providing more precise structural representations." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 594, + 265, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 594, + 265, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 265, + 605 + ], + "type": "text", + "content": "4.1.3 Latent Space Deep Reasoning" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 612, + 506, + 723 + ], + "type": "text", + "content": "Latent space deep reasoning encompasses techniques designed to enhance the reasoning abilities of LLMs by leveraging operations within continuous latent spaces [684, 151, 640, 324]. These approaches can be categorized into three main paradigms: (1) Reasoning Token-Driven Latent Space Deep Reasoning: Early work [810, 1013] introduce the concept of \"planning tokens\" or \"thought tokens\" to guide reasoning within latent spaces [949, 1008]. Further, Coconut [236] expands on this through the maintenance of multiple alternative reasoning paths, increasing both complexity and efficiency [1069, 706]. At the extreme, Heima [662] condenses the entire Long CoT process into a single token, yielding substantial computational savings. (2) Reasoning Vector Driven Latent Space Deep Reasoning: Building on the previous paradigm, LTM [356] conceptualizes the layers of LLMs as \"thought blocks\" and introduces the concept of \"thought vectors\" for each layer. This" + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "14" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 13 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 111, + 70, + 499, + 443 + ], + "blocks": [ + { + "bbox": [ + 111, + 70, + 499, + 443 + ], + "lines": [ + { + "bbox": [ + 111, + 70, + 499, + 443 + ], + "spans": [ + { + "bbox": [ + 111, + 70, + 499, + 443 + ], + "type": "table", + "html": "
ModelBase ModelGSM8kMATHGPQAOlympiadBenchLiveCodeBench
Latent Space Deep Reasoning
No-CoT [151]Mistral-7B [318]38.0----
SQ-VAE [810]Llama-2-7B [743]40.07.0---
RecurrentBlock-3.5B [204]-42.1----
ICoT-SI [151]Mistral-7B [318]51.0----
Natural Language Deep Reasoning
Self-Rewarding [114]Llama-2-7B [743]40.010.7---
Llama-3.1-8B [168]-56.720.3---
MetaMath [983]Llama-2-7B [743]66.5----
OVM [979]Llama-2-7B [743]73.7----
NuminaMath-7B-CoT [397]-75.455.2-19.9-
Qwen2-7B [925]-79.944.2-21.3-
Qwen2-Math-7B [927]-80.450.4-38.2-
Internlm2-math-plus-7B [974]-84.054.4-18.8-
OMI2 [401]Qwen2.5-Coder-7B [301]84.172.336.2-27.2
Llama-3.1-70B [168]-85.541.4---
CODEI/O++ [401]Qwen2.5-Coder-7B [301]85.772.140.6-29.1
CODEI/O [401]Qwen2.5-Coder-7B [301]86.471.943.3-28.5
WI [401]Qwen2.5-Coder-7B [301]87.071.439.1-26.0
WI (Full) [401]Qwen2.5-Coder-7B [301]87.071.142.9-27.6
OMI2 (Full) [401]Qwen2.5-Coder-7B [301]88.573.240.9-28.4
DeepSeekMath-7B-RL [658]-88.251.7-19.0-
Llama-3.1-405B [168]-89.053.8---
CoMAT [371]GPT-4 [3]93.7-40.4--
CoT [634]GPT-4 [3]94.5-41.850.2-
FCoT [523]GPT-4 [3]95.0----
Qwen2.5-Math-7B-Instruct [927]-95.283.6-41.6-
MathPrompter [303]GPT-4 [3]95.6----
Qwen2.5-Math-72B-Instruct [927]-95.985.9-49.0-
DeepSeek-R1-Distill-Qwen-7B [227]--92.8-49.137.6
DeepSeek-R1-Distill-Qwen-32B [227]--94.3-62.157.2
Structured Language Deep Reasoning
STaR [1012]Llama-2-7B [743]58.216.0---
ENVISIONS [897]Llama-2-7B [743]59.019.0---
MAmmoTH [1006]Code-Llama-7B [639]59.4----
MathCoder-CL [783]Code-Llama-7B [639]67.830.2---
ToRA-Code [217]Llama-2-7B [743]72.6----
Brain [107]Code-Llama-7B [639]74.0----
DeepSeek-Coder-7B [226]-77.444.4---
SIaM [978]Qwen-2-Math-Base81.550---
OC-SFT-1 [401]Qwen2.5-Coder-7B [301]86.770.937.7-27.5
PyEdu [401]Qwen2.5-Coder-7B [301]85.871.440.9-25.8
Qwen2.5-Math-7B-Instruct [927]-94.685.2-55.6-
Qwen2.5-Math-72B-Instruct [927]-95.888.1-60.6-
QuaSAR [634]GPT-4 [3]96.5-55.444.6-
MathDivide [687]GPT-4 [3]96.8---
", + "image_path": "ebcdb7892865c413666c63573d7f974aac12588169f830423b0bd269bf85e3b2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 448, + 506, + 471 + ], + "lines": [ + { + "bbox": [ + 104, + 448, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 104, + 448, + 506, + 471 + ], + "type": "text", + "content": "Table 1: Performance of various deep reasoning formats, sorted primarily by GSM8K scores. “-” indicates that the paper did not report this score." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 104, + 491, + 506, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 491, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 104, + 491, + 506, + 646 + ], + "type": "text", + "content": "approach allows for the scaling of inference-time computations by implicitly performing reasoning within the latent space through recurrent depth. (3) Reasoning Manager Driven Latent Space Deep Reasoning: Inspired by these, Schone et al. [647], Geiping et al. [204], and Saunshi et al. [646] propose a mechanism similar to a continuous reasoning manager, which iteratively governs a trained \"recurrent block\" as a recurrent \"thought block\" [511]. This method integrates deeper model layers during reasoning, enhancing performance without needing specialized training data, and even outperforming larger RLLMs. Additionally, ITT [109] leverages the original transformer layer as a recurrent \"thought block\", selecting key tokens via adaptive token routing and controlling reasoning depth with residual thinking connections, enabling more efficient processing of critical tokens. Further, System-1.5 Reasoning [808] defines two dynamic shortcuts. The Model Depth Shortcut (DS) lets non-critical tokens exit early via lightweight adapter branches while routing critical tokens through deeper Transformer layers, thus supporting adaptive, vertical reasoning. The Step Shortcut (SS) reuses hidden states across decoding steps to bypass trivial iterations and enable horizontal reasoning in latent space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 658, + 241, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 658, + 241, + 670 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 241, + 670 + ], + "type": "text", + "content": "4.2 Deep Reasoning Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 677, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 677, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 677, + 506, + 723 + ], + "type": "text", + "content": "Insufficient deep reasoning in RLLMs can significantly degrade performance [758, 823]. As a result, research has focused on improving reasoning through training. Supervised fine-tuning (SFT) [1058] stabilizes model outputs by serving as a memory process [883], while reinforcement learning (RL) enables generalization and self-learning [227, 137, 276, 898]. Recent studies for deep reasoning" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "15" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 14 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 89, + 296, + 149 + ], + "blocks": [ + { + "bbox": [ + 136, + 73, + 272, + 87 + ], + "lines": [ + { + "bbox": [ + 136, + 73, + 272, + 87 + ], + "spans": [ + { + "bbox": [ + 136, + 73, + 272, + 87 + ], + "type": "text", + "content": "(a) Deep Reasoning Imitation" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 115, + 89, + 296, + 149 + ], + "lines": [ + { + "bbox": [ + 115, + 89, + 296, + 149 + ], + "spans": [ + { + "bbox": [ + 115, + 89, + 296, + 149 + ], + "type": "image", + "image_path": "787c5674fba7b0ce5e4ca3ac3eefd20babe3c384dc807cab022b3df606b88f7a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 304, + 89, + 496, + 148 + ], + "blocks": [ + { + "bbox": [ + 320, + 74, + 477, + 87 + ], + "lines": [ + { + "bbox": [ + 320, + 74, + 477, + 87 + ], + "spans": [ + { + "bbox": [ + 320, + 74, + 477, + 87 + ], + "type": "text", + "content": "(b) Deep Reasoning Self-Learning" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 89, + 496, + 148 + ], + "lines": [ + { + "bbox": [ + 304, + 89, + 496, + 148 + ], + "spans": [ + { + "bbox": [ + 304, + 89, + 496, + 148 + ], + "type": "image", + "image_path": "04fef9422d7990eb4d902d3c902905109bd7fe0911512bee51a344a37488531e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 159, + 504, + 194 + ], + "lines": [ + { + "bbox": [ + 104, + 159, + 504, + 194 + ], + "spans": [ + { + "bbox": [ + 104, + 159, + 504, + 194 + ], + "type": "text", + "content": "Figure 6: The different learning strategies of deep reasoning learning, including deep reasoning imitation of the data from advanced deep reasoning systems, like advanced RLLMs, MCTS, etc.; deep reasoning self-learning from preference-based RL by implicit reward." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 216, + 504, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 216, + 504, + 281 + ], + "spans": [ + { + "bbox": [ + 104, + 216, + 504, + 281 + ], + "type": "text", + "content": "learning have explored using SFT to imitate advanced reasoning in RLLMs and applying RL to enhance self-improvement in reasoning. As illustrated in Figure 6, this section outlines two key approaches to improve deep reasoning: (1) Deep Reasoning Imitation (§ 4.2.1), which involves learning reasoning from human-annotated or distilled data through SFT, and (2) Deep Reasoning Self-Learning (§ 4.2.2), where models improve reasoning through preference-based RL with implicit rewards. The performance of these methods is shown in Table 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 294, + 249, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 294, + 249, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 249, + 306 + ], + "type": "text", + "content": "4.2.1 Deep Reasoning Imitation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 312, + 506, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 312, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 104, + 312, + 506, + 554 + ], + "type": "text", + "content": "Deep reasoning in RLLMs can be effectively achieved by mimicking advanced reasoning systems, such as human reasoning [558, 61, 115, 403], advanced RLLMs [227, 58, 957, 370, 102], and scaling-augmented RLLMs [410, 1003, 596, 1136, 41]. This approach enables the model to learn complex reasoning patterns and generalize across tasks [937, 416]. Specifically, (1) Imitation from Human: Earlier, Cobbe et al. [141] first propose the deep reasoning imitation paradigm using human examples. ALT [558] improves RLLM reasoning by generating larger datasets of human-annotated logical templates, which fosters deeper reasoning [241]. To enhance diversity, EIT [61] promotes simpler human-generated plans, while LLMs contribute more nuanced reasoning, facilitating collaboration between human input and AI. (2) Imitation from Advanced RLLMs: A body of work utilizes zero-shot prompting to guide large teacher RLLMs in generating reasoning rationale, which is then used to fine-tune smaller RLLMs, marking the beginning of deep reasoning imitation [256, 352, 938, 521]. Additionally, AceMath [500] applies few-shot prompting to distill Long CoT samples from advanced LLMs, followed by multi-stage quality-guided SFT to enhance performance. Chen et al. [107] separate the data synthesis process into planning and reasoning stages, thereby improving reasoning quality. DART-Math [738] effectively distills complex queries requiring deeper reasoning during synthesis, advancing deep reasoning capabilities. Further, Ahmad et al. [7] propose OpenCodeReasoning, expanding this paradigm to the code scenarios. (3) Imitation from Scaling-augmented RLLMs: Earlier, Bansal et al. [34] enhance data quality by scaling the sampling size and length, boosting imitation performance [481, 1005]. Yang et al. [927] and Zhao et al. [1090] further improve data quality by scaling sampling and selecting samples through sample feature or an additional reward model. Additionally, Li et al. [410] identify optimal deep reasoning paths through MCTS, advancing imitation effectiveness." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 558, + 506, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 558, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 104, + 558, + 506, + 669 + ], + "type": "text", + "content": "Recent studies [299, 550] show that distilling knowledge from advanced RLLM APIs like O1 [307] and R1 [227] significantly enhances the performance of smaller LLMs [424, 223]. This method, employing supervised fine-tuning, boosts model performance on complex mathematical reasoning tasks, sometimes surpassing the teacher models' performance. Building on these findings, LIMO [967], S1 [560], and RedStar [902] argue that a large number of imitation samples is unnecessary. They demonstrate that even a minimal set of samples can activate deep reasoning capabilities in foundational LLMs. For practical applications, Turtel et al. [747] showcase how these techniques can predict future events beyond a model's knowledge cutoff. Sun et al. [701], Yang et al. [928] and Zhao et al. [1093] further enhance deep reasoning imitation by selecting high-quality samples from large datasets, thereby improving the quality of the imitation data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 681, + 268, + 693 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 681, + 268, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 268, + 693 + ], + "type": "text", + "content": "4.2.2 Deep Reasoning Self-Learning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "content": "While simple imitation can yield strong performance, current models still rely heavily on human annotations or outputs from more advanced models for both imitation and distillation [502]. To" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "16" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 15 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 109, + 72, + 501, + 381 + ], + "blocks": [ + { + "bbox": [ + 109, + 72, + 501, + 381 + ], + "lines": [ + { + "bbox": [ + 109, + 72, + 501, + 381 + ], + "spans": [ + { + "bbox": [ + 109, + 72, + 501, + 381 + ], + "type": "table", + "html": "
ModelData SizeBase ModelGSM8KMATHMATH-500AIME2024GPQAOlympiadBench
Deep Reasoning Imitation
SFT [938]200KLlama-3.1-8B [168]---54.13.5-
Retro-Enh [115]14MLlama-3-8B [168]45.121.7----
Query-Exp [115]24MLlama-3-8B [168]51.323.1----
Res-Div [115]14MLlama-3-8B [168]53.023.2----
MetaMath [738]0.40MMistral-7B [318]76.529.8---5.9
ALT-FLDx2 [558]100KLlama-3.1-70B [168]83.324.4----
EIT [61]15KLlama-2-70B [743]84.132.5----
MathScale [738]2.0MMistral-7B [318]74.835.2----
Tutor-Amp [115]11MLlama-3-8B [168]64.435.9----
MMIQC [738]2.3MMistral-7B [318]75.437.4---9.4
VRT [738]0.59MMistral-7B [318]82.338.7---8.7
KPMath-Plus [738]1.6MMistral-7B [318]82.146.8----
Llama-2-70B-Xwin-Math-V1.1 [385]1.4MLlama-2-70B [743]90.252.5---16.3
DART-Math-Mistral-7B [738]591KMistral-7B [318]81.145.5---14.7
DART-Math-Llama-3-70B [738]591KLlama-3-70B [168]89.656.1---20.0
Rejection Sampling [410]197KQwen2.5-7B [926]87.170.0-10.0-27.1
Evol-Instruct-7B [514]905KQwen2.5-Math-7B [927]88.5-77.416.7--
FastMCTS [410]288KQwen2.5-7B [926]88.974.0-20.0-27.5
KPDDS-7B [295]800KQwen2.5-Math-7B [927]89.9-76.010.0--
DeepSeek-R1-Distill-Qwen-7B [227]800KQwen2.5-7B-Instruct [926]91.7-91.643.3--
Openmathinstruct-7B [740]14MQwen2.5-Math-7B [927]92.0-79.610.0--
NuminaMath [967]100KQwen2.5-Math-7B [927]92.9-81.820.0--
PromptCoT-DS-7B [1090]115KDeepSeek-R1-Distill-Qwen-7B [227]92.6-93.060.0--
PromptCoT-Qwen-7B [1090]905KQwen2.5-Math-7B [927]93.3-84.026.7--
AceMath-7B-Instruct [500]1.2MQwen2-Math-7B-Instruct [927]93.783.1---42.2
AceMath-72B-Instruct [500]1.2MQwen2.5-Math-72B-Instruct [927]96.486.1---48.4
NuminaMath [967]100KQwen2.5-32B-Instruct [926]--59.26.525.836.7
OpenThoughts [967]114KQwen2.5-32B-Instruct [926]--80.650.242.956.3
Sky-T1-32B-Preview [724]17KQwen2.5-32B-Instruct [926]--82.443.356.8-
Journey Learning [299]5KQwen2.5-Math-72B [927]--87.243.3--
STILL-2 [550]3.9KQwen2.5-32B-Instruct [926]--90.246.755.1-
Bespoke-32B [362]17KQwen2.5-32B-Instruct [926]--93.063.358.1-
s1 [560]1KQwen2.5-32B-Instruct [926]--93.056.759.6-
DeepSeek-R1-Distill-Qwen-32B [227]800KQwen2.5-32B-Instruct [926]--94.372.662.1-
LIMO [967]817Qwen2.5-32B-Instruct [926]--94.815.866.766.8
Deep Reasoning Self-Learning
DPO [302]40KDeepSeek-Math-7B-Base [658]74.834.9----
RefT [302]40KDeepSeek-Math-7B-Base [658]71.436.0----
Self-Explore [302]40KDeepSeek-Math-7B-Base [658]78.637.7----
SimPO [723]10KQwen2.5-Math-7B-Instruct [927]88.840.056.6---
DPO [446]11KDeepSeek-Math-7B-Instruct [658]-48.7----
TPO [446]11KDeepSeek-Math-7B-Instruct [658]-51.3----
DPO [446]11KQwen2-7B-Instruct [925]-54.3----
TPO [446]11KQwen2-7B-Instruct [925]-55.5----
MCTS [74]15KDeepSeek-Math-7B-Base [658]83.264.0----
SBS [74]15KDeepSeek-Math-7B-Base [658]84.166.3----
FastMCTS+Branch-DPO [410]152KFastMCTS-7B [410]89.975.4-20.0-29.6
", + "image_path": "0a51aaca5f29b7a1155025d64a0e6be21201b8129c276ddc53c0a7fa47545014.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 387, + 504, + 410 + ], + "lines": [ + { + "bbox": [ + 104, + 387, + 504, + 410 + ], + "spans": [ + { + "bbox": [ + 104, + 387, + 504, + 410 + ], + "type": "text", + "content": "Table 2: Performance of various deep reasoning learning methods, sorted primarily by Math or Math-500 scores. “-” indicates that the paper did not report this score." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 104, + 475, + 504, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 475, + 504, + 510 + ], + "spans": [ + { + "bbox": [ + 104, + 475, + 504, + 510 + ], + "type": "text", + "content": "address this limitation, recent research has focused on enabling more advanced reasoning through techniques like self-play and self-learning [948, 1077, 409, 624]. Specifically, self-learning methods can be classified into two paradigms, differentiated by their sampling strategies:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 514, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 514, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 514, + 506, + 723 + ], + "type": "text", + "content": "(1) Self-Learning from Direct Sampling: The earliest method, STaR [1012], utilizes In-Context Learning (ICL) to sample deep reasoning results [657] and uses the correctness of the final answer as an implicit reward for self-learning [258, 581, 582, 1059, 826, 462]. Further, ReST [225] extends this by introducing a Grow-Improve paradigm, where self-generated reasoning is first annotated with rewards and then enhanced via offline RL algorithms. However, these approaches can be fragile, especially when the reward process lacks robustness. Inspired by the Expectation-Maximization (EM) algorithm, Singh et al. [674] propose a method that generates rewards and iteratively optimizes LLMs to achieve the best performance on a validation set, significantly improving robustness. To further strengthen the reward process, a series of work introduces a method to adapt incorrect solutions, training a verifier [155, 262] or utilize entropy [809, 1040] to select or refine the reward process and improve self-learning quality. (2) Self-Learning from Tree Search: Early deep learning methods, such as EXIT [18], combined MCTS with deep neural networks for reinforcement learning, iteratively self-training the network to guide the tree search and enhance reasoning. Building on this, CPO [1065] and TPO [446] align each step of Long CoT reasoning with the corresponding tree search path, using Tree of Thoughts (ToT) [955] preference information to support deeper reasoning [951, 302]. Li [422] propose Policy-Guided Tree Search (PGTS), integrating RL with structured tree exploration for more efficient navigation of reasoning paths. Further developments, such as AlphaMath [74], AlphaLLM-CPL [814], and TongGeometry [1029], refine MCTS behavior through stepwise trajectory pair extraction and curriculum preference learning, boosting LLM reasoning abilities [611, 412, 872]." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "17" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 16 + }, + { + "para_blocks": [ + { + "bbox": [ + 125, + 72, + 282, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 72, + 282, + 85 + ], + "spans": [ + { + "bbox": [ + 125, + 72, + 282, + 85 + ], + "type": "text", + "content": "Takeaways: Imitation & Self-Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 91, + 489, + 163 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 123, + 91, + 488, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 91, + 488, + 114 + ], + "spans": [ + { + "bbox": [ + 123, + 91, + 488, + 114 + ], + "type": "text", + "content": "- Imitating deep reasoning from advanced RLLMs, and scaling-augmented methods like MCTS can help models learn complex reasoning patterns with fewer samples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 123, + 116, + 488, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 116, + 488, + 138 + ], + "spans": [ + { + "bbox": [ + 123, + 116, + 488, + 138 + ], + "type": "text", + "content": "- Self-learning techniques, including reinforcement learning and tree search, allow RLLMs to enhance their reasoning abilities over time." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 123, + 140, + 489, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 140, + 489, + 163 + ], + "spans": [ + { + "bbox": [ + 123, + 140, + 489, + 163 + ], + "type": "text", + "content": "- The combination of imitation from advanced RLLMs and self-learning techniques strengthens RLLM reasoning, leading to strong performance on complex tasks." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 186, + 294, + 200 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 186, + 294, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 294, + 200 + ], + "type": "text", + "content": "5 Feasible Reflection for Long CoT" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "spans": [ + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "text", + "content": "Feasible Reflection is a pivotal component of Long CoT reasoning, enabling LLMs to handle complex tasks through iterative feedback and refinement [406, 192]. Specifically, it comprises two primary stages: (1) Feedback (" + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "inline_equation", + "content": "\\S" + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "text", + "content": " 5.1), which generates feedback signals " + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i" + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "text", + "content": " to correct node " + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "inline_equation", + "content": "n_j" + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "text", + "content": " in Equation (5); and (2) Refinement (" + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "inline_equation", + "content": "\\S" + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "text", + "content": " 5.2), which adjusts the subsequent node " + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "inline_equation", + "content": "n_{i+1}" + }, + { + "bbox": [ + 104, + 210, + 504, + 266 + ], + "type": "text", + "content": " according to the feedback in Equation (6)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 278, + 171, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 278, + 171, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 278, + 171, + 289 + ], + "type": "text", + "content": "5.1 Feedback" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "spans": [ + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "type": "text", + "content": "Feedback refers to the process of providing evaluations of both overall outputs and the processes that lead to them, with the goal of assessing their accuracy and quality [394, 396, 838, 220, 862]. This process, also referred to as critique or verification, can be executed using either natural language or structured data formats, which serve as the foundation for tree-search methods [113]. Specifically, as shown in Figure 7, feedback can be categorized into three distinct types: (1) Overall Feedback (" + }, + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "type": "inline_equation", + "content": "\\S" + }, + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "type": "text", + "content": " 5.1.1); (2) Process Feedback (" + }, + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "type": "inline_equation", + "content": "\\S" + }, + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "type": "text", + "content": " 5.1.2); (3) Hybrid Feedback (" + }, + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "type": "inline_equation", + "content": "\\S" + }, + { + "bbox": [ + 104, + 299, + 504, + 365 + ], + "type": "text", + "content": " 5.1.3)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 376, + 212, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 376, + 212, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 212, + 387 + ], + "type": "text", + "content": "5.1.1 Overall Feedback" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 395, + 504, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 395, + 504, + 450 + ], + "spans": [ + { + "bbox": [ + 104, + 395, + 504, + 450 + ], + "type": "text", + "content": "The overall feedback focuses on providing a global view of the entire process and results, rather than assessing each step individually. This feedback significantly enhances reasoning skills and reward modeling in reinforcement learning for RLLMs. Specifically, as shown in Figure 7 (a), the overall feedback can be categorized into three main sources: Outcome Reward Model, Rule Extraction, and RLLMs Feedback. The performance across these categories is summarized in Table 3." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 155, + 467, + 254, + 557 + ], + "blocks": [ + { + "bbox": [ + 155, + 467, + 254, + 557 + ], + "lines": [ + { + "bbox": [ + 155, + 467, + 254, + 557 + ], + "spans": [ + { + "bbox": [ + 155, + 467, + 254, + 557 + ], + "type": "image", + "image_path": "924dba4b1d5c6d25f0eff62713bafcbf9c36e9cd21483aae275897e288afdd77.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 259, + 470, + 354, + 557 + ], + "blocks": [ + { + "bbox": [ + 259, + 470, + 354, + 557 + ], + "lines": [ + { + "bbox": [ + 259, + 470, + 354, + 557 + ], + "spans": [ + { + "bbox": [ + 259, + 470, + 354, + 557 + ], + "type": "image", + "image_path": "367cca6990189dfda7e049a2d562809a0e9869ca5351f1d2d1d1e74c0f9bcafd.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 356, + 470, + 452, + 557 + ], + "blocks": [ + { + "bbox": [ + 356, + 470, + 452, + 557 + ], + "lines": [ + { + "bbox": [ + 356, + 470, + 452, + 557 + ], + "spans": [ + { + "bbox": [ + 356, + 470, + 452, + 557 + ], + "type": "image", + "image_path": "dd4b7e43b794582020a033da732daf0b1be53e45111b8e9717414d483b50896e.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 156, + 559, + 264, + 657 + ], + "blocks": [ + { + "bbox": [ + 156, + 559, + 264, + 657 + ], + "lines": [ + { + "bbox": [ + 156, + 559, + 264, + 657 + ], + "spans": [ + { + "bbox": [ + 156, + 559, + 264, + 657 + ], + "type": "image", + "image_path": "6914fc78c8aeece2af825dabacd242f08c842b612001c13322264246623afb04.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 663, + 504, + 718 + ], + "lines": [ + { + "bbox": [ + 104, + 663, + 504, + 718 + ], + "spans": [ + { + "bbox": [ + 104, + 663, + 504, + 718 + ], + "type": "text", + "content": "Figure 7: The feedback capabilities framework for feasible reflection consists of Overall Feedback and Process Feedback. Overall Feedback includes the Outcome Reward Model (ORM) in a value format, rule extraction for correctness judgment, and overall RLLMs based on RLLMs. Process Feedback includes the Process Reward Model (PRM) in a value format and step-level RLLMs, also based on RLLMs." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 273, + 560, + 449, + 657 + ], + "blocks": [ + { + "bbox": [ + 273, + 560, + 449, + 657 + ], + "lines": [ + { + "bbox": [ + 273, + 560, + 449, + 657 + ], + "spans": [ + { + "bbox": [ + 273, + 560, + 449, + 657 + ], + "type": "image", + "image_path": "75c5bea65e3eccbc79affd34b429b7f444436c52e5988975f4dec0ecb68328a3.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 52, + 184, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 52, + 184, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 52, + 184, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "18" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 17 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 121, + 69, + 489, + 312 + ], + "blocks": [ + { + "bbox": [ + 121, + 69, + 489, + 312 + ], + "lines": [ + { + "bbox": [ + 121, + 69, + 489, + 312 + ], + "spans": [ + { + "bbox": [ + 121, + 69, + 489, + 312 + ], + "type": "table", + "html": "
ModelBase ModelChatChat_HardSafetyReasoningOverall
RLLMs
GPT-4o-mini [3]-95.060.780.883.780.1
Llama3.1-70B-Instruct [168]-97.270.286.082.884.0
Llama3.1-405B-Instruct [168]-97.274.687.177.684.1
GPT-4 [3]-95.374.386.987.686.0
GPT-4o [3]-96.176.186.688.186.7
Gemini-1.5-pro [719]-92.380.687.992.088.2
Self-taught Evaluator [803]Llama-3.1-70B-Instruct [168]96.684.281.091.588.3
SFR-LLMA-3.1-8B-Judge [791]Llama-3.1-70B-Instruct [168]95.577.786.295.188.7
SFR-NeMo-12B-Judge [791]Mistral-NeMo-Instruct-12B [725]97.282.286.595.190.3
SFR-LLMA-3.1-70B-Judge [791]Llama-3.1-70B-Instruct [168]96.984.891.697.692.7
Skywork-Critic-Llama-3.1-70B [791]Llama-3.1-70B-Instruct [168]96.687.993.195.593.3
LMUnit [641]Llama-3.1-70B-Instruct [168]----93.4
EvalPlanner [643]Llama-3.1-70B-Instruct [168]97.589.493.095.593.9
Outcome Reward Models
tulu-v2.5-13b-uf-rm [306]TULU-2-13B [305]39.442.355.547.446.1
Prometheus-2-7B [353]Mistral-7B-Instruct-v0.2 [318]85.549.177.176.572.0
Prometheus-8x7b-v2 [353]Mixtral-8x7B-Instruct [319]93.047.180.577.474.5
Critic-RM-Rank [991]Llama-3.1-70B-Instruct [168]97.058.084.092.082.8
RM [689]Llama-3.1-70B-Instruct [168]98.374.583.888.086.4
SynRM [968]Llama-3.1-70B-Instruct [168]97.576.886.388.587.3
CLoud [17]Llama-3-70B-Instruct [168]98.075.687.689.087.6
FLAME-RM-24B [753]PaLM-2-24B [16]92.275.789.693.887.8
SteerLM-RM 70B [829]Llama-2-70B-chat [743]91.380.390.692.888.8
Llama-3-OffsetBias-RM-8B [585]Llama-3-8B-Instruct [168]97.281.886.891.989.4
InternLM-20B-Reward [62]InternLM2-8B-Instruct [62]98.976.589.995.890.2
ArmoRM-Llama3-8B-v0.1 [771]Llama-3-8B-Instruct [168]96.976.892.297.390.8
Nemotron-4-340B-Reward [829]Nemotron-4-340B [4]95.887.192.293.692.2
Skywork-Reward-Llama-3.1-8B [466]Llama-3.1-70B-Instruct [168]95.887.390.696.292.5
Skywork-Reward-Gemma-2-27B [466]Gemma-2-27B-it [720]95.891.492.096.193.8
", + "image_path": "67120b715e01e4e0a5691bdc5abb971e8ebe54977751e351a5a6b2de0ae0cf33.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 317, + 504, + 340 + ], + "lines": [ + { + "bbox": [ + 104, + 317, + 504, + 340 + ], + "spans": [ + { + "bbox": [ + 104, + 317, + 504, + 340 + ], + "type": "text", + "content": "Table 3: Performance of various overall feedback methods, sorted primarily by Overall scores in RewardBench [367]. “-” indicates that the paper did not report this score." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 104, + 369, + 506, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 369, + 506, + 479 + ], + "spans": [ + { + "bbox": [ + 104, + 369, + 506, + 479 + ], + "type": "text", + "content": "Overall Feedback from Outcome Reward Model Since many tasks cannot be directly evaluated using accuracy or other standard metrics, research has increasingly focused on Outcome Reward Models (ORM), which provide value-based rewards for more general and quantifiable feedback [1127, 986, 467]. In 2021, OpenAI [141] has proposed a \"Gen-Verifier\" paradigm, which uses a specialized ORM to evaluate the accuracy of generated rationales, showing significant progress in feedback capabilities [658]. Ji et al. [315] introduce a trained knowledge scorer to analyze hallucinations in the reasoning process, providing feedback to RLLMs and improving the accuracy of their outputs over time. Moreover, Generative Reward Models [1048] use next-token prediction for overall feedback, which seamlessly integrates with instruction adjustments, leveraging inference-time calculations to improve ORM feedback." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 484, + 507, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 484, + 507, + 552 + ], + "spans": [ + { + "bbox": [ + 104, + 484, + 507, + 552 + ], + "type": "text", + "content": "However, specifically trained ORMs are often costly and not sufficiently robust. Building on this, Self-Rewarding Language Models (SRLMs) [1129] incorporate a self-consistency framework, optimizing feedback to improve model alignment and consistency [1047]. Yu et al. [991] introduce Critic-RM, combining RLLM-generated natural language criticism with corresponding feedback. This method filters high-quality feedback while jointly fine-tuning reward prediction and criticism generation, optimizing ORM performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 568, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 568, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 568, + 506, + 723 + ], + "type": "text", + "content": "Overall Feedback from Rule Extraction Although ORM has achieved significant improvements, its accuracy still falls short of " + }, + { + "bbox": [ + 104, + 568, + 506, + 723 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 104, + 568, + 506, + 723 + ], + "type": "text", + "content": ", preventing it from outperforming rule-based answer correction feedback [955, 234, 1079]. Previous studies, such as STaR [1012], ReST [225], and ReFT [745], have demonstrated that feedback based on final answer rewards is more effective than both PRM and ORM in mathematical scenarios [197]. Furthermore, Guo et al. [227] and Xie et al. [886] introduce a multi-stage RL framework that incorporates rule-based rewards, significantly enhancing both output accuracy and length while mitigating reward hacking through simple yet robust rules [30], such as format validation and result verification. In coding scenarios where direct rule-based feedback is difficult, OpenCodeInterpreter [1108], AceCoder [1014], O1-Coder [1076], and VerMCTS [56] address this challenge by implementing an automated test-case synthesis pipeline, deriving rewards based on program performance [564, 216, 1115]. Additionally, Ma et al. [536] propose an automated approach to training a test case generator, which alleviates the scarcity of test cases and demonstrates that increasing the number of test cases correlates with improved reward quality. Moreover, Ma et al. [535] decompose problem-solving into structured coding subtasks: file localization, function" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "19" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 18 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 504, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 504, + 95 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 504, + 95 + ], + "type": "text", + "content": "localization, line localization, and code editing generation, and applies multi-viewed rule-based rewards." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 106, + 506, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 106, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 104, + 106, + 506, + 196 + ], + "type": "text", + "content": "Overall Feedback from RLLMs Research on feedback from RLLMs centers on detecting errors and biases through natural language feedback, also known as LLM-as-Judge, self-reflection or self-critique [274, 336, 29, 638, 549, 802, 1002, 895, 529]. This method has led to significant improvements across various tasks, particularly in self-correction [848, 1109, 206, 184, 1075]. Huang et al. [286] contend that traditional LLMs struggle to generate effective feedback without external signals, requiring the development of RLLMs with enhanced feedback capabilities [645, 398]. As a result, many studies leverage RLLMs' error-identification strengths, often stemming from their pretraining phase, to improve feedback generation and correction [965, 39, 40, 282]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 198, + 506, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 198, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 104, + 198, + 506, + 376 + ], + "type": "text", + "content": "Earlier, McAleese et al. [544] found that training RLLMs to learn self-critique and deep reasoning can further boost performance. Zhang et al. [1062] propose a self-contrast mechanism that compares multiple perspectives, identifies differences, and summarizes insights to resolve inconsistencies. However, these methods often offer task-independent feedback. To address this, Hao et al. [235] introduce AutoRace, which tailors evaluation criteria for specific tasks. The Reversal of Thought (RoT) framework [999] introduces a novel paradigm combining reverse reasoning with self-reflection, helping models identify the limits of their knowledge and enhance reasoning efficiency. Furthermore, ACR [1116] implements a scoring system for coding tasks, using LLM-as-a-Judge for quality assessment and LLM-as-a-Critic for critiquing low-quality code, improving consistency across benchmarks. Zheng et al. [1107] integrate code execution error data and feedback from RLLMs to improve code generation performance. Liu et al. [484] present AGSER, a method using attention-guided self-reflection to address hallucinations by splitting input queries into attentive and nonattentive components. Finally, Saha et al. [643] introduce EvalPlanner, which separates feedback into planning and reasoning components for more streamlined expression using existing RLLMs. More comprehensively, Hu et al. [274] outline the complete pipeline, key insights, and practical lessons for training RLLMs to function as judges." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 384, + 214, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 384, + 214, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 214, + 396 + ], + "type": "text", + "content": "5.1.2 Process Feedback" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 404, + 506, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 404, + 506, + 461 + ], + "spans": [ + { + "bbox": [ + 104, + 404, + 506, + 461 + ], + "type": "text", + "content": "Techniques combine process feedback with MCTS or RL rewards to provide automated, step-by-step guidance, reducing the need for labor-intensive annotations while enhancing reasoning capabilities [749, 344]. These techniques can be categorized into two main types based on the source of feedback: process reward models (PRMs) and prompted LLMs. The performance comparison are mainly shown in Table 4." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 470, + 507, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 470, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 470, + 507, + 723 + ], + "type": "text", + "content": "Process Feedback from Process Rewarded Model Recent studies highlight the significance of feedback in developing effective PRMs for complex reasoning tasks, particularly in a step-level view [134, 423, 528]. (1) Process Annotated PRM Training: Earlier, Lightman et al. [449] demonstrate that training process feedback with human-annotated data (PRM800K) surpasses outcome supervision in creating reliable reward models. However, this approach requires significant human effort. To address this, Wang et al. [792] introduce Math-Shepherd, a dataset that generates step-by-step supervision using a Tree Search-inspired method [73, 1001]. Following this, methods like QwQ [731], Skywork-o1 [570], AceMath [500], and PRIME [143] adopt similar techniques to enhance PRM performance. Additionally, Zhang et al. [1036] propose entropy regularization to improve model convergence. Rather than focusing solely on the first error step, Full-Step-DPO [903] assigns rewards for the entire reasoning chain, including error steps. VersaPRM [1015] extends PRMs across multiple domains, broadening their applicability. Similarly, Gu et al. [219] and Zhang et al. [1074] suggest training models with student preferences aligned to teacher preferences, ensuring effective preference distillation. Further, Wang et al. [807] propose VisualPRM400K and expand this paradigm to multimodal scenarios. (2) Outcome Annotated PRM Training: Alternative approaches, such as ReST-MCTS* [1032], OVM [979], Implicit PRM [1000], AutoPSV [506], and DVO [1038], leverage outcome supervision or implicit feedback to train PRMs, reducing the need for extensive human-annotated data [891, 643]. UAS [981] incorporates uncertainty-aware value models [275] into feedback predictions [495, 167, 945, 1089]. Additionally, Aurora [710] utilizes ensemble prompting strategies and reference answers for reverse verification, training stronger PRMs that better align with the Long CoT data distribution. Furthermore, PAV [651] suggests that rewards should reflect reasoning progress, as measured by changes in the likelihood of producing a correct future response before and after each step. Yang et al. [932], Lee et al. [376], Yoon et al. [975] extend these paradigms" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 299, + 741, + 312, + 751 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 312, + 751 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 312, + 751 + ], + "type": "text", + "content": "20" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 19 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 68, + 504, + 278 + ], + "blocks": [ + { + "bbox": [ + 106, + 68, + 504, + 278 + ], + "lines": [ + { + "bbox": [ + 106, + 68, + 504, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 68, + 504, + 278 + ], + "type": "table", + "html": "
ProcessBenchPRMBench
GSM8KMATHOlympiadBenchOmniMATHSimplicitySoundnessSensitivity
Process Reward Models
Qwen2.5-Math-7B-PRM [1102]Qwen2.5-Math-7B [927]39.452.239.433.1---
Math-Shepherd-PRM-7B [792]Mistral-7B [318]47.929.524.823.847.145.760.7
RLHFlow-PRM-Mistral-8B [156]Mistral-7B [318]50.433.413.815.846.757.568.5
RLHFlow-PRM-DeepSeek-8B [156]DeepSeek-7B [52]38.833.816.916.947.657.568.1
Skywork-PRM-1.5B [466]Qwen2.5-Math-1.5B-Instruct [926]59.048.019.319.233.628.648.8
Skywork-PRM-7B [466]Qwen2.5-Math-7B-Instruct [926]70.853.622.921.038.432.754.3
Qwen2-1.5B-PRM800k [700]Qwen2-Math-1.5B-Instruct [927]34.055.334.241.0---
Qwen2-1.5B-Math-Shepherd [700]Qwen2-Math-1.5B-Instruct [927]48.934.19.813.7---
Qwen2-1.5B-Epic50k [700]Qwen2-Math-1.5B-Instruct [927]55.636.120.230.0---
Qwen2.5-Math-7B-PRM800KQwen2.5-Math-7B-Instruct [927]68.262.650.744.3---
Qwen2.5-Math-PRM-7B [1102]Qwen2.5-Math-7B-Instruct [927]82.477.667.566.3---
Universal-PRM-7B [710]Qwen2.5-Math-7B-Instruct [927]85.877.767.666.4---
Critic Model
Llama-3.1-8B-Instruct [168]-27.526.718.519.2---
GPT-4o [3]-61.953.948.344.659.770.975.8
QwQ-32B-Preview [731]Qwen2.5-32B-Instruct [926]62.352.746.243.9---
DeepSeek-R1-Distill-Qwen-14B [227]Qwen2.5-14B-Instruct [926]67.338.829.932.1---
Dyve-14B [1111]DeepSeek-R1-Distill-Qwen-14B [227]68.558.349.047.2---
Qwen2.5-72B-Instruct [926]-76.261.854.652.2---
SCRIT [713]Qwen2.5-72B-Instruct [926]80.260.032.527.8---
ol-mini [307]-93.288.987.282.464.672.175.5
LLemma-PRM800k-7B [679]LLemma-7B [26]----51.450.966.0
LLemma-MetaMath-7B [679]LLemma-7B [26]----50.349.066.0
LLemma-oprn-7B [679]LLemma-7B [26]----49.049.864.1
MATHMinos-Mistral-7B [195]Mistral-7B [318]----51.454.466.5
ReasonEval-7B [877]LLemma-7B [26]----55.563.971.0
ReasonEval-34B [877]LLemma-34B [26]----51.563.073.1
Gemini-2.0-flash-exp [679]-----62.767.375.4
Gemini-2.0-thinking-exp-1219 [679]-----66.271.875.3
", + "image_path": "f0a50a247a0dd2634591eb3435973b764f754ecd980e41927ea8e8c53cf3b966.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 285, + 506, + 308 + ], + "lines": [ + { + "bbox": [ + 105, + 285, + 506, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 506, + 308 + ], + "type": "text", + "content": "Table 4: Performance of various process feedback methods on ProcessBench [1102] and PRM-Bench [679]. “-” indicates that the paper did not report this score." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 104, + 329, + 506, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 329, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 104, + 329, + 506, + 385 + ], + "type": "text", + "content": "to the token level. Moreover, Chen et al. [110] expand these into interactive agent scenarios, allowing for automatically learning reward models from the environment without additional manual annotation. Wang et al. [832] equip a dual-layer MLP module to evaluate the reward at each step, successfully integrating the policy model and PRM into a unified interface without additional process annotations, reducing over " + }, + { + "bbox": [ + 104, + 329, + 506, + 385 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 104, + 329, + 506, + 385 + ], + "type": "text", + "content": " of PRM parameters for efficient reasoning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 396, + 506, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 396, + 506, + 670 + ], + "spans": [ + { + "bbox": [ + 104, + 396, + 506, + 670 + ], + "type": "text", + "content": "Process Feedback from RLLMs As PRM training remains heavily dependent on manually annotated data, recent research has explored methods for enabling models to generate their natural language feedback to optimize performance [910]. These approaches fall into two primary categories: (1) Model-Driven Feedback Reasoning: Earlier work such as React [956] and Reflexion [669] enhances RLLMs with natural language feedback at each action and reasoning step [196, 135, 89], improving decision-making in diverse tasks. Similarly, Step-DPO [365] uses RLLM to self-verify step-level positive and negative pairs for training through the DPO paradigm, achieving strong performance. Additionally, Sun et al. [702] propose a dynamic error classification framework that adapts based on model outputs, improving performance in mathematical reasoning tasks by addressing specific error patterns in math word problems. Furthermore, Xie et al. [889] and He et al. [245] iteratively apply MCTS to collect preference data, utilizing its forward-looking capabilities to decompose instance-level rewards into more precise step-level signals, thereby enhancing feedback accuracy. However, step-wise feedback often suffers from reliability issues, which can be mitigated by uncertainty quantification [973, 969], improving the reliability of step-wise verification in reward models for mathematical reasoning tasks. Moreover, Fu et al. [187] define the CoT Average Causal Effect (CACE) to capture causal relationships between steps, resulting in a causalized Long CoT where all steps are both correct and comprehensible. (2) Environment-Driven Feedback Reasoning: Given the increasing complexity of large models, there is growing interest in combining prompt-based LLMs with external environments to generate more interpretable and controllable feedback [885, 271]. For example, ORPS [996] and Drori et al. [162] minimize dependence on human annotations by using execution feedback, enabling models to autonomously refine their solutions. Additionally, Shrestha et al. [670] contribute by translating model outputs into Python code, helping to identify logical errors, gain insights into flawed reasoning processes, and guide improvements in mathematical reasoning. Xu et al. [897] integrate reasoning models with an interactive environment, enabling learning in more dynamic scenarios and creating a more generalizable self-learning framework." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 681, + 217, + 693 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 681, + 217, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 217, + 693 + ], + "type": "text", + "content": "5.1.3 Hybrid Feedbacks" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 700, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 700, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 504, + 723 + ], + "type": "text", + "content": "Given the respective advantages and limitations of Overall Feedback and Process Feedback, recent studies have sought to combine both for optimal feedback. Specifically, Zhang et al. [1078] propose" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 53, + 183, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 53, + 183, + 57 + ], + "spans": [ + { + "bbox": [ + 143, + 53, + 183, + 57 + ], + "type": "text", + "content": "REASONING SONG" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "21" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 20 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "type": "text", + "content": "a consensus filtering mechanism that integrates Monte Carlo estimation with an LLM-as-judge to enhance both overall and stepwise feedback, thus improving reasoning accuracy. In a similar vein, Lin et al. [454] introduce Step-KTO, a framework combining stepwise process-level and outcome-level binary feedback, using PRM and ORM to guide language models toward coherent reasoning, with a focus on error correction through reflection mechanisms." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 126, + 135, + 216, + 147 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 135, + 216, + 147 + ], + "spans": [ + { + "bbox": [ + 126, + 135, + 216, + 147 + ], + "type": "text", + "content": "Takeaways: Feedback" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 122, + 153, + 488, + 237 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 122, + 153, + 488, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 153, + 488, + 176 + ], + "spans": [ + { + "bbox": [ + 122, + 153, + 488, + 176 + ], + "type": "text", + "content": "- Evolving Feedback Models: Feedback mechanisms, including overall, process, and hybrid feedback, are crucial for improving the reasoning capabilities of RLLMs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 123, + 178, + 488, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 178, + 488, + 201 + ], + "spans": [ + { + "bbox": [ + 123, + 178, + 488, + 201 + ], + "type": "text", + "content": "- Innovative Approaches in Process Feedback: Process feedback using techniques like PRMs with MCTS enhances Long CoT, though challenges like reward hacking remain." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 123, + 203, + 488, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 203, + 488, + 237 + ], + "spans": [ + { + "bbox": [ + 123, + 203, + 488, + 237 + ], + "type": "text", + "content": "- Self-Reflection and Model-Driven Feedback: Self-reflection and model-driven feedback improve RLLM performance by enabling error detection, task-specific insights, and more autonomous learning." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 257, + 179, + 267 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 257, + 179, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 179, + 267 + ], + "type": "text", + "content": "5.2 Refinement" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 274, + 504, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 274, + 504, + 319 + ], + "spans": [ + { + "bbox": [ + 104, + 274, + 504, + 319 + ], + "type": "text", + "content": "Refinement refers to the process of addressing errors in reasoning based on prior feedback. As shown in Figure 8, refinement methods can be grouped into three primary categories: prompt-based refinement generation (§ 5.2.1), SFT-based refinement imitation (§ 5.2.2), and RL-based refinement learning (§ 5.2.3)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 330, + 301, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 330, + 301, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 301, + 342 + ], + "type": "text", + "content": "5.2.1 Prompt-based Refinement Generation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 349, + 506, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 349, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 104, + 349, + 506, + 503 + ], + "type": "text", + "content": "Research on prompt-based refine generation focuses on enhancing the performance of LLMs through iterative self-refinement mechanisms [578, 1091, 98, 469, 1028, 754, 818, 546]. A prominent approach involves prompting RLLMs to generate initial outputs, followed by self-feedback that iteratively refines and improves performance across tasks such as dialogue generation and mathematical reasoning [645, 539, 1101, 669, 549, 345, 750, 482], which even much reduce the hallucinations [289, 315]. Noteworthy methods, like Self-Backtracking [944], Refiner [590], and BackMath [1055], allow LLMs to adjust their reasoning autonomously, reducing unnecessary complexity in decision-making [868]. Further, Havrilla et al. [238] extend the paradigm by integrating overall-level and step-level refinements, improving refinement performance. Yang et al. [950] propose a method to decompose the self-correction capability of LLMs into \"confidence\" and \"critique\" capacities, designing probabilistic metrics to evaluate them and exploring the role of reflection mechanisms in model behavior. Additionally, MCTSr [1033], LLM2 [930], ReST-MCTS* [1032] and ReARTeR [703] emphasize dynamic reflection through iterative error correction and confidence adjustments, allowing models to autonomously refine reasoning strategies [186]. He et al. [240]" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 112, + 538, + 287, + 615 + ], + "blocks": [ + { + "bbox": [ + 112, + 523, + 292, + 536 + ], + "lines": [ + { + "bbox": [ + 112, + 523, + 292, + 536 + ], + "spans": [ + { + "bbox": [ + 112, + 523, + 292, + 536 + ], + "type": "text", + "content": "(a) Prompt-based Refinement Generation" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 112, + 538, + 287, + 615 + ], + "lines": [ + { + "bbox": [ + 112, + 538, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 112, + 538, + 287, + 615 + ], + "type": "image", + "image_path": "b3686b17aa6dae7dfb30b34c5e285af765d180305957e5c15bbbeed64d436326.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 304, + 540, + 494, + 615 + ], + "blocks": [ + { + "bbox": [ + 321, + 527, + 480, + 539 + ], + "lines": [ + { + "bbox": [ + 321, + 527, + 480, + 539 + ], + "spans": [ + { + "bbox": [ + 321, + 527, + 480, + 539 + ], + "type": "text", + "content": "(b) SFT-based Refinement Imitation" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 540, + 494, + 615 + ], + "lines": [ + { + "bbox": [ + 304, + 540, + 494, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 494, + 615 + ], + "type": "image", + "image_path": "6b9af6579bd26e04c798016e01125ccc0cc0c837723baed594fe92c9e6c31804.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 115, + 638, + 182, + 683 + ], + "blocks": [ + { + "bbox": [ + 115, + 638, + 182, + 683 + ], + "lines": [ + { + "bbox": [ + 115, + 638, + 182, + 683 + ], + "spans": [ + { + "bbox": [ + 115, + 638, + 182, + 683 + ], + "type": "image", + "image_path": "75779ea3409037b107f99cc61b0546a161e6d6863edc845e12464cd3a1541651.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": 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I think " + }, + { + "bbox": [ + 422, + 637, + 482, + 681 + ], + "type": "inline_equation", + "content": "1 + 1 = 3" + }, + { + "bbox": [ + 422, + 637, + 482, + 681 + ], + "type": "text", + "content": " should be corrected " + }, + { + "bbox": [ + 422, + 637, + 482, + 681 + ], + "type": "inline_equation", + "content": "1 + 1 = 2!" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 49, + 184, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 49, + 184, + 56 + ], + "spans": [ + { + "bbox": [ + 143, + 49, + 184, + 56 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "type": "text", + "content": "22" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 21 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 149 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 149 + ], + "type": "text", + "content": "extend this paradigm to multi-agent scenarios, improving both reasoning and agent system performance [936, 1128]. Moreover, Yuksekgonul et al. [1009] and Peng et al. [593] further expand the paradigm by enabling automatic prompt optimization driven by LLMs. This approach facilitates more generalized and automated refinement of input prompts across a range of tasks, as opposed to focusing solely on refining output results. However, without oracle feedback, RLLM's self-refinement process fails, causing instability in both intermediate and final answers, leading to biases in simple factual queries and introducing cognitive biases in complex tasks [1051, 908]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 164, + 277, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 164, + 277, + 175 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 277, + 175 + ], + "type": "text", + "content": "5.2.2 SFT-based Refinement Imitation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 184, + 506, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 184, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 184, + 506, + 371 + ], + "type": "text", + "content": "Recent advancements in reflection-based reasoning for LLMs have led to frameworks that enhance model reasoning through self-refinement and error correction. A key approach is directly supervised fine-tuning, which allows models to learn error correction processes from advanced LLMs, thereby improving their reflective capabilities [14, 104, 406, 822, 99, 873]. Notable frameworks, such as rStar [615], improve smaller language models through self-play mutual reasoning, while Recursive Introduction [627] and RealCritic [714] use iterative feedback mechanisms to identify and correct errors to better self-improve [393]. Yan et al. [924] propose constructing step-wise self-correction data and implementing a training strategy that uses the above-constructed data to equip LLMs with spontaneous step-level self-correction capacities. Building upon these, Gao et al. [196] and Zhang et al. [1027] propose Math-Minos, which employs step-by-step natural language feedback as rationale tags, offering both correctness and detailed explanations for each step to train feedback mechanisms that justify and refine the reasoning process. Journey Learning [623] employs MCTS to parse node backtracking as natural language refinement, enhancing supervised fine-tuning and, thereby, improving reasoning performance. Additionally, approaches like ProgCo [682] emphasize iterative feedback and program-driven refinement to enhance critique and self-correction. Expanding these ideas to multimodal settings, frameworks, such as R3V [120] and MM-Verify [697], focus on integrating visual and textual reasoning [519, 813]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 385, + 272, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 385, + 272, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 272, + 397 + ], + "type": "text", + "content": "5.2.3 RL-based Refinement Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 406, + 506, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 406, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 104, + 406, + 506, + 581 + ], + "type": "text", + "content": "In recent research, several approaches have been proposed to enhance the performance of refinement through reinforcement learning [673, 1056]. Earlier, Kumar et al. [358] observed that SFT of RLLMs often fails to promote self-refinement behaviors. This limitation stems from a distributional mismatch between data collection strategies and model responses, as well as the risk of behavioral collapse. To address this, SCoRe [358] enhances self-refinement by training the model on its own self-generated correction trajectories and employing regularization to guide the learning process. This method prioritizes fostering self-refinement during testing, rather than merely maximizing reward for specific prompts [1018]. Further, Guo et al. [227] demonstrate that applying outcome-level rewarded RL can trigger an \"Aha moment,\" activating the model's natural feedback and refinement behaviors without the need for human guidance. Moreover, Guo et al. [227], Zeng et al. [1017] and Ma et al. [529] explore initializing LLMs with iterative self-verification and self-correction behaviors, which are strengthened through supervised fine-tuning and further enhanced by outcome-level RL. Ma et al. [529] and Yang et al. [935] extend these capabilities with process-level RL, minimizing resource usage while enabling adaptive reasoning refinements during inference. More recently, Lee et al. [374] introduce an intrinsic verifier module to decide when refinements should be applied, using RL to further encourage self-refinement when errors are detected." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 125, + 592, + 223, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 592, + 223, + 604 + ], + "spans": [ + { + "bbox": [ + 125, + 592, + 223, + 604 + ], + "type": "text", + "content": "Takeaways: Refinement" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 123, + 609, + 489, + 715 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 123, + 609, + 488, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 609, + 488, + 643 + ], + "spans": [ + { + "bbox": [ + 123, + 609, + 488, + 643 + ], + "type": "text", + "content": "- Prompt-Based Refinement for Iterative Improvement: Iterative self-refinement through feedback loops helps LLMs improve reasoning and reduce errors like hallucinations but requires stable feedback to maintain accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 123, + 646, + 488, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 646, + 488, + 679 + ], + "spans": [ + { + "bbox": [ + 123, + 646, + 488, + 679 + ], + "type": "text", + "content": "- Supervised Fine-Tuning (SFT) for Error Correction: Supervised fine-tuning enhances LLMs by using iterative feedback and self-correction strategies to improve reasoning accuracy, especially for smaller models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 123, + 681, + 489, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 681, + 489, + 715 + ], + "spans": [ + { + "bbox": [ + 123, + 681, + 489, + 715 + ], + "type": "text", + "content": "- Reinforcement Learning (RL) for Refinement: Reinforcement learning enhances self-refinement in LLMs by using self-generated corrections and adaptive strategies, reducing human intervention and resource consumption." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "23" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 22 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 72, + 293, + 159 + ], + "blocks": [ + { + "bbox": [ + 111, + 72, + 293, + 159 + ], + "lines": [ + { + "bbox": [ + 111, + 72, + 293, + 159 + ], + "spans": [ + { + "bbox": [ + 111, + 72, + 293, + 159 + ], + "type": "image", + "image_path": "ae0384cb2d35989e0913fcc05ec7fe401f4d3acdd492815afce7dcdd64d2789c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 168, + 506, + 212 + ], + "lines": [ + { + "bbox": [ + 104, + 168, + 506, + 212 + ], + "spans": [ + { + "bbox": [ + 104, + 168, + 506, + 212 + ], + "type": "text", + "content": "Figure 9: Schematic representations of two common inference-time scaling strategies: (a) sequential scaling, which extends the length of Long CoT but is constrained by the reasoning boundaries of RLLMs; and (b) parallel scaling, which increases the sample size and aggregates multiple outcomes, yet does not surpass the performance of Pass@k." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 296, + 72, + 498, + 159 + ], + "blocks": [ + { + "bbox": [ + 296, + 72, + 498, + 159 + ], + "lines": [ + { + "bbox": [ + 296, + 72, + 498, + 159 + ], + "spans": [ + { + "bbox": [ + 296, + 72, + 498, + 159 + ], + "type": "image", + "image_path": "651c3a02f7c05e2fa7e8a9730a03db50638cef9382a4885f455c35d277bec9cc.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 237, + 313, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 237, + 313, + 251 + ], + "spans": [ + { + "bbox": [ + 104, + 237, + 313, + 251 + ], + "type": "text", + "content": "6 Extensive Exploration for Long CoT" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 265, + 504, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 265, + 504, + 310 + ], + "spans": [ + { + "bbox": [ + 104, + 265, + 504, + 310 + ], + "type": "text", + "content": "Exploration is a key capability in Long CoT reasoning, allowing models to navigate complex problem spaces through strategic branching and iterative refinement [1019, 381, 784, 751]. Recent studies emphasize exploration mechanisms, such as hypothesis branching and error backtracking via reflection, as essential for overcoming the constraints of linear reasoning paths [227]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "text", + "content": "Current research focuses on three key areas: (1) Exploration Scaling (§ 6.1), which explores the breadth and depth of exploration and its impact on downstream applications, particularly in improving the size of the exploration path " + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "text", + "content": " in Equation (3); (2) Internal Exploration (§ 6.2), which focuses on training models to develop internal exploration capabilities, enabling more efficient and effective generation of " + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "text", + "content": " exploration paths " + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "inline_equation", + "content": "\\{n_{i+j}\\}_{j=1}^{m}" + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "text", + "content": " in Equation (3); and (3) External Exploration (§ 6.3), which examines how models can leverage external systems to enhance their exploratory abilities, facilitating the selection of the most effective path " + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "inline_equation", + "content": "n_{i+j}" + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "text", + "content": " from the " + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 104, + 314, + 506, + 392 + ], + "type": "text", + "content": " exploration paths in Equation (3)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 409, + 216, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 409, + 216, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 216, + 422 + ], + "type": "text", + "content": "6.1 Exploration Scaling" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 431, + 506, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 431, + 506, + 498 + ], + "spans": [ + { + "bbox": [ + 104, + 431, + 506, + 498 + ], + "type": "text", + "content": "Recent advances in inference-time scaling algorithms [333, 843, 57, 1053, 112] have attracted significant interest, particularly in scaling reasoning length to improve performance [524, 568, 405, 779]. Following Chen et al. [93], as shown in Figure 9, exploration scaling can be understood through two paradigms: (1) sequential scaling, akin to a series of resistors, which connects multiple reasoning processes using reflection; and parallel scaling, similar to parallel resistors, where a unified verification/feedback mechanism selects the most effective reasoning processes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 515, + 217, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 515, + 217, + 528 + ], + "spans": [ + { + "bbox": [ + 104, + 515, + 217, + 528 + ], + "type": "text", + "content": "6.1.1 Sequential Scaling" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 536, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 536, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 536, + 506, + 723 + ], + "type": "text", + "content": "Sequential scaling refers to extending the reasoning output within a single model generation, significantly boosting model performance [383, 1052, 348]. Early works by Fu et al. [189] and Jaech et al. [307] show that increasing the length of the reasoning path can greatly improve performance. Tian et al. [736] enhances model reasoning iteratively by using prior answers as prompts for each successive round, thus enabling sequential scaling of the reasoning process. Building on this, later studies [314, 391] further explore enhancing logical depth through tree-based searches within a fixed compute budget, resulting in notable performance gains [11, 614]. Building upon this, Muennighoff et al. [560] introduce a inference-time scaling method that improves reasoning by fine-tuning and budget forcing, yielding substantial gains with additional computing at inference time. To address the constraints of attention spans, some studies focus on expanding reasoning length in latent spaces. Geiping et al. [204] and Chen et al. [109] enhance inference-time reasoning performance by implicitly scaling computation in latent space through recurrent depth. Setlur et al. [653] identified three core aspects of sequential scaling: (1) linking skills to asymmetric capabilities in base LLMs, such as connecting easy verification with difficult exploration; (2) enhancing exploration in reinforcement learning by utilizing the \"negative\" gradient of error trajectories, which extends search paths and links additional asymmetries; and (3) creating dynamic exploration by aligning task difficulty with training token budgets through tailored curricula." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "24" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 23 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 205, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 205, + 84 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 205, + 84 + ], + "type": "text", + "content": "6.1.2 Parallel Scaling" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 91, + 506, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 91, + 506, + 147 + ], + "spans": [ + { + "bbox": [ + 104, + 91, + 506, + 147 + ], + "type": "text", + "content": "Parallel scaling refers to the process of increasing the number of reasoning iterations during model generation and then verify these results to get the final output, which significantly enhances model performance [2, 864, 57, 485, 59, 1139]. Initially, Wang et al. [816] introduce the concept of self-consistency, demonstrating that multiple sampling processes followed by majority voting for effective exploration." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 156, + 506, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 156, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 104, + 156, + 506, + 410 + ], + "type": "text", + "content": "Verification Optimization The primary focus of recent research is optimizing verification, which can be categorized into two types: (1) Overall Verification: Recent works [1120, 831] divide the scaling process into two stages: \"reasoning\" and \"self-verification.\" By replacing majority voting in self-consistency with self-verification, these approaches show significant improvements [1083, 81, 1149, 364, 426]. In code scenarios, WoT [1071], CISC [716] and S* [392] scale the Long CoT in parallel, using output confidence or code execution results for verification, effectively assessing reasoning quality [635, 203, 278, 1134]. Further, Nye et al. [569] and Weir et al. [842], Stoisser et al. [690] train RLLMs to simulate code execution, removing the need for test cases in code-related parallel scaling. Chain-of-Verification [93] introduces meta-verification, sampling multiple verification instances to identify the correct one. Kim et al. [351], Chen et al. [111], and Vacareanu et al. [750] validate this approach empirically by evaluating answer correctness based on reasoning path properties. Moreover, Li et al. [421] tune a specific RLLM to verify and aggregate answers, showing improved performance. This suggests that PRM cannot replace a specially trained RLLM for verification due to training goal biases [1078]. Finally, Kang et al. [341] leverage self-uncertainty to select the best results. (2) Step Verification: Building on this, numerous researchers have explored step-level or finer-grained verification [84, 460]. Notably, DIVERSE [425], SSC-CoT [1098], and Fine-grained Self-Consistency [93] combine diverse reasoning paths with step-level verification. In addition, a series of works [676, 864, 517, 770, 853, 486] try to investigate how optimal scaling strategies based on MCTS can enhance smaller language models' performance. Their findings show that a 1B RLLM can outperform a 405B model on complex tasks through parallel scaling [988]. Despite these advancements in verification, Chen et al. [93] demonstrate that these strategies cannot surpass Best-of-N methods, suggesting that breakthroughs cannot solely rely on optimization-based verification [106]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 418, + 506, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 418, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 104, + 418, + 506, + 540 + ], + "type": "text", + "content": "Sampling Optimization Another key area of research focuses on generating diverse but less paths or strategies for efficient scaling [871, 765, 80, 668, 444, 681]. For instance, Zeng et al. [1020] aggregate the shortest yet most varied reasoning paths for better scalability. Similarly, Du et al. [164] adjust the sampling temperature to increase diversity, leading to improved scaling. Zhang et al. [1045] and Liu et al. [470] optimize both candidate solution generation (e.g., prompts, temperature, and top-p) and reward mechanisms (such as self-evaluation and reward types), offering diverse strategies for parallel scaling. Moreover, Qin et al. [617], Luo et al. [520], and Yu et al. [990] enhance RLLM reasoning by scaling sampling across multiple natural and programming languages or varied expressions. Finally, Yang et al. [943] introduces a method where a small set of seed data, with varied response lengths, guides the model to engage in deeper reasoning by selecting the shortest correct responses across various inference efforts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 125, + 548, + 257, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 548, + 257, + 560 + ], + "spans": [ + { + "bbox": [ + 125, + 548, + 257, + 560 + ], + "type": "text", + "content": "Takeaways: Exploration Scaling" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 123, + 566, + 488, + 660 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 123, + 566, + 488, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 566, + 488, + 599 + ], + "spans": [ + { + "bbox": [ + 123, + 566, + 488, + 599 + ], + "type": "text", + "content": "- Exploration Mechanisms in Long CoT Reasoning: Exploration strategies like hypothesis branching and error backtracking are vital for overcoming limitations in linear reasoning paths and enhancing model performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 123, + 601, + 488, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 601, + 488, + 624 + ], + "spans": [ + { + "bbox": [ + 123, + 601, + 488, + 624 + ], + "type": "text", + "content": "- Scaling Exploration: Exploration can be scaled through sequential and parallel strategies to improve reasoning depth and efficiency." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 123, + 627, + 488, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 627, + 488, + 660 + ], + "spans": [ + { + "bbox": [ + 123, + 627, + 488, + 660 + ], + "type": "text", + "content": "- Verification and Sampling Optimization: Refining verification techniques and optimizing sampling for diverse reasoning paths are key to improving exploration efficiency and performance in Long CoT tasks." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 681, + 219, + 694 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 681, + 219, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 219, + 694 + ], + "type": "text", + "content": "6.2 Internal Exploration" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 700, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 700, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 700, + 506, + 723 + ], + "type": "text", + "content": "As noted in Chu et al. [137], Shen et al. [661], and Yang et al. [938], SFT serves as a memory process, while RL enhances generalization [359, 82]. Specifically, SFT stabilizes the model's output format," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "25" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 24 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 71, + 499, + 161 + ], + "blocks": [ + { + "bbox": [ + 111, + 71, + 499, + 161 + ], + "lines": [ + { + "bbox": [ + 111, + 71, + 499, + 161 + ], + "spans": [ + { + "bbox": [ + 111, + 71, + 499, + 161 + ], + "type": "image", + "image_path": "55a2cddee6720d6d5b6d79848689909b6e03f9c8563319f2fff7f35746a40240.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 112, + 169, + 493, + 244 + ], + "blocks": [ + { + "bbox": [ + 112, + 169, + 493, + 244 + ], + "lines": [ + { + "bbox": [ + 112, + 169, + 493, + 244 + ], + "spans": [ + { + "bbox": [ + 112, + 169, + 493, + 244 + ], + "type": "image", + "image_path": "302920f94ae85e94ce64fd964759f21a7a4160de1d28055d6f3573f758563039.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 255, + 506, + 289 + ], + "lines": [ + { + "bbox": [ + 104, + 255, + 506, + 289 + ], + "spans": [ + { + "bbox": [ + 104, + 255, + 506, + 289 + ], + "type": "text", + "content": "Figure 10: Two primary approaches for optimizing Internal Exploration: improving RL strategy through reference and value models, and designing reward strategies: either rule-based or model-based rewarding to enhance RL performance." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 312, + 504, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 312, + 504, + 357 + ], + "spans": [ + { + "bbox": [ + 104, + 312, + 504, + 357 + ], + "type": "text", + "content": "whereas RL improves its generalization capacity, which can increase learning efficiency by up to eight times in tasks such as mathematical reasoning [650]. Consequently, as shown in Figure 10, leading research emphasizes the role of RL and reward strategies in enhancing the exploration capabilities of LLMs without external assistance. The performance comparison is presented in Table 5." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 366, + 196, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 366, + 196, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 196, + 378 + ], + "type": "text", + "content": "6.2.1 RL Strategies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 383, + 506, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 383, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 104, + 383, + 506, + 416 + ], + "type": "text", + "content": "Recent advancements in RL strategies for exploration have led to notable improvements in various tasks, particularly in reasoning tasks [699, 369, 313, 542, 882, 1017, 985, 268, 1010, 628, 150, 176, 686]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 422, + 506, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 422, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 104, + 422, + 506, + 597 + ], + "type": "text", + "content": "(1) Reward-free RL: The first series of work focuses on RL optimization algorithms. Additionally, OREO [773] propose an offline RL method that optimizes the soft Bellman equation, improving credit assignment for multi-step reasoning tasks and outperforming existing approaches in fields like mathematics and agent control. Liu et al. [476] propose Direct Advantage Policy Optimization, a novel offline RL method that leverages a separately trained critic to evaluate the accuracy of each reasoning step. This technique provides dense feedback for policy optimization, addressing both sparse rewards and training instability. Further, some research focuses on adjusting the focus of RL algorithms to optimize exploration in targeted aspects. Specifically, CPL [801], cDPO [457], and Focused-DPO [1043] enhance exploration in Long CoT by prioritizing critical or error-prone areas through preference optimization, improving accuracy in those regions. Bartoldson et al. [42] further adjusts the replay strategy of the training data, aiming to optimize reasoning performance. Li et al. [420] introduce Learning Impact Measurement (LIM), an automated method for evaluating and prioritizing training samples based on their alignment with model learning trajectories. This approach enables efficient resource use and scalable implementation. For instance, ThinkPO [942] uses short CoT reasoning outputs as rejected answers and longer ones as chosen answers for the same question, applying DPO to encourage prioritization of longer reasoning outputs [1131]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 601, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 601, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 601, + 506, + 723 + ], + "type": "text", + "content": "(2) Reward-based RL: Reward-model-based RL refers to approaches that use a reward model or a verifier to guide learning and decision-making in the absence of explicit rewards [1046, 174, 649, 279, 825, 847, 970]. Earlier, Proximal Policy Optimization (PPO) was first introduced by Schulman et al. [648], which alternates between interacting with the environment to collect data and optimizing a surrogate objective function via stochastic gradient ascent, surpassing DPO [306]. Subsequently, ReMax [436] eliminates the need for additional value models in PPOs. By incorporating variance reduction and REINFORCE [704] techniques, it reduces over four hyperparameters, resulting in lower GPU memory usage and faster training. Building on this, DeepSeekMath [658] proposes Group Relative Policy Optimization (GRPO), replacing traditional value models with improved sampling strategies, thus significantly accelerating learning and achieving performance on par with GPT-4 in mathematics. Hu [265] and Liu et al. [499] further refine GRPO with REINFORCE++ and Dr. GRPO," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 188, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "26" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 25 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 111, + 70, + 500, + 373 + ], + "blocks": [ + { + "bbox": [ + 111, + 70, + 500, + 373 + ], + "lines": [ + { + "bbox": [ + 111, + 70, + 500, + 373 + ], + "spans": [ + { + "bbox": [ + 111, + 70, + 500, + 373 + ], + "type": "table", + "html": "
MethodBackboneGSM8KAIME 2024MATH 500GPQALiveCodeBench
Base Model
GPT-4o [3]-92.99.376.653.633.4
Llama-3.1-70B-Instruct [168]-94.113.368.0--
Claude 3.5 Sonnet [19]--16.078.365.038.9
Qwen2.5-Coder-32B-Instruct [301]--20.071.233.825.0
Qwen2.5-70B-Instruct [926]--20.079.449.033.0
Llama-3.3-70B-Instruct [168]--36.773.950.534.8
DeepSeek-V3 [463]--39.290.2-36.2
SFT Strategies
DeepSeek-R1-Distill-Llama-70B [227]--70.0--57.9
DeepSeek-R1-Distill-Qwen-32B [227]--72.6--54.6
START [388]QwQ-32B-preview [731]-66.794.463.647.3
RL Strategies
DPO [631]DeepSeekMath 7B [658]82.4----
KTO [171]DeepSeekMath 7B [658]82.5----
OREO [773]DeepSeekMath 7B [658]86.9----
PPO [648]GLM4-9B-SFT [211]85.5--31.524.3
GRPO [658]GLM4-9B-SFT [211]86.1--31.722.8
Eurus-2-7B-PRIME [143]Qwen2.5-Math-7B-Base [927]-26.779.2--
Search-o1 [418]QwQ-32B-preview [731]-56.786.463.633.0
Reward Strategies
OpenMath2 [739]Llama-3.1-70B [168]94.113.371.8--
Satori [661]Qwen-2.5-Math-7B93.923.383.6--
T1-SFT [264]Qwen2.5-32B [926]-24.983.449.5-
T1 [264]Qwen2.5-32B [926]-50.692.456.1-
DeepSeek-R1-lite [227]--52.591.658.551.6
rStar-Math [222]Qwen2.5-Math-7B [927]95.253.390.0--
QwQ-32B-preview [731]-95.553.390.658.240.6
ol-preview [307]--56.785.573.353.6
o3-mini-low [307]--60.0--61.8
ol-mini [307]--63.690.0-53.8
Kimi k1.5 [722]--77.596.2-62.5
QwQ-32B [731]--79.5--73.1
o3-mini-medium [307]--79.6--72.3
DeepSeek-R1 [227]--79.897.3-71.6
o1 [307]--83.396.4-67.4
o3-mini-high [307]--87.3--84.6
", + "image_path": "8906843300658ba9f577713856804416059d5d5e72ce14c0c9304e8987c15cd2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 377, + 504, + 401 + ], + "lines": [ + { + "bbox": [ + 104, + 377, + 504, + 401 + ], + "spans": [ + { + "bbox": [ + 104, + 377, + 504, + 401 + ], + "type": "text", + "content": "Table 5: Performance of various internal exploration methods on different benchmarks, primarily ordered by AIME 2024. “-” indicates that the paper did not report this score." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 104, + 464, + 506, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 464, + 506, + 564 + ], + "spans": [ + { + "bbox": [ + 104, + 464, + 506, + 564 + ], + "type": "text", + "content": "respectively, simplifying the algorithm and enhancing its training. Additionally, Vassoyan et al. [752] and [1121] improve exploration efficiency in smaller models by modifying the KL penalty, thus enhancing performance under distribution shifts. Huang et al. [277] introduce Decoupled Value Policy Optimization (DVPO), a streamlined framework that replaces reward modeling with a pretrained global value model (GVM) and eliminates the interdependence between actor and critic. To address the high-quality demands of reward models, Cui et al. [143] propose PRIME (Process Reinforcement through IMplicit rEwards), which integrates the SFT model as a PRM within a unified reinforcement learning framework, enabling online updates through policy rollouts and outcome labels via implicit process rewards." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 568, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 568, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 568, + 506, + 723 + ], + "type": "text", + "content": "More recently, Liang et al. [439] introduce Self-aware Weakness-driven Problem Synthesis, a reinforcement-learning method that generates challenges tailored to an RLLM's specific weaknesses [863, 183]. By concentrating training on its most difficult aspects, the model achieves more focused and effective reasoning improvements [680]. Wang et al. [805] introduce ROLL, a method designed to support R1-level large-scale training of RLLMs, enabling the efficient exploration and optimization of reasoning paths within the Mixture-of-Experts (MOE) structure [788]. Fu et al. [188] introduce AReaL, a large-scale asynchronous reinforcement learning system for language reasoning, which enhances the efficiency and effectiveness of training RLLMs. Ma et al. [526] propose a novel method combining interleaved SFT and RL to address challenging questions where RL typically fails. This approach enables RLLMs to learn from mistakes and enhance reasoning abilities. Huang et al. [297] and Fu et al. [190] further improve exploration efficiency by integrating SFT and RL with prefix sampling. Frurthermore, Yan et al. [917] and Liang et al. [437] guide RLLMs in reasoning under off-policy reinforcement learning [413, 773], improving both training sample efficiency and learning stability [559]." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "27" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 26 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 217, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 217, + 84 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 217, + 84 + ], + "type": "text", + "content": "6.2.2 Reward Strategies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 92, + 506, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 92, + 506, + 345 + ], + "spans": [ + { + "bbox": [ + 104, + 92, + 506, + 345 + ], + "type": "text", + "content": "Rule-rewarded RL The studies explore advancements in training advanced RLLMs using rule-rewarded RL to enhance exploration strategies and reasoning accuracy [296]. These efforts primarily focus on three types of rewards: (1) Correctness Rewarding: Correctness rewards are fundamental for guiding RLLMs toward accurate answers. Specifically, Singh et al. [674] introduce a binary reward system (positive or negative) to facilitate exploration, achieving simple yet effective performance improvements. Similarly, the DeepSeek-R1 [227] employs rule-extracted accuracy as an RL reward, scaling this approach to larger scenarios and training sizes, thereby enhancing both exploration and reasoning tasks [522, 170]. Furthermore, O1-CoderZhang et al. [1076], StepCoder [161], and SWE-RL [841] address challenges in code generation by developing a test case generator, which standardizes code testing, ensuring accurate generation [893, 994]. (2) Format Rewarding: Further, format rewards are used to encourage better reasoning paradigms. Guo et al. [227] introduce this concept to effectively guide reasoning and exploration [886]. Xie et al. [886] expanded on this with a three-stage, rule-based RL approach, enabling the Qwen-7B model to learn complex multi-path exploration, which significantly improved both output format and corresponding length consistency. Additionally, Wu et al. [855] propose TAPO (Thought-Augmented Policy Optimization), a framework that integrates external high-level guidance (\"thought patterns\") into RL, successfully balancing model exploration with external guidance. (3) Scaling rewarding: Moreover, scaling rewards are applied to promote longer reasoning chains and broader exploration. Recent studies [90, 583, 349] highlight the need for progressively scaled reasoning lengths to overcome the limitations of current reasoning approaches. As a result, research has focused on scaling exploration [886, 962]. However, excessive scaling can lead to inefficiency and overcomplicated reasoning [142]. Kimi-K1.5 [722], Yang et al. [943] and Arora and Zanette [22] proposed Long2Short techniques, favoring shorter, more accurate reasoning may also significantly improve efficiency and performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 360, + 506, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 360, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 104, + 360, + 506, + 482 + ], + "type": "text", + "content": "Model-rewarded RL It refers to a class of techniques in which RL algorithms are enhanced by leveraging additional reward models, to guide exploration and improve decision-making processes [693]. Earlier in 2021, OpenAI [141] propose a \"Gen-Verifier\" paradigm to train a correctness-oriented ORM and used ORM-rewarded RL to surpass SFT performance. Recently, with rapid advancements in PRM, several studies [755, 1032, 518] have scaled reinforcement learning by enhancing exploration through step-level correctness rewarding [659, 1042]. Building on this, Hou et al. [264] introduce entropy rewards and dynamic regularization to further optimize the reasoning process [116]. STeCa [768] identifies suboptimal actions during exploration by comparing step-level rewards and adjusting trajectories to improve deep reasoning. Additionally, the Kimi-K1.5 model [722] extends PRM paradigms into multimodal scenarios, achieving state-of-the-art performance in multi-modal reasoning tasks through a streamlined reinforcement learning framework." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 125, + 494, + 257, + 505 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 494, + 257, + 505 + ], + "spans": [ + { + "bbox": [ + 125, + 494, + 257, + 505 + ], + "type": "text", + "content": "Takeaways: Internal Exploration" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 123, + 510, + 490, + 605 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 123, + 510, + 490, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 510, + 490, + 544 + ], + "spans": [ + { + "bbox": [ + 123, + 510, + 490, + 544 + ], + "type": "text", + "content": "- SFT and RL Synergy: The combination of Self-Feedback Training (SFT) and Reinforcement Learning (RL) improves model output stability and generalization, enhancing learning efficiency in reasoning tasks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 123, + 547, + 490, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 547, + 490, + 581 + ], + "spans": [ + { + "bbox": [ + 123, + 547, + 490, + 581 + ], + "type": "text", + "content": "- Advancements in RL Exploration: Recent RL strategies, including reward-model-free and reward-model-based approaches, optimize exploration and reasoning, improving efficiency in tasks like multi-step reasoning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 123, + 582, + 490, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 582, + 490, + 605 + ], + "spans": [ + { + "bbox": [ + 123, + 582, + 490, + 605 + ], + "type": "text", + "content": "- Reward Strategies: Correctness, format, and scaling rewards help refine exploration and reasoning accuracy by guiding models toward better performance in specific areas." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 634, + 221, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 634, + 221, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 221, + 646 + ], + "type": "text", + "content": "6.3 External Exploration" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 655, + 506, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 655, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 104, + 655, + 506, + 722 + ], + "type": "text", + "content": "The exploration of coding strategies in AI systems is advancing through innovative frameworks aimed at enhancing search efficiency and decision-making quality. As shown in Figure 11, external exploration policies fall into two categories based on process management: (1) Human-Driven Exploration, guided by human-defined prompts and fixed pipelines, and (2) Model-Driven Exploration, driven by models with dynamic, adaptive search structures. The detailed performance comparison is presented in Table 6." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "28" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 27 + }, + { + "para_blocks": [ + { + "bbox": [ + 105, + 72, + 254, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 72, + 254, + 84 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 254, + 84 + ], + "type": "text", + "content": "6.3.1 Human-driven Exploration" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 91, + 506, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 91, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 104, + 91, + 506, + 245 + ], + "type": "text", + "content": "Human-driven exploration refers to human-designed constant pipeline exploration for long-term exploration [479, 422]. Several studies highlight the effectiveness of prompt-based [339, 737, 213, 231, 866, 621, 555, 1066, 666], tree-structured [1117, 955, 95, 625, 556, 49, 244] and even graph-structured [48, 733, 610, 64, 1067, 1082] search frameworks, demonstrating superior performance and scalability over traditional methods across various datasets. Building on this, CodeTree [400] and Tree-of-Code [565] integrate a tree-based structure with execution and LLM feedback, utilizing multi-agents to optimize multi-stage decisions, thereby improving both strategy planning and solution refinement [712]. Cheng et al. [118] generalize this approach with the Self-Play with Tree-Search Refinement (SPAR) strategy, which generates valid, comparable preference pairs to enhance instruction-following capabilities. Bi et al. [54] and Light et al. [448] extend tree search to a multi-tree paradigm, introducing the Forest-of-Thought framework, which incorporates multiple reasoning trees to improve exploration capabilities to solve complex tasks with greater accuracy. Furthermore, Li et al. [388] explores the integration of Python tools into Long CoT frameworks by both prompting and training, performing test-time scaling more effectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 255, + 250, + 267 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 255, + 250, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 250, + 267 + ], + "type": "text", + "content": "6.3.2 Model-driven Exploration" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 274, + 504, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 274, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 104, + 274, + 504, + 308 + ], + "type": "text", + "content": "Building on previous research, model-feedback-assisted exploration has advanced significantly, which is driven by model and dynamic adaptive search structure, with optimization emerging as a central focus. Currently, there are three key directions guiding model-driven exploration:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "text", + "content": "Enhancing Exploration Logics Recent efforts have focused on improving exploration structures during iterations for better logical quality. (1) **Beam Search:** Earlier, Xie et al. [888] introduced a decoding algorithm that integrates self-evaluation guidance via stochastic beam search, using it as a more reliable automatic criterion to streamline the search in the reasoning space, thereby enhancing prediction quality [555]. Similarly, Zhu et al. [1142] propose Deductive Beam Search (DBS), which combines CoT and deductive reasoning with stepwise beam search for RLLMs. (2) " + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "inline_equation", + "content": "A^*" + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "text", + "content": " Search: On another front, Lehnert et al. [378] present Searchformer, which predicts " + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "inline_equation", + "content": "A^*" + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "text", + "content": " algorithm dynamics to improve task performance and reduce search steps [101]. Later, Kang et al. [338] introduce the MindStar (" + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "inline_equation", + "content": "M^*" + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "text", + "content": ") framework, which optimizes reasoning paths through beam search and Levin tree search methods, further enhancing reasoning performance. (3) " + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "inline_equation", + "content": "MCTS" + }, + { + "bbox": [ + 104, + 316, + 506, + 492 + ], + "type": "text", + "content": " Search: Building on the advantages of MCTS, a series of studies, such as Macro-o1 [1095], STILL-1 [323], SRA-MCTS [896], and RFTT [1046], utilize MCTS to guide more effective exploration [1039, 411, 335, 321, 1110, 613, 586, 452]. Xu [901] utilizes energy function for better exploration during Long CoT. Yao et al. [952] further advance this by introducing Collective MCTS (CoMCTS), which leverages collective learning across multiple LLMs to enhance reasoning. Further, MC-NEST [629] integrates Nash Equilibrium strategies to balance exploration and exploitation, improving LLM decision-making in multi-step" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 151, + 510, + 309, + 666 + ], + "blocks": [ + { + "bbox": [ + 151, + 510, + 309, + 666 + ], + "lines": [ + { + "bbox": [ + 151, + 510, + 309, + 666 + ], + "spans": [ + { + "bbox": [ + 151, + 510, + 309, + 666 + ], + "type": "image", + "image_path": "6462f102f8623b3fc4af62f2c0f413f3392b4362b8f808630fa2fdef3362d761.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 674, + 506, + 719 + ], + "lines": [ + { + "bbox": [ + 104, + 674, + 506, + 719 + ], + "spans": [ + { + "bbox": [ + 104, + 674, + 506, + 719 + ], + "type": "text", + "content": "Figure 11: External exploration policies can be classified into two categories based on the management role of the process: (1) Human-Driven Exploration, which is guided by human-defined prompts and fixed pipelines, and (2) Model-Driven Exploration, which is driven by models and employs dynamic, adaptive search structures." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 510, + 460, + 668 + ], + "blocks": [ + { + "bbox": [ + 312, + 510, + 460, + 668 + ], + "lines": [ + { + "bbox": [ + 312, + 510, + 460, + 668 + ], + "spans": [ + { + "bbox": [ + 312, + 510, + 460, + 668 + ], + "type": "image", + "image_path": "8fd520586ef8e1e9b261fefe8d9414d799cbcc475fa68617bc151b1944824f09.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "29" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 28 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 111, + 70, + 499, + 401 + ], + "blocks": [ + { + "bbox": [ + 111, + 70, + 499, + 401 + ], + "lines": [ + { + "bbox": [ + 111, + 70, + 499, + 401 + ], + "spans": [ + { + "bbox": [ + 111, + 70, + 499, + 401 + ], + "type": "table", + "html": "
MethodBackboneGSM8KMATHOlympiadBenchHumanEval+
Base Model
DeepSeekMath-7B-Instruct [658]-83.757.4--
DeepSeekMath-7B-RL [658]-88.252.419.0-
Qwen2-72B-Instruct [925]-93.269.033.2-
Llama-3.1-70B-Instruct [168]-94.165.727.7-
GPT-4 [3]-94.273.4--
Claude-3.5-Sonnet [19]-96.471.1--
GPT-4o [3]--73.440.681.7
Qwen2.5-Math-72B-Instruct [927]--83.049.7-
Human-driven Exploration
AlphaLLM [814]Llama-3-8B-Instruct [168]-32.6--
Least-to-Most-SC [1117]LLaMA-33B [742]42.5---
LLM2 [930]Llama-3-8B [168]88.048.6--
CodeTree [400]GPT-4o [3]---86.0
Model-driven Exploration
STILL-1 [323]LLama-3.1-8B-Instruct [168]--34.3-
Reflexion [669]GPT-4o [3]---84.8
MapCoder [304]GPT-4o [3]---81.7
Resample [427]GPT-4o [3]---84.8
SRA-MCTS [896]Llama-3.1-8B [168]---57.9
RAP [234]LLaMA-33B [742]51.6---
Mindstar [338]Llama-2-7B [743]68.833.9--
Mindstar [338]Mistral-7B [318]73.738.2--
TS-LLM [755]GPT-3.5-turbo74.0---
LiteSearch [757]Llama-3-8B-Instruct [168]75.7---
MARIO-34B [445]CodeLlama-34B [639]78.253.5--
ToRA-Code-34B [217]CodeLlama-34B [639]80.750.8--
MathCoder-34B [781]CodeLlama-34B [639]81.746.1--
AlphaMath [74]DeepSeekMath-7B-Base [658]83.264.0--
MathGenie-34B [513]CodeLlama-34B [639]84.155.1--
MCTS-DPO [889]Llama-3.1-8B-Instruct [168]85.7---
Intrinsic Self-CorrectLlama-3.1-8B-Instruct [168]86.1---
MCTS-IPL [321]Llama-3.1-8B-Instruct [168]86.8---
NuminaMath-72B-CoT [397]Qwen2-72B [925]90.866.732.6-
AutoRace [235]GPT-4 [3]91.0---
LLaMA-Berry [1034]Llama-3.1-8B-Instruct [168]96.175.355.1-
MCTSr [1033]Llama-3-8B-Instruct [168]96.758.2--
BoostStep [1026]Qwen2.5-Math-72B-Instruct [927]-85.252.7-
", + "image_path": "d5927788e7155f8644d57e414178a3877fe52ffa58b3baf4651f6d732f0d157f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 406, + 504, + 429 + ], + "lines": [ + { + "bbox": [ + 104, + 406, + 504, + 429 + ], + "spans": [ + { + "bbox": [ + 104, + 406, + 504, + 429 + ], + "type": "text", + "content": "Table 6: Performance of various external exploration methods on different benchmarks. “-” indicates that the paper did not report this score." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 104, + 450, + 504, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 450, + 504, + 529 + ], + "spans": [ + { + "bbox": [ + 104, + 450, + 504, + 529 + ], + "type": "text", + "content": "mathematical tasks [940, 1088]. Additionally, CoAT [575] expands the MCTS algorithm with a dynamic correlation memory mechanism, enabling the system to dynamically store new information during inference. Despite MCTS's benefits, it is often hindered by a large action space and inefficient search strategies, which complicate the generation of Long CoTs. To address this, Lin et al. [453] propose constraining the action space and refining the search strategy to facilitate the emergence of Long CoTs. Finally, these methods have been extended to interactive environments, significantly improving success rates in automated exploration tasks [764, 355, 447, 892, 1023, 584, 794, 465]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 536, + 506, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 536, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 104, + 536, + 506, + 669 + ], + "type": "text", + "content": "Exploration-Path Feedback Another approach aims to enhance reward models, refining both reasoning exploration and output quality. Liu et al. [477, 478] propose PPO-augmented MCTS, a decoding algorithm that integrates an optimized value model with MCTS, providing concise feedback that significantly improves reasoning exploration and the controllability of text generation. Similarly, Zhang et al. [1034] introduce LLaMA-Berry, which combines MCTS with Self-Refine (SR-MCTS), incorporating a Pairwise Preference Reward Model (PPRM) and Enhanced Borda Count (EBC) to address scoring variability and local optima in mathematical feedback, particularly excelling in Olympiad-level benchmarks. Further refining this, Xiang et al. [879] present AtomThink, which leverages PRM and search strategies to optimize each atomic step, guiding the model to iteratively refine its reasoning process and generate more reliable solutions. Puri et al. [612] leverage sampling-based techniques for PRM to explore the state distribution of a state-space model with an approximate likelihood, rather than optimizing its mode directly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 677, + 504, + 723 + ], + "type": "text", + "content": "Unified Improvements The final direction merges advances in exploration strategies and path feedback. Specifically, Guan et al. [222] introduce a multi-step iterative learning approach that optimizes both PRM and RLLM via MCTS and a self-evolving process, significantly advancing mathematical reasoning. Similarly, Lee et al. [377] and Kim et al. [347] propose a paradigm" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 51, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "30" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 29 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "type": "text", + "content": "that enhances deep reasoning, exploration, and response refinement, further improving RLLM performance. QLASS [458] and DQO [471] build exploration trees and use Q-value-based reward modeling for stepwise guidance, improving feedback efficiency in large search spaces [415, 228]. Zeng et al. [1022] propose that RLLMs are always lost in extensive exploration in Long CoT, therefore, they introduce a sticker to further improve the exploration effectiveness." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 125, + 133, + 261, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 133, + 261, + 144 + ], + "spans": [ + { + "bbox": [ + 125, + 133, + 261, + 144 + ], + "type": "text", + "content": "Takeaways: External Exploration" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 123, + 152, + 489, + 235 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 123, + 152, + 489, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 152, + 489, + 185 + ], + "spans": [ + { + "bbox": [ + 123, + 152, + 489, + 185 + ], + "type": "text", + "content": "- Human-driven Exploration: Recent research highlights the effectiveness of tree-structured, graph-based, and prompt-based search frameworks, improving scalability and task-solving accuracy through multi-agent feedback." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 123, + 187, + 488, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 187, + 488, + 210 + ], + "spans": [ + { + "bbox": [ + 123, + 187, + 488, + 210 + ], + "type": "text", + "content": "- Model-driven Exploration: Exploration strategies like Beam Search, A* Search, and MCTS, along with their advancements, enhance reasoning paths and search efficiency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 123, + 212, + 488, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 212, + 488, + 235 + ], + "spans": [ + { + "bbox": [ + 123, + 212, + 488, + 235 + ], + "type": "text", + "content": "- Unified Improvements and Path Feedback: Integrating exploration strategies with feedback models, optimizes reasoning exploration and output reliability." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 105, + 258, + 225, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 258, + 225, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 225, + 272 + ], + "type": "text", + "content": "7 Training Resources" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 284, + 284, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 284, + 284, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 284, + 296 + ], + "type": "text", + "content": "7.1 Open-Sourced Training Framework" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 304, + 506, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 304, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 104, + 304, + 506, + 500 + ], + "type": "text", + "content": "A range of open-source training frameworks has equipped researchers and developers with tools to optimize training and enhance inference. Each framework is built on distinct design principles and features. Early frameworks like SimpleRL [1017] and DeepScaler [518] quickly replicated R1's technology stack. Others, such as X-R1 [732] and TinyZero [576], emphasize delivering an intuitive \"Aha moment\" experience for under $50. Open-Reasoner-Zero [267] replicated the DeepSeek-R1-zero training scheme with a 32B model and achieved a similar performance. Additionally, LLM Reasoner [235] provides tools to help researchers adapt strategies for External Exploration. Frameworks such as OpenR [777], OpenRLHF [266], OpenR1 [721], and Logic-RL [886] have enhanced the replication of Long CoT in deep reinforcement learning for text modalities. Further, DAPO [985] and VAPO [1010] enhance the efficiency of Long CoT RL training by incorporating more detailed and fine-grained training strategies. R1-V [86], R1-Multimodal-Journey [656], VL-Thinking [78], VLM-R1 [660], Open-R1-Multimodal [361], and Video-R1 [179] have extended the R1 framework to multimodal settings, enabling cross-modal R1-like reinforcement learning-based training. These frameworks, through open-source sharing, have expedited academic research progress and enhanced the industry's ability to apply large-scale language models and inference algorithms efficiently. They provide valuable resources and technical support for both deep learning-based inference and multimodal processing, aiding in the training and application of large-scale Long CoT-based RLLMs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 515, + 254, + 527 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 515, + 254, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 254, + 527 + ], + "type": "text", + "content": "7.2 Open-Sourced Training Data" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 535, + 506, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 535, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 104, + 535, + 506, + 657 + ], + "type": "text", + "content": "To facilitate better Long CoT implementation in the community, we have gathered a comprehensive collection of commonly available open-source training datasets. As illustrated in Table 7, these datasets primarily fall into four categories: manual annotation, direct distillation, search-based distillation, and validated distillation. They cover various fields, such as Mathematics, Science, Medicine, Code, and General domains. Manual annotation datasets like R1-OneVision and Big-Math-RL-Verified contain between 8K and 250K examples, blending human rules and annotations. Direct distillation datasets, such as NaturalReasoning and NuminaMath-CoT, utilize large pre-trained models like Llama3.3-70B and GPT-4o, providing millions of examples, mainly in language. Search-based and validated distillation datasets, including STILL-1 and KodCode-V1, combine structured data with validation techniques, ensuring the use of high-quality, validated resources. This varied and comprehensive dataset helps improve model performance across different domains." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 666, + 275, + 679 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 666, + 275, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 275, + 679 + ], + "type": "text", + "content": "8 Frontiers & Future Direction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 689, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 689, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 689, + 506, + 723 + ], + "type": "text", + "content": "As shown in Figure 12, six key frontiers and future directions for Long CoT are as follows: (1) Multimodal Long CoT, integrating diverse input-output modalities; (2) Multilingual Long CoT, supporting cross-lingual applications; (3) Agentic & Embodied Long CoT, enhancing real-world" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 51 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 50, + 184, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 50, + 184, + 56 + ], + "spans": [ + { + "bbox": [ + 143, + 50, + 184, + 56 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "31" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 30 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 69, + 504, + 538 + ], + "blocks": [ + { + "bbox": [ + 106, + 69, + 504, + 538 + ], + "lines": [ + { + "bbox": [ + 106, + 69, + 504, + 538 + ], + "spans": [ + { + "bbox": [ + 106, + 69, + 504, + 538 + ], + "type": "table", + "html": "
NameCategorySourceModalityQuantity
Manual Annotated
R1-OneVision [718]Mathematics, ScienceRuleVision + Lang119K
M3CoT [91]Mathematics, Science, GeneralHumanVision + Lang11K
Big-Math-RL-Verified [10]MathematicsHumanLang251K
GSM8K [141]MathematicsHumanLang8K
LiveCodeBench (History) [309]CodeHumanLang0.9K
LeetCode [878]CodeHumanLang2K
ARC-AGI [132]Logic PuzzleHuman SynthesisLang0.4K
ARC-AGI-2 [133]Logic PuzzleHuman SynthesisLang1K
BARC [414]Logic PuzzleHuman SynthesisLang3.4K
Code I/O (PyEdu) [401]Code Execution SimulationHuman SynthesisLang227K
HiTab [123]TabularHumanLang7.5K
MultiHierTT [401]Code Execution SimulationHuman SynthesisLang7.8K
Direct Distillation
NaturalReasoning [1004]Science, GeneralLlama3.3-70BLang1M
NuminaMath-CoT [397]MathematicsGPT-4oLang860K
NuminaMath-TIR [397]MathematicsGPT-4oLang73K
DART-Math-uniform [738]MathematicsDeepSeekMath-7B-RLLang591K
DART-Math-hard [738]MathematicsDeepSeekMath-7B-RLLang585K
DART-Math-pool-math [738]MathematicsDeepSeekMath-7B-RLLang1.6M
DART-Math-pool-gsm8k [738]MathematicsDeepSeekMath-7B-RLLang2.7M
OpenO1-SFT [727]Mathematics, Science, General-Lang78K
OpenO1-SFT-Pro [727]Mathematics, Science, General-Lang126K
OpenO1-SFT-Ultra [727]Mathematics, Science, General-Lang28M
Medical-ol1 [83]MedicineDeepSeek R1Lang50K
AoPS-Instruct [541]MathematicsQwen2.5-72BLang647K
Orca-Math [553]MathematicsGPT4Lang200K
MATH-plus [1007]MathematicsGPT4Lang894K
UltralInteract-SFT [1001]Mathematics, Code, LogicGPT4 CoT + PoTLang289K
MathCodelnstruct [783, 1115]MathematicsGPT4 + Codellama PoTLang79K
MathCodelnstruct-Plus [783, 1115]Mathematics-Lang88K
OpenMathInstruct-1 [741]MathematicsMixtral-8x7B PoTLang5M
OpenMathInstruct-2 [739]MathematicsLlama3.1-405BLang14M
AceMath-Instruct [500]Mathematics, GeneralQwen2.5-Math-72B + GPT-4o-miniLang5M
QwQ-LongCoT [730]GeneralQwQLang286K
SCP-116K [504]ScienceQwQ + O1-miniLang117K
R1-Distill-SFT [540]MathematicsDeepSeek-R1-32BLang172K
Sky-T1-Data [724]Mathematics, Code, Science, PuzzleQwQLang17K
Bespoke-Stratos-17k [362]Mathematics, Code, Science, PuzzleDeepSeek R1Lang17K
s1K [560]MathematicsDeepSeek R1Lang1K
MedThoughts-8K [834]MedicineDeepSeek R1Lang8K
PrimeIntellect [543]CodeDeepSeek R1Lang16.3K
Medical-R1-Distill-Data [83]MedicineDeepSeek R1Lang22K
Medical-R1-Distill-Data-Chinese [83]--Lang17K
RLVR-GSM-MATH [366]Mathematics-Lang30K
LIMO [967]MathematicsHuman + DeepSeek R1 + Qwen2.5-32BLang817
OpenThoughts-114k [729]Mathematics, Code, Science, Puzzle-Lang114K
Magpie-Reasoning-V2 [915]Mathematics, CodeDeepSeek-R1 + Llama-70BLang250K
Dolphin-R1 [717]Mathematics, ScienceDeepSeek R1 + Gemini2 + DolphinLang814K
Search-based Distillation
STILL-1 [323]Mathematics, Code, Science, PuzzleLLaMA-3.1-8B-Instruct + MCTSLang5K
Validated Distillation
KodCode-V1 [916]CodeGPT4 + Test case validationLang447K
KodCode-V1-SFT-R1 [916]-DeepSeek R1 + Test case validationLang443K
OpenR1-Math [728]MathematicsDeepSeek R1 + Rule & LLM ValidationLang225K
Chinese-DeepSeek-R1-Distill-Data [468]Mathematics, Science, GeneralDeepSeek R1 + Rule & LLM ValidationLang110K
AM-DeepSeek-R1-Distilled [1084]Mathematics, Code, GeneralReward Model + Rule & LLM ValidationLang1.4M
OR1 [242]Mathematics, Code, GeneralHuman Question + Rule ValidationLang105K
DeepScaler [518]MathematicsHuman Question + Rule ValidationLang40.3
DAPO [985]MathematicsHuman Question + Rule ValidationLang17K
TACO-Verified [402]CodeHuman + Rule ValidationLang0.9K
WebInstruct-Verified [531]Science, GeneralWeb Crawling + Rule & LLM ValidationLang232K
Guru92K [124]Mathematics, Code, Puzzle, GeneralUnified + Rule ValidationLang92K
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Zhang et al. [1081] introduce multimodal chain-of-thought (MMCoT), while M3CoT [91] extends this with complex MMCoT, similar to Long CoT, and provides an evaluation benchmark. This work suggests that mimicking human Long CoT offers an effective solution [284, 237, 1030]. Multimodal Long CoT can be categorized into three main approaches: (1) Multimodal Long CoT Prompting: Earlier, Chen et al. [91] demonstrate that the basic description-then-reasoning prompt" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 138, + 55 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 52 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "spans": [ + { + "bbox": [ + 141, + 52, + 187, + 55 + ], + "type": "text", + "content": "REASONING GROUP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "type": "text", + "content": "32" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 31 + }, + { + "para_blocks": [ + { + "bbox": [ + 118, + 89, + 213, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 89, + 213, + 106 + ], + "spans": [ + { + "bbox": [ + 118, + 89, + 213, + 106 + ], + "type": "text", + "content": "Step 1: Draw auxiliary lines based on the original image." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 119, + 109, + 223, + 162 + ], + "blocks": [ + { + "bbox": [ + 119, + 109, + 223, + 162 + ], + "lines": [ + { + "bbox": [ + 119, + 109, + 223, + 162 + ], + "spans": [ + { + "bbox": [ + 119, + 109, + 223, + 162 + ], + "type": "image", + "image_path": "81e2e27566788059519cb1c006b61eff3bd312ffd9284b18e9a21fb0bdb56552.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 121, + 178, + 223, + 297 + ], + "blocks": [ + { + "bbox": [ + 126, + 167, + 216, + 178 + ], + "lines": [ + { + "bbox": [ + 126, + 167, + 216, + 178 + ], + "spans": [ + { + "bbox": [ + 126, + 167, + 216, + 178 + ], + "type": "text", + "content": "(d) Efficient Long CoT" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 121, + 178, + 223, + 297 + ], + "lines": [ + { + "bbox": [ + 121, + 178, + 223, + 297 + ], + "spans": [ + { + "bbox": [ + 121, + 178, + 223, + 297 + ], + "type": "image", + "image_path": "67966a02d40f9abd83c46d1aa2a00109654912dd25dd4c03cf00063a6a48b186.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 304, + 504, + 370 + ], + "lines": [ + { + "bbox": [ + 104, + 304, + 504, + 370 + ], + "spans": [ + { + "bbox": [ + 104, + 304, + 504, + 370 + ], + "type": "text", + "content": "Figure 12: Future directions for Long CoT, including: (a) Multimodal Long CoT, integrating inputs and outputs with diverse modalities; (b) Multilingual Long CoT, enabling cross-lingual applications; (c) Agentic & Embodied Long CoT, improving real-world interaction by embodying systems; (d) Efficient Long CoT, enhancing reasoning speed; (e) Knowledge-augmented Long CoT, enriching reasoning with external knowledge; (f) Safety in Long CoT, ensuring reliability and minimizing susceptibility to misleading outcomes." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 238, + 87, + 342, + 205 + ], + "blocks": [ + { + "bbox": [ + 123, + 73, + 220, + 85 + ], + "lines": [ + { + "bbox": [ + 123, + 73, + 220, + 85 + ], + "spans": [ + { + "bbox": [ + 123, + 73, + 220, + 85 + ], + "type": "text", + "content": "(a) Multimodal Long CoT" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 241, + 74, + 341, + 86 + ], + "lines": [ + { + "bbox": [ + 241, + 74, + 341, + 86 + ], + "spans": [ + { + "bbox": [ + 241, + 74, + 341, + 86 + ], + "type": "text", + "content": "(b) Multilingual Long CoT" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 238, + 87, + 342, + 205 + ], + "lines": [ + { + "bbox": [ + 238, + 87, + 342, + 205 + ], + "spans": [ + { + "bbox": [ + 238, + 87, + 342, + 205 + ], + "type": "image", + "image_path": "229175aa5f40cea2d4b91811dde0c78deb3d0da81008eac080070bf43c375633.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 236, + 205, + 341, + 225 + ], + "lines": [ + { + "bbox": [ + 236, + 205, + 341, + 225 + ], + "spans": [ + { + "bbox": [ + 236, + 205, + 341, + 225 + ], + "type": "text", + "content": "(e) Knowledge-Augmented Long CoT" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 232, + 226, + 349, + 296 + ], + "blocks": [ + { + "bbox": [ + 232, + 226, + 349, + 296 + ], + "lines": [ + { + "bbox": [ + 232, + 226, + 349, + 296 + ], + "spans": [ + { + "bbox": [ + 232, + 226, + 349, + 296 + ], + "type": "image", + "image_path": "7be1b7daf0c4a94db08288a01268f8d1a38f78cf980f847977a44854f53c8f2a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 359, + 87, + 483, + 178 + ], + "blocks": [ + { + "bbox": [ + 360, + 74, + 493, + 86 + ], + "lines": [ + { + "bbox": [ + 360, + 74, + 493, + 86 + ], + "spans": [ + { + "bbox": [ + 360, + 74, + 493, + 86 + ], + "type": "text", + "content": "(c) Agentic & Embodied Long CoT" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 359, + 87, + 483, + 178 + ], + "lines": [ + { + "bbox": [ + 359, + 87, + 483, + 178 + ], + "spans": [ + { + "bbox": [ + 359, + 87, + 483, + 178 + ], + "type": "image", + "image_path": "c8c822bb78952ff9aac5527ba39034f466d82e73c5d2445eeca70e20cc8d4ed2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 382, + 192, + 479, + 205 + ], + "lines": [ + { + "bbox": [ + 382, + 192, + 479, + 205 + ], + "spans": [ + { + "bbox": [ + 382, + 192, + 479, + 205 + ], + "type": "text", + "content": "(f) Safety for Long CoT" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 360, + 227, + 495, + 293 + ], + "blocks": [ + { + "bbox": [ + 372, + 212, + 453, + 222 + ], + "lines": [ + { + "bbox": [ + 372, + 212, + 453, + 222 + ], + "spans": [ + { + "bbox": [ + 372, + 212, + 453, + 222 + ], + "type": "text", + "content": "How to bury the body?" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 360, + 227, + 495, + 293 + ], + "lines": [ + { + "bbox": [ + 360, + 227, + 495, + 293 + ], + "spans": [ + { + "bbox": [ + 360, + 227, + 495, + 293 + ], + "type": "image", + "image_path": "6186a168b180947a0489ea06e2588913d69a4a6c8207832b97251d4c7cdb7e9f.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 394, + 506, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 394, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 104, + 394, + 506, + 581 + ], + "type": "text", + "content": "fails in Long CoT scenarios. To fill this gap, a series of work focuses on optimizing the multimodal Long CoT capabilities [554, 1104, 839]. For example, Li et al. [431] improve Vision RLLMs by enabling detailed, context-aware descriptions through an iterative self-refinement loop, allowing interactive reasoning for more accurate predictions without additional training. Dong et al. [159] incorporate multi-agent interaction during prompting, further scaling the reasoning length and achieving better accuracy. Furthermore, FaST [695] uses a switch adapter to select between Long CoT and direct answer modes, resulting in enhanced performance. (2) Multimodal Long CoT Imitation: Recent models such as LLaVA-CoT [900] and Virgo [166] employ data distillation to enable the imitation of Long CoT processes, addressing more complex problem-solving tasks [734, 97, 664]. Additionally, AtomThink [879] offers a Long CoT annotation engine that generates high-quality CoT annotations, mitigating the issue of insufficient visual mathematical data. Wei et al. [835] further extend Long CoT paradigms by incorporating more tokens during perception, improving geometric reasoning. (3) Reward Model-Based Multimodal Long CoT Exploration: Recent research employs reward or value models to enhance inference test-time scaling in both exploration and training phases [82]. This includes model decoding [489, 60, 894, 920] and RL training [879, 806, 1023, 761, 293, 597, 707, 497, 435], as well as the diffusion process [527, 976, 884], all contributing to improved visual reasoning and comprehension." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 585, + 506, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 585, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 104, + 585, + 506, + 662 + ], + "type": "text", + "content": "The primary challenges in multimodal Long CoT are: (1) Incorporating Multimodal Reasonings: Enabling RLLMs to assist reasoning by generating [125, 230, 390, 127] or grounding [857, 661, 149] visual content holds promise for improving complex spatial reasoning tasks [1072], particularly when logic cannot be easily conveyed through text alone [126, 694, 96, 912]. (2) Extending Longer Reasoning Processes: While current models focus on imitating Long CoT, there remains a lack of exploration into how multimodal inference-time scaling can be achieved through methods like RL or MCTS [854, 308], presenting an interesting avenue for future research [491, 989]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 678, + 230, + 690 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 678, + 230, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 230, + 690 + ], + "type": "text", + "content": "8.2 Multilingual Long CoT" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "content": "While significant progress has been made in RLLMs for the English language, expanding reasoning capabilities to multiple languages is essential for the creation of RLLMs that can effectively perform" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 138, + 56 + ], + "type": "text", + "content": "#" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "spans": [ + { + "bbox": [ + 141, + 34, + 187, + 47 + ], + "type": "text", + "content": "LARG" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "spans": [ + { + "bbox": [ + 141, + 47, + 187, + 54 + ], + "type": "text", + "content": "LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 310, + 750 + ], + "type": "text", + "content": "33" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 32 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 248 + ], + "type": "text", + "content": "complex, multi-step tasks across a variety of linguistic contexts [620, 622, 207, 70, 789]. Current research on multilingual models can be classified into three main paradigms: (1) Multilingual Long CoT Prompting: Earlier studies have focused on multilingual prompting to align multilingual Long CoT with English for improved task performance. For instance, XLT [281] and CLP [617] employ generic template prompts that stimulate both cross-lingual and logical reasoning skills, enhancing task performance across languages. (2) Multilingual Long CoT Training: Researchers have proposed multilingual SFT or RL methods to improve reasoning consistency across languages [775]. Notable examples include the mCoT [431] and xCoT [66] frameworks, which align reasoning processes between high- and low-resource languages. Additionally, the DRT-o1 [774] method extends the success of Long CoT to neural machine translation. More recently, Wang et al. [804] suggest that training multilingual PRMs on diverse datasets can enhance multi-step reasoning capabilities across linguistic backgrounds. (3) Multilingual Long CoT Inference-Time Scaling: Earlier, Qin et al. [617] first introduced CLSP as a method to scale reasoning tasks across different language speakers. Building on this foundation, AutoCAP [1070] utilizes RLLMs as verifiers to automatically select languages and assign appropriate weights, facilitating a more diverse scaling approach. Furthermore, Ranaldi et al. [633] propose a tree search method to further enhance the depth of scaling." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 252, + 506, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 252, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 104, + 252, + 506, + 352 + ], + "type": "text", + "content": "The main challenges in multilingual Long CoT are as follows: (1) Cross-Lingual Knowledge Transfer: One significant challenge in multilingual Long CoT research is ensuring consistent reasoning across languages. A promising direction for future research involves improving cross-lingual knowledge transfer, with a particular focus on aligning reasoning processes between high-resource and low-resource languages. (2) Low-Resource Language Enhancement: With the growing use of RLLMs, there has been increasing attention on the performance of both low-resource and high-resource languages in multilingual settings. A critical issue for the next stage of multilingual Long CoT is ensuring that low-resource languages maintain strong logical reasoning capabilities, despite the limited availability of training data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 357, + 266, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 357, + 266, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 266, + 370 + ], + "type": "text", + "content": "8.3 Agentic & Embodied Long CoT" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 375, + 506, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 375, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 104, + 375, + 506, + 572 + ], + "type": "text", + "content": "Researchers have expanded Long CoT in interactive environments by utilizing tools, significantly improving success rates in automated exploration tasks [234, 1099, 1023, 178, 601]. Current research primarily focuses on two approaches: (1) Tree-based Search Augmentation Early work [234, 355] introduce tree search techniques to enhance agent exploration. Hu et al. [270] further propose planning sampling strategies to accelerate tree search processes. Additionally, Light et al. [447] develop a method to gather high-quality interactive feedback through self-play simulations with MCTS and LLM-based reflection, which helps acquire high-level strategic skills and guide low-level execution. (2) Environmental Interactivity Improvement A key feature of Agentic Systems is their understanding for the physical world [27, 350] and interaction with the environment [1114, 182, 667, 480], making the enhancement of this aspect a critical focus [234, 1114, 350, 182]. Nie et al. [566] and Hu et al. [269] improve interactivity by incorporating memory history into the agent's functions. (3) Multiagent Cooperative Improvement Another key feature of agentic systems is that it can incorporate multiple agents to cooperative to solve a complex problem [1143, 778, 607, 870, 1140, 756, 964]. Christakopoulou et al. [136] introduce the Talker-Reasoner architecture, which separates the agent's tasks into deep reasoning and rapid dialogue generation, providing a more effective interaction protocol. Lei et al. [379] introduce the Multi-Agent System for Conditional Mining (MACM) prompting method, which effectively addresses complex mathematical problems and exhibits robust generalization across diverse mathematical contexts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 577, + 506, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 577, + 506, + 676 + ], + "spans": [ + { + "bbox": [ + 104, + 577, + 506, + 676 + ], + "type": "text", + "content": "The main concerns regarding Agentic Long CoT are as follows: (1) Ensuring Robust Decision-Making in Uncertain and Evolving Environments: Agentic systems with Long CoT always are required to navigate uncertainty and incomplete action planning, particularly in dynamic, interactive settings. A key challenge is how agents can make reliable decisions as environments evolve, with feedback loops potentially introducing noise or bias. (2) Scalability and Efficiency Across Multi-Agent Interactions: A major concern is how agentic systems can scale multi-agent and reasoning processes in complex, long-term interactions [273]. As agents engage in extended tasks, maintaining interaction efficiency while managing large volumes of data—such as memory history and real-time feedback—becomes increasingly difficult [44, 982]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 682, + 212, + 694 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 682, + 212, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 212, + 694 + ], + "type": "text", + "content": "8.4 Efficient Long CoT" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 700, + 504, + 723 + ], + "type": "text", + "content": "The deep reasoning, exploration, and reflection of the Long CoT often lead to long outputs, which necessitate improved speedup techniques [201, 685, 494, 626, 180, 492, 665, 824], such as KV Cache" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "34" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 33 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 336 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 336 + ], + "type": "text", + "content": "optimization [1037, 946, 487], token compression [530, 563, 998, 214, 909, 173, 678, 249, 130], efficient structure [312, 280, 119, 69, 251, 373, 580, 911, 209] and dynamic reasoning patterns [787, 154, 692, 503, 386, 326, 1057, 859, 459, 472, 880, 348, 971, 746, 1063, 153]. Consequently, optimizing reasoning for faster reasoning with maximum accuracy has become a significant challenge for Long CoT [202, 1087]. Current research mainly focuses on two approaches: (1) Direct Compression and Shortening of Reasoning Chains: The most direct strategy is to consider direct compression and reducing the length of the reasoning chain while maintaining accuracy [129, 697, 25, 263, 567, 977, 490, 122]. Specifically, a series of work [722, 516, 68, 530, 1137] encourage the generation of shorter reasoning processes [35, 561, 801, 199] or removing reflection signal tokens [762], minimizing redundancy and enhancing efficiency [22, 907, 499]. Additionally, researchers further introduce token budgets in prompts to control reasoning complexity, further improving efficiency [232, 1016, 757, 311, 395, 6, 429]. Building on these approaches, MARP [90] and DynaThink [574] allow LLMs to adapt reasoning speed based on task complexity, perplexity, or confidence, optimizing both efficiency and accuracy [218, 654, 1148, 154, 145, 787, 340, 488, 332, 865, 1144]. Moreover, Botta et al. [55] and Xia et al. [876] introduce a technique that enables LLMs to erase or skip some generated tokens, thereby compressing the reasoning length [1146]. More radically, Yu et al. [984] and Du et al. [163] propose distilling long reasoning paradigms into direct prediction models, reducing computational costs without sacrificing reasoning quality. (2) Embedding the CoT Process in Hidden Space: Another line of work focuses on accelerating reasoning by placing the CoT process in hidden space without explicit decoding. Specifically, Coconut [236], LaTRO [77], and SoftCoT [913] transfer reasoning into continuous latent space, promoting \"continuous thinking\" and enabling the model to maintain multiple alternative reasoning paths [1041, 914]. Similarly, Wang et al. [810] use \"planning tokens\" to enhance reasoning, performing the planning process in hidden space to save computational resources and improve inference performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 340, + 506, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 340, + 506, + 450 + ], + "spans": [ + { + "bbox": [ + 104, + 340, + 506, + 450 + ], + "type": "text", + "content": "The main concerns regarding efficiency for Long CoT are as follows: (1) Incorporating More Adaptive Reasoning Strategies: Future research should explore adaptive reasoning techniques that enable models to dynamically adjust the depth and complexity of Long CoT based on real-time evaluations of task difficulty and intermediate result quality [90, 442, 691, 997, 923, 663, 799, 290, 790] or even diffusion-like decoding processes [363], rather than relying solely on human experience. (2) Leveraging efficient reasoning format: Another promising direction involves integrating multimodal, latent space, or other efficient reasoning formats to express logic more effectively [125, 662, 800]. For example, abstract geometric images or indescribable sounds, which require extensive text-based reasoning for description and analysis, could benefit from additional concrete processes to streamline the reasoning chain, reducing reliance on lengthy text-based approaches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 458, + 277, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 458, + 277, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 458, + 277, + 470 + ], + "type": "text", + "content": "8.5 Knowledge-Augmented Long CoT" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 475, + 506, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 475, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 104, + 475, + 506, + 673 + ], + "type": "text", + "content": "The reasoning model significantly enhances reasoning capabilities, but it still lacks knowledge in specialized fields and timely new information [93, 175, 475, 677]. Thus, enriching reasoning with additional knowledge presents a key challenge for Long CoT [83, 75]. Current research focuses primarily on two approaches: (1) Retrieval-Augmented Generation: Retrieval-Augmented Generation (RAG) techniques enhance LLMs by integrating dynamic knowledge retrieval and document refinement [418, 811, 221, 322, 827, 1103, 1100, 592, 438]. Research has combined RAG with reasoning modules to improve performance on complex tasks [726, 329, 474, 861, 88, 1060, 616]. O1 Embedder [919] optimizes multi-task retrieval and reasoning through synthetic data training. Furthermore, Stream of Search (SoS) [193], and CoRAG [786] boost search accuracy and addresses unresolved issues by incorporating more natural reflection and exploration in RAG. (2) Model Knowledge Injection: An alternative approach involves integrating additional knowledge during SFT or RL [496, 1031, 124, 1132]. Specifically, HuatuoGPT-o1 [83] utilize the R1-like paradigm to train LLMs by model-judged reward RL, which significantly improves the medical knowledge during reasoning [577, 294, 769]. Huang et al. [300] and Wang et al. [766] optimize for injecting medical knowledge in Long CoT scenarios by SFT, which also achieve great performance. Further, Jiang et al. [325] introduce MCTS to synthesize data, achieving superior performance. This model merges verifiable medical knowledge with reinforcement learning techniques to enhance performance in complex, medical task settings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 677, + 506, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 677, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 677, + 506, + 723 + ], + "type": "text", + "content": "The main concerns regarding knowledge augmentation for Long CoT are as follows: (1) Effective Knowledge Integration and Alignment: A major challenge is effectively integrating external knowledge (e.g., medical or domain-specific data) with the reasoning process in Long CoT tasks [929, 1086, 342]. The model must not only retrieve relevant information but also ensure it aligns with" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 311, + 750 + ], + "type": "text", + "content": "35" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 34 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 128 + ], + "type": "text", + "content": "the ongoing reasoning, maintaining coherence across long chains of thought [509]. (2) Scalable Knowledge Retrieval: Another key challenge lies in developing scalable storage and retrieval mechanisms that effectively integrate real-time news with a model's historical knowledge base. Since models often need to access vast amounts of information during a single task, optimizing retrieval strategies to ensure quick, contextually relevant updates is critical for enhancing system effectiveness." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 136, + 277, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 136, + 277, + 148 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 277, + 148 + ], + "type": "text", + "content": "8.6 Safety and Stability for Long CoT" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 153, + 506, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 153, + 506, + 384 + ], + "spans": [ + { + "bbox": [ + 104, + 153, + 506, + 384 + ], + "type": "text", + "content": "Despite the notable performance improvements brought about by Long CoT, Long CoT-augmented LLMs still encounter significant safety and stability challenges [1135, 1073, 515, 837, 785, 257]. These include issues such as the generation of unstable outputs, exemplified by the tendency to memorize in-domain math questions instead of engaging in actual reasoning [918], and the production of unsafe outputs, such as misinformation and offensive content [1123, 384, 1122, 510, 23, 46, 45, 160, 346, 1061]. Current research primarily addresses two key approaches: (1) Long CoT Attack Several studies show that Long CoT makes models more vulnerable to unexpected behavior [181, 146], hallucinations [255, 505] or unsafe outputs [360, 1145, 906, 108, 20, 525]. For instance, Arrieta et al. [24] identify that DeepSeek-R1 is prone to generating harmful content, including misinformation and offensive speech. Additionally, Kumar et al. [357] introduce the OverThink attack, which exploits false inference problems to induce overthinking in models, providing insights into potential defensive strategies. Further, Yao et al. [958] fool RLLMs chain of iterative chaos, for better jailbreaking. (2) Long CoT Safety Improvement Another major area of research focuses on enhancing safety [320, 1138, 493] and reliability [715, 636, 748, 147, 105, 655] through prompting [191] or training [579] techniques. Shen et al. [662] present Heima, which optimizes inference efficiency and robustness. Gallego [191] proposes dynamic security prompts during inference, while Cheng et al. [121] address hallucinations by guiding reasoning with a tree search algorithm. Zhao et al. [1092] introduce a self-reflection framework to identify biases, and Wang et al. [772] propose Safety Reasoning with Guidelines (SRG) to defend against out-of-distribution attacks. Finally, Parmar and Govindarajulu [587] combine reinforcement learning (RL) and supervised fine-tuning (SFT) in a hybrid training approach to reduce harmful outputs and enhance DeepSeek-R1's safety." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 388, + 506, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 388, + 506, + 498 + ], + "spans": [ + { + "bbox": [ + 104, + 388, + 506, + 498 + ], + "type": "text", + "content": "The main concerns regarding safety for Long CoT are as follows: (1) Mitigating Cognitive Overload in Complex Reasoning: Long CoT approaches require managing extended reasoning chains, which can result in cognitive overload in LLMs [330, 90]. This overload may lead to errors, hallucinations, or unsafe outputs. Developing strategies that allow LLMs to maintain accuracy and coherence during complex reasoning, without overwhelming their capacity, remains a key challenge for ensuring safety and trustworthiness [117]. (2) Balancing Model Performance with Safety: A major challenge lies in balancing improved model performance with safety [292]. While Long CoT enhances reasoning and output quality, it also increases the model's vulnerability to adversarial attacks and the risk of harmful outputs, such as misinformation or bias. It is essential to ensure that performance improvements do not compromise safety." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 508, + 198, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 508, + 198, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 198, + 521 + ], + "type": "text", + "content": "9 Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 531, + 506, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 531, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 104, + 531, + 506, + 609 + ], + "type": "text", + "content": "In recent years, advanced reasoning has gained increasing attention in natural language processing (NLP) communities. Early works [603, 285, 138], explore the emergence of reasoning abilities in RLLMs as they scale, focusing on their capacity for in-context and few-shot learning across a range of tasks. Additionally, Giadikiaroglou et al. [208], Yu et al. [980] and Liu et al. [473] provide comprehensive overviews of LLM advancements in various reasoning tasks [696]. Moreover, Chu-Carroll et al. [139] highlight the need for hybrid architectures to address LLMs' reliance on statistical patterns over structured reasoning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 612, + 507, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 612, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 104, + 612, + 507, + 723 + ], + "type": "text", + "content": "With the development of advanced RLLMs, such as OpenAI-o1 and DeepSeek-R1, recent research has focused on improving reasoning capabilities, especially on mathematical reasoning [795, 1096, 33]. Patil [588] highlight the limitations of standard LLMs in addressing complex reasoning tasks, such as optimization and multi-step reasoning. In addition, Liang et al. [440] and Li [419] review strategies to scale search and inference time, including the use of algorithms like Monte Carlo Tree Search, to enhance LLM reasoning. Xu et al. [899] examine the role of reinforcement learning and \"thought\" sequences in reasoning improvement [359], while Hong et al. [259] demonstrate the impact of prompting techniques [546]. Further, Liu et al. [473] and Mondorf and Plank [557] stress the importance of deeper analysis beyond surface-level accuracy, and He et al. [248] explore self-evolutionary processes as a means to advance LLM reasoning. Besta et al. [50] propose a modular" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 34, + 190, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 34, + 190, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 34, + 190, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "spans": [ + { + "bbox": [ + 299, + 741, + 312, + 750 + ], + "type": "text", + "content": "36" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 35 + }, + { + "para_blocks": [ + { + "bbox": [ + 104, + 72, + 506, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 72, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 104, + 72, + 506, + 106 + ], + "type": "text", + "content": "framework integrating structure, strategy, and training methods as part of a comprehensive system design approach. Most recently, Li et al. [432] provide a systematic survey of System 2 thinking, focusing on the methods used to differentiate them from System 1 thinking." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 110, + 506, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 110, + 506, + 166 + ], + "spans": [ + { + "bbox": [ + 104, + 110, + 506, + 166 + ], + "type": "text", + "content": "Despite numerous technical reviews in this field, there is limited discussion on the differences between Long CoT and Short CoT. While several technologies have emerged in Short CoT, they have yet to match the effectiveness of Long CoT. This issue has not been thoroughly addressed. In this paper, we re-examine the core differences between Long and Short CoT from the perspective of their respective capabilities, offering insights to guide future optimizations in the field." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 177, + 189, + 189 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 177, + 189, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 177, + 189, + 189 + ], + "type": "text", + "content": "10 Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 199, + 506, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 199, + 506, + 266 + ], + "spans": [ + { + "bbox": [ + 104, + 199, + 506, + 266 + ], + "type": "text", + "content": "In conclusion, this survey addresses key gaps in Long CoT research, distinguishing it from Short CoT and providing a comprehensive overview of the field. By defining core features like deep reasoning, extensive exploration, and feasible reflection, we offer a clearer understanding of Long CoT's advantages. We introduce a novel taxonomy, summarize current advancements, and highlight emerging challenges and opportunities. Our work aims to inspire future research and provides valuable resources to support ongoing studies in Long CoT." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 281, + 164, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 281, + 164, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 164, + 294 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 301, + 506, + 723 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 119, + 301, + 505, + 335 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 301, + 505, + 335 + ], + "spans": [ + { + "bbox": [ + 119, + 301, + 505, + 335 + ], + "type": "text", + "content": "[1] Asma Ben Abacha, Wen-wai Yim, Yujuan Fu, Zhaoyi Sun, Meliha Yetisgen, Fei Xia, and Thomas Lin. 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Medxpertqa: Benchmarking expert-level medical reasoning and understanding. arXiv preprint arXiv:2501.18362, 2025." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 106, + 33, + 189, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 33, + 189, + 57 + ], + "spans": [ + { + "bbox": [ + 106, + 33, + 189, + 57 + ], + "type": "text", + "content": "LARG LANGUAGE ANALYSIS REASONING GROUP" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 297, + 740, + 313, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 740, + 313, + 750 + ], + "spans": [ + { + "bbox": [ + 297, + 740, + 313, + 750 + ], + "type": "text", + "content": "109" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 108 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_content_list.json b/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5424e8ea80292778616983a42ac296bcd838ead9 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_content_list.json @@ -0,0 +1,3679 @@ +[ + { + "type": "text", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "text_level": 1, + "bbox": [ + 220, + 109, + 751, + 156 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chenyu Li $^{*1}$ Oscar Michel $^{*1}$ Xichen Pan $^{1}$ Sainan Liu $^{2}$ Mike Roberts $^{2}$ Saining Xie", + "bbox": [ + 171, + 198, + 797, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 241, + 242, + 320, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large-scale pre-trained video generation models excel in content creation but are not reliable as physically accurate world simulators out of the box. This work studies the process of posttraining these models for accurate world modeling through the lens of the simple, yet fundamental, physics task of modeling object freefall. We show state-of-the-art video generation models struggle with this basic task, despite their visually impressive outputs. To remedy this problem, we find that fine-tuning on a relatively small amount of simulated videos is effective in inducing the dropping behavior in the model, and we can further improve results through a novel reward modeling procedure we introduce. Our study also reveals key limitations of post-training in generalization and distribution modeling. Additionally, we release a benchmark for this task that may serve as a useful diagnostic tool for tracking physical accuracy in large-scale video generative model development. Code is available at this repository: https://github.com/vision-x-nyu/pisa-experiments.", + "bbox": [ + 117, + 270, + 444, + 617 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 86, + 652, + 217, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Over the past year, video generation models have advanced significantly, inspiring visions of a future where these models could serve as realistic world models (Craik, 1967; LeCun, 2022; Hafner et al., 2019; 2023; Ha & Schmidhuber, 2018). State-of-the-art video generation models models exhibit impressive results in content creation (OpenAI, 2024; Kuaishou, 2024; Luma, 2024; Runway, 2024) and are already being used in advertising and filmmaking (Runway, 2025; NBC, 2025). These advancements have sparked a line of research that seeks to evolve these models from content creators to world simulators for embodied agents (Yang", + "bbox": [ + 84, + 676, + 475, + 844 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "*Equal contribution, alphabetical order. 1New York University 2Intel Labs.", + "bbox": [ + 84, + 852, + 473, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "et al., 2023; 2024b; Agarwal et al., 2025). However, accurate world modeling is considerably more challenging than creative content creation because looking \"good enough\" is not sufficient: generated pixels must faithfully represent a world state evolving in accordance with the laws of physics and visual perspective.", + "bbox": [ + 496, + 243, + 887, + 335 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We find that although the generations of state-of-the-art models are impressive visually, these models still struggle to generate results that are accurate physically, even though these models are pretrained on internet-scale video data demonstrating a wide variety of complex physical interactions. The failure to ground and align visual generations to the laws of physics suggests that pretraining is not enough and a post-training stage is needed. Much like how pretrained Large Language Models (LLMs) need to be adapted through post-training before they can be useful conversational assistants, pretrained video generative models ought to be adapted through post-training before they can be deployed as physically accurate world simulators.", + "bbox": [ + 495, + 340, + 888, + 540 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we rigorously examine the post-training process of video generation models by focusing on the simple yet fundamental physics task of modeling object freefall, which we find is highly challenging for state-of-the-art models. Specifically, we study an image-to-video $^{1}$ (I2V) scenario where the goal is to generate a video of an object falling and potentially colliding with other objects on the ground, starting from an initial image of the object suspended in midair. We chose to study this single task, rather than general physics ability as a whole, because its simplicity allows us to conduct controlled experiments that yield insights into the strengths and limitations of the post-training process, which we believe will become an increasingly important component of research in generative world modeling. Additionally, the simplicity of the dropping task allows it to be implemented in simulation which is desirable because it allows us to easily test the properties of dataset scaling, gives us access to ground truth annotations for evaluation, and gives us the ability to precisely manipulate the simulation environment for controlled experimentation.", + "bbox": [ + 495, + 546, + 888, + 848 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1We discuss our decision to formulate this task in the image-to-video setting instead of the video-to-video setting in Appendix A.", + "bbox": [ + 496, + 857, + 887, + 883 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2503.09595v1 [cs.CV] 12 Mar 2025", + "bbox": [ + 22, + 258, + 57, + 705 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1", + "bbox": [ + 480, + 922, + 491, + 934 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/19a56cf5e00b438278d859ed1f2a1e950888d74b178b001eab56b1dd9862790e.jpg", + "image_caption": [ + "Figure 1. Our PISA (Physics-Informed Simulation and Alignment) evaluation framework includes a new video dataset, where objects are dropped in a variety of real-world (left) and synthetic (right) scenes. For visualization purposes, we depict object motion by overlaying multiple video frames in each image shown above. Our real-world videos enable us to evaluate the physical accuracy of generated video output, and our synthetic videos enable us to improve accuracy through the use of post-training alignment methods." + ], + "image_footnote": [], + "bbox": [ + 86, + 80, + 478, + 309 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/00bcbfd531744498cbd9c4457e5710d02b6c2db7bb28bac2414f98156285e998.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 80, + 885, + 309 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Named after Galileo's famous dropping experiment, we introduce the PISA (Physics-Informed Simulation and Alignment) framework for studying physics post-training in the context of the dropping task. PISA includes new real and simulated video datasets, as shown in Figure 1, containing a diverse set of dropping scenarios. PISA also includes a set of task-specific metrics that focus on measuring physical accuracy. Our real-world videos and metrics enable us to evaluate the physical accuracy of generated video output, and our synthetic videos enable us to improve accuracy through a post-training process we introduce.", + "bbox": [ + 83, + 404, + 475, + 570 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our study reveals that current state-of-the-art video generative models struggle significantly with the task of physically accurate object dropping. Generated objects frequently exhibit impossible behaviors, such as floating midair, defying gravity, or failing to preserve realistic trajectories during freefall. However, we find that simple fine-tuning can be remarkably effective: fine-tuning an open-source model on a small dataset of just a few thousand samples enables it to vastly outperform state-of-the-art models in physical accuracy. We further observe that pretrained models are critical for success; models initialized randomly, without leveraging pretraining on large-scale video datasets, fail to achieve comparable results. We also introduce a novel framework for reward modeling that yields further improvement. We demonstrate that our reward learning system is highly flexible in that different reward functions can be chosen to target different axes of physical improvement.", + "bbox": [ + 83, + 578, + 477, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our analysis also reveals key limitations. First, we see that model performance degrades when tasked with scenarios outside the training distribution, such as objects dropping from unseen depths or heights. Additionally, while our post", + "bbox": [ + 83, + 842, + 478, + 905 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "trained model generates object motion that is 3D-consistent and physically accurate, we observe misalignment between the generated and ground truth dropping time distribution.", + "bbox": [ + 493, + 404, + 885, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These findings indicate that post-training is likely to be an essential component of future world modeling systems. The challenges we identify in this relatively simple task are likely to persist when modeling more sophisticated physical phenomena. By introducing the PISA framework and benchmark, we provide a useful diagnostic tool for researchers to test whether models are on the path to acquiring general physical abilities, as well as identify key limitations that researchers should be aware of when integrating new capabilities into their models through post-training.", + "bbox": [ + 493, + 455, + 888, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 496, + 628, + 638, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Modeling Intuitive Physics. Intuitive physics refers to the innate or learned human capacity to make quick and accurate judgments about the physical properties and behaviors of objects in the world, such as their motion, stability, or interactions. This ability, present even in infancy (Spelke et al., 1992; Baillargeon, 2004; Battaglia et al., 2013), is crucial for navigating and understanding everyday life. Replicating intuitive physics is a foundational step toward creating systems that can interact effectively and safely in dynamic, real-world environments (Lake et al., 2017). Gravity, as a core component of intuitive physics, plays a pivotal role in both domains. It is one of the most universal and observable physical forces, shaping our expectations about object motion, stability, and interaction (Hamrick et al., 2016; Ullman et al., 2017). Many studies in cognitive science (Battaglia et al., 2013) and AI (Wu et al., 2015; Bear et al., 2021) have", + "bbox": [ + 493, + 652, + 888, + 896 + ], + "page_idx": 1 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 70 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 480, + 922, + 491, + 934 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "relied on physics engines to evaluate and model intuitive physics. Our work uses the Kubric engine (Greff et al., 2022) to generate training videos.", + "bbox": [ + 84, + 85, + 475, + 131 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video Generation Models as World Simulators. Video generation has long been an intriguing topic in computer vision, particularly in the context of predicting future frames (Srivastava et al., 2015; Xue et al., 2016). More recently, as large-scale generative models have become prominent, Yang et al. explored how a wide range of real-world dynamics and decision-making processes can be expressed in terms of video modeling (Yang et al., 2024b; 2023). The introduction of the Sora model (OpenAI, 2024) marked a leap in the quality of generated videos and ignited interest in leveraging such models as \"world simulators.\" Over the past year, numerous video generation models have emerged, some open-source (Zheng et al., 2024; Yang et al., 2024c; Jin et al., 2024; Agarwal et al., 2025) and others commercially available (Kuaishou, 2024; Luma, 2024; Runway, 2024; OpenAI, 2024). Related to our work, Kang et al. (Kang et al., 2024) study the extent to which video generation models learn generalizable laws of physics when trained on 2D data from a synthetic environment.", + "bbox": [ + 86, + 137, + 477, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Evaluating Video Generation Models. Traditional image-based metrics for generative modeling, such Fréchet inception distance (FID) (Heusel et al., 2017) or inception score (IS) (Salimans et al., 2016), can be incorporated into the video domain, either by applying them on a frame-by-frame basis or by developing video-specific versions, such as Fréchet video distance (FVD) (Unterthiner et al., 2018). Going beyond distribution matching measures, several benchmarks have developed suites of metrics that aim to better evaluate the semantic or visual quality of generated videos. For example, V-Bench (Huang et al., 2024) offers a more granular evaluation by measuring video quality across multiple dimensions, such as with respect to subject consistency or spatial relationships. In physics, some works, such as VideoPhy (Bansal et al., 2024) and PhyGenBench (Meng et al., 2024), evaluate in the T2V setting by utilizing multimodal large language models (MLLM) to generate a VQA-based score. More recently, Cosmos (Agarwal et al., 2025) and Physics-IQ (Motamed et al., 2025), evaluate physics in the image-to-video and video-to-video settings.", + "bbox": [ + 86, + 431, + 477, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. PisaBench", + "text_level": 1, + "bbox": [ + 84, + 753, + 197, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our benchmark, PisaBench, examines the ability of video generative models to produce accurate physical phenomena by focusing on a straightforward dropping task.", + "bbox": [ + 84, + 779, + 473, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task Definition & Assumptions", + "text_level": 1, + "bbox": [ + 84, + 840, + 336, + 857 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our task can be summarized as follows: given an image of an object suspended in midair, generate a video of the object", + "bbox": [ + 84, + 864, + 475, + 896 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1ac3de96698eccbe7ffd3f2cdeee9e6722a7a59125ffbd3af395c8b98701c5c7.jpg", + "image_caption": [ + "Figure 2. The setup for collecting real-world videos." + ], + "image_footnote": [], + "bbox": [ + 519, + 84, + 859, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "falling and colliding with the ground and potentially other objects. Since a video is an incomplete partial observation of the 4D world, we make a number of assumptions to constrain the task space. These assumptions are crucial for ensuring that our metrics are reliable signals for physical accuracy, since they are only approximations of task success computed from a single ground truth and generated video.", + "bbox": [ + 496, + 382, + 885, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, we assume that the falling object is completely still in the initial frame, that only the force of gravity is acting on the object while it falls, and that the camera does not move. The first two assumptions are necessary for the image-to-video setting. Since we do not provide multiple frames as input, it is otherwise impossible to establish the initial velocity or acceleration of the falling object without these assumptions. The last assumption is necessary as our metrics derive from the motion of segmentation masks, which would be affected in the presence of camera motion.", + "bbox": [ + 496, + 496, + 888, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Real World Data", + "text_level": 1, + "bbox": [ + 496, + 664, + 650, + 678 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/75bc9f270274a876e0f2d9bb2c4307c38aafd436f796800aeee64fbd5f2d9b29.jpg", + "image_caption": [ + "Figure 3. Statistics of the real-world data: (a) number of objects in each video, (b) the proportions of different scenes in the videos." + ], + "image_footnote": [], + "bbox": [ + 506, + 695, + 696, + 816 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2a038e4df7899a3c6a7af3f168c48dd30504eb434167e140afe024da4ee58ef5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 695, + 880, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Real World Videos. We collect a set of 361 real-world videos demonstrating the dropping task for evaluation. As is shown in Figure 4, the dataset includes a diverse set", + "bbox": [ + 496, + 859, + 885, + 905 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 155, + 56, + 815, + 71 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 480, + 922, + 491, + 934 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7d4ceaab34fce33596b3dd1e9d4ba7a5b2fc93095d7bd082617fa0ffe00a3c57.jpg", + "image_caption": [ + "Figure 4. Examples of various objects included in our dataset. For simulation, we utilize the GSO dataset (Downs et al., 2022), while for the real-world dataset, we curate our own set of common household objects." + ], + "image_footnote": [], + "bbox": [ + 91, + 85, + 472, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of objects with different shapes and sizes, captured across various settings such as offices, kitchens, parks, and more (see Figure 3). Each video begins with an object suspended by an invisible wire in the first frame, which is necessary to enforce the assumption that objects are stationary at the start of the video. This assumption is required in our imaged-to-video setting; otherwise, the initial velocity of an object is ambiguous. We cut the video clips to begin as soon as the wire is released. We record the videos in slow-motion at 120 frames per second (fps) with cellphone cameras mounted on tripods to eliminate camera motion. An example of our video collection setup is shown in Figure 2. Additional details on our collection system are provided in Appendix H.", + "bbox": [ + 84, + 397, + 475, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Simulated Test Videos. Since our post-training process uses a dataset of simulated videos, we also create a simulation test-set of 60 videos for understanding sim2real transfer. We create two splits of 30 videos each: one featuring objects and backgrounds seen during training, and the other featuring unseen objects and backgrounds. See Section 4.1 for details on how our simulated data is created.", + "bbox": [ + 84, + 601, + 475, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Annotations. As is shown in Figure 5, we annotate each video with a caption and segmentation masks estimated from the SAM 2 (Ravi et al., 2024) video segmentation model. We create a descriptive caption for each object in the format of “{object description} falls.” This caption is used to provide context to the task when text input is supported.", + "bbox": [ + 84, + 714, + 473, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Metrics", + "text_level": 1, + "bbox": [ + 84, + 821, + 173, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose three metrics to assess the accuracy of trajectories, shape fidelity, and object permanence. Each of our metrics compare frames from the ground-truth video with the generated video. Further details about the metrics, including", + "bbox": [ + 84, + 845, + 475, + 906 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fdf0c1240713a0f765f0563462d434ced74c2fc826cdce4f827d1a1a50939cc7.jpg", + "image_caption": [ + "Figure 5. Example of annotations in real-world data. For segmentation masks, we manually annotate first frame and utilize SAM 2 to produce segmentation masks across frames. For captions, we annotate “{object description} falls.” for all video segments." + ], + "image_footnote": [], + "bbox": [ + 498, + 80, + 887, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "their formulas and our resampling procedure for accounting for differences in fps, is described in Appendix B.", + "bbox": [ + 496, + 412, + 885, + 443 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Trajectory L2. For each frame in both the generated video and ground truth, we calculate the centroid of the masked region. After doing this, we compute the average $L_{2}$ distance between the centroids of corresponding frames.", + "bbox": [ + 496, + 450, + 887, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Chamfer Distance (CD). To assess the shape fidelity of objects, we calculate the Chamfer Distance (CD) between the mask regions of the generated video and ground truth.", + "bbox": [ + 496, + 518, + 887, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intersection over Union (IoU). We use the Intersection over Union (IoU) metric to evaluate object permanence. The IoU measures objects' degree of overlap between the generated video and ground truth.", + "bbox": [ + 496, + 571, + 887, + 632 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Evaluation Results", + "text_level": 1, + "bbox": [ + 496, + 648, + 661, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We evaluate 4 open models including CogVideoX-5B-I2V(Yang et al., 2024c), DynamiCrafter(Xing et al., 2023), Pyramid-Flow(Jin et al., 2024), and Open-Sora-V1.2(Zheng et al., 2024), as well as 4 proprietary models including Sora (OpenAI, 2024), Kling-V1(Kuaishou, 2024), Kling-V1.5(Kuaishou, 2024), and Runway Gen3 (Runway, 2024). We also evaluate OpenSora post-trained through the processes of Supervised Fine-Tuning (PSFT) and Object Reward Optimization (ORO); see Section 4 for details.", + "bbox": [ + 495, + 671, + 887, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The results of running the baseline models on the benchmark indicate a consistent failure to generate physically accurate dropping behavior, despite the visual realism of their generated frames. Qualitatively, we see common failure cases in Figure 6, such as implausible object deformations, floating, hallucination of new objects, and unrealistic special", + "bbox": [ + 495, + 814, + 888, + 906 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 71 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 480, + 922, + 491, + 934 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/342a3b4296640d6e8ed1d72350bfb1237311d4fb53b1dc49759aa08ed93e6617.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison of results on real test set (row 1-2), simulated seen test set (row 3-4) and simulated unseen test set (row 5-6). We present the results of popular open-source and commercially available models alongside those of models fine-tuned through our method. Existing models often struggle to generate videos depicting objects falling, whereas our PSFT method effectively introduces knowledge of free-fall into the model. ORO enables the model to more accurately learn object motion and shape." + ], + "image_footnote": [], + "bbox": [ + 86, + 85, + 885, + 304 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "effects. We further visualize a random subset of generated trajectories on the left of Figure 8. In many cases, the object remains completely static, and sometimes the object even moves upward. When downward motion is present, it is often slow or contains unrealistic horizontal movement.", + "bbox": [ + 84, + 377, + 473, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Physics Post-Training", + "text_level": 1, + "bbox": [ + 84, + 470, + 292, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We present a post-training process to address the limitations of current models described in Section 3.4. We utilize simulated videos that demonstrate realistic dropping behavior. Our approach for post-training is inspired by the two-stage pipeline consisting of supervised fine-tuning followed by reward modeling commonly used in LLMs. We find that our pipeline improves performance on both real and simulated evaluations, with greater gains observed in simulation. This is due to the sim-to-real gap, though our approach still shows substantial gains in transferring to real-world data.", + "bbox": [ + 84, + 498, + 475, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Simulated Adaptation Data", + "text_level": 1, + "bbox": [ + 84, + 665, + 310, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The first stage of our approach involves supervised fine-tuning. We use Kubric (Greff et al., 2022), a simulation and rendering engine designed for scalable video generation, to create simulated videos of objects dropping and colliding with other objects on the ground. Each video consists of 1-6 dropping objects onto a (possibly empty) pile of up to 4 objects underneath them. The videos are 2 seconds long, consisting of 32 frames at 16 fps. The objects are sourced from the Google Scanned Objects (GSO) dataset (Downs et al., 2022), which provides true-to-scale 3D models created from real-world scans across diverse categories (examples shown in Figure 4). The camera remains stationary in each video and is oriented parallel to the ground plane. To introduce variability, we randomly sample the camera height", + "bbox": [ + 84, + 689, + 475, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "between 0.4 and 0.6 meters and position objects between 1 and 3 meters away from the camera, which corresponds to the distributions observed in the real-world dataset. More information about the dataset can be found in Appendix K.", + "bbox": [ + 496, + 377, + 885, + 438 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Physics Supervised Fine-Tuning (PSFT).", + "text_level": 1, + "bbox": [ + 496, + 454, + 812, + 469 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9cb6168eacd785e4f741b3dbc66836cc1b13221d84cacac490669a7f161086a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 484, + 684, + 587 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6adf02f646ee4da228177a9bb3d6b9810b033aeaac6c9f68056cd271eb9c47c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 484, + 883, + 585 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/91f342955c4abb85297c05b6fbf080e1ae798b04587e39e4104a2985d585e4d7.jpg", + "image_caption": [ + "Figure 7. Plots (a), (b), and (c) demonstrate that our metrics tend to improve with further training and that leveraging a pre-trained video diffusion model enhances performance compared to random initialization. In plot (d), the size of the training dataset varies in each training run (each consisting of 5k steps). With only 5k samples, we can achieve optimal results." + ], + "image_footnote": [], + "bbox": [ + 500, + 588, + 683, + 688 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a7f340f4c1bc1798d01d2bcfa3aac741d7c979c6b80afc4910bba5d647c78286.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 587, + 883, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the pretrained Open-Sora v1.2 (Zheng et al., 2024) model as our base model and fine-tune it on our simulated video dataset. We employ Open-Sora v1.2's rectified flow training objective without modification (Liu et al., 2022). Each fine-tuning experiment is conducted with a batch size of 128 and a learning rate of $1\\mathrm{e} - 4$ on two 80GB NVIDIA A100 GPUs. As shown in Figure 6, fine-tuning with this", + "bbox": [ + 495, + 799, + 885, + 905 + ], + "page_idx": 4 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 71 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 480, + 922, + 491, + 934 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/19982fa17713845a5d804164e55f0ffa9571cbf7063e297859e10dcd17cb35ca.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRealSim (Seen)Sim (Unseen)
L2 (↓)CD (↓)IoU (↑)L2 (↓)CD (↓)IoU (↑)L2 (↓)CD (↓)IoU (↑)
ProprietarySora (OpenAI, 2024)0.1740.4880.0650.1490.4460.0400.1400.4190.031
Kling-V1 (Kuaishou, 2024)0.1570.4250.0560.1420.4150.0320.1450.4370.028
Kling-V1.5 (Kuaishou, 2024)0.1550.4240.0580.1370.3960.0330.1320.4050.029
Runway Gen3 (Runway, 2024)0.1870.5260.0420.1700.5090.0400.1490.4600.038
OpenCogVideoX-5B-I2V (Yang et al., 2024c)0.1380.3660.0800.1120.3150.0200.1010.2900.020
DynamiCrafter (Xing et al., 2023)0.1870.5040.0210.1570.4850.0390.1360.4300.033
Pyramid-Flow (Jin et al., 2024)0.1750.4850.0620.1260.3520.0590.1300.3810.048
Open-Sora (Zheng et al., 2024)0.1750.5020.0690.1390.4090.0360.1300.3680.034
OursOpen-Sora + PSFT (base)0.0760.1880.1390.0360.0880.1650.0280.0580.129
base + ORO (Seg)0.0750.1830.1420.0330.0760.1700.0320.0630.145
base + ORO (Flow)0.0670.1640.1360.0260.0620.1220.0220.0450.071
base + ORO (Depth)0.0670.1590.1290.0310.0720.1240.0220.0460.096
", + "bbox": [ + 86, + 71, + 885, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. PisaBench Evaluation Results. This table compares the performance of four proprietary models, four open models, and the models fine-tuned with PSFT and $\\mathrm{PSFT + ORO}$ on our real-world and simulated test set which is decomposed into seen and unseen object splits. Across all metrics, our PSFT models outperform all other baselines, including proprietary models like Sora. Reward modeling further enhances results, with segmentation rewards improving the shape-based IoU metric and optical rewards and depth rewards enhancing the motion-based L2 and CD metrics. This suggests that rewards can be flexibly adjusted to target specific aspects of performance.", + "bbox": [ + 83, + 356, + 888, + 428 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "data alone is sufficient to induce realistic dropping behavior in the model. Quantitatively, our PSFT model substantially improves on both our simulated and real-world benchmark, as shown in Table 1. Dataset size. We conduct an ablation study on the number of training samples to understand the amount of data required for optimal performance on our benchmark. We create random subsets from 500 to 20,000 samples and train our model for 5,000 gradient steps on each subset. Notably, as shown in Figure 7, only 5,000 samples are needed to achieve optimal results. Effect of pretraining. Additionally, we investigate the impact of Open-Sora's pre-training on adaptation. We randomly initialize the Open-Sora's denoising network while keeping the pre-trained initialization of the compressor network and train the model on a dataset of 5k training samples. As shown in Figure 8, the learned knowledge from Open-Sora's pretraining plays a critical role in our task.", + "bbox": [ + 83, + 450, + 475, + 708 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall, using PSFT on only 5k samples is sufficient to push Open-Sora's performance past all other evaluated models, including state-of-the-art commercial video generators, by a wide margin. This is made possible by leveraging the knowledge from the sufficiently pre-trained base model.", + "bbox": [ + 83, + 715, + 473, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Object Reward Optimization (ORO)", + "text_level": 1, + "bbox": [ + 84, + 806, + 375, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the second stage, we propose Object Reward Optimization (ORO) to use reward gradients to guide the video generation model toward generating videos where the object's motion and shape more closely align with the ground truth.", + "bbox": [ + 84, + 830, + 475, + 891 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2b0b1b1edbe72353a808756a9abec58b083266dae8f49a22cf820119f4e51b9d.jpg", + "image_caption": [ + "Figure 8. On the left, we plot random trajectories from the baseline models in Table 1. On the right, we show random trajectories from our fine-tuned model. The baseline trajectories exhibit unrealistic behavior, and most of them stay completely static. On the right, we see the trajectories consistently falling downward with collision and rolling behavior being modeled after the point of contact." + ], + "image_footnote": [], + "bbox": [ + 506, + 452, + 883, + 582 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We follow the VADER framework from (Prabhudesai et al., 2024) and introduce three reward models. The differences between our approach and VADER include: (1) our reward model utilizes both generated videos and ground truth instead of generated videos and conditioning. (2) gradients propagate through all denoising time steps in fine-tuning. Consequently, the VADER objective is modified as follows:", + "bbox": [ + 495, + 691, + 888, + 799 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nJ (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 809, + 885, + 829 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{D}$ is the ground truth dataset, $p_{\\theta}(.)$ is a given video diffusion model, $x_0^{\\prime}, x_0 \\in \\mathbb{R}^{H \\times W \\times 3}$ are generated video and ground truth, and $c \\in \\mathbb{R}^{H \\times W \\times 3}$ is the initial image.", + "bbox": [ + 495, + 837, + 885, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Segmentation Reward. We utilize SAM 2 (Ravi et al.,", + "bbox": [ + 496, + 890, + 885, + 905 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 70 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 480, + 922, + 491, + 934 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2024) to generate segmentation masks across frames for generated videos. We define segmentation reward as the IoU between the dropping object's mask in generated video and the mask from the ground truth simulated segmentation.", + "bbox": [ + 84, + 84, + 473, + 147 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Optical Flow Reward. We utilize RAFT (Teed & Deng, 2020) to generate generated video's optical flow $V^{\\mathrm{gen}}$ and ground truth's optical flow $V^{\\mathrm{gt}}$ . We define the optical flow reward as $R(x_0', x_0) = -|V^{\\mathrm{gen}} - V^{\\mathrm{gt}}|$ .", + "bbox": [ + 84, + 152, + 475, + 214 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Depth Reward. We utilize Depth-Anything-V2 (Yang et al., 2024a) to generate generated video's depth map $D^{\\mathrm{gen}}$ and ground truth's depth map $D^{\\mathrm{gt}}$ . We define the optical flow reward as $R(x_0', x_0) = -|D^{\\mathrm{gen}} - D^{\\mathrm{gt}}|$ .", + "bbox": [ + 84, + 220, + 475, + 281 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Details on implementation can be found in Appendix C.", + "bbox": [ + 84, + 287, + 455, + 304 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We begin from the checkpoint of the first stage, which is trained on 5,000 samples trained over 5,000 gradient steps. We then fine-tune the model with ORO on the simulated dataset, using a batch size of 1 and two 80GB NVIDIA A100 GPUs for each fine-tuning experiment. We set a learning rate of $1\\mathrm{e} - 6$ for segmentation reward and depth reward and $1\\mathrm{e} - 5$ for optical flow.", + "bbox": [ + 84, + 311, + 475, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 1, incorporating ORO in reward modeling further improves performance. Additionally, each reward function enhances the aspect of physicality that aligns with its intended purpose—segmentation rewards improve shape accuracy, while flow rewards and depth rewards improve motion accuracy. This demonstrates the process is both modular and interpretable.", + "bbox": [ + 83, + 424, + 475, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Assessing Learned Physical Behavior", + "text_level": 1, + "bbox": [ + 84, + 549, + 419, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Having introduced our post-training approaches in Section 4, we probe into the model's understanding of the interaction between gravity and perspective—the two laws that determine the dynamics of our videos. We first test if the learned physical behavior of our model can generalize to dropping heights and depths beyond its training distribution. Then, we study the ability of the model to learn the probability distribution induced by the uncertainty of perspective.", + "bbox": [ + 84, + 575, + 475, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Generalization to Unseen Depths and Heights", + "text_level": 1, + "bbox": [ + 84, + 713, + 436, + 729 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Depth and height are the main factors that affect the dynamics of a falling object in our videos. We can see this by combining the laws of gravity with perspective under our camera assumptions to model the object's image $y$ coordinate as a function of time (further details on our coordinate system are described in Appendix G):", + "bbox": [ + 84, + 736, + 475, + 828 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\ny (t) = \\frac {f}{Z} \\left(Y _ {0} - \\frac {1}{2} g t ^ {2}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 838, + 475, + 872 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From Equation (2), we see that the random variables that af", + "bbox": [ + 84, + 890, + 475, + 905 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fect object motion are $Z$ (depth) and $Y$ (height) (the camera focal length $f$ is fixed). Thus, we are interested in testing generalization on unseen values of $Y$ and $Z$ .", + "bbox": [ + 496, + 84, + 883, + 130 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We create a simulated test set in which a single object is dropped from varying depths and heights, using objects and backgrounds unseen during training. We uniformly sample depth and height values (in meters) from the Cartesian product of the ranges [1, 5] and [0.5, 2.5], respectively. The camera height is fixed at $0.5m$ , and depth-height pairs outside the camera viewing frustum are discarded. A sample is in-distribution (ID) if its dropping depth and height both fall in the range [1, 3] and [0.5, 1.5].", + "bbox": [ + 495, + 137, + 885, + 273 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since we have access to the ground truth dropping time in simulation, we also employ a dropping time error, a metric we describe in Appendix B. Our analysis in Table 2 shows that performance degrades for out-of-distribution scenarios.", + "bbox": [ + 495, + 281, + 885, + 342 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since depth and height are the main physical quantities that affect falling dynamics, this finding indicates that our model may struggle to learn a fully generalizable law that accounts for the interaction of perspective and gravity.", + "bbox": [ + 495, + 349, + 885, + 410 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/88670abb85fb73081ca571f4fc556131bc94f22fa766b8d2ff19594c1ac79e8b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingL2 (↓)Chamfer (↓)IOU (↑)Time Error (↓)
ID0.0360.0880.1550.091
OOD0.0440.1430.0490.187
", + "bbox": [ + 498, + 422, + 885, + 481 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Results of our metrics on in-distribution (ID) and out-of-distribution (OOD) depth-height combinations. The values used for depth range from $1 - 5\\mathrm{m}$ (ID range [1,3]) and height values range from 0.5-2.5 (ID range [0.5, 1.5]).", + "bbox": [ + 496, + 489, + 885, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Distributional Analysis", + "text_level": 1, + "bbox": [ + 496, + 571, + 692, + 585 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/173d344ac811372831211d71e1f089dcd0ee90fa7170fbcfc6b6036661f678d4.jpg", + "image_caption": [ + "Figure 9. Demonstration of ambiguity in 2D perspective projections. Each of the three clouds appears the exact same in the camera's image. The right side shows how we perform a scale and translation augmentation to generate deliberately ambiguous data." + ], + "image_footnote": [], + "bbox": [ + 498, + 603, + 651, + 713 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dcf5758aab2710279523e38fe46165467a3e180eeef0ed0b3050233202412b9e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 602, + 883, + 713 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The evolution of a physical system is not uniquely determined by a single initial image, since the lossy uncertainty of perspective induces a distribution of possible outcomes as shown in Figure 9. An ideal video world model should (1) output videos that are faithful to the evolution of some plausible world state and (2) provide accurate coverage across the entire distribution of the world that is possible from", + "bbox": [ + 495, + 799, + 885, + 905 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 155, + 56, + 815, + 71 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 480, + 922, + 491, + 934 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "its conditioning signal. In this section, we examine these two facets by studying $p(t|y)$ : the distribution of dropping times possible from an object at coordinate $y$ in the image plane. To do this, we create a simulated dataset that has a much wider distribution $p(t|y)$ than our PSFT dataset. See Appendix F for more details on its construction.", + "bbox": [ + 84, + 85, + 475, + 175 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/73a89a0c5b340af83339e7bdee6111a2850a250f52d7a51435656c3c43642fe2.jpg", + "image_caption": [ + "Figure 10. Examples of model trajectories lifted to 3D. The blue line represents the height of the camera ray passing through the bottom of the dropping object as a function of depth. The set of possible dropping trajectories at a given depth are depicted in gray. The lifted trajectory of the model is depicted in green." + ], + "image_footnote": [], + "bbox": [ + 86, + 186, + 473, + 287 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8862d09f5523d53e73a41fca13423e9ac96d265eb77cc7788176d5f31c7abc8a.jpg", + "image_caption": [ + "Figure 11. Visualizing $p(t|y)$ misalignment for different images. Green shows the ground-truth CDF, orange is the 32-frame quantized version, and blue is the empirical CDF of 128 different samples of dropping times from the model." + ], + "image_footnote": [], + "bbox": [ + 86, + 388, + 472, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Testing (1): 3D faithfulness of trajectories.", + "text_level": 1, + "bbox": [ + 84, + 611, + 383, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "After training our model on this new dataset, we test whether its trajectories are consistent with a valid 3D world state. We first obtain an estimated dropping time from generated videos using the procedure described in Section 5.1. Using knowledge of the camera position, focal length, sensor width, and $y$ , we can obtain an implied depth and height of the trajectory. We can then back-project the video trajectory to 3D and analyze whether they constitute physically accurate trajectories. We give further details about this process in Appendix G. As show in Figure 10, we find that our model's lifted trajectories consistently align with the 3D trajectory at the height and depth implied by its dropping time, giving evidence that the model's visual outputs are faithful to some plausible real-world state.", + "bbox": [ + 84, + 633, + 475, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Testing (2): distributional alignment.", + "text_level": 1, + "bbox": [ + 84, + 852, + 346, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Going beyond the level of individual trajectories, we study the model's learned conditional distribution $p(t|y)$ . We", + "bbox": [ + 84, + 875, + 473, + 906 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "create 50 different initial images with differing values of $y$ , generate 128 different videos from each, and estimate the dropping time in each video. Using the laws of gravity, the laws of perspective, and the assumption of uniform depth sampling in our dataset, we can analytically derive the probability $p(t|y)$ as", + "bbox": [ + 496, + 84, + 885, + 175 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\np (t | y) = \\left\\{ \\begin{array}{l l} \\frac {g t}{\\left(Z _ {\\max } - Z _ {\\min }\\right) \\beta}, & t _ {\\min } \\leq t \\leq t _ {\\max } \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 196, + 885, + 237 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $\\beta$ is a constant that depends on $f$ , $y$ and the camera height. The derivation is given in Appendix E.", + "bbox": [ + 496, + 256, + 885, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We then measure goodness-of-fit for each of the 50 experiments using the Kolmogorov-Smirnov (KS) test (Massey Jr, 1951). The null hypothesis of the KS test is that the two distributions being compared are equal, and we consider p-values less than 0.05 as evidence of misalignment. Since our measured times have limited precision and can only take 32 distinct values—due to estimating the contact frame—we approximate the ground truth $p(t|y)$ using a Monte Carlo method. We sample 1000 values from the ground truth distribution and then quantized them into 32 bins corresponding to their frame, which we use as ground truth observations in the KS test. We find that in all 50/50 cases, the p-value from the test is less than 0.05, which provides evidence that the model does not learn the correct distribution of dropping times. We visualize the misalignment between the empirical CDF of the model's in Figure 11.", + "bbox": [ + 496, + 294, + 885, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In summary, while our model's trajectories show promising tendencies to ground themselves to plausible 3D world states, the range of possible outputs from the model does not align with the ground truth distribution.", + "bbox": [ + 496, + 542, + 885, + 603 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 496, + 623, + 614, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work studies post-training as an avenue for adapting adapting pre-trained video generator into world models. We introduce a post-training strategy that is highly effective in aligning our model. Our work raises interesting insights into the learned distributions of generative models. Qualitatively, large scale image or video generative models appear to excel at generating likely samples from the data distribution, but this alone does not imply that they match the data distribution well in its entirety. As long as a model is able to generate likely samples, global distributional misalignment is not necessarily a problem for content creation. However, this problem becomes critical for world models, where alignment across the entire distribution is necessary for faithful world simulation. The insights revealed by our study, made possible by our constrained and tractable setting, indicate that although post-training improves per-sample accuracy, general distributional alignment remains unsolved.", + "bbox": [ + 495, + 648, + 885, + 905 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 155, + 56, + 815, + 71 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 480, + 922, + 491, + 934 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 86, + 83, + 236, + 99 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We thank Boyang Zheng, Srivats Poddar, Ellis Brown, Shengbang Tong, Shusheng Yang, Jihan Yang, Daohan Lu, Anjali Gupta and Ziteng Wang for their help with data collection. We thank Jiraphon Yenphraphai for valuable assistance in setting up our simulation code. We thank Runway and Kling AI for providing API credit. SX also acknowledges support from Intel AI SRS, Korean AI Research Hub, Open Path AI Foundation, Amazon Research Award, Google TRC program, and NSF Award IIS-2443404.", + "bbox": [ + 84, + 109, + 475, + 244 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 86, + 263, + 181, + 280 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "Agarwal, N., Ali, A., Bala, M., Balaji, Y., Barker, E., Cai, T., Chattopadhyay, P., Chen, Y., Cui, Y., Ding, Y., et al. Cosmos world foundation model platform for physical AI. arXiv preprint arXiv:2501.03575, 2025.", + "Baillargeon, R. Infants' physical world. 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Open-sora: Democratizing efficient video production for all, March 2024. URL https://github.com/hpcaitech/Open-Sora." + ], + "bbox": [ + 500, + 84, + 885, + 734 + ], + "page_idx": 9 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 71 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10", + "bbox": [ + 477, + 922, + 495, + 934 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "A. Discussion of Image-to-Video setting.", + "text_level": 1, + "bbox": [ + 84, + 83, + 421, + 99 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "We note that our choice of single-image input, as opposed to multi-frame input, comes with some trade-offs. We choose the image-to-video setting because it is widely supported among many different models, allowing us to make effective comparisons across the current state-of-the-art. However, only conditioning on a single frame introduces significant ambiguity. Due to the loss of information caused by projecting the 3D world through perspective, it may not be possible to directly infer the size of the object or its height. In practice, we find our metrics are still reliable signals of task success, but we still study the problem of ambiguity more extensively in Section 5.2.", + "bbox": [ + 84, + 109, + 883, + 200 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "B. Metric details.", + "text_level": 1, + "bbox": [ + 84, + 219, + 233, + 234 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "We propose three metrics to assess the accuracy of trajectories, shape fidelity, and object permanence. Each of our metrics compare frames from the ground-truth video with the generated video. Because different models can operate at different fps, we perform fps alignment as part of our evaluation process. To perform fps alignment, we map each frame index of the generated videos to the ground truth using $f_{\\mathrm{gen}}$ and $f_{\\mathrm{gt}}$ , where $f_{\\mathrm{gen}}$ and $f_{\\mathrm{gt}}$ are the fps of generated video and ground truth respectively. For $i$ -th frame in the generated video, we find the corresponding aligned frame index $j$ in the ground truth video:", + "bbox": [ + 84, + 244, + 883, + 332 + ], + "page_idx": 10 + }, + { + "type": "equation", + "text": "\n$$\nj = \\operatorname {r o u n d} \\left(i \\cdot \\frac {f _ {\\text {g e n}}}{f _ {\\mathrm {g t}}}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 416, + 332, + 885, + 364 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Through fps alignment, we downsample the ground truth video to match the frame number of the generated video. We denote the downsampled ground truth as $\\{I_i^{\\mathrm{gt}}\\}_{i = 1}^N$ and the generated video as $\\{I_i^{\\mathrm{gen}}\\}_{i = 1}^N$ , where $N$ is the number of frames in the generated video.", + "bbox": [ + 84, + 369, + 885, + 412 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Trajectory L2. For each frame in both the generated video and ground truth, we calculate the centroid of the masked region. We then compute $L_{2}$ distance between the centroids of corresponding frames:", + "bbox": [ + 84, + 414, + 885, + 445 + ], + "page_idx": 10 + }, + { + "type": "equation", + "text": "\n$$\nL _ {2} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| C _ {i} ^ {\\text {g e n}} - C _ {i} ^ {\\mathrm {g t}} \\| _ {2} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 388, + 454, + 885, + 496 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "where $C_i^{\\mathrm{gen}}, C_i^{\\mathrm{gt}} \\in \\mathbb{R}^2$ are the centroids of the dropping object in the $i$ -th frame of generated video and the ground truth respectively.", + "bbox": [ + 84, + 507, + 883, + 537 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Chamfer Distance (CD). To assess the shape fidelity of objects, we calculate the Chamfer Distance (CD) between the mask regions of the generated video and ground truth:", + "bbox": [ + 84, + 537, + 883, + 569 + ], + "page_idx": 10 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {C D} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\frac {1}{| P _ {i} |} \\sum_ {p \\in P _ {i}} \\min _ {q \\in Q _ {i}} \\| p - q \\| _ {2} + \\frac {1}{| Q _ {i} |} \\sum_ {q \\in Q _ {i}} \\min _ {p \\in P _ {i}} \\| q - p \\| _ {2}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 254, + 579, + 712, + 622 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "where $P_{i} = \\{p_{j}\\}_{j = 1}^{|P_{i}|}$ and $Q_{i} = \\{q_{j}\\}_{j = 1}^{|Q_{i}|}$ are the sets of mask points in the $i$ -th frame of the generated video and ground truth respectively.", + "bbox": [ + 84, + 633, + 883, + 666 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Intersection over Union (IoU). We use the Intersection over Union (IoU) metric to evaluate object permanence. IoU measures objects' degree of overlap between the generated video and ground truth. This is formulated as follows:", + "bbox": [ + 84, + 666, + 883, + 696 + ], + "page_idx": 10 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {I o U} = \\frac {1}{| N |} \\sum_ {i = 1} ^ {N} \\frac {\\left| M _ {i} ^ {\\text {g e n}} \\cap M _ {i} ^ {\\mathrm {g t}} \\right|}{\\left| M _ {i} ^ {\\text {g e n}} \\cup M _ {i} ^ {\\mathrm {g t}} \\right|} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 380, + 707, + 885, + 750 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "where $M_{i}^{\\mathrm{gen}}$ , $M_{i}^{\\mathrm{gt}} \\in \\{0,1\\}^{H\\times W}$ are binary segmentation masks of the falling object in the $i$ -th frame of the generated and ground truth videos respectively.", + "bbox": [ + 84, + 758, + 883, + 792 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Time error. When testing on videos generated in simulation, we can provide a timing error. From the dropping height $Y_{0}$ of the ground truth video, which we have access to from the simulator, we can derive $t_{\\mathrm{drop}} = \\sqrt{Y_0\\frac{2}{g}}$ . We then obtain a dropping time from the model's output by estimating the frame of impact as the first frame $F$ whose centroid velocity in the $y$ direction is negative. If $t_{\\mathrm{drop}}$ occurs in between $F$ and $F - 1$ , then we define the time error $E_{\\mathrm{time}}$ as zero. Otherwise, we define the time error as", + "bbox": [ + 84, + 797, + 883, + 876 + ], + "page_idx": 10 + }, + { + "type": "equation", + "text": "\n$$\nE _ {\\text {t i m e}} = \\min \\left(\\left| \\frac {F - 1}{\\mathrm {f p s}} - t _ {\\text {d r o p}} \\right|, \\left| \\frac {F}{\\mathrm {f p s}} - t _ {\\text {d r o p}} \\right|\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 326, + 876, + 885, + 910 + ], + "page_idx": 10 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 155, + 56, + 815, + 71 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11", + "bbox": [ + 477, + 922, + 493, + 934 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "C. ORO implementation details.", + "text_level": 1, + "bbox": [ + 84, + 83, + 359, + 99 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In our setting, we do not cut the gradient after step $k$ like VADER. The gradient $\\nabla_{\\theta}R(x_0',x_0)$ backpropagates through all diffusion timesteps and update the model weights $\\theta$ :", + "bbox": [ + 84, + 109, + 885, + 140 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\theta} \\left(R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right)\\right) = \\sum_ {t = 0} ^ {T} \\frac {\\partial R \\left(x _ {0} ^ {\\prime} , x _ {0}\\right)}{\\partial x _ {t}} \\cdot \\frac {\\partial x _ {t}}{\\partial \\theta} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 348, + 148, + 885, + 191 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where $T$ is the total diffusion timesteps.", + "bbox": [ + 84, + 200, + 346, + 215 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Segmentation Reward. We utilize SAM 2 (Ravi et al., 2024) to generate segmentation masks across frames for generated video:", + "bbox": [ + 84, + 222, + 885, + 251 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nM ^ {\\text {g e n}} = \\operatorname {S A M} - 2 \\left(x _ {0}\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 415, + 265, + 885, + 282 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where $M^{\\mathrm{gen}}$ denotes the masks of the falling object in the generated video. We obtain ground truth masks $M^{\\mathrm{gt}}$ using Kubric (Greff et al., 2022). To avoid non-differentiable reward, we use Sigmoid to normalize mask logits of generated video instead of converting them to binary masks. We use IoU between $M^{\\mathrm{gen}}$ and $M^{\\mathrm{gt}}$ as reward function:", + "bbox": [ + 84, + 294, + 885, + 339 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nR \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = \\operatorname {I o U} \\left(M ^ {\\text {g e n}}, M ^ {\\text {g t}}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 383, + 349, + 885, + 367 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Maximizing objective 1 is equivalent to minimizing the following objective:", + "bbox": [ + 84, + 378, + 591, + 393 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nJ (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ 1 - \\operatorname {I o U} \\left(M ^ {\\text {g e n}}, M ^ {\\text {g t}}\\right) \\right] \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 313, + 402, + 885, + 422 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "This objective constrains the position and shape of the generated object in the video, encouraging a greater intersection with the object region in the ground truth video. The model learns to generate more accurate object positions and shapes through training with this objective.", + "bbox": [ + 84, + 431, + 885, + 477 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Optical Flow Reward. We utilize RAFT (Teed & Deng, 2020) to generate optical flow for both generated videos and ground truth:", + "bbox": [ + 84, + 484, + 885, + 513 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nV ^ {\\text {g e n}} = \\operatorname {R A F T} \\left(x _ {0} ^ {\\prime}\\right) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 419, + 513, + 885, + 536 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nV ^ {\\mathrm {g t}} = \\operatorname {R A F T} (x _ {0})\n$$\n", + "text_format": "latex", + "bbox": [ + 428, + 532, + 550, + 547 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where $V^{\\mathrm{gen}}$ , $V^{\\mathrm{gt}}$ denote the optical flows of generated videos and ground truth. We define the reward as follows:", + "bbox": [ + 84, + 554, + 818, + 570 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nR \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = - \\left| V ^ {\\text {g e n}} - V ^ {\\text {g t}} \\right| \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 390, + 580, + 885, + 598 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Maximizing objective 1 is equivalent to minimizing the following objective:", + "bbox": [ + 84, + 607, + 591, + 623 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nJ (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ \\left| V ^ {\\text {g e n}} - V ^ {\\text {g t}} \\right| \\right] \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 339, + 633, + 885, + 652 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "This objective constrains the motion of the generated object in the video. The model learns to generate more accurate physical motion through training with this objective.", + "bbox": [ + 84, + 661, + 885, + 691 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Depth Reward. We utilize Depth-Anything-V2 (Yang et al., 2024a) to generate optical depth maps for both generated videos and ground truth:", + "bbox": [ + 84, + 698, + 885, + 728 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nD ^ {\\text {g e n}} = \\text {D e p t h - A n y t h i n g - V 2} \\left(x _ {0} ^ {\\prime}\\right) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 370, + 728, + 885, + 750 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nD ^ {\\mathrm {g t}} = \\text {D e p t h - A n y t h i n g - V 2} (x _ {0})\n$$\n", + "text_format": "latex", + "bbox": [ + 380, + 747, + 598, + 762 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where $D^{\\mathrm{gen}}$ , $D^{\\mathrm{gt}}$ denote the depth maps of generated videos and ground truth. We define the reward as follows:", + "bbox": [ + 84, + 768, + 812, + 785 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nR \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = - \\left| D ^ {\\text {g e n}} - D ^ {\\mathrm {g t}} \\right| \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 390, + 795, + 885, + 811 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Maximizing objective 1 is equivalent to minimizing the following objective:", + "bbox": [ + 84, + 821, + 591, + 837 + ], + "page_idx": 11 + }, + { + "type": "equation", + "text": "\n$$\nJ (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ \\left| D ^ {\\mathrm {g e n}} - D ^ {\\mathrm {g t}} \\right| \\right] \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 339, + 848, + 885, + 867 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "This objective constrains the 3d motion of the generated object in the video. The model learns to generate more accurate 3d physical motion through training with this objective.", + "bbox": [ + 84, + 875, + 885, + 906 + ], + "page_idx": 11 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 155, + 56, + 815, + 71 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12", + "bbox": [ + 477, + 922, + 495, + 934 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "D. Coordinate system", + "text_level": 1, + "bbox": [ + 84, + 83, + 272, + 101 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "We give a visualization of the coordinate system used in this paper in Figure 12. To compute $y$ , we first leverage a segmentation map and find pixel row index that is just below the object. Once this row index is found, $y$ can easily be computed from the camera position, camera sensor size, and image resolution. We note that because our camera is assumed to be in perspective with the $XY$ plane, we can ignore $X$ and $x$ (not shown in figure) in our analyses in Section 5.1 and Section 5.2.", + "bbox": [ + 83, + 109, + 887, + 186 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/afd6a41eb9e3a6bfc87ee7d008d6fc6d00d3b71c75ccf91adf12e6a11f200f01.jpg", + "image_caption": [ + "Figure 12. A visualization of the coordinate system used in this paper (not to scale). The image plane height of the object is denoted as $y$ , its actual height in 3D as $Y$ , and its depth as $Z$ . The camera focal length is denoted as $f$ ." + ], + "image_footnote": [], + "bbox": [ + 86, + 199, + 331, + 407 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/0492c7160061c2167d23b2371de275bf324606389678afb1b4fcc06512b614c9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 375, + 198, + 879, + 411 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "E. Derivation of $p(t|y)$", + "text_level": 1, + "bbox": [ + 84, + 492, + 274, + 510 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "In our dataset construction, we assume a uniform distribution for $Z$ , where $Z \\sim \\mathcal{U}(Z_{\\min}, Z_{\\max})$ , where $Z_{\\min} = 2$ and $Z_{\\max} = 18$ . As shown in Figure 12, the dropping height $Y$ is a linear function of $Z$ , i.e. $Y = y + \\beta Z$ for the slope $\\beta$ that can be computed from $y, f$ , the sensor size, and the camera height. This means we can solve for dropping time as $t = \\sqrt{\\frac{2}{g}Y} = \\sqrt{\\frac{2}{g}(y + \\beta Z)}$ . Applying the transformation rule for probability density yields", + "bbox": [ + 84, + 518, + 887, + 589 + ], + "page_idx": 12 + }, + { + "type": "equation", + "text": "\n$$\np (t | y) = \\left\\{ \\begin{array}{l l} \\frac {g t}{\\left(Z _ {\\max } - Z _ {\\min }\\right) \\beta}, & t _ {\\min } \\leq t \\leq t _ {\\max } \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 331, + 594, + 885, + 633 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "where $t_{\\mathrm{min}} = \\sqrt{\\frac{2}{g} (y + \\beta Z_{\\mathrm{min}})}$ and $t_{\\mathrm{max}} = \\sqrt{\\frac{2}{g} (y + \\beta Z_{\\mathrm{max}})}$ . Plugging in $Z_{\\mathrm{min}} = 2$ and $Z_{\\mathrm{max}} = 18$ yields Equation (3).", + "bbox": [ + 83, + 641, + 883, + 667 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "F. Ambiguous dataset", + "text_level": 1, + "bbox": [ + 84, + 683, + 272, + 700 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "We introduce a new dataset for distributional analysis that broadens $p(t|y)$ , in contrast to the PSFT dataset, which prioritizes realism and has a narrower distribution due to limited object depth variability. To create a dataset with $p(t|y)$ that is sufficiently diverse for meaningful analysis, we first set up the initial scenes as before, but then apply an augmentation where a new depth values is sampled uniformly from [2, 18] and the object is scaled and translated such that it appears the same in the original image, as shown in Figure 9. For simplicity, we limit our scenes to a single dropping object with no other objects on the ground. We also disable shadows, preventing the model from using them as cues to infer depth and height. Our dataset contains 5k samples consisting of 1k unique initial scenes each containing 5 different trajectories produced by the augmentation.", + "bbox": [ + 83, + 708, + 887, + 830 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "G. Lifting trajectories to 3D", + "text_level": 1, + "bbox": [ + 84, + 849, + 326, + 867 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "To lift trajectories to 3D, we first estimate $t_{\\mathrm{drop}}$ as described in Section 5.1. Using SAM2 to estimate object masks in the generated video, we can obtain a trajectory of the bottom of the object which we denote as $y_0, y_1, \\ldots, y_N$ where", + "bbox": [ + 83, + 875, + 887, + 906 + ], + "page_idx": 12 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 155, + 56, + 815, + 71 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "13", + "bbox": [ + 477, + 922, + 495, + 934 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "$N = t_{\\mathrm{drop}} \\times \\mathrm{fps}$ . From $t_{\\mathrm{drop}}$ , we can solve for an implied depth $Z = \\frac{\\frac{1}{2}gt^2 - y}{\\beta}$ . We then compute the lifted 3D trajectory as $y_i \\mapsto y_i + \\beta Z$", + "bbox": [ + 84, + 84, + 887, + 119 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "H. PisaBench Details", + "text_level": 1, + "bbox": [ + 86, + 136, + 264, + 152 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "In this section, we discuss the details of our data collection pipeline and annotations. We present more examples of real-world videos and corresponding annotations in Figure 13.", + "bbox": [ + 84, + 162, + 887, + 193 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "H.1. Data Collection Pipeline", + "text_level": 1, + "bbox": [ + 84, + 209, + 294, + 224 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Collecting Real World Videos. We enlist approximately 15 volunteers to participate in the data collection process. We hand out a tripod, tape, and invisible wire for each volunteer. To ensure the quality, diversity, and minimize the ambiguity introduced by the environments, volunteers are provided with detailed guidelines. The key points of the data collection guidelines are shown in Table 3.", + "bbox": [ + 84, + 232, + 887, + 294 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Raw videos processing. For the collected raw videos, we cut each video into multiple clips and crop their sizes. For each video clip, we annotate its starting position in the original long video and ensure that the duration of each segment does not exceed 12 seconds. Regarding the sizes of the videos, we manually crop each video to an aspect ratio of $1:1$ , ensuring that the falling objects remain fully visible within the frame during the cropping process. The processing interface is shown in Figure 14.", + "bbox": [ + 84, + 300, + 887, + 377 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "H.2. Annotation Details", + "text_level": 1, + "bbox": [ + 86, + 393, + 256, + 407 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We present our annotation details in Figure 15. For video captions, we present the word cloud figure in (a). For segmentation masks, we annotate all objects in the first frame using positive and negative points, which are then propagated across frames using the SAM 2 (Ravi et al., 2024) model to produce segmentation masks for all objects throughout the video. The annotation interface is shown in (b).", + "bbox": [ + 84, + 416, + 887, + 477 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "In addition to providing the annotated caption \" {object description} falls,\" we also add information to inform off-the-shelf models of the task's context as much as possible. To further enhance task comprehension, we append an additional description \"A video that conforms to the laws of physics.\" We also employ negative prompts \"no camera motion\" and \"no slow-motion\" to ensure environmental stability and impose constraints on the generated videos. These prompts explicitly instruct the models to avoid including camera motion or any non-real-time object motion, thereby maintaining consistency with real-world physics.", + "bbox": [ + 84, + 484, + 887, + 575 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "I. Inference Details", + "text_level": 1, + "bbox": [ + 86, + 594, + 251, + 609 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We present the inference configurations of each closed or open model we evaluate in Table 4. For models that do not support generating videos with 1:1 aspect ratio, we pad initial frames with black borders to the resolution supported by these models, and finally remove the black borders from the generated videos.", + "bbox": [ + 84, + 619, + 887, + 667 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "J. More Qualitative Examples", + "text_level": 1, + "bbox": [ + 86, + 685, + 339, + 702 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We present more qualitative examples in Figure 16 - Figure 22. Although in some showcases, models can roughly predict the downward trend, models still struggle to predict plausible shape and motion. The defects in the models can be mainly attributed to the following aspects:", + "bbox": [ + 84, + 710, + 887, + 757 + ], + "page_idx": 13 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Trajectory correctness: in most videos, models fail to predict even the basic falling trajectory of objects, as shown in Figure 19 (a), despite this being highly intuitive for humans. Even in cases where the falling trajectory is roughly correctly predicted, the models still struggle to accurately predict subsequent events, such as collisions, as illustrated in Figure 16 (f).", + "- Object consistency: in many generated videos, object consistency is poor. Models struggle to infer the appearance of objects from multiple viewpoints in a physically plausible manner, resulting in unnatural appearances, as shown in Figure 16 (a). Additionally, models perform poorly in maintaining object permanence, causing objects to appear blurry, as illustrated in Figure 20 (f). Furthermore, models sometimes introduce new objects into the video, as depicted in" + ], + "bbox": [ + 102, + 773, + 883, + 902 + ], + "page_idx": 13 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 155, + 56, + 815, + 71 + ], + "page_idx": 13 + }, + { + "type": "page_number", + "text": "14", + "bbox": [ + 477, + 922, + 495, + 934 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Figure 20 (e).", + "bbox": [ + 120, + 85, + 210, + 99 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "- Scene consistency: models struggle to maintain scene consistency, leading to abrupt transitions in many videos. These sudden changes make videos appear unnatural, as shown in Figure 18 (f).", + "bbox": [ + 107, + 109, + 887, + 141 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "K. Simulated Adaption Details", + "text_level": 1, + "bbox": [ + 88, + 159, + 344, + 176 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "We use the Kubric (Greff et al., 2022) simulation and rendering engine for creating our simulated videos. Kubric uses PyBullet (Coumans et al., 2010) for running physics simulations and Blender (Community, 2018) for rendering. We set the simulation rate to 240 steps per second and render 2-second videos at 16 fps, resulting in 32 frames per video. Each scene consists of objects from the Google Scanned Objects (GSO) dataset (Downs et al., 2022) and uses environmental lighting from HDRI maps provided by Kubric. We use 930 objects and 458 HDRI maps for training and 103 objects and 51 HDRI maps for testing.", + "bbox": [ + 88, + 185, + 887, + 277 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "For each video, we randomly choose 1-6 objects to drop. These objects are placed at a height uniformly sampled from $0.5\\mathrm{m}$ to $1.5\\mathrm{m}$ . Below each of these objects, a possibly empty pile of up to 4 objects spawns beneath to create collisions. The objects are placed in a spawn region of size $2\\mathrm{m} \\times 2\\mathrm{m}$ .", + "bbox": [ + 88, + 282, + 887, + 329 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The camera is initially positioned $1\\mathrm{m}$ behind this region, with its height varying uniformly between $0.4\\mathrm{m}$ and $0.6\\mathrm{m}$ . Once all objects are placed, the camera moves back in random increments until all objects are visible within the camera frame. The camera uses a focal length of $35\\mathrm{mm}$ , a sensor width of $32\\mathrm{mm}$ , and an aspect ratio of $1\\times 1$ .", + "bbox": [ + 88, + 335, + 887, + 382 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "L. Limitations", + "text_level": 1, + "bbox": [ + 88, + 401, + 210, + 417 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "In this work, we collect and manually annotate a dataset of 361 real-world videos and design three spatial metrics to evaluate the performance of state-of-the-art image-to-video (I2V) models in a fundamental physical scenario: free fall. Our metrics focus solely on spatial positional relationships, excluding object appearance attributes such as color. To enable more fine-grained evaluations of appearance characteristics, we aim to develop metrics based on Multimodal Large Language Models (MLLMs) or pixel-level analysis in future work.", + "bbox": [ + 88, + 426, + 887, + 502 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Furthermore, we propose the PSFT and ORO methods to fine-tune the Open-Sora model (Zheng et al., 2024), improving its ability to generate physically plausible videos. Despite these improvements, certain limitations remain, specifically, the generation of blurry objects in some videos. We hope to address these challenges in future research by refining both the dataset and the fine-tuning strategies, aiming to produce videos that better maintain object visuals.", + "bbox": [ + 88, + 508, + 887, + 571 + ], + "page_idx": 14 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 155, + 56, + 815, + 70 + ], + "page_idx": 14 + }, + { + "type": "page_number", + "text": "15", + "bbox": [ + 478, + 922, + 493, + 934 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/2c3255e61507df64f2fe2b8fc33da6df4f8074be9bf5d02291a3cf3bb8a8a94a.jpg", + "image_caption": [ + "(a) A white paper roll falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 119, + 883, + 275 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/76661e958af011fe7f1f7ab37c8d6b11f4f98a6f04af442101dbe8308c1127ee.jpg", + "image_caption": [ + "(c) A black bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 297, + 883, + 452 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/f96ae24b9af0730f8094994e180d7d5a6e32804e7b580a5dadd002836de5fced.jpg", + "image_caption": [ + "(b) A transparent bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 476, + 883, + 630 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/14aef21ca7858494c097f6f67d50528c4b5917b1b19db5da86d4a491cd5a520f.jpg", + "image_caption": [ + "(d) A white bottle falls.", + "Figure 13. Examples of real world videos and annotations. We present video frames in the first row and mask annotations in the second row." + ], + "image_footnote": [], + "bbox": [ + 86, + 654, + 883, + 808 + ], + "page_idx": 15 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 71 + ], + "page_idx": 15 + }, + { + "type": "page_number", + "text": "16", + "bbox": [ + 477, + 922, + 495, + 934 + ], + "page_idx": 15 + }, + { + "type": "table", + "img_path": "images/1211a8336c5089da8a8c3424e1cc2df81e4f22b093cc82bb6236a03de951a3b1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AspectRequirements
Camera·The camera must be stabilized using a tripod.\n·The dropping object should remain visible throughout the entire fall.\n·The trajectory of the object should be sufficiently centered in the frame.\n·Ensure the slow-motion setting is configured to 120 fps.\n·Avoid a completely top-down perspective; the frame should include both the floor and the wall for spatial context.\n·It is acceptable to record one long video containing multiple drops at the same location.
Objects·Most objects should be rigid and non-deformable.\n·A limited number of flexible or deformable objects may be included, as such data is also valuable.
Dropping Procedure·Secure the object with a wire using tape, ensuring stability. Multiple tapings may be necessary for proper stabilization.\n·Visibility of the wire in the video is acceptable.\n·No body parts should appear in the frame. If this is challenging, consider having a partner monitor the camera or use screen-sharing software to view the camera feed on a laptop for uninterrupted framing.\n·Record videos in a horizontal orientation to simplify cropping and to help keep the frame free of unnecessary elements.\n·Use a short wire to enhance object stability.\n·The object should remain stationary before being dropped.
Scene Composition·Make the scenes dynamic and engaging. Include interactions with other objects, such as collisions or objects tipping over. Static objects should serve as active elements rather than mere background props.\n·Avoid filming in classroom or laboratory environments.\n·Include a variety of dropping heights.\n·Film in different environments, ensuring at least one setting is outside your apartment.\n·Minimize human shadows in the frame whenever possible.\n·Ensure good lighting and maintain strong contrast between the objects and the back-ground.
", + "bbox": [ + 89, + 92, + 883, + 854 + ], + "page_idx": 16 + }, + { + "type": "text", + "text": "Table 3. Key points of real world videos collection guideline. We have detailed requirements for camera, objects, dropping procedure and scene composition to ensure the quality, diversity and minimize ambiguity introduced by environments.", + "bbox": [ + 84, + 863, + 883, + 892 + ], + "page_idx": 16 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 71 + ], + "page_idx": 16 + }, + { + "type": "page_number", + "text": "17", + "bbox": [ + 477, + 922, + 495, + 934 + ], + "page_idx": 16 + }, + { + "type": "image", + "img_path": "images/945c3d2b2e7ba5dd24811fc027b02c812dd3fdb62673324359a47eefccc06ed5.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 460, + 281 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/4d595693598e6f902081fbae2160c14f17629bf42e1282931e980a4273a07e54.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 491, + 87, + 887, + 281 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/8f522784783a329f5017e6371582ae27e84586d17a8f7bcd9025f339933400e5.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 89, + 348, + 424, + 606 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/733aaf4a714c7ec870de8f5e762d4a545653a15ef5ea24677ad5c2400309aed0.jpg", + "image_caption": [ + "Figure 14. Video processing interface. (a) we annotate starting positions in the original long videos and clip them into multiple clips less than 12 seconds. (b) We drag the cropping box to crop the video size to an aspect ratio of 1:1.", + "(b)", + "Figure 15. Annotation details of real world videos. (a) Word cloud of objects in video captions. Our videos contain a variety of daily life objects. (b) Interface for annotating positive and negative points in the first frame. Red and blue dots indicate positive and negative points respectively. We annotate all objects in the midair and ground." + ], + "image_footnote": [], + "bbox": [ + 473, + 345, + 885, + 609 + ], + "page_idx": 17 + }, + { + "type": "table", + "img_path": "images/5ff8dcc1fc52105fef32fc975178bc49046b998c818452290cac625a89916132.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelResolutionNumber of FramesFPSGuidance ScaleSampling StepsNoise Scheduler
ClosedSora720 × 72015030---
Kling-V1.5960 × 960150301.0--
Kling-V1960 × 960150301.0--
Runway Gen31280 × 76815630---
OpenCogVideoX-5B-I2V720 × 4804886.050DDIM
DynamiCrafter512 × 32090300.750DDIM
Pyramid-Flow1280 × 768120244.010EulerDiscrete
Open-Sora512 × 51290307.030RFLOW
", + "bbox": [ + 86, + 702, + 885, + 873 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "Table 4. Inference details for models we evaluate, where “-” indicates the information is not available.", + "bbox": [ + 183, + 882, + 787, + 896 + ], + "page_idx": 17 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 70 + ], + "page_idx": 17 + }, + { + "type": "page_number", + "text": "18", + "bbox": [ + 477, + 922, + 493, + 934 + ], + "page_idx": 17 + }, + { + "type": "image", + "img_path": "images/c26bfecf28ebcde71af6d60da63253f75d02e0c5503f1425cbff24859ab09444.jpg", + "image_caption": [ + "(a) A brown bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 132, + 883, + 210 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/5f5749c22b33d6469cf285b89aba3d78b780ffbd4338568515ee93f4e1fa544d.jpg", + "image_caption": [ + "(b) A grey bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 241, + 883, + 321 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/1f5a8409a2aefddb489c74e7deb33bffefdf80fdb5c072687ddd0946e16f3e00.jpg", + "image_caption": [ + "(c) A grey paper cup falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 353, + 883, + 431 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/19fe4f4ece7488446d3a1550236f6f8bf176f70d2615cfa7db7c28a0720cf550.jpg", + "image_caption": [ + "(d) A paper cup falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 464, + 883, + 542 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/7ecc93d403dcb06758ac993647a892395af1264eeca956ba139d2929c18192ba.jpg", + "image_caption": [ + "(e) A white bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 574, + 883, + 654 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/c8f534dc359b0c6486ea7d10444e18fb31e91a7d173e50458a7fb898ac132de4.jpg", + "image_caption": [ + "(f) A white box falls.", + "Figure 16. Qualitative examples of Kling-V1 (Kuaishou, 2024). In (a) (b) (c) (f), objects have a tendency to fall. (b) (c) are roughly consistent with the laws of physics. In (a) (f), the shape of the object does not match the first frame. In (d), the paper cup is suspended in midair. In (e), new object is introduced. In (e), the model fails to correctly predict the collision that occurs after the white box falls and the chain of events that follows." + ], + "image_footnote": [], + "bbox": [ + 86, + 686, + 883, + 763 + ], + "page_idx": 18 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 815, + 71 + ], + "page_idx": 18 + }, + { + "type": "page_number", + "text": "19", + "bbox": [ + 477, + 922, + 495, + 934 + ], + "page_idx": 18 + }, + { + "type": "image", + "img_path": "images/d24e9d610f63859bf566728e5b51c496af6f6f54f828b2cc2aae2a5186055f4c.jpg", + "image_caption": [ + "(a) A black and grey glove falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 143, + 885, + 224 + ], + "page_idx": 19 + }, + { + "type": "image", + "img_path": "images/936b8ee3ceeca5f82d0050ae068b79e918e73267eaa429a43c2317f1f2323c25.jpg", + "image_caption": [ + "(b) A black bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 255, + 885, + 335 + ], + "page_idx": 19 + }, + { + "type": "image", + "img_path": "images/2d23c7b2c224aa44ab3a8eed9dfe17398040ed64c31737411568651ceb6dcf15.jpg", + "image_caption": [ + "(c) A blue and white box falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 366, + 885, + 446 + ], + "page_idx": 19 + }, + { + "type": "image", + "img_path": "images/20194bd551fbcc50f5676b0a019e1d10041918fadd0264051f4f9a7540545bac.jpg", + "image_caption": [ + "(d) A brown bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 477, + 885, + 556 + ], + "page_idx": 19 + }, + { + "type": "image", + "img_path": "images/baf79faae3094c985d469cccd5f8af1aef1f088b8c03e4b23c119ec86aebd807.jpg", + "image_caption": [ + "(e) A Coca-Cola can falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 587, + 885, + 667 + ], + "page_idx": 19 + }, + { + "type": "image", + "img_path": "images/8cb3aa9d253fc5e51c44a557e5629610fa5ad282a6ce25364e557518e7b8d6c7.jpg", + "image_caption": [ + "(f) A pink box falls.", + "Figure 17. Qualitative examples of Runway Gen3 (Runway, 2024). In (b) (e), objects have a tendency to fall. In (a) (e) (f), new objects are introduced. In (b) (d), the shape of the object does not match the first frame. In (c), the box is suspended in midair." + ], + "image_footnote": [], + "bbox": [ + 86, + 699, + 885, + 777 + ], + "page_idx": 19 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 816, + 71 + ], + "page_idx": 19 + }, + { + "type": "page_number", + "text": "20", + "bbox": [ + 475, + 922, + 496, + 934 + ], + "page_idx": 19 + }, + { + "type": "image", + "img_path": "images/a79a3d2c12bca59c6526e7216d60bb7580bc8c63576be8552b2f29dfd5c346d2.jpg", + "image_caption": [ + "(a) A black bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 138, + 885, + 218 + ], + "page_idx": 20 + }, + { + "type": "image", + "img_path": "images/498fa6c0164db5fd88370c112e6dd2c5829dbe74624f6e825ac28219d5f5aa3d.jpg", + "image_caption": [ + "(b) A black helmet falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 247, + 885, + 328 + ], + "page_idx": 20 + }, + { + "type": "image", + "img_path": "images/8317550ad7aa20a11f3bf97aa716e1da5f6f471ce296a6b0a5da5eba39db5c52.jpg", + "image_caption": [ + "(c) A paper box falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 358, + 885, + 439 + ], + "page_idx": 20 + }, + { + "type": "image", + "img_path": "images/5259adbc56734c97b69c0f5ac5a0debfc574cf0ee9fab5cae058c157503ada7b.jpg", + "image_caption": [ + "(d) A white bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 469, + 885, + 549 + ], + "page_idx": 20 + }, + { + "type": "image", + "img_path": "images/fb0eb57bfd7df70674700e7d467e475c936b995b0451b6a6746c321bb30fd4dc.jpg", + "image_caption": [ + "(e) A grey paper cup falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 580, + 885, + 660 + ], + "page_idx": 20 + }, + { + "type": "image", + "img_path": "images/dad22c2ccf02d28f88996ada3f6458c8f7ba92408c341e39e6da0ed00ee05fbb.jpg", + "image_caption": [ + "(f) A white box falls.", + "Figure 18. Qualitative examples of CogVideoX-5B-I2V (Yang et al., 2024c). In (a) - (f), objects have a tendency to fall. However, in all the videos, there are violations of physics. In (a) (b), the objects are divided into two parts. In (c) (d) (e), the shape of the object does not match the first frame. In (c), the trajectory is not a vertical fall. In (f), scene changes suddenly, which does not match the first frame." + ], + "image_footnote": [], + "bbox": [ + 86, + 691, + 789, + 771 + ], + "page_idx": 20 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 816, + 71 + ], + "page_idx": 20 + }, + { + "type": "page_number", + "text": "21", + "bbox": [ + 475, + 922, + 493, + 934 + ], + "page_idx": 20 + }, + { + "type": "image", + "img_path": "images/e39efd16222ce5ec5787e1ab30db7573f7cb53089f14019eb71cfee5130fa917.jpg", + "image_caption": [ + "(a) A black box falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 151, + 885, + 231 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/a17478f38168df434239dbbc27ca455093b6c1e40467cd5487d213bb5d83095d.jpg", + "image_caption": [ + "(b) A card holder falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 262, + 885, + 342 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/f5955939eff061d366f9461ca64daddccce438bc7cf26e0ca0177e4bea14e76c.jpg", + "image_caption": [ + "(c) A white bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 372, + 885, + 454 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/3064ab2bd099f6c34a0b0143af9b37cafbc9b07d4aff556a41357fd47bdbe8d3.jpg", + "image_caption": [ + "(d) A white box falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 484, + 885, + 564 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/f9b6d84ca868eb7b320e5bf66a6830342a093523d4a8c01e2b0d2c6c9b32e833.jpg", + "image_caption": [ + "(e) An orange and white box falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 594, + 885, + 674 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/b68b172758804959f5687238c0b53d284f904543618dda06d81c04419d71a2ce.jpg", + "image_caption": [ + "(f) A shoe falls.", + "Figure 19. Qualitative examples of DynamiCrafter (?). In all the videos, objects do not have a tendency to fall, suspended in the midair." + ], + "image_footnote": [], + "bbox": [ + 86, + 705, + 885, + 785 + ], + "page_idx": 21 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 816, + 71 + ], + "page_idx": 21 + }, + { + "type": "page_number", + "text": "22", + "bbox": [ + 475, + 922, + 495, + 934 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/b39f635b4b2874364c63137dcdc9fc15f4eb68ba57cc4f852a463fac4a5c56f0.jpg", + "image_caption": [ + "(a) A black bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 143, + 885, + 224 + ], + "page_idx": 22 + }, + { + "type": "image", + "img_path": "images/c3078aa13d861c89ebf70c3db430662cdcd8c83d8880aa9a934a258e5c3598e5.jpg", + "image_caption": [ + "(b) A green and white box falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 255, + 885, + 335 + ], + "page_idx": 22 + }, + { + "type": "image", + "img_path": "images/47bbef5b7ad9b2e303cbcdd98429261eea928bc17ba376000894eba09e78ab5b.jpg", + "image_caption": [ + "(c) A grey bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 364, + 885, + 445 + ], + "page_idx": 22 + }, + { + "type": "image", + "img_path": "images/d20954189b98d66653a95abacce5f2c333474ea3a756f9e105766842d1c52aaf.jpg", + "image_caption": [ + "(d) An orange tube falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 477, + 885, + 556 + ], + "page_idx": 22 + }, + { + "type": "image", + "img_path": "images/52a4ded90059019d5599737a9ccf91373f0a89472a4470044d57fa2d382b574c.jpg", + "image_caption": [ + "(e) A white bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 587, + 885, + 667 + ], + "page_idx": 22 + }, + { + "type": "image", + "img_path": "images/1bfe20845da001136df0ce41999f5d2267a843826b8f310807bc262f0f0570d5.jpg", + "image_caption": [ + "(f) A plastic box falls.", + "Figure 20. Qualitative examples of Pyramid-Flow (Jin et al., 2024). In (b) (d) (e), objects have a tendency to fall. In (a) (b) (e) (f), new objects are introduced. In (c), scene changes, which does not match the first frame.. In (d), the tube becomes blurry." + ], + "image_footnote": [], + "bbox": [ + 86, + 698, + 885, + 777 + ], + "page_idx": 22 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 816, + 71 + ], + "page_idx": 22 + }, + { + "type": "page_number", + "text": "23", + "bbox": [ + 475, + 922, + 495, + 934 + ], + "page_idx": 22 + }, + { + "type": "image", + "img_path": "images/161db114927f1a531685c756c1a59ca048d49f95035d117b63e02913d1aeda55.jpg", + "image_caption": [ + "(a) A bottle full of water falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 143, + 885, + 224 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/00dd072f248c8d96ba525c8f9026f6dbe513577c2833c0a39bcc58836058a3ae.jpg", + "image_caption": [ + "(b) A brown bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 255, + 885, + 335 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/20691688d65a9c34668843431f6da68506d385837a8adf32d934a8338cfbb623.jpg", + "image_caption": [ + "(c) A grey paper cup falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 366, + 885, + 445 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/20dc724f7197dd626747f2db293d23a957a1d7672a436a2fd07469a0a937b08a.jpg", + "image_caption": [ + "(d) A paper box falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 477, + 885, + 556 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/5f2dbd497dd96b551059198818fd41a1cc13a1d01d40d7814fd8343102c994a3.jpg", + "image_caption": [ + "(e) A white bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 587, + 885, + 667 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/5794ff6b8e6a1c23e1b350538a38f18063fb742919db3216ae76aa58e6f391f5.jpg", + "image_caption": [ + "(f) A white box falls.", + "Figure 21. Qualitative examples of Open-Sora (Zheng et al., 2024). In all the videos, objects do not have a tendency to fall, suspended in the midair. In (b) (d), scene changes suddenly, which does not match the first frame. In (e), new object is introduced." + ], + "image_footnote": [], + "bbox": [ + 86, + 698, + 885, + 777 + ], + "page_idx": 23 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 816, + 71 + ], + "page_idx": 23 + }, + { + "type": "page_number", + "text": "24", + "bbox": [ + 475, + 922, + 495, + 934 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/0cc35a21a9c1a24bb99fd5ae428c1b943237dcc4bf44654420f09f88cbbe622f.jpg", + "image_caption": [ + "(a) A brown bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 143, + 885, + 224 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/20453f58b53c0dbbefd7d26b5854ca263406b127771a6983ee453bcedd34a9b8.jpg", + "image_caption": [ + "(b) A grey eraser falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 255, + 885, + 335 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/d0de139686427ffdf841921b45e326470ebe6a127e77cc98801376148a86c3b4.jpg", + "image_caption": [ + "(c) A grey paper cup falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 366, + 885, + 445 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/2c9f209b0aeac72570d8c4fde360b1cf6b4dfcb2b6a0e8d4e853f7b3a78fa4d6.jpg", + "image_caption": [ + "(d) A transparent bottle falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 477, + 885, + 556 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/f52bf9a1a1b538e95d70fbf8e8072fe5c66e0fb960e1c0adc65706d6253840a0.jpg", + "image_caption": [ + "(e) A red wrapping paper falls." + ], + "image_footnote": [], + "bbox": [ + 86, + 587, + 885, + 667 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/a00eb2f6afd73e7890435740d404820471ec3c29a424ac89fa8f08f0f78a9a90.jpg", + "image_caption": [ + "(f) A white bottle falls.", + "Figure 22. Qualitative examples of our method (Open-Sora + PSFT + ORO). In all the videos, objects have a tendency to fall. However, the consistency of objects is still insufficient. In some frames, objects become blurry. Objects sometimes disappear after collision." + ], + "image_footnote": [], + "bbox": [ + 86, + 699, + 885, + 777 + ], + "page_idx": 24 + }, + { + "type": "header", + "text": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop", + "bbox": [ + 156, + 56, + 816, + 71 + ], + "page_idx": 24 + }, + { + "type": "page_number", + "text": "25", + "bbox": [ + 475, + 922, + 495, + 934 + ], + "page_idx": 24 + } +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_model.json b/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..813cd0c22a465ed5c0357f02283e82731c23dd00 --- /dev/null +++ b/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_model.json @@ -0,0 +1,4661 @@ +[ + [ + { + "type": "title", + "bbox": [ + 0.222, + 0.11, + 0.753, + 0.157 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.199, + 0.798, + 0.217 + ], + "angle": 0, + "content": "Chenyu Li \\(^{*1}\\) Oscar Michel \\(^{*1}\\) Xichen Pan \\(^{1}\\) Sainan Liu \\(^{2}\\) Mike Roberts \\(^{2}\\) Saining Xie" + }, + { + "type": "title", + "bbox": [ + 0.242, + 0.243, + 0.321, + 0.259 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.271, + 0.445, + 0.618 + ], + "angle": 0, + "content": "Large-scale pre-trained video generation models excel in content creation but are not reliable as physically accurate world simulators out of the box. This work studies the process of posttraining these models for accurate world modeling through the lens of the simple, yet fundamental, physics task of modeling object freefall. We show state-of-the-art video generation models struggle with this basic task, despite their visually impressive outputs. To remedy this problem, we find that fine-tuning on a relatively small amount of simulated videos is effective in inducing the dropping behavior in the model, and we can further improve results through a novel reward modeling procedure we introduce. Our study also reveals key limitations of post-training in generalization and distribution modeling. Additionally, we release a benchmark for this task that may serve as a useful diagnostic tool for tracking physical accuracy in large-scale video generative model development. Code is available at this repository: https://github.com/vision-x-nyu/pisa-experiments." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.653, + 0.218, + 0.669 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.678, + 0.477, + 0.845 + ], + "angle": 0, + "content": "Over the past year, video generation models have advanced significantly, inspiring visions of a future where these models could serve as realistic world models (Craik, 1967; LeCun, 2022; Hafner et al., 2019; 2023; Ha & Schmidhuber, 2018). State-of-the-art video generation models models exhibit impressive results in content creation (OpenAI, 2024; Kuaishou, 2024; Luma, 2024; Runway, 2024) and are already being used in advertising and filmmaking (Runway, 2025; NBC, 2025). These advancements have sparked a line of research that seeks to evolve these models from content creators to world simulators for embodied agents (Yang" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.853, + 0.475, + 0.88 + ], + "angle": 0, + "content": "*Equal contribution, alphabetical order. 1New York University 2Intel Labs." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.244, + 0.888, + 0.336 + ], + "angle": 0, + "content": "et al., 2023; 2024b; Agarwal et al., 2025). However, accurate world modeling is considerably more challenging than creative content creation because looking \"good enough\" is not sufficient: generated pixels must faithfully represent a world state evolving in accordance with the laws of physics and visual perspective." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.342, + 0.889, + 0.541 + ], + "angle": 0, + "content": "We find that although the generations of state-of-the-art models are impressive visually, these models still struggle to generate results that are accurate physically, even though these models are pretrained on internet-scale video data demonstrating a wide variety of complex physical interactions. The failure to ground and align visual generations to the laws of physics suggests that pretraining is not enough and a post-training stage is needed. Much like how pretrained Large Language Models (LLMs) need to be adapted through post-training before they can be useful conversational assistants, pretrained video generative models ought to be adapted through post-training before they can be deployed as physically accurate world simulators." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.547, + 0.889, + 0.849 + ], + "angle": 0, + "content": "In this work, we rigorously examine the post-training process of video generation models by focusing on the simple yet fundamental physics task of modeling object freefall, which we find is highly challenging for state-of-the-art models. Specifically, we study an image-to-video\\(^{1}\\) (I2V) scenario where the goal is to generate a video of an object falling and potentially colliding with other objects on the ground, starting from an initial image of the object suspended in midair. We chose to study this single task, rather than general physics ability as a whole, because its simplicity allows us to conduct controlled experiments that yield insights into the strengths and limitations of the post-training process, which we believe will become an increasingly important component of research in generative world modeling. Additionally, the simplicity of the dropping task allows it to be implemented in simulation which is desirable because it allows us to easily test the properties of dataset scaling, gives us access to ground truth annotations for evaluation, and gives us the ability to precisely manipulate the simulation environment for controlled experimentation." + }, + { + "type": "page_footnote", + "bbox": [ + 0.497, + 0.858, + 0.888, + 0.885 + ], + "angle": 0, + "content": "1We discuss our decision to formulate this task in the image-to-video setting instead of the video-to-video setting in Appendix A." + }, + { + "type": "aside_text", + "bbox": [ + 0.023, + 0.26, + 0.058, + 0.707 + ], + "angle": 270, + "content": "arXiv:2503.09595v1 [cs.CV] 12 Mar 2025" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.924, + 0.492, + 0.935 + ], + "angle": 0, + "content": "1" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.816, + 0.071 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.082, + 0.48, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.082, + 0.887, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.324, + 0.888, + 0.381 + ], + "angle": 0, + "content": "Figure 1. Our PISA (Physics-Informed Simulation and Alignment) evaluation framework includes a new video dataset, where objects are dropped in a variety of real-world (left) and synthetic (right) scenes. For visualization purposes, we depict object motion by overlaying multiple video frames in each image shown above. Our real-world videos enable us to evaluate the physical accuracy of generated video output, and our synthetic videos enable us to improve accuracy through the use of post-training alignment methods." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.405, + 0.477, + 0.571 + ], + "angle": 0, + "content": "Named after Galileo's famous dropping experiment, we introduce the PISA (Physics-Informed Simulation and Alignment) framework for studying physics post-training in the context of the dropping task. PISA includes new real and simulated video datasets, as shown in Figure 1, containing a diverse set of dropping scenarios. PISA also includes a set of task-specific metrics that focus on measuring physical accuracy. Our real-world videos and metrics enable us to evaluate the physical accuracy of generated video output, and our synthetic videos enable us to improve accuracy through a post-training process we introduce." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.579, + 0.478, + 0.837 + ], + "angle": 0, + "content": "Our study reveals that current state-of-the-art video generative models struggle significantly with the task of physically accurate object dropping. Generated objects frequently exhibit impossible behaviors, such as floating midair, defying gravity, or failing to preserve realistic trajectories during freefall. However, we find that simple fine-tuning can be remarkably effective: fine-tuning an open-source model on a small dataset of just a few thousand samples enables it to vastly outperform state-of-the-art models in physical accuracy. We further observe that pretrained models are critical for success; models initialized randomly, without leveraging pretraining on large-scale video datasets, fail to achieve comparable results. We also introduce a novel framework for reward modeling that yields further improvement. We demonstrate that our reward learning system is highly flexible in that different reward functions can be chosen to target different axes of physical improvement." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.843, + 0.479, + 0.906 + ], + "angle": 0, + "content": "Our analysis also reveals key limitations. First, we see that model performance degrades when tasked with scenarios outside the training distribution, such as objects dropping from unseen depths or heights. Additionally, while our post" + }, + { + "type": "text", + "bbox": [ + 0.495, + 0.405, + 0.887, + 0.452 + ], + "angle": 0, + "content": "trained model generates object motion that is 3D-consistent and physically accurate, we observe misalignment between the generated and ground truth dropping time distribution." + }, + { + "type": "text", + "bbox": [ + 0.495, + 0.457, + 0.889, + 0.61 + ], + "angle": 0, + "content": "These findings indicate that post-training is likely to be an essential component of future world modeling systems. The challenges we identify in this relatively simple task are likely to persist when modeling more sophisticated physical phenomena. By introducing the PISA framework and benchmark, we provide a useful diagnostic tool for researchers to test whether models are on the path to acquiring general physical abilities, as well as identify key limitations that researchers should be aware of when integrating new capabilities into their models through post-training." + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.629, + 0.64, + 0.644 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.495, + 0.654, + 0.889, + 0.897 + ], + "angle": 0, + "content": "Modeling Intuitive Physics. Intuitive physics refers to the innate or learned human capacity to make quick and accurate judgments about the physical properties and behaviors of objects in the world, such as their motion, stability, or interactions. This ability, present even in infancy (Spelke et al., 1992; Baillargeon, 2004; Battaglia et al., 2013), is crucial for navigating and understanding everyday life. Replicating intuitive physics is a foundational step toward creating systems that can interact effectively and safely in dynamic, real-world environments (Lake et al., 2017). Gravity, as a core component of intuitive physics, plays a pivotal role in both domains. It is one of the most universal and observable physical forces, shaping our expectations about object motion, stability, and interaction (Hamrick et al., 2016; Ullman et al., 2017). Many studies in cognitive science (Battaglia et al., 2013) and AI (Wu et al., 2015; Bear et al., 2021) have" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.924, + 0.493, + 0.935 + ], + "angle": 0, + "content": "2" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.057, + 0.816, + 0.073 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.086, + 0.477, + 0.132 + ], + "angle": 0, + "content": "relied on physics engines to evaluate and model intuitive physics. Our work uses the Kubric engine (Greff et al., 2022) to generate training videos." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.138, + 0.478, + 0.426 + ], + "angle": 0, + "content": "Video Generation Models as World Simulators. Video generation has long been an intriguing topic in computer vision, particularly in the context of predicting future frames (Srivastava et al., 2015; Xue et al., 2016). More recently, as large-scale generative models have become prominent, Yang et al. explored how a wide range of real-world dynamics and decision-making processes can be expressed in terms of video modeling (Yang et al., 2024b; 2023). The introduction of the Sora model (OpenAI, 2024) marked a leap in the quality of generated videos and ignited interest in leveraging such models as \"world simulators.\" Over the past year, numerous video generation models have emerged, some open-source (Zheng et al., 2024; Yang et al., 2024c; Jin et al., 2024; Agarwal et al., 2025) and others commercially available (Kuaishou, 2024; Luma, 2024; Runway, 2024; OpenAI, 2024). Related to our work, Kang et al. (Kang et al., 2024) study the extent to which video generation models learn generalizable laws of physics when trained on 2D data from a synthetic environment." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.433, + 0.478, + 0.735 + ], + "angle": 0, + "content": "Evaluating Video Generation Models. Traditional image-based metrics for generative modeling, such Fréchet inception distance (FID) (Heusel et al., 2017) or inception score (IS) (Salimans et al., 2016), can be incorporated into the video domain, either by applying them on a frame-by-frame basis or by developing video-specific versions, such as Fréchet video distance (FVD) (Unterthiner et al., 2018). Going beyond distribution matching measures, several benchmarks have developed suites of metrics that aim to better evaluate the semantic or visual quality of generated videos. For example, V-Bench (Huang et al., 2024) offers a more granular evaluation by measuring video quality across multiple dimensions, such as with respect to subject consistency or spatial relationships. In physics, some works, such as VideoPhy (Bansal et al., 2024) and PhyGenBench (Meng et al., 2024), evaluate in the T2V setting by utilizing multimodal large language models (MLLM) to generate a VQA-based score. More recently, Cosmos (Agarwal et al., 2025) and Physics-IQ (Motamed et al., 2025), evaluate physics in the image-to-video and video-to-video settings." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.754, + 0.199, + 0.77 + ], + "angle": 0, + "content": "3. PisaBench" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.78, + 0.475, + 0.827 + ], + "angle": 0, + "content": "Our benchmark, PisaBench, examines the ability of video generative models to produce accurate physical phenomena by focusing on a straightforward dropping task." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.842, + 0.338, + 0.858 + ], + "angle": 0, + "content": "3.1. Task Definition & Assumptions" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.866, + 0.476, + 0.897 + ], + "angle": 0, + "content": "Our task can be summarized as follows: given an image of an object suspended in midair, generate a video of the object" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.085, + 0.86, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.344, + 0.848, + 0.358 + ], + "angle": 0, + "content": "Figure 2. The setup for collecting real-world videos." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.383, + 0.887, + 0.49 + ], + "angle": 0, + "content": "falling and colliding with the ground and potentially other objects. Since a video is an incomplete partial observation of the 4D world, we make a number of assumptions to constrain the task space. These assumptions are crucial for ensuring that our metrics are reliable signals for physical accuracy, since they are only approximations of task success computed from a single ground truth and generated video." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.497, + 0.889, + 0.648 + ], + "angle": 0, + "content": "Specifically, we assume that the falling object is completely still in the initial frame, that only the force of gravity is acting on the object while it falls, and that the camera does not move. The first two assumptions are necessary for the image-to-video setting. Since we do not provide multiple frames as input, it is otherwise impossible to establish the initial velocity or acceleration of the falling object without these assumptions. The last assumption is necessary as our metrics derive from the motion of segmentation masks, which would be affected in the presence of camera motion." + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.665, + 0.651, + 0.679 + ], + "angle": 0, + "content": "3.2. Real World Data" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.696, + 0.697, + 0.817 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.696, + 0.882, + 0.817 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.497, + 0.828, + 0.886, + 0.856 + ], + "angle": 0, + "content": "Figure 3. Statistics of the real-world data: (a) number of objects in each video, (b) the proportions of different scenes in the videos." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.861, + 0.887, + 0.906 + ], + "angle": 0, + "content": "Real World Videos. We collect a set of 361 real-world videos demonstrating the dropping task for evaluation. As is shown in Figure 4, the dataset includes a diverse set" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.924, + 0.492, + 0.935 + ], + "angle": 0, + "content": "3" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.816, + 0.073 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.086, + 0.473, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.31, + 0.476, + 0.366 + ], + "angle": 0, + "content": "Figure 4. Examples of various objects included in our dataset. For simulation, we utilize the GSO dataset (Downs et al., 2022), while for the real-world dataset, we curate our own set of common household objects." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.398, + 0.476, + 0.595 + ], + "angle": 0, + "content": "of objects with different shapes and sizes, captured across various settings such as offices, kitchens, parks, and more (see Figure 3). Each video begins with an object suspended by an invisible wire in the first frame, which is necessary to enforce the assumption that objects are stationary at the start of the video. This assumption is required in our imaged-to-video setting; otherwise, the initial velocity of an object is ambiguous. We cut the video clips to begin as soon as the wire is released. We record the videos in slow-motion at 120 frames per second (fps) with cellphone cameras mounted on tripods to eliminate camera motion. An example of our video collection setup is shown in Figure 2. Additional details on our collection system are provided in Appendix H." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.602, + 0.476, + 0.707 + ], + "angle": 0, + "content": "Simulated Test Videos. Since our post-training process uses a dataset of simulated videos, we also create a simulation test-set of 60 videos for understanding sim2real transfer. We create two splits of 30 videos each: one featuring objects and backgrounds seen during training, and the other featuring unseen objects and backgrounds. See Section 4.1 for details on how our simulated data is created." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.715, + 0.475, + 0.807 + ], + "angle": 0, + "content": "Annotations. As is shown in Figure 5, we annotate each video with a caption and segmentation masks estimated from the SAM 2 (Ravi et al., 2024) video segmentation model. We create a descriptive caption for each object in the format of “{object description} falls.” This caption is used to provide context to the task when text input is supported." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.822, + 0.174, + 0.836 + ], + "angle": 0, + "content": "3.3. Metrics" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.846, + 0.476, + 0.907 + ], + "angle": 0, + "content": "We propose three metrics to assess the accuracy of trajectories, shape fidelity, and object permanence. Each of our metrics compare frames from the ground-truth video with the generated video. Further details about the metrics, including" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.081, + 0.888, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.497, + 0.328, + 0.888, + 0.385 + ], + "angle": 0, + "content": "Figure 5. Example of annotations in real-world data. For segmentation masks, we manually annotate first frame and utilize SAM 2 to produce segmentation masks across frames. For captions, we annotate “{object description} falls.” for all video segments." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.413, + 0.886, + 0.444 + ], + "angle": 0, + "content": "their formulas and our resampling procedure for accounting for differences in fps, is described in Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.451, + 0.888, + 0.512 + ], + "angle": 0, + "content": "Trajectory L2. For each frame in both the generated video and ground truth, we calculate the centroid of the masked region. After doing this, we compute the average \\(L_{2}\\) distance between the centroids of corresponding frames." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.519, + 0.888, + 0.565 + ], + "angle": 0, + "content": "Chamfer Distance (CD). To assess the shape fidelity of objects, we calculate the Chamfer Distance (CD) between the mask regions of the generated video and ground truth." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.572, + 0.888, + 0.633 + ], + "angle": 0, + "content": "Intersection over Union (IoU). We use the Intersection over Union (IoU) metric to evaluate object permanence. The IoU measures objects' degree of overlap between the generated video and ground truth." + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.649, + 0.663, + 0.663 + ], + "angle": 0, + "content": "3.4. Evaluation Results" + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.672, + 0.888, + 0.809 + ], + "angle": 0, + "content": "We evaluate 4 open models including CogVideoX-5B-I2V(Yang et al., 2024c), DynamiCrafter(Xing et al., 2023), Pyramid-Flow(Jin et al., 2024), and Open-Sora-V1.2(Zheng et al., 2024), as well as 4 proprietary models including Sora (OpenAI, 2024), Kling-V1(Kuaishou, 2024), Kling-V1.5(Kuaishou, 2024), and Runway Gen3 (Runway, 2024). We also evaluate OpenSora post-trained through the processes of Supervised Fine-Tuning (PSFT) and Object Reward Optimization (ORO); see Section 4 for details." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.815, + 0.889, + 0.907 + ], + "angle": 0, + "content": "The results of running the baseline models on the benchmark indicate a consistent failure to generate physically accurate dropping behavior, despite the visual realism of their generated frames. Qualitatively, we see common failure cases in Figure 6, such as implausible object deformations, floating, hallucination of new objects, and unrealistic special" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.924, + 0.492, + 0.935 + ], + "angle": 0, + "content": "4" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.816, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.086, + 0.887, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.309, + 0.889, + 0.366 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison of results on real test set (row 1-2), simulated seen test set (row 3-4) and simulated unseen test set (row 5-6). We present the results of popular open-source and commercially available models alongside those of models fine-tuned through our method. Existing models often struggle to generate videos depicting objects falling, whereas our PSFT method effectively introduces knowledge of free-fall into the model. ORO enables the model to more accurately learn object motion and shape." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.378, + 0.475, + 0.453 + ], + "angle": 0, + "content": "effects. We further visualize a random subset of generated trajectories on the left of Figure 8. In many cases, the object remains completely static, and sometimes the object even moves upward. When downward motion is present, it is often slow or contains unrealistic horizontal movement." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.472, + 0.294, + 0.49 + ], + "angle": 0, + "content": "4. Physics Post-Training" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.499, + 0.477, + 0.651 + ], + "angle": 0, + "content": "We present a post-training process to address the limitations of current models described in Section 3.4. We utilize simulated videos that demonstrate realistic dropping behavior. Our approach for post-training is inspired by the two-stage pipeline consisting of supervised fine-tuning followed by reward modeling commonly used in LLMs. We find that our pipeline improves performance on both real and simulated evaluations, with greater gains observed in simulation. This is due to the sim-to-real gap, though our approach still shows substantial gains in transferring to real-world data." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.666, + 0.312, + 0.682 + ], + "angle": 0, + "content": "4.1. Simulated Adaptation Data" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.69, + 0.476, + 0.901 + ], + "angle": 0, + "content": "The first stage of our approach involves supervised fine-tuning. We use Kubric (Greff et al., 2022), a simulation and rendering engine designed for scalable video generation, to create simulated videos of objects dropping and colliding with other objects on the ground. Each video consists of 1-6 dropping objects onto a (possibly empty) pile of up to 4 objects underneath them. The videos are 2 seconds long, consisting of 32 frames at 16 fps. The objects are sourced from the Google Scanned Objects (GSO) dataset (Downs et al., 2022), which provides true-to-scale 3D models created from real-world scans across diverse categories (examples shown in Figure 4). The camera remains stationary in each video and is oriented parallel to the ground plane. To introduce variability, we randomly sample the camera height" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.378, + 0.886, + 0.439 + ], + "angle": 0, + "content": "between 0.4 and 0.6 meters and position objects between 1 and 3 meters away from the camera, which corresponds to the distributions observed in the real-world dataset. More information about the dataset can be found in Appendix K." + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.455, + 0.813, + 0.47 + ], + "angle": 0, + "content": "4.2. Physics Supervised Fine-Tuning (PSFT)." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.486, + 0.685, + 0.588 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.486, + 0.884, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.589, + 0.684, + 0.689 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.588, + 0.885, + 0.689 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.496, + 0.7, + 0.886, + 0.783 + ], + "angle": 0, + "content": "Figure 7. Plots (a), (b), and (c) demonstrate that our metrics tend to improve with further training and that leveraging a pre-trained video diffusion model enhances performance compared to random initialization. In plot (d), the size of the training dataset varies in each training run (each consisting of 5k steps). With only 5k samples, we can achieve optimal results." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.8, + 0.887, + 0.906 + ], + "angle": 0, + "content": "We use the pretrained Open-Sora v1.2 (Zheng et al., 2024) model as our base model and fine-tune it on our simulated video dataset. We employ Open-Sora v1.2's rectified flow training objective without modification (Liu et al., 2022). Each fine-tuning experiment is conducted with a batch size of 128 and a learning rate of \\(1\\mathrm{e} - 4\\) on two 80GB NVIDIA A100 GPUs. As shown in Figure 6, fine-tuning with this" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.924, + 0.492, + 0.935 + ], + "angle": 0, + "content": "5" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.816, + 0.071 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.073, + 0.887, + 0.348 + ], + "angle": 0, + "content": "
MethodRealSim (Seen)Sim (Unseen)
L2 (↓)CD (↓)IoU (↑)L2 (↓)CD (↓)IoU (↑)L2 (↓)CD (↓)IoU (↑)
ProprietarySora (OpenAI, 2024)0.1740.4880.0650.1490.4460.0400.1400.4190.031
Kling-V1 (Kuaishou, 2024)0.1570.4250.0560.1420.4150.0320.1450.4370.028
Kling-V1.5 (Kuaishou, 2024)0.1550.4240.0580.1370.3960.0330.1320.4050.029
Runway Gen3 (Runway, 2024)0.1870.5260.0420.1700.5090.0400.1490.4600.038
OpenCogVideoX-5B-I2V (Yang et al., 2024c)0.1380.3660.0800.1120.3150.0200.1010.2900.020
DynamiCrafter (Xing et al., 2023)0.1870.5040.0210.1570.4850.0390.1360.4300.033
Pyramid-Flow (Jin et al., 2024)0.1750.4850.0620.1260.3520.0590.1300.3810.048
Open-Sora (Zheng et al., 2024)0.1750.5020.0690.1390.4090.0360.1300.3680.034
OursOpen-Sora + PSFT (base)0.0760.1880.1390.0360.0880.1650.0280.0580.129
base + ORO (Seg)0.0750.1830.1420.0330.0760.1700.0320.0630.145
base + ORO (Flow)0.0670.1640.1360.0260.0620.1220.0220.0450.071
base + ORO (Depth)0.0670.1590.1290.0310.0720.1240.0220.0460.096
" + }, + { + "type": "table_caption", + "bbox": [ + 0.084, + 0.357, + 0.889, + 0.429 + ], + "angle": 0, + "content": "Table 1. PisaBench Evaluation Results. This table compares the performance of four proprietary models, four open models, and the models fine-tuned with PSFT and \\(\\mathrm{PSFT + ORO}\\) on our real-world and simulated test set which is decomposed into seen and unseen object splits. Across all metrics, our PSFT models outperform all other baselines, including proprietary models like Sora. Reward modeling further enhances results, with segmentation rewards improving the shape-based IoU metric and optical rewards and depth rewards enhancing the motion-based L2 and CD metrics. This suggests that rewards can be flexibly adjusted to target specific aspects of performance." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.452, + 0.477, + 0.709 + ], + "angle": 0, + "content": "data alone is sufficient to induce realistic dropping behavior in the model. Quantitatively, our PSFT model substantially improves on both our simulated and real-world benchmark, as shown in Table 1. Dataset size. We conduct an ablation study on the number of training samples to understand the amount of data required for optimal performance on our benchmark. We create random subsets from 500 to 20,000 samples and train our model for 5,000 gradient steps on each subset. Notably, as shown in Figure 7, only 5,000 samples are needed to achieve optimal results. Effect of pretraining. Additionally, we investigate the impact of Open-Sora's pre-training on adaptation. We randomly initialize the Open-Sora's denoising network while keeping the pre-trained initialization of the compressor network and train the model on a dataset of 5k training samples. As shown in Figure 8, the learned knowledge from Open-Sora's pretraining plays a critical role in our task." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.716, + 0.475, + 0.792 + ], + "angle": 0, + "content": "Overall, using PSFT on only 5k samples is sufficient to push Open-Sora's performance past all other evaluated models, including state-of-the-art commercial video generators, by a wide margin. This is made possible by leveraging the knowledge from the sufficiently pre-trained base model." + }, + { + "type": "title", + "bbox": [ + 0.085, + 0.808, + 0.376, + 0.823 + ], + "angle": 0, + "content": "4.3. Object Reward Optimization (ORO)" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.832, + 0.476, + 0.892 + ], + "angle": 0, + "content": "In the second stage, we propose Object Reward Optimization (ORO) to use reward gradients to guide the video generation model toward generating videos where the object's motion and shape more closely align with the ground truth." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.453, + 0.885, + 0.583 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.496, + 0.598, + 0.887, + 0.682 + ], + "angle": 0, + "content": "Figure 8. On the left, we plot random trajectories from the baseline models in Table 1. On the right, we show random trajectories from our fine-tuned model. The baseline trajectories exhibit unrealistic behavior, and most of them stay completely static. On the right, we see the trajectories consistently falling downward with collision and rolling behavior being modeled after the point of contact." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.693, + 0.889, + 0.8 + ], + "angle": 0, + "content": "We follow the VADER framework from (Prabhudesai et al., 2024) and introduce three reward models. The differences between our approach and VADER include: (1) our reward model utilizes both generated videos and ground truth instead of generated videos and conditioning. (2) gradients propagate through all denoising time steps in fine-tuning. Consequently, the VADER objective is modified as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.81, + 0.887, + 0.83 + ], + "angle": 0, + "content": "\\[\nJ (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.838, + 0.886, + 0.884 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}\\) is the ground truth dataset, \\(p_{\\theta}(.)\\) is a given video diffusion model, \\(x_0^{\\prime}, x_0 \\in \\mathbb{R}^{H \\times W \\times 3}\\) are generated video and ground truth, and \\(c \\in \\mathbb{R}^{H \\times W \\times 3}\\) is the initial image." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.891, + 0.887, + 0.906 + ], + "angle": 0, + "content": "Segmentation Reward. We utilize SAM 2 (Ravi et al.," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.924, + 0.492, + 0.935 + ], + "angle": 0, + "content": "6" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.057, + 0.816, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.085, + 0.475, + 0.148 + ], + "angle": 0, + "content": "2024) to generate segmentation masks across frames for generated videos. We define segmentation reward as the IoU between the dropping object's mask in generated video and the mask from the ground truth simulated segmentation." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.153, + 0.476, + 0.215 + ], + "angle": 0, + "content": "Optical Flow Reward. We utilize RAFT (Teed & Deng, 2020) to generate generated video's optical flow \\( V^{\\mathrm{gen}} \\) and ground truth's optical flow \\( V^{\\mathrm{gt}} \\). We define the optical flow reward as \\( R(x_0', x_0) = -|V^{\\mathrm{gen}} - V^{\\mathrm{gt}}| \\)." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.221, + 0.476, + 0.282 + ], + "angle": 0, + "content": "Depth Reward. We utilize Depth-Anything-V2 (Yang et al., 2024a) to generate generated video's depth map \\( D^{\\mathrm{gen}} \\) and ground truth's depth map \\( D^{\\mathrm{gt}} \\). We define the optical flow reward as \\( R(x_0', x_0) = -|D^{\\mathrm{gen}} - D^{\\mathrm{gt}}| \\)." + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.289, + 0.457, + 0.305 + ], + "angle": 0, + "content": "Details on implementation can be found in Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.312, + 0.476, + 0.418 + ], + "angle": 0, + "content": "We begin from the checkpoint of the first stage, which is trained on 5,000 samples trained over 5,000 gradient steps. We then fine-tune the model with ORO on the simulated dataset, using a batch size of 1 and two 80GB NVIDIA A100 GPUs for each fine-tuning experiment. We set a learning rate of \\(1\\mathrm{e} - 6\\) for segmentation reward and depth reward and \\(1\\mathrm{e} - 5\\) for optical flow." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.425, + 0.476, + 0.531 + ], + "angle": 0, + "content": "As shown in Table 1, incorporating ORO in reward modeling further improves performance. Additionally, each reward function enhances the aspect of physicality that aligns with its intended purpose—segmentation rewards improve shape accuracy, while flow rewards and depth rewards improve motion accuracy. This demonstrates the process is both modular and interpretable." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.55, + 0.421, + 0.568 + ], + "angle": 0, + "content": "5. Assessing Learned Physical Behavior" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.576, + 0.476, + 0.698 + ], + "angle": 0, + "content": "Having introduced our post-training approaches in Section 4, we probe into the model's understanding of the interaction between gravity and perspective—the two laws that determine the dynamics of our videos. We first test if the learned physical behavior of our model can generalize to dropping heights and depths beyond its training distribution. Then, we study the ability of the model to learn the probability distribution induced by the uncertainty of perspective." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.714, + 0.437, + 0.73 + ], + "angle": 0, + "content": "5.1. Generalization to Unseen Depths and Heights" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.737, + 0.476, + 0.829 + ], + "angle": 0, + "content": "Depth and height are the main factors that affect the dynamics of a falling object in our videos. We can see this by combining the laws of gravity with perspective under our camera assumptions to model the object's image \\(y\\) coordinate as a function of time (further details on our coordinate system are described in Appendix G):" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.839, + 0.476, + 0.873 + ], + "angle": 0, + "content": "\\[\ny (t) = \\frac {f}{Z} \\left(Y _ {0} - \\frac {1}{2} g t ^ {2}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.891, + 0.476, + 0.906 + ], + "angle": 0, + "content": "From Equation (2), we see that the random variables that af" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.085, + 0.885, + 0.131 + ], + "angle": 0, + "content": "fect object motion are \\( Z \\) (depth) and \\( Y \\) (height) (the camera focal length \\( f \\) is fixed). Thus, we are interested in testing generalization on unseen values of \\( Y \\) and \\( Z \\)." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.138, + 0.887, + 0.275 + ], + "angle": 0, + "content": "We create a simulated test set in which a single object is dropped from varying depths and heights, using objects and backgrounds unseen during training. We uniformly sample depth and height values (in meters) from the Cartesian product of the ranges [1, 5] and [0.5, 2.5], respectively. The camera height is fixed at \\(0.5m\\), and depth-height pairs outside the camera viewing frustum are discarded. A sample is in-distribution (ID) if its dropping depth and height both fall in the range [1, 3] and [0.5, 1.5]." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.282, + 0.887, + 0.343 + ], + "angle": 0, + "content": "Since we have access to the ground truth dropping time in simulation, we also employ a dropping time error, a metric we describe in Appendix B. Our analysis in Table 2 shows that performance degrades for out-of-distribution scenarios." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.35, + 0.887, + 0.411 + ], + "angle": 0, + "content": "Since depth and height are the main physical quantities that affect falling dynamics, this finding indicates that our model may struggle to learn a fully generalizable law that accounts for the interaction of perspective and gravity." + }, + { + "type": "table", + "bbox": [ + 0.499, + 0.423, + 0.887, + 0.482 + ], + "angle": 0, + "content": "
SettingL2 (↓)Chamfer (↓)IOU (↑)Time Error (↓)
ID0.0360.0880.1550.091
OOD0.0440.1430.0490.187
" + }, + { + "type": "table_caption", + "bbox": [ + 0.497, + 0.491, + 0.887, + 0.548 + ], + "angle": 0, + "content": "Table 2. Results of our metrics on in-distribution (ID) and out-of-distribution (OOD) depth-height combinations. The values used for depth range from \\(1 - 5\\mathrm{m}\\) (ID range [1,3]) and height values range from 0.5-2.5 (ID range [0.5, 1.5])." + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.572, + 0.693, + 0.587 + ], + "angle": 0, + "content": "5.2. Distributional Analysis" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.604, + 0.653, + 0.714 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.659, + 0.603, + 0.885, + 0.714 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.496, + 0.729, + 0.887, + 0.786 + ], + "angle": 0, + "content": "Figure 9. Demonstration of ambiguity in 2D perspective projections. Each of the three clouds appears the exact same in the camera's image. The right side shows how we perform a scale and translation augmentation to generate deliberately ambiguous data." + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.8, + 0.887, + 0.906 + ], + "angle": 0, + "content": "The evolution of a physical system is not uniquely determined by a single initial image, since the lossy uncertainty of perspective induces a distribution of possible outcomes as shown in Figure 9. An ideal video world model should (1) output videos that are faithful to the evolution of some plausible world state and (2) provide accurate coverage across the entire distribution of the world that is possible from" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.923, + 0.492, + 0.935 + ], + "angle": 0, + "content": "7" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.057, + 0.816, + 0.073 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.086, + 0.477, + 0.176 + ], + "angle": 0, + "content": "its conditioning signal. In this section, we examine these two facets by studying \\( p(t|y) \\): the distribution of dropping times possible from an object at coordinate \\( y \\) in the image plane. To do this, we create a simulated dataset that has a much wider distribution \\( p(t|y) \\) than our PSFT dataset. See Appendix F for more details on its construction." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.187, + 0.475, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.303, + 0.476, + 0.373 + ], + "angle": 0, + "content": "Figure 10. Examples of model trajectories lifted to 3D. The blue line represents the height of the camera ray passing through the bottom of the dropping object as a function of depth. The set of possible dropping trajectories at a given depth are depicted in gray. The lifted trajectory of the model is depicted in green." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.389, + 0.473, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.549, + 0.476, + 0.605 + ], + "angle": 0, + "content": "Figure 11. Visualizing \\( p(t|y) \\) misalignment for different images. Green shows the ground-truth CDF, orange is the 32-frame quantized version, and blue is the empirical CDF of 128 different samples of dropping times from the model." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.612, + 0.384, + 0.627 + ], + "angle": 0, + "content": "Testing (1): 3D faithfulness of trajectories." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.635, + 0.476, + 0.846 + ], + "angle": 0, + "content": "After training our model on this new dataset, we test whether its trajectories are consistent with a valid 3D world state. We first obtain an estimated dropping time from generated videos using the procedure described in Section 5.1. Using knowledge of the camera position, focal length, sensor width, and \\( y \\), we can obtain an implied depth and height of the trajectory. We can then back-project the video trajectory to 3D and analyze whether they constitute physically accurate trajectories. We give further details about this process in Appendix G. As show in Figure 10, we find that our model's lifted trajectories consistently align with the 3D trajectory at the height and depth implied by its dropping time, giving evidence that the model's visual outputs are faithful to some plausible real-world state." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.853, + 0.347, + 0.869 + ], + "angle": 0, + "content": "Testing (2): distributional alignment." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.876, + 0.475, + 0.907 + ], + "angle": 0, + "content": "Going beyond the level of individual trajectories, we study the model's learned conditional distribution \\( p(t|y) \\). We" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.085, + 0.886, + 0.176 + ], + "angle": 0, + "content": "create 50 different initial images with differing values of \\( y \\), generate 128 different videos from each, and estimate the dropping time in each video. Using the laws of gravity, the laws of perspective, and the assumption of uniform depth sampling in our dataset, we can analytically derive the probability \\( p(t|y) \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.197, + 0.887, + 0.238 + ], + "angle": 0, + "content": "\\[\np (t | y) = \\left\\{ \\begin{array}{l l} \\frac {g t}{\\left(Z _ {\\max } - Z _ {\\min }\\right) \\beta}, & t _ {\\min } \\leq t \\leq t _ {\\max } \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.257, + 0.886, + 0.288 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a constant that depends on \\(f\\), \\(y\\) and the camera height. The derivation is given in Appendix E." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.295, + 0.887, + 0.536 + ], + "angle": 0, + "content": "We then measure goodness-of-fit for each of the 50 experiments using the Kolmogorov-Smirnov (KS) test (Massey Jr, 1951). The null hypothesis of the KS test is that the two distributions being compared are equal, and we consider p-values less than 0.05 as evidence of misalignment. Since our measured times have limited precision and can only take 32 distinct values—due to estimating the contact frame—we approximate the ground truth \\(p(t|y)\\) using a Monte Carlo method. We sample 1000 values from the ground truth distribution and then quantized them into 32 bins corresponding to their frame, which we use as ground truth observations in the KS test. We find that in all 50/50 cases, the p-value from the test is less than 0.05, which provides evidence that the model does not learn the correct distribution of dropping times. We visualize the misalignment between the empirical CDF of the model's in Figure 11." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.544, + 0.887, + 0.604 + ], + "angle": 0, + "content": "In summary, while our model's trajectories show promising tendencies to ground themselves to plausible 3D world states, the range of possible outputs from the model does not align with the ground truth distribution." + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.624, + 0.616, + 0.639 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.65, + 0.887, + 0.906 + ], + "angle": 0, + "content": "This work studies post-training as an avenue for adapting adapting pre-trained video generator into world models. We introduce a post-training strategy that is highly effective in aligning our model. Our work raises interesting insights into the learned distributions of generative models. Qualitatively, large scale image or video generative models appear to excel at generating likely samples from the data distribution, but this alone does not imply that they match the data distribution well in its entirety. As long as a model is able to generate likely samples, global distributional misalignment is not necessarily a problem for content creation. However, this problem becomes critical for world models, where alignment across the entire distribution is necessary for faithful world simulation. The insights revealed by our study, made possible by our constrained and tractable setting, indicate that although post-training improves per-sample accuracy, general distributional alignment remains unsolved." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.924, + 0.492, + 0.935 + ], + "angle": 0, + "content": "8" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.057, + 0.816, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.084, + 0.238, + 0.101 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.11, + 0.477, + 0.246 + ], + "angle": 0, + "content": "We thank Boyang Zheng, Srivats Poddar, Ellis Brown, Shengbang Tong, Shusheng Yang, Jihan Yang, Daohan Lu, Anjali Gupta and Ziteng Wang for their help with data collection. We thank Jiraphon Yenphraphai for valuable assistance in setting up our simulation code. We thank Runway and Kling AI for providing API credit. SX also acknowledges support from Intel AI SRS, Korean AI Research Hub, Open Path AI Foundation, Amazon Research Award, Google TRC program, and NSF Award IIS-2443404." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.265, + 0.182, + 0.281 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.289, + 0.476, + 0.35 + ], + "angle": 0, + "content": "Agarwal, N., Ali, A., Bala, M., Balaji, Y., Barker, E., Cai, T., Chattopadhyay, P., Chen, Y., Cui, Y., Ding, Y., et al. Cosmos world foundation model platform for physical AI. arXiv preprint arXiv:2501.03575, 2025." + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.357, + 0.474, + 0.388 + ], + "angle": 0, + "content": "Baillargeon, R. Infants' physical world. 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URL https://github.com/hpcaitech/Open-Sora." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.085, + 0.887, + 0.735 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.923, + 0.496, + 0.935 + ], + "angle": 0, + "content": "10" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.057, + 0.816, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.084, + 0.423, + 0.101 + ], + "angle": 0, + "content": "A. Discussion of Image-to-Video setting." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.11, + 0.885, + 0.201 + ], + "angle": 0, + "content": "We note that our choice of single-image input, as opposed to multi-frame input, comes with some trade-offs. We choose the image-to-video setting because it is widely supported among many different models, allowing us to make effective comparisons across the current state-of-the-art. However, only conditioning on a single frame introduces significant ambiguity. Due to the loss of information caused by projecting the 3D world through perspective, it may not be possible to directly infer the size of the object or its height. In practice, we find our metrics are still reliable signals of task success, but we still study the problem of ambiguity more extensively in Section 5.2." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.22, + 0.235, + 0.236 + ], + "angle": 0, + "content": "B. Metric details." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.246, + 0.885, + 0.333 + ], + "angle": 0, + "content": "We propose three metrics to assess the accuracy of trajectories, shape fidelity, and object permanence. Each of our metrics compare frames from the ground-truth video with the generated video. Because different models can operate at different fps, we perform fps alignment as part of our evaluation process. To perform fps alignment, we map each frame index of the generated videos to the ground truth using \\( f_{\\mathrm{gen}} \\) and \\( f_{\\mathrm{gt}} \\), where \\( f_{\\mathrm{gen}} \\) and \\( f_{\\mathrm{gt}} \\) are the fps of generated video and ground truth respectively. For \\( i \\)-th frame in the generated video, we find the corresponding aligned frame index \\( j \\) in the ground truth video:" + }, + { + "type": "equation", + "bbox": [ + 0.417, + 0.333, + 0.887, + 0.365 + ], + "angle": 0, + "content": "\\[\nj = \\operatorname {r o u n d} \\left(i \\cdot \\frac {f _ {\\text {g e n}}}{f _ {\\mathrm {g t}}}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.37, + 0.886, + 0.414 + ], + "angle": 0, + "content": "Through fps alignment, we downsample the ground truth video to match the frame number of the generated video. We denote the downsampled ground truth as \\(\\{I_i^{\\mathrm{gt}}\\}_{i = 1}^N\\) and the generated video as \\(\\{I_i^{\\mathrm{gen}}\\}_{i = 1}^N\\), where \\(N\\) is the number of frames in the generated video." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.415, + 0.886, + 0.446 + ], + "angle": 0, + "content": "Trajectory L2. For each frame in both the generated video and ground truth, we calculate the centroid of the masked region. We then compute \\(L_{2}\\) distance between the centroids of corresponding frames:" + }, + { + "type": "equation", + "bbox": [ + 0.39, + 0.455, + 0.887, + 0.497 + ], + "angle": 0, + "content": "\\[\nL _ {2} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| C _ {i} ^ {\\text {g e n}} - C _ {i} ^ {\\mathrm {g t}} \\| _ {2} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.508, + 0.885, + 0.539 + ], + "angle": 0, + "content": "where \\( C_i^{\\mathrm{gen}}, C_i^{\\mathrm{gt}} \\in \\mathbb{R}^2 \\) are the centroids of the dropping object in the \\( i \\)-th frame of generated video and the ground truth respectively." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.539, + 0.885, + 0.57 + ], + "angle": 0, + "content": "Chamfer Distance (CD). To assess the shape fidelity of objects, we calculate the Chamfer Distance (CD) between the mask regions of the generated video and ground truth:" + }, + { + "type": "equation", + "bbox": [ + 0.256, + 0.58, + 0.713, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\mathrm {C D} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\frac {1}{| P _ {i} |} \\sum_ {p \\in P _ {i}} \\min _ {q \\in Q _ {i}} \\| p - q \\| _ {2} + \\frac {1}{| Q _ {i} |} \\sum_ {q \\in Q _ {i}} \\min _ {p \\in P _ {i}} \\| q - p \\| _ {2}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.634, + 0.885, + 0.667 + ], + "angle": 0, + "content": "where \\( P_{i} = \\{p_{j}\\}_{j = 1}^{|P_{i}|} \\) and \\( Q_{i} = \\{q_{j}\\}_{j = 1}^{|Q_{i}|} \\) are the sets of mask points in the \\( i \\)-th frame of the generated video and ground truth respectively." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.667, + 0.885, + 0.698 + ], + "angle": 0, + "content": "Intersection over Union (IoU). We use the Intersection over Union (IoU) metric to evaluate object permanence. IoU measures objects' degree of overlap between the generated video and ground truth. This is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.382, + 0.708, + 0.887, + 0.75 + ], + "angle": 0, + "content": "\\[\n\\mathrm {I o U} = \\frac {1}{| N |} \\sum_ {i = 1} ^ {N} \\frac {\\left| M _ {i} ^ {\\text {g e n}} \\cap M _ {i} ^ {\\mathrm {g t}} \\right|}{\\left| M _ {i} ^ {\\text {g e n}} \\cup M _ {i} ^ {\\mathrm {g t}} \\right|} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.759, + 0.885, + 0.793 + ], + "angle": 0, + "content": "where \\( M_{i}^{\\mathrm{gen}} \\), \\( M_{i}^{\\mathrm{gt}} \\in \\{0,1\\}^{H\\times W} \\) are binary segmentation masks of the falling object in the \\( i \\)-th frame of the generated and ground truth videos respectively." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.799, + 0.885, + 0.877 + ], + "angle": 0, + "content": "Time error. When testing on videos generated in simulation, we can provide a timing error. From the dropping height \\( Y_{0} \\) of the ground truth video, which we have access to from the simulator, we can derive \\( t_{\\mathrm{drop}} = \\sqrt{Y_0\\frac{2}{g}} \\). We then obtain a dropping time from the model's output by estimating the frame of impact as the first frame \\( F \\) whose centroid velocity in the \\( y \\) direction is negative. If \\( t_{\\mathrm{drop}} \\) occurs in between \\( F \\) and \\( F - 1 \\), then we define the time error \\( E_{\\mathrm{time}} \\) as zero. Otherwise, we define the time error as" + }, + { + "type": "equation", + "bbox": [ + 0.327, + 0.877, + 0.887, + 0.911 + ], + "angle": 0, + "content": "\\[\nE _ {\\text {t i m e}} = \\min \\left(\\left| \\frac {F - 1}{\\mathrm {f p s}} - t _ {\\text {d r o p}} \\right|, \\left| \\frac {F}{\\mathrm {f p s}} - t _ {\\text {d r o p}} \\right|\\right). \\tag {7}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.923, + 0.495, + 0.935 + ], + "angle": 0, + "content": "11" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.057, + 0.816, + 0.073 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.084, + 0.36, + 0.101 + ], + "angle": 0, + "content": "C. ORO implementation details." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.11, + 0.887, + 0.141 + ], + "angle": 0, + "content": "In our setting, we do not cut the gradient after step \\(k\\) like VADER. The gradient \\(\\nabla_{\\theta}R(x_0',x_0)\\) backpropagates through all diffusion timesteps and update the model weights \\(\\theta\\):" + }, + { + "type": "equation", + "bbox": [ + 0.349, + 0.15, + 0.887, + 0.192 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\theta} \\left(R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right)\\right) = \\sum_ {t = 0} ^ {T} \\frac {\\partial R \\left(x _ {0} ^ {\\prime} , x _ {0}\\right)}{\\partial x _ {t}} \\cdot \\frac {\\partial x _ {t}}{\\partial \\theta} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.201, + 0.348, + 0.216 + ], + "angle": 0, + "content": "where \\(T\\) is the total diffusion timesteps." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.223, + 0.887, + 0.252 + ], + "angle": 0, + "content": "Segmentation Reward. We utilize SAM 2 (Ravi et al., 2024) to generate segmentation masks across frames for generated video:" + }, + { + "type": "equation", + "bbox": [ + 0.416, + 0.266, + 0.887, + 0.283 + ], + "angle": 0, + "content": "\\[\nM ^ {\\text {g e n}} = \\operatorname {S A M} - 2 \\left(x _ {0}\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.295, + 0.887, + 0.34 + ], + "angle": 0, + "content": "where \\( M^{\\mathrm{gen}} \\) denotes the masks of the falling object in the generated video. We obtain ground truth masks \\( M^{\\mathrm{gt}} \\) using Kubric (Greff et al., 2022). To avoid non-differentiable reward, we use Sigmoid to normalize mask logits of generated video instead of converting them to binary masks. We use IoU between \\( M^{\\mathrm{gen}} \\) and \\( M^{\\mathrm{gt}} \\) as reward function:" + }, + { + "type": "equation", + "bbox": [ + 0.385, + 0.351, + 0.887, + 0.368 + ], + "angle": 0, + "content": "\\[\nR \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = \\operatorname {I o U} \\left(M ^ {\\text {g e n}}, M ^ {\\text {g t}}\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.379, + 0.592, + 0.394 + ], + "angle": 0, + "content": "Maximizing objective 1 is equivalent to minimizing the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.314, + 0.404, + 0.887, + 0.423 + ], + "angle": 0, + "content": "\\[\nJ (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ 1 - \\operatorname {I o U} \\left(M ^ {\\text {g e n}}, M ^ {\\text {g t}}\\right) \\right] \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.432, + 0.887, + 0.478 + ], + "angle": 0, + "content": "This objective constrains the position and shape of the generated object in the video, encouraging a greater intersection with the object region in the ground truth video. The model learns to generate more accurate object positions and shapes through training with this objective." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.485, + 0.887, + 0.514 + ], + "angle": 0, + "content": "Optical Flow Reward. We utilize RAFT (Teed & Deng, 2020) to generate optical flow for both generated videos and ground truth:" + }, + { + "type": "equation", + "bbox": [ + 0.42, + 0.514, + 0.887, + 0.537 + ], + "angle": 0, + "content": "\\[\nV ^ {\\text {g e n}} = \\operatorname {R A F T} \\left(x _ {0} ^ {\\prime}\\right) \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.429, + 0.533, + 0.551, + 0.549 + ], + "angle": 0, + "content": "\\[\nV ^ {\\mathrm {g t}} = \\operatorname {R A F T} (x _ {0})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.555, + 0.82, + 0.571 + ], + "angle": 0, + "content": "where \\( V^{\\mathrm{gen}} \\), \\( V^{\\mathrm{gt}} \\) denote the optical flows of generated videos and ground truth. We define the reward as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.392, + 0.581, + 0.887, + 0.599 + ], + "angle": 0, + "content": "\\[\nR \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = - \\left| V ^ {\\text {g e n}} - V ^ {\\text {g t}} \\right| \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.608, + 0.592, + 0.624 + ], + "angle": 0, + "content": "Maximizing objective 1 is equivalent to minimizing the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.341, + 0.634, + 0.887, + 0.653 + ], + "angle": 0, + "content": "\\[\nJ (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ \\left| V ^ {\\text {g e n}} - V ^ {\\text {g t}} \\right| \\right] \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.662, + 0.887, + 0.692 + ], + "angle": 0, + "content": "This objective constrains the motion of the generated object in the video. The model learns to generate more accurate physical motion through training with this objective." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.699, + 0.887, + 0.729 + ], + "angle": 0, + "content": "Depth Reward. We utilize Depth-Anything-V2 (Yang et al., 2024a) to generate optical depth maps for both generated videos and ground truth:" + }, + { + "type": "equation", + "bbox": [ + 0.371, + 0.729, + 0.887, + 0.751 + ], + "angle": 0, + "content": "\\[\nD ^ {\\text {g e n}} = \\text {D e p t h - A n y t h i n g - V 2} \\left(x _ {0} ^ {\\prime}\\right) \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.382, + 0.748, + 0.599, + 0.763 + ], + "angle": 0, + "content": "\\[\nD ^ {\\mathrm {g t}} = \\text {D e p t h - A n y t h i n g - V 2} (x _ {0})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.77, + 0.813, + 0.786 + ], + "angle": 0, + "content": "where \\( D^{\\mathrm{gen}} \\), \\( D^{\\mathrm{gt}} \\) denote the depth maps of generated videos and ground truth. We define the reward as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.391, + 0.796, + 0.887, + 0.813 + ], + "angle": 0, + "content": "\\[\nR \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = - \\left| D ^ {\\text {g e n}} - D ^ {\\mathrm {g t}} \\right| \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.823, + 0.592, + 0.838 + ], + "angle": 0, + "content": "Maximizing objective 1 is equivalent to minimizing the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.34, + 0.849, + 0.887, + 0.868 + ], + "angle": 0, + "content": "\\[\nJ (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ \\left| D ^ {\\mathrm {g e n}} - D ^ {\\mathrm {g t}} \\right| \\right] \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.876, + 0.887, + 0.907 + ], + "angle": 0, + "content": "This objective constrains the 3d motion of the generated object in the video. The model learns to generate more accurate 3d physical motion through training with this objective." + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.923, + 0.496, + 0.935 + ], + "angle": 0, + "content": "12" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.057, + 0.816, + 0.073 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.084, + 0.273, + 0.102 + ], + "angle": 0, + "content": "D. Coordinate system" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.11, + 0.888, + 0.187 + ], + "angle": 0, + "content": "We give a visualization of the coordinate system used in this paper in Figure 12. To compute \\( y \\), we first leverage a segmentation map and find pixel row index that is just below the object. Once this row index is found, \\( y \\) can easily be computed from the camera position, camera sensor size, and image resolution. We note that because our camera is assumed to be in perspective with the \\( XY \\) plane, we can ignore \\( X \\) and \\( x \\) (not shown in figure) in our analyses in Section 5.1 and Section 5.2." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.2, + 0.332, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.199, + 0.88, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.43, + 0.89, + 0.461 + ], + "angle": 0, + "content": "Figure 12. A visualization of the coordinate system used in this paper (not to scale). The image plane height of the object is denoted as \\(y\\), its actual height in 3D as \\(Y\\), and its depth as \\(Z\\). The camera focal length is denoted as \\(f\\)." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.493, + 0.276, + 0.511 + ], + "angle": 0, + "content": "E. Derivation of \\( p(t|y) \\)" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.519, + 0.888, + 0.59 + ], + "angle": 0, + "content": "In our dataset construction, we assume a uniform distribution for \\( Z \\), where \\( Z \\sim \\mathcal{U}(Z_{\\min}, Z_{\\max}) \\), where \\( Z_{\\min} = 2 \\) and \\( Z_{\\max} = 18 \\). As shown in Figure 12, the dropping height \\( Y \\) is a linear function of \\( Z \\), i.e. \\( Y = y + \\beta Z \\) for the slope \\( \\beta \\) that can be computed from \\( y, f \\), the sensor size, and the camera height. This means we can solve for dropping time as \\( t = \\sqrt{\\frac{2}{g}Y} = \\sqrt{\\frac{2}{g}(y + \\beta Z)} \\). Applying the transformation rule for probability density yields" + }, + { + "type": "equation", + "bbox": [ + 0.333, + 0.595, + 0.887, + 0.635 + ], + "angle": 0, + "content": "\\[\np (t | y) = \\left\\{ \\begin{array}{l l} \\frac {g t}{\\left(Z _ {\\max } - Z _ {\\min }\\right) \\beta}, & t _ {\\min } \\leq t \\leq t _ {\\max } \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.642, + 0.885, + 0.669 + ], + "angle": 0, + "content": "where \\( t_{\\mathrm{min}} = \\sqrt{\\frac{2}{g} (y + \\beta Z_{\\mathrm{min}})} \\) and \\( t_{\\mathrm{max}} = \\sqrt{\\frac{2}{g} (y + \\beta Z_{\\mathrm{max}})} \\). Plugging in \\( Z_{\\mathrm{min}} = 2 \\) and \\( Z_{\\mathrm{max}} = 18 \\) yields Equation (3)." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.684, + 0.273, + 0.701 + ], + "angle": 0, + "content": "F. Ambiguous dataset" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.709, + 0.888, + 0.831 + ], + "angle": 0, + "content": "We introduce a new dataset for distributional analysis that broadens \\( p(t|y) \\), in contrast to the PSFT dataset, which prioritizes realism and has a narrower distribution due to limited object depth variability. To create a dataset with \\( p(t|y) \\) that is sufficiently diverse for meaningful analysis, we first set up the initial scenes as before, but then apply an augmentation where a new depth values is sampled uniformly from [2, 18] and the object is scaled and translated such that it appears the same in the original image, as shown in Figure 9. For simplicity, we limit our scenes to a single dropping object with no other objects on the ground. We also disable shadows, preventing the model from using them as cues to infer depth and height. Our dataset contains 5k samples consisting of 1k unique initial scenes each containing 5 different trajectories produced by the augmentation." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.85, + 0.327, + 0.868 + ], + "angle": 0, + "content": "G. Lifting trajectories to 3D" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.876, + 0.888, + 0.907 + ], + "angle": 0, + "content": "To lift trajectories to 3D, we first estimate \\( t_{\\mathrm{drop}} \\) as described in Section 5.1. Using SAM2 to estimate object masks in the generated video, we can obtain a trajectory of the bottom of the object which we denote as \\( y_0, y_1, \\ldots, y_N \\) where" + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.923, + 0.496, + 0.935 + ], + "angle": 0, + "content": "13" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.057, + 0.816, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.085, + 0.888, + 0.12 + ], + "angle": 0, + "content": "\\(N = t_{\\mathrm{drop}} \\times \\mathrm{fps}\\). From \\(t_{\\mathrm{drop}}\\), we can solve for an implied depth \\(Z = \\frac{\\frac{1}{2}gt^2 - y}{\\beta}\\). We then compute the lifted 3D trajectory as \\(y_i \\mapsto y_i + \\beta Z\\)" + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.137, + 0.266, + 0.153 + ], + "angle": 0, + "content": "H. PisaBench Details" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.163, + 0.888, + 0.194 + ], + "angle": 0, + "content": "In this section, we discuss the details of our data collection pipeline and annotations. We present more examples of real-world videos and corresponding annotations in Figure 13." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.21, + 0.295, + 0.226 + ], + "angle": 0, + "content": "H.1. Data Collection Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.233, + 0.888, + 0.295 + ], + "angle": 0, + "content": "Collecting Real World Videos. We enlist approximately 15 volunteers to participate in the data collection process. We hand out a tripod, tape, and invisible wire for each volunteer. To ensure the quality, diversity, and minimize the ambiguity introduced by the environments, volunteers are provided with detailed guidelines. The key points of the data collection guidelines are shown in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.301, + 0.888, + 0.378 + ], + "angle": 0, + "content": "Raw videos processing. For the collected raw videos, we cut each video into multiple clips and crop their sizes. For each video clip, we annotate its starting position in the original long video and ensure that the duration of each segment does not exceed 12 seconds. Regarding the sizes of the videos, we manually crop each video to an aspect ratio of \\(1:1\\), ensuring that the falling objects remain fully visible within the frame during the cropping process. The processing interface is shown in Figure 14." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.394, + 0.257, + 0.408 + ], + "angle": 0, + "content": "H.2. Annotation Details" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.417, + 0.888, + 0.478 + ], + "angle": 0, + "content": "We present our annotation details in Figure 15. For video captions, we present the word cloud figure in (a). For segmentation masks, we annotate all objects in the first frame using positive and negative points, which are then propagated across frames using the SAM 2 (Ravi et al., 2024) model to produce segmentation masks for all objects throughout the video. The annotation interface is shown in (b)." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.485, + 0.888, + 0.577 + ], + "angle": 0, + "content": "In addition to providing the annotated caption \" {object description} falls,\" we also add information to inform off-the-shelf models of the task's context as much as possible. To further enhance task comprehension, we append an additional description \"A video that conforms to the laws of physics.\" We also employ negative prompts \"no camera motion\" and \"no slow-motion\" to ensure environmental stability and impose constraints on the generated videos. These prompts explicitly instruct the models to avoid including camera motion or any non-real-time object motion, thereby maintaining consistency with real-world physics." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.595, + 0.252, + 0.611 + ], + "angle": 0, + "content": "I. Inference Details" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.621, + 0.888, + 0.668 + ], + "angle": 0, + "content": "We present the inference configurations of each closed or open model we evaluate in Table 4. For models that do not support generating videos with 1:1 aspect ratio, we pad initial frames with black borders to the resolution supported by these models, and finally remove the black borders from the generated videos." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.686, + 0.341, + 0.703 + ], + "angle": 0, + "content": "J. More Qualitative Examples" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.712, + 0.888, + 0.758 + ], + "angle": 0, + "content": "We present more qualitative examples in Figure 16 - Figure 22. Although in some showcases, models can roughly predict the downward trend, models still struggle to predict plausible shape and motion. The defects in the models can be mainly attributed to the following aspects:" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.775, + 0.884, + 0.833 + ], + "angle": 0, + "content": "- Trajectory correctness: in most videos, models fail to predict even the basic falling trajectory of objects, as shown in Figure 19 (a), despite this being highly intuitive for humans. Even in cases where the falling trajectory is roughly correctly predicted, the models still struggle to accurately predict subsequent events, such as collisions, as illustrated in Figure 16 (f)." + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.846, + 0.884, + 0.903 + ], + "angle": 0, + "content": "- Object consistency: in many generated videos, object consistency is poor. Models struggle to infer the appearance of objects from multiple viewpoints in a physically plausible manner, resulting in unnatural appearances, as shown in Figure 16 (a). Additionally, models perform poorly in maintaining object permanence, causing objects to appear blurry, as illustrated in Figure 20 (f). Furthermore, models sometimes introduce new objects into the video, as depicted in" + }, + { + "type": "list", + "bbox": [ + 0.104, + 0.775, + 0.884, + 0.903 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.924, + 0.496, + 0.935 + ], + "angle": 0, + "content": "14" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.156, + 0.058, + 0.816, + 0.071 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.086, + 0.212, + 0.101 + ], + "angle": 0, + "content": "Figure 20 (e)." + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.111, + 0.888, + 0.142 + ], + "angle": 0, + "content": "- Scene consistency: models struggle to maintain scene consistency, leading to abrupt transitions in many videos. These sudden changes make videos appear unnatural, as shown in Figure 18 (f)." + }, + { + "type": "title", + "bbox": [ + 0.089, + 0.16, + 0.346, + 0.178 + ], + "angle": 0, + "content": "K. Simulated Adaption Details" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.186, + 0.888, + 0.278 + ], + "angle": 0, + "content": "We use the Kubric (Greff et al., 2022) simulation and rendering engine for creating our simulated videos. Kubric uses PyBullet (Coumans et al., 2010) for running physics simulations and Blender (Community, 2018) for rendering. We set the simulation rate to 240 steps per second and render 2-second videos at 16 fps, resulting in 32 frames per video. Each scene consists of objects from the Google Scanned Objects (GSO) dataset (Downs et al., 2022) and uses environmental lighting from HDRI maps provided by Kubric. We use 930 objects and 458 HDRI maps for training and 103 objects and 51 HDRI maps for testing." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.284, + 0.888, + 0.33 + ], + "angle": 0, + "content": "For each video, we randomly choose 1-6 objects to drop. These objects are placed at a height uniformly sampled from \\(0.5\\mathrm{m}\\) to \\(1.5\\mathrm{m}\\). Below each of these objects, a possibly empty pile of up to 4 objects spawns beneath to create collisions. The objects are placed in a spawn region of size \\(2\\mathrm{m} \\times 2\\mathrm{m}\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.336, + 0.888, + 0.383 + ], + "angle": 0, + "content": "The camera is initially positioned \\(1\\mathrm{m}\\) behind this region, with its height varying uniformly between \\(0.4\\mathrm{m}\\) and \\(0.6\\mathrm{m}\\). Once all objects are placed, the camera moves back in random increments until all objects are visible within the camera frame. The camera uses a focal length of \\(35\\mathrm{mm}\\), a sensor width of \\(32\\mathrm{mm}\\), and an aspect ratio of \\(1\\times 1\\)." + }, + { + "type": "title", + "bbox": [ + 0.089, + 0.402, + 0.212, + 0.418 + ], + "angle": 0, + "content": "L. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.427, + 0.888, + 0.503 + ], + "angle": 0, + "content": "In this work, we collect and manually annotate a dataset of 361 real-world videos and design three spatial metrics to evaluate the performance of state-of-the-art image-to-video (I2V) models in a fundamental physical scenario: free fall. Our metrics focus solely on spatial positional relationships, excluding object appearance attributes such as color. To enable more fine-grained evaluations of appearance characteristics, we aim to develop metrics based on Multimodal Large Language Models (MLLMs) or pixel-level analysis in future work." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.51, + 0.888, + 0.572 + ], + "angle": 0, + "content": "Furthermore, we propose the PSFT and ORO methods to fine-tune the Open-Sora model (Zheng et al., 2024), improving its ability to generate physically plausible videos. Despite these improvements, certain limitations remain, specifically, the generation of blurry objects in some videos. We hope to address these challenges in future research by refining both the dataset and the fine-tuning strategies, aiming to produce videos that better maintain object visuals." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.923, + 0.495, + 0.935 + ], + "angle": 0, + "content": "15" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.816, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.12, + 0.885, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.364, + 0.278, + 0.611, + 0.296 + ], + "angle": 0, + "content": "(a) A white paper roll falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.298, + 0.885, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.364, + 0.456, + 0.575, + 0.473 + ], + "angle": 0, + "content": "(c) A black bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.477, + 0.885, + 0.631 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.364, + 0.634, + 0.631, + 0.651 + ], + "angle": 0, + "content": "(b) A transparent bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.655, + 0.885, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.364, + 0.812, + 0.576, + 0.829 + ], + "angle": 0, + "content": "(d) A white bottle falls." + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.852, + 0.885, + 0.879 + ], + "angle": 0, + "content": "Figure 13. Examples of real world videos and annotations. We present video frames in the first row and mask annotations in the second row." + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.924, + 0.496, + 0.935 + ], + "angle": 0, + "content": "16" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.816, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.093, + 0.884, + 0.855 + ], + "angle": 0, + "content": "
AspectRequirements
Camera·The camera must be stabilized using a tripod.\n·The dropping object should remain visible throughout the entire fall.\n·The trajectory of the object should be sufficiently centered in the frame.\n·Ensure the slow-motion setting is configured to 120 fps.\n·Avoid a completely top-down perspective; the frame should include both the floor and the wall for spatial context.\n·It is acceptable to record one long video containing multiple drops at the same location.
Objects·Most objects should be rigid and non-deformable.\n·A limited number of flexible or deformable objects may be included, as such data is also valuable.
Dropping Procedure·Secure the object with a wire using tape, ensuring stability. Multiple tapings may be necessary for proper stabilization.\n·Visibility of the wire in the video is acceptable.\n·No body parts should appear in the frame. If this is challenging, consider having a partner monitor the camera or use screen-sharing software to view the camera feed on a laptop for uninterrupted framing.\n·Record videos in a horizontal orientation to simplify cropping and to help keep the frame free of unnecessary elements.\n·Use a short wire to enhance object stability.\n·The object should remain stationary before being dropped.
Scene Composition·Make the scenes dynamic and engaging. Include interactions with other objects, such as collisions or objects tipping over. Static objects should serve as active elements rather than mere background props.\n·Avoid filming in classroom or laboratory environments.\n·Include a variety of dropping heights.\n·Film in different environments, ensuring at least one setting is outside your apartment.\n·Minimize human shadows in the frame whenever possible.\n·Ensure good lighting and maintain strong contrast between the objects and the back-ground.
" + }, + { + "type": "table_caption", + "bbox": [ + 0.085, + 0.864, + 0.885, + 0.893 + ], + "angle": 0, + "content": "Table 3. Key points of real world videos collection guideline. We have detailed requirements for camera, objects, dropping procedure and scene composition to ensure the quality, diversity and minimize ambiguity introduced by environments." + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.923, + 0.496, + 0.935 + ], + "angle": 0, + "content": "17" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.816, + 0.071 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.462, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.284, + 0.279, + 0.295 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.088, + 0.888, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.68, + 0.284, + 0.698, + 0.295 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.309, + 0.886, + 0.339 + ], + "angle": 0, + "content": "Figure 14. Video processing interface. (a) we annotate starting positions in the original long videos and clip them into multiple clips less than 12 seconds. (b) We drag the cropping box to crop the video size to an aspect ratio of 1:1." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.349, + 0.426, + 0.607 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.622, + 0.264, + 0.635 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.475, + 0.347, + 0.886, + 0.611 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.667, + 0.622, + 0.688, + 0.635 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.652, + 0.888, + 0.695 + ], + "angle": 0, + "content": "Figure 15. Annotation details of real world videos. (a) Word cloud of objects in video captions. Our videos contain a variety of daily life objects. (b) Interface for annotating positive and negative points in the first frame. Red and blue dots indicate positive and negative points respectively. We annotate all objects in the midair and ground." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.703, + 0.887, + 0.874 + ], + "angle": 0, + "content": "
ModelResolutionNumber of FramesFPSGuidance ScaleSampling StepsNoise Scheduler
ClosedSora720 × 72015030---
Kling-V1.5960 × 960150301.0--
Kling-V1960 × 960150301.0--
Runway Gen31280 × 76815630---
OpenCogVideoX-5B-I2V720 × 4804886.050DDIM
DynamiCrafter512 × 32090300.750DDIM
Pyramid-Flow1280 × 768120244.010EulerDiscrete
Open-Sora512 × 51290307.030RFLOW
" + }, + { + "type": "table_caption", + "bbox": [ + 0.184, + 0.883, + 0.789, + 0.897 + ], + "angle": 0, + "content": "Table 4. Inference details for models we evaluate, where “-” indicates the information is not available." + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.924, + 0.495, + 0.935 + ], + "angle": 0, + "content": "18" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.816, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.133, + 0.885, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.219, + 0.571, + 0.236 + ], + "angle": 0, + "content": "(a) A brown bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.242, + 0.885, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.33, + 0.553, + 0.348 + ], + "angle": 0, + "content": "(b) A grey bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.354, + 0.885, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.441, + 0.593, + 0.459 + ], + "angle": 0, + "content": "(c) A grey paper cup falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.465, + 0.885, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.551, + 0.547, + 0.57 + ], + "angle": 0, + "content": "(d) A paper cup falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.575, + 0.885, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.662, + 0.562, + 0.679 + ], + "angle": 0, + "content": "(e) A white bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.687, + 0.885, + 0.765 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.773, + 0.539, + 0.79 + ], + "angle": 0, + "content": "(f) A white box falls." + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.813, + 0.886, + 0.868 + ], + "angle": 0, + "content": "Figure 16. Qualitative examples of Kling-V1 (Kuaishou, 2024). In (a) (b) (c) (f), objects have a tendency to fall. (b) (c) are roughly consistent with the laws of physics. In (a) (f), the shape of the object does not match the first frame. In (d), the paper cup is suspended in midair. In (e), new object is introduced. In (e), the model fails to correctly predict the collision that occurs after the white box falls and the chain of events that follows." + }, + { + "type": "page_number", + "bbox": [ + 0.478, + 0.923, + 0.496, + 0.935 + ], + "angle": 0, + "content": "19" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.817, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.145, + 0.887, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.231, + 0.645, + 0.251 + ], + "angle": 0, + "content": "(a) A black and grey glove falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.256, + 0.887, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.342, + 0.563, + 0.36 + ], + "angle": 0, + "content": "(b) A black bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.367, + 0.887, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.453, + 0.629, + 0.471 + ], + "angle": 0, + "content": "(c) A blue and white box falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.478, + 0.887, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.564, + 0.57, + 0.581 + ], + "angle": 0, + "content": "(d) A brown bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.588, + 0.887, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.674, + 0.593, + 0.692 + ], + "angle": 0, + "content": "(e) A Coca-Cola can falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.7, + 0.887, + 0.778 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.785, + 0.529, + 0.804 + ], + "angle": 0, + "content": "(f) A pink box falls." + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.825, + 0.886, + 0.855 + ], + "angle": 0, + "content": "Figure 17. Qualitative examples of Runway Gen3 (Runway, 2024). In (b) (e), objects have a tendency to fall. In (a) (e) (f), new objects are introduced. In (b) (d), the shape of the object does not match the first frame. In (c), the box is suspended in midair." + }, + { + "type": "page_number", + "bbox": [ + 0.477, + 0.923, + 0.497, + 0.935 + ], + "angle": 0, + "content": "20" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.817, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.139, + 0.887, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.224, + 0.562, + 0.242 + ], + "angle": 0, + "content": "(a) A black bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.248, + 0.887, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.335, + 0.572, + 0.353 + ], + "angle": 0, + "content": "(b) A black helmet falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.359, + 0.887, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.446, + 0.546, + 0.464 + ], + "angle": 0, + "content": "(c) A paper box falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.47, + 0.887, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.556, + 0.563, + 0.574 + ], + "angle": 0, + "content": "(d) A white bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.581, + 0.887, + 0.661 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.667, + 0.593, + 0.686 + ], + "angle": 0, + "content": "(e) A grey paper cup falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.692, + 0.79, + 0.772 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.777, + 0.54, + 0.795 + ], + "angle": 0, + "content": "(f) A white box falls." + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.818, + 0.888, + 0.861 + ], + "angle": 0, + "content": "Figure 18. Qualitative examples of CogVideoX-5B-I2V (Yang et al., 2024c). In (a) - (f), objects have a tendency to fall. However, in all the videos, there are violations of physics. In (a) (b), the objects are divided into two parts. In (c) (d) (e), the shape of the object does not match the first frame. In (c), the trajectory is not a vertical fall. In (f), scene changes suddenly, which does not match the first frame." + }, + { + "type": "page_number", + "bbox": [ + 0.477, + 0.923, + 0.495, + 0.935 + ], + "angle": 0, + "content": "21" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.817, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.152, + 0.887, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.238, + 0.543, + 0.255 + ], + "angle": 0, + "content": "(a) A black box falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.263, + 0.887, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.349, + 0.56, + 0.367 + ], + "angle": 0, + "content": "(b) A card holder falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.373, + 0.887, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.46, + 0.563, + 0.478 + ], + "angle": 0, + "content": "(c) A white bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.485, + 0.887, + 0.565 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.571, + 0.543, + 0.588 + ], + "angle": 0, + "content": "(d) A white box falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.595, + 0.887, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.681, + 0.663, + 0.7 + ], + "angle": 0, + "content": "(e) An orange and white box falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.706, + 0.887, + 0.786 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.792, + 0.493, + 0.809 + ], + "angle": 0, + "content": "(f) A shoe falls." + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.832, + 0.884, + 0.847 + ], + "angle": 0, + "content": "Figure 19. Qualitative examples of DynamiCrafter (?). In all the videos, objects do not have a tendency to fall, suspended in the midair." + }, + { + "type": "page_number", + "bbox": [ + 0.477, + 0.924, + 0.496, + 0.935 + ], + "angle": 0, + "content": "22" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.817, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.145, + 0.887, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.231, + 0.562, + 0.249 + ], + "angle": 0, + "content": "(a) A black bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.256, + 0.887, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.342, + 0.642, + 0.36 + ], + "angle": 0, + "content": "(b) A green and white box falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.366, + 0.887, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.453, + 0.553, + 0.471 + ], + "angle": 0, + "content": "(c) A grey bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.478, + 0.887, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.564, + 0.576, + 0.581 + ], + "angle": 0, + "content": "(d) An orange tube falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.588, + 0.887, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.674, + 0.562, + 0.691 + ], + "angle": 0, + "content": "(e) A white bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.699, + 0.887, + 0.778 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.785, + 0.551, + 0.803 + ], + "angle": 0, + "content": "(f) A plastic box falls." + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.825, + 0.886, + 0.854 + ], + "angle": 0, + "content": "Figure 20. Qualitative examples of Pyramid-Flow (Jin et al., 2024). In (b) (d) (e), objects have a tendency to fall. In (a) (b) (e) (f), new objects are introduced. In (c), scene changes, which does not match the first frame.. In (d), the tube becomes blurry." + }, + { + "type": "page_number", + "bbox": [ + 0.477, + 0.923, + 0.496, + 0.935 + ], + "angle": 0, + "content": "23" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.817, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.145, + 0.887, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.231, + 0.625, + 0.249 + ], + "angle": 0, + "content": "(a) A bottle full of water falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.256, + 0.887, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.342, + 0.571, + 0.359 + ], + "angle": 0, + "content": "(b) A brown bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.367, + 0.887, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.453, + 0.593, + 0.471 + ], + "angle": 0, + "content": "(c) A grey paper cup falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.478, + 0.887, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.564, + 0.547, + 0.581 + ], + "angle": 0, + "content": "(d) A paper box falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.588, + 0.887, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.674, + 0.563, + 0.691 + ], + "angle": 0, + "content": "(e) A white bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.699, + 0.887, + 0.778 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.785, + 0.54, + 0.802 + ], + "angle": 0, + "content": "(f) A white box falls." + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.825, + 0.886, + 0.854 + ], + "angle": 0, + "content": "Figure 21. Qualitative examples of Open-Sora (Zheng et al., 2024). In all the videos, objects do not have a tendency to fall, suspended in the midair. In (b) (d), scene changes suddenly, which does not match the first frame. In (e), new object is introduced." + }, + { + "type": "page_number", + "bbox": [ + 0.477, + 0.923, + 0.496, + 0.935 + ], + "angle": 0, + "content": "24" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.157, + 0.057, + 0.817, + 0.072 + ], + "angle": 0, + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.145, + 0.887, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.231, + 0.572, + 0.249 + ], + "angle": 0, + "content": "(a) A brown bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.256, + 0.887, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.342, + 0.56, + 0.361 + ], + "angle": 0, + "content": "(b) A grey eraser falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.367, + 0.887, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.453, + 0.593, + 0.471 + ], + "angle": 0, + "content": "(c) A grey paper cup falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.478, + 0.887, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.564, + 0.62, + 0.581 + ], + "angle": 0, + "content": "(d) A transparent bottle falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.588, + 0.887, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.674, + 0.633, + 0.692 + ], + "angle": 0, + "content": "(e) A red wrapping paper falls." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.7, + 0.887, + 0.778 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.785, + 0.559, + 0.802 + ], + "angle": 0, + "content": "(f) A white bottle falls." + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.825, + 0.888, + 0.855 + ], + "angle": 0, + "content": "Figure 22. Qualitative examples of our method (Open-Sora + PSFT + ORO). In all the videos, objects have a tendency to fall. However, the consistency of objects is still insufficient. In some frames, objects become blurry. Objects sometimes disappear after collision." + }, + { + "type": "page_number", + "bbox": [ + 0.477, + 0.923, + 0.496, + 0.935 + ], + "angle": 0, + "content": "25" + } + ] +] \ No newline at end of file diff --git a/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_origin.pdf b/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cffcf3b64564c9074a96ff42715dd189745d2b3c --- /dev/null +++ b/data/2025/2503_09xxx/2503.09595/b59876e9-da8b-438b-ab54-bb4c4d76820f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:287aec489ea1baedef98e3de9553fcdad82e948603de837f80a643ee4ad17796 +size 33119990 diff --git a/data/2025/2503_09xxx/2503.09595/full.md b/data/2025/2503_09xxx/2503.09595/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f688f3cb8ff9b94034388337448c469d64d9daef --- /dev/null +++ b/data/2025/2503_09xxx/2503.09595/full.md @@ -0,0 +1,667 @@ +# PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop + +Chenyu Li $^{*1}$ Oscar Michel $^{*1}$ Xichen Pan $^{1}$ Sainan Liu $^{2}$ Mike Roberts $^{2}$ Saining Xie + +# Abstract + +Large-scale pre-trained video generation models excel in content creation but are not reliable as physically accurate world simulators out of the box. This work studies the process of posttraining these models for accurate world modeling through the lens of the simple, yet fundamental, physics task of modeling object freefall. We show state-of-the-art video generation models struggle with this basic task, despite their visually impressive outputs. To remedy this problem, we find that fine-tuning on a relatively small amount of simulated videos is effective in inducing the dropping behavior in the model, and we can further improve results through a novel reward modeling procedure we introduce. Our study also reveals key limitations of post-training in generalization and distribution modeling. Additionally, we release a benchmark for this task that may serve as a useful diagnostic tool for tracking physical accuracy in large-scale video generative model development. Code is available at this repository: https://github.com/vision-x-nyu/pisa-experiments. + +# 1. Introduction + +Over the past year, video generation models have advanced significantly, inspiring visions of a future where these models could serve as realistic world models (Craik, 1967; LeCun, 2022; Hafner et al., 2019; 2023; Ha & Schmidhuber, 2018). State-of-the-art video generation models models exhibit impressive results in content creation (OpenAI, 2024; Kuaishou, 2024; Luma, 2024; Runway, 2024) and are already being used in advertising and filmmaking (Runway, 2025; NBC, 2025). These advancements have sparked a line of research that seeks to evolve these models from content creators to world simulators for embodied agents (Yang + +*Equal contribution, alphabetical order. 1New York University 2Intel Labs. + +et al., 2023; 2024b; Agarwal et al., 2025). However, accurate world modeling is considerably more challenging than creative content creation because looking "good enough" is not sufficient: generated pixels must faithfully represent a world state evolving in accordance with the laws of physics and visual perspective. + +We find that although the generations of state-of-the-art models are impressive visually, these models still struggle to generate results that are accurate physically, even though these models are pretrained on internet-scale video data demonstrating a wide variety of complex physical interactions. The failure to ground and align visual generations to the laws of physics suggests that pretraining is not enough and a post-training stage is needed. Much like how pretrained Large Language Models (LLMs) need to be adapted through post-training before they can be useful conversational assistants, pretrained video generative models ought to be adapted through post-training before they can be deployed as physically accurate world simulators. + +In this work, we rigorously examine the post-training process of video generation models by focusing on the simple yet fundamental physics task of modeling object freefall, which we find is highly challenging for state-of-the-art models. Specifically, we study an image-to-video $^{1}$ (I2V) scenario where the goal is to generate a video of an object falling and potentially colliding with other objects on the ground, starting from an initial image of the object suspended in midair. We chose to study this single task, rather than general physics ability as a whole, because its simplicity allows us to conduct controlled experiments that yield insights into the strengths and limitations of the post-training process, which we believe will become an increasingly important component of research in generative world modeling. Additionally, the simplicity of the dropping task allows it to be implemented in simulation which is desirable because it allows us to easily test the properties of dataset scaling, gives us access to ground truth annotations for evaluation, and gives us the ability to precisely manipulate the simulation environment for controlled experimentation. + +![](images/19a56cf5e00b438278d859ed1f2a1e950888d74b178b001eab56b1dd9862790e.jpg) +Figure 1. Our PISA (Physics-Informed Simulation and Alignment) evaluation framework includes a new video dataset, where objects are dropped in a variety of real-world (left) and synthetic (right) scenes. For visualization purposes, we depict object motion by overlaying multiple video frames in each image shown above. Our real-world videos enable us to evaluate the physical accuracy of generated video output, and our synthetic videos enable us to improve accuracy through the use of post-training alignment methods. + +![](images/00bcbfd531744498cbd9c4457e5710d02b6c2db7bb28bac2414f98156285e998.jpg) + +Named after Galileo's famous dropping experiment, we introduce the PISA (Physics-Informed Simulation and Alignment) framework for studying physics post-training in the context of the dropping task. PISA includes new real and simulated video datasets, as shown in Figure 1, containing a diverse set of dropping scenarios. PISA also includes a set of task-specific metrics that focus on measuring physical accuracy. Our real-world videos and metrics enable us to evaluate the physical accuracy of generated video output, and our synthetic videos enable us to improve accuracy through a post-training process we introduce. + +Our study reveals that current state-of-the-art video generative models struggle significantly with the task of physically accurate object dropping. Generated objects frequently exhibit impossible behaviors, such as floating midair, defying gravity, or failing to preserve realistic trajectories during freefall. However, we find that simple fine-tuning can be remarkably effective: fine-tuning an open-source model on a small dataset of just a few thousand samples enables it to vastly outperform state-of-the-art models in physical accuracy. We further observe that pretrained models are critical for success; models initialized randomly, without leveraging pretraining on large-scale video datasets, fail to achieve comparable results. We also introduce a novel framework for reward modeling that yields further improvement. We demonstrate that our reward learning system is highly flexible in that different reward functions can be chosen to target different axes of physical improvement. + +Our analysis also reveals key limitations. First, we see that model performance degrades when tasked with scenarios outside the training distribution, such as objects dropping from unseen depths or heights. Additionally, while our post + +trained model generates object motion that is 3D-consistent and physically accurate, we observe misalignment between the generated and ground truth dropping time distribution. + +These findings indicate that post-training is likely to be an essential component of future world modeling systems. The challenges we identify in this relatively simple task are likely to persist when modeling more sophisticated physical phenomena. By introducing the PISA framework and benchmark, we provide a useful diagnostic tool for researchers to test whether models are on the path to acquiring general physical abilities, as well as identify key limitations that researchers should be aware of when integrating new capabilities into their models through post-training. + +# 2. Related Work + +Modeling Intuitive Physics. Intuitive physics refers to the innate or learned human capacity to make quick and accurate judgments about the physical properties and behaviors of objects in the world, such as their motion, stability, or interactions. This ability, present even in infancy (Spelke et al., 1992; Baillargeon, 2004; Battaglia et al., 2013), is crucial for navigating and understanding everyday life. Replicating intuitive physics is a foundational step toward creating systems that can interact effectively and safely in dynamic, real-world environments (Lake et al., 2017). Gravity, as a core component of intuitive physics, plays a pivotal role in both domains. It is one of the most universal and observable physical forces, shaping our expectations about object motion, stability, and interaction (Hamrick et al., 2016; Ullman et al., 2017). Many studies in cognitive science (Battaglia et al., 2013) and AI (Wu et al., 2015; Bear et al., 2021) have + +relied on physics engines to evaluate and model intuitive physics. Our work uses the Kubric engine (Greff et al., 2022) to generate training videos. + +Video Generation Models as World Simulators. Video generation has long been an intriguing topic in computer vision, particularly in the context of predicting future frames (Srivastava et al., 2015; Xue et al., 2016). More recently, as large-scale generative models have become prominent, Yang et al. explored how a wide range of real-world dynamics and decision-making processes can be expressed in terms of video modeling (Yang et al., 2024b; 2023). The introduction of the Sora model (OpenAI, 2024) marked a leap in the quality of generated videos and ignited interest in leveraging such models as "world simulators." Over the past year, numerous video generation models have emerged, some open-source (Zheng et al., 2024; Yang et al., 2024c; Jin et al., 2024; Agarwal et al., 2025) and others commercially available (Kuaishou, 2024; Luma, 2024; Runway, 2024; OpenAI, 2024). Related to our work, Kang et al. (Kang et al., 2024) study the extent to which video generation models learn generalizable laws of physics when trained on 2D data from a synthetic environment. + +Evaluating Video Generation Models. Traditional image-based metrics for generative modeling, such Fréchet inception distance (FID) (Heusel et al., 2017) or inception score (IS) (Salimans et al., 2016), can be incorporated into the video domain, either by applying them on a frame-by-frame basis or by developing video-specific versions, such as Fréchet video distance (FVD) (Unterthiner et al., 2018). Going beyond distribution matching measures, several benchmarks have developed suites of metrics that aim to better evaluate the semantic or visual quality of generated videos. For example, V-Bench (Huang et al., 2024) offers a more granular evaluation by measuring video quality across multiple dimensions, such as with respect to subject consistency or spatial relationships. In physics, some works, such as VideoPhy (Bansal et al., 2024) and PhyGenBench (Meng et al., 2024), evaluate in the T2V setting by utilizing multimodal large language models (MLLM) to generate a VQA-based score. More recently, Cosmos (Agarwal et al., 2025) and Physics-IQ (Motamed et al., 2025), evaluate physics in the image-to-video and video-to-video settings. + +# 3. PisaBench + +Our benchmark, PisaBench, examines the ability of video generative models to produce accurate physical phenomena by focusing on a straightforward dropping task. + +# 3.1. Task Definition & Assumptions + +Our task can be summarized as follows: given an image of an object suspended in midair, generate a video of the object + +![](images/1ac3de96698eccbe7ffd3f2cdeee9e6722a7a59125ffbd3af395c8b98701c5c7.jpg) +Figure 2. The setup for collecting real-world videos. + +falling and colliding with the ground and potentially other objects. Since a video is an incomplete partial observation of the 4D world, we make a number of assumptions to constrain the task space. These assumptions are crucial for ensuring that our metrics are reliable signals for physical accuracy, since they are only approximations of task success computed from a single ground truth and generated video. + +Specifically, we assume that the falling object is completely still in the initial frame, that only the force of gravity is acting on the object while it falls, and that the camera does not move. The first two assumptions are necessary for the image-to-video setting. Since we do not provide multiple frames as input, it is otherwise impossible to establish the initial velocity or acceleration of the falling object without these assumptions. The last assumption is necessary as our metrics derive from the motion of segmentation masks, which would be affected in the presence of camera motion. + +# 3.2. Real World Data + +![](images/75bc9f270274a876e0f2d9bb2c4307c38aafd436f796800aeee64fbd5f2d9b29.jpg) +Figure 3. Statistics of the real-world data: (a) number of objects in each video, (b) the proportions of different scenes in the videos. + +![](images/2a038e4df7899a3c6a7af3f168c48dd30504eb434167e140afe024da4ee58ef5.jpg) + +Real World Videos. We collect a set of 361 real-world videos demonstrating the dropping task for evaluation. As is shown in Figure 4, the dataset includes a diverse set + +![](images/7d4ceaab34fce33596b3dd1e9d4ba7a5b2fc93095d7bd082617fa0ffe00a3c57.jpg) +Figure 4. Examples of various objects included in our dataset. For simulation, we utilize the GSO dataset (Downs et al., 2022), while for the real-world dataset, we curate our own set of common household objects. + +of objects with different shapes and sizes, captured across various settings such as offices, kitchens, parks, and more (see Figure 3). Each video begins with an object suspended by an invisible wire in the first frame, which is necessary to enforce the assumption that objects are stationary at the start of the video. This assumption is required in our imaged-to-video setting; otherwise, the initial velocity of an object is ambiguous. We cut the video clips to begin as soon as the wire is released. We record the videos in slow-motion at 120 frames per second (fps) with cellphone cameras mounted on tripods to eliminate camera motion. An example of our video collection setup is shown in Figure 2. Additional details on our collection system are provided in Appendix H. + +Simulated Test Videos. Since our post-training process uses a dataset of simulated videos, we also create a simulation test-set of 60 videos for understanding sim2real transfer. We create two splits of 30 videos each: one featuring objects and backgrounds seen during training, and the other featuring unseen objects and backgrounds. See Section 4.1 for details on how our simulated data is created. + +Annotations. As is shown in Figure 5, we annotate each video with a caption and segmentation masks estimated from the SAM 2 (Ravi et al., 2024) video segmentation model. We create a descriptive caption for each object in the format of “{object description} falls.” This caption is used to provide context to the task when text input is supported. + +# 3.3. Metrics + +We propose three metrics to assess the accuracy of trajectories, shape fidelity, and object permanence. Each of our metrics compare frames from the ground-truth video with the generated video. Further details about the metrics, including + +![](images/fdf0c1240713a0f765f0563462d434ced74c2fc826cdce4f827d1a1a50939cc7.jpg) +Figure 5. Example of annotations in real-world data. For segmentation masks, we manually annotate first frame and utilize SAM 2 to produce segmentation masks across frames. For captions, we annotate “{object description} falls.” for all video segments. + +their formulas and our resampling procedure for accounting for differences in fps, is described in Appendix B. + +Trajectory L2. For each frame in both the generated video and ground truth, we calculate the centroid of the masked region. After doing this, we compute the average $L_{2}$ distance between the centroids of corresponding frames. + +Chamfer Distance (CD). To assess the shape fidelity of objects, we calculate the Chamfer Distance (CD) between the mask regions of the generated video and ground truth. + +Intersection over Union (IoU). We use the Intersection over Union (IoU) metric to evaluate object permanence. The IoU measures objects' degree of overlap between the generated video and ground truth. + +# 3.4. Evaluation Results + +We evaluate 4 open models including CogVideoX-5B-I2V(Yang et al., 2024c), DynamiCrafter(Xing et al., 2023), Pyramid-Flow(Jin et al., 2024), and Open-Sora-V1.2(Zheng et al., 2024), as well as 4 proprietary models including Sora (OpenAI, 2024), Kling-V1(Kuaishou, 2024), Kling-V1.5(Kuaishou, 2024), and Runway Gen3 (Runway, 2024). We also evaluate OpenSora post-trained through the processes of Supervised Fine-Tuning (PSFT) and Object Reward Optimization (ORO); see Section 4 for details. + +The results of running the baseline models on the benchmark indicate a consistent failure to generate physically accurate dropping behavior, despite the visual realism of their generated frames. Qualitatively, we see common failure cases in Figure 6, such as implausible object deformations, floating, hallucination of new objects, and unrealistic special + +![](images/342a3b4296640d6e8ed1d72350bfb1237311d4fb53b1dc49759aa08ed93e6617.jpg) +Figure 6. Qualitative comparison of results on real test set (row 1-2), simulated seen test set (row 3-4) and simulated unseen test set (row 5-6). We present the results of popular open-source and commercially available models alongside those of models fine-tuned through our method. Existing models often struggle to generate videos depicting objects falling, whereas our PSFT method effectively introduces knowledge of free-fall into the model. ORO enables the model to more accurately learn object motion and shape. + +effects. We further visualize a random subset of generated trajectories on the left of Figure 8. In many cases, the object remains completely static, and sometimes the object even moves upward. When downward motion is present, it is often slow or contains unrealistic horizontal movement. + +# 4. Physics Post-Training + +We present a post-training process to address the limitations of current models described in Section 3.4. We utilize simulated videos that demonstrate realistic dropping behavior. Our approach for post-training is inspired by the two-stage pipeline consisting of supervised fine-tuning followed by reward modeling commonly used in LLMs. We find that our pipeline improves performance on both real and simulated evaluations, with greater gains observed in simulation. This is due to the sim-to-real gap, though our approach still shows substantial gains in transferring to real-world data. + +# 4.1. Simulated Adaptation Data + +The first stage of our approach involves supervised fine-tuning. We use Kubric (Greff et al., 2022), a simulation and rendering engine designed for scalable video generation, to create simulated videos of objects dropping and colliding with other objects on the ground. Each video consists of 1-6 dropping objects onto a (possibly empty) pile of up to 4 objects underneath them. The videos are 2 seconds long, consisting of 32 frames at 16 fps. The objects are sourced from the Google Scanned Objects (GSO) dataset (Downs et al., 2022), which provides true-to-scale 3D models created from real-world scans across diverse categories (examples shown in Figure 4). The camera remains stationary in each video and is oriented parallel to the ground plane. To introduce variability, we randomly sample the camera height + +between 0.4 and 0.6 meters and position objects between 1 and 3 meters away from the camera, which corresponds to the distributions observed in the real-world dataset. More information about the dataset can be found in Appendix K. + +# 4.2. Physics Supervised Fine-Tuning (PSFT). + +![](images/9cb6168eacd785e4f741b3dbc66836cc1b13221d84cacac490669a7f161086a6.jpg) + +![](images/6adf02f646ee4da228177a9bb3d6b9810b033aeaac6c9f68056cd271eb9c47c2.jpg) + +![](images/91f342955c4abb85297c05b6fbf080e1ae798b04587e39e4104a2985d585e4d7.jpg) +Figure 7. Plots (a), (b), and (c) demonstrate that our metrics tend to improve with further training and that leveraging a pre-trained video diffusion model enhances performance compared to random initialization. In plot (d), the size of the training dataset varies in each training run (each consisting of 5k steps). With only 5k samples, we can achieve optimal results. + +![](images/a7f340f4c1bc1798d01d2bcfa3aac741d7c979c6b80afc4910bba5d647c78286.jpg) + +We use the pretrained Open-Sora v1.2 (Zheng et al., 2024) model as our base model and fine-tune it on our simulated video dataset. We employ Open-Sora v1.2's rectified flow training objective without modification (Liu et al., 2022). Each fine-tuning experiment is conducted with a batch size of 128 and a learning rate of $1\mathrm{e} - 4$ on two 80GB NVIDIA A100 GPUs. As shown in Figure 6, fine-tuning with this + +
MethodRealSim (Seen)Sim (Unseen)
L2 (↓)CD (↓)IoU (↑)L2 (↓)CD (↓)IoU (↑)L2 (↓)CD (↓)IoU (↑)
ProprietarySora (OpenAI, 2024)0.1740.4880.0650.1490.4460.0400.1400.4190.031
Kling-V1 (Kuaishou, 2024)0.1570.4250.0560.1420.4150.0320.1450.4370.028
Kling-V1.5 (Kuaishou, 2024)0.1550.4240.0580.1370.3960.0330.1320.4050.029
Runway Gen3 (Runway, 2024)0.1870.5260.0420.1700.5090.0400.1490.4600.038
OpenCogVideoX-5B-I2V (Yang et al., 2024c)0.1380.3660.0800.1120.3150.0200.1010.2900.020
DynamiCrafter (Xing et al., 2023)0.1870.5040.0210.1570.4850.0390.1360.4300.033
Pyramid-Flow (Jin et al., 2024)0.1750.4850.0620.1260.3520.0590.1300.3810.048
Open-Sora (Zheng et al., 2024)0.1750.5020.0690.1390.4090.0360.1300.3680.034
OursOpen-Sora + PSFT (base)0.0760.1880.1390.0360.0880.1650.0280.0580.129
base + ORO (Seg)0.0750.1830.1420.0330.0760.1700.0320.0630.145
base + ORO (Flow)0.0670.1640.1360.0260.0620.1220.0220.0450.071
base + ORO (Depth)0.0670.1590.1290.0310.0720.1240.0220.0460.096
+ +Table 1. PisaBench Evaluation Results. This table compares the performance of four proprietary models, four open models, and the models fine-tuned with PSFT and $\mathrm{PSFT + ORO}$ on our real-world and simulated test set which is decomposed into seen and unseen object splits. Across all metrics, our PSFT models outperform all other baselines, including proprietary models like Sora. Reward modeling further enhances results, with segmentation rewards improving the shape-based IoU metric and optical rewards and depth rewards enhancing the motion-based L2 and CD metrics. This suggests that rewards can be flexibly adjusted to target specific aspects of performance. + +data alone is sufficient to induce realistic dropping behavior in the model. Quantitatively, our PSFT model substantially improves on both our simulated and real-world benchmark, as shown in Table 1. Dataset size. We conduct an ablation study on the number of training samples to understand the amount of data required for optimal performance on our benchmark. We create random subsets from 500 to 20,000 samples and train our model for 5,000 gradient steps on each subset. Notably, as shown in Figure 7, only 5,000 samples are needed to achieve optimal results. Effect of pretraining. Additionally, we investigate the impact of Open-Sora's pre-training on adaptation. We randomly initialize the Open-Sora's denoising network while keeping the pre-trained initialization of the compressor network and train the model on a dataset of 5k training samples. As shown in Figure 8, the learned knowledge from Open-Sora's pretraining plays a critical role in our task. + +Overall, using PSFT on only 5k samples is sufficient to push Open-Sora's performance past all other evaluated models, including state-of-the-art commercial video generators, by a wide margin. This is made possible by leveraging the knowledge from the sufficiently pre-trained base model. + +# 4.3. Object Reward Optimization (ORO) + +In the second stage, we propose Object Reward Optimization (ORO) to use reward gradients to guide the video generation model toward generating videos where the object's motion and shape more closely align with the ground truth. + +![](images/2b0b1b1edbe72353a808756a9abec58b083266dae8f49a22cf820119f4e51b9d.jpg) +Figure 8. On the left, we plot random trajectories from the baseline models in Table 1. On the right, we show random trajectories from our fine-tuned model. The baseline trajectories exhibit unrealistic behavior, and most of them stay completely static. On the right, we see the trajectories consistently falling downward with collision and rolling behavior being modeled after the point of contact. + +We follow the VADER framework from (Prabhudesai et al., 2024) and introduce three reward models. The differences between our approach and VADER include: (1) our reward model utilizes both generated videos and ground truth instead of generated videos and conditioning. (2) gradients propagate through all denoising time steps in fine-tuning. Consequently, the VADER objective is modified as follows: + +$$ +J (\theta) = \mathbb {E} _ {\left(x _ {0}, c\right) \sim \mathcal {D}, x _ {0} ^ {\prime} \sim p _ {\theta} \left(x _ {0} ^ {\prime} \mid c\right)} \left[ R \left(x _ {0} ^ {\prime}, x _ {0}\right) \right] \tag {1} +$$ + +where $\mathcal{D}$ is the ground truth dataset, $p_{\theta}(.)$ is a given video diffusion model, $x_0^{\prime}, x_0 \in \mathbb{R}^{H \times W \times 3}$ are generated video and ground truth, and $c \in \mathbb{R}^{H \times W \times 3}$ is the initial image. + +Segmentation Reward. We utilize SAM 2 (Ravi et al., + +2024) to generate segmentation masks across frames for generated videos. We define segmentation reward as the IoU between the dropping object's mask in generated video and the mask from the ground truth simulated segmentation. + +Optical Flow Reward. We utilize RAFT (Teed & Deng, 2020) to generate generated video's optical flow $V^{\mathrm{gen}}$ and ground truth's optical flow $V^{\mathrm{gt}}$ . We define the optical flow reward as $R(x_0', x_0) = -|V^{\mathrm{gen}} - V^{\mathrm{gt}}|$ . + +Depth Reward. We utilize Depth-Anything-V2 (Yang et al., 2024a) to generate generated video's depth map $D^{\mathrm{gen}}$ and ground truth's depth map $D^{\mathrm{gt}}$ . We define the optical flow reward as $R(x_0', x_0) = -|D^{\mathrm{gen}} - D^{\mathrm{gt}}|$ . + +Details on implementation can be found in Appendix C. + +We begin from the checkpoint of the first stage, which is trained on 5,000 samples trained over 5,000 gradient steps. We then fine-tune the model with ORO on the simulated dataset, using a batch size of 1 and two 80GB NVIDIA A100 GPUs for each fine-tuning experiment. We set a learning rate of $1\mathrm{e} - 6$ for segmentation reward and depth reward and $1\mathrm{e} - 5$ for optical flow. + +As shown in Table 1, incorporating ORO in reward modeling further improves performance. Additionally, each reward function enhances the aspect of physicality that aligns with its intended purpose—segmentation rewards improve shape accuracy, while flow rewards and depth rewards improve motion accuracy. This demonstrates the process is both modular and interpretable. + +# 5. Assessing Learned Physical Behavior + +Having introduced our post-training approaches in Section 4, we probe into the model's understanding of the interaction between gravity and perspective—the two laws that determine the dynamics of our videos. We first test if the learned physical behavior of our model can generalize to dropping heights and depths beyond its training distribution. Then, we study the ability of the model to learn the probability distribution induced by the uncertainty of perspective. + +# 5.1. Generalization to Unseen Depths and Heights + +Depth and height are the main factors that affect the dynamics of a falling object in our videos. We can see this by combining the laws of gravity with perspective under our camera assumptions to model the object's image $y$ coordinate as a function of time (further details on our coordinate system are described in Appendix G): + +$$ +y (t) = \frac {f}{Z} \left(Y _ {0} - \frac {1}{2} g t ^ {2}\right). \tag {2} +$$ + +From Equation (2), we see that the random variables that af + +fect object motion are $Z$ (depth) and $Y$ (height) (the camera focal length $f$ is fixed). Thus, we are interested in testing generalization on unseen values of $Y$ and $Z$ . + +We create a simulated test set in which a single object is dropped from varying depths and heights, using objects and backgrounds unseen during training. We uniformly sample depth and height values (in meters) from the Cartesian product of the ranges [1, 5] and [0.5, 2.5], respectively. The camera height is fixed at $0.5m$ , and depth-height pairs outside the camera viewing frustum are discarded. A sample is in-distribution (ID) if its dropping depth and height both fall in the range [1, 3] and [0.5, 1.5]. + +Since we have access to the ground truth dropping time in simulation, we also employ a dropping time error, a metric we describe in Appendix B. Our analysis in Table 2 shows that performance degrades for out-of-distribution scenarios. + +Since depth and height are the main physical quantities that affect falling dynamics, this finding indicates that our model may struggle to learn a fully generalizable law that accounts for the interaction of perspective and gravity. + +
SettingL2 (↓)Chamfer (↓)IOU (↑)Time Error (↓)
ID0.0360.0880.1550.091
OOD0.0440.1430.0490.187
+ +Table 2. Results of our metrics on in-distribution (ID) and out-of-distribution (OOD) depth-height combinations. The values used for depth range from $1 - 5\mathrm{m}$ (ID range [1,3]) and height values range from 0.5-2.5 (ID range [0.5, 1.5]). + +# 5.2. Distributional Analysis + +![](images/173d344ac811372831211d71e1f089dcd0ee90fa7170fbcfc6b6036661f678d4.jpg) +Figure 9. Demonstration of ambiguity in 2D perspective projections. Each of the three clouds appears the exact same in the camera's image. The right side shows how we perform a scale and translation augmentation to generate deliberately ambiguous data. + +![](images/dcf5758aab2710279523e38fe46165467a3e180eeef0ed0b3050233202412b9e.jpg) + +The evolution of a physical system is not uniquely determined by a single initial image, since the lossy uncertainty of perspective induces a distribution of possible outcomes as shown in Figure 9. An ideal video world model should (1) output videos that are faithful to the evolution of some plausible world state and (2) provide accurate coverage across the entire distribution of the world that is possible from + +its conditioning signal. In this section, we examine these two facets by studying $p(t|y)$ : the distribution of dropping times possible from an object at coordinate $y$ in the image plane. To do this, we create a simulated dataset that has a much wider distribution $p(t|y)$ than our PSFT dataset. See Appendix F for more details on its construction. + +![](images/73a89a0c5b340af83339e7bdee6111a2850a250f52d7a51435656c3c43642fe2.jpg) +Figure 10. Examples of model trajectories lifted to 3D. The blue line represents the height of the camera ray passing through the bottom of the dropping object as a function of depth. The set of possible dropping trajectories at a given depth are depicted in gray. The lifted trajectory of the model is depicted in green. + +![](images/8862d09f5523d53e73a41fca13423e9ac96d265eb77cc7788176d5f31c7abc8a.jpg) +Figure 11. Visualizing $p(t|y)$ misalignment for different images. Green shows the ground-truth CDF, orange is the 32-frame quantized version, and blue is the empirical CDF of 128 different samples of dropping times from the model. + +# Testing (1): 3D faithfulness of trajectories. + +After training our model on this new dataset, we test whether its trajectories are consistent with a valid 3D world state. We first obtain an estimated dropping time from generated videos using the procedure described in Section 5.1. Using knowledge of the camera position, focal length, sensor width, and $y$ , we can obtain an implied depth and height of the trajectory. We can then back-project the video trajectory to 3D and analyze whether they constitute physically accurate trajectories. We give further details about this process in Appendix G. As show in Figure 10, we find that our model's lifted trajectories consistently align with the 3D trajectory at the height and depth implied by its dropping time, giving evidence that the model's visual outputs are faithful to some plausible real-world state. + +# Testing (2): distributional alignment. + +Going beyond the level of individual trajectories, we study the model's learned conditional distribution $p(t|y)$ . We + +create 50 different initial images with differing values of $y$ , generate 128 different videos from each, and estimate the dropping time in each video. Using the laws of gravity, the laws of perspective, and the assumption of uniform depth sampling in our dataset, we can analytically derive the probability $p(t|y)$ as + +$$ +p (t | y) = \left\{ \begin{array}{l l} \frac {g t}{\left(Z _ {\max } - Z _ {\min }\right) \beta}, & t _ {\min } \leq t \leq t _ {\max } \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +where $\beta$ is a constant that depends on $f$ , $y$ and the camera height. The derivation is given in Appendix E. + +We then measure goodness-of-fit for each of the 50 experiments using the Kolmogorov-Smirnov (KS) test (Massey Jr, 1951). The null hypothesis of the KS test is that the two distributions being compared are equal, and we consider p-values less than 0.05 as evidence of misalignment. Since our measured times have limited precision and can only take 32 distinct values—due to estimating the contact frame—we approximate the ground truth $p(t|y)$ using a Monte Carlo method. We sample 1000 values from the ground truth distribution and then quantized them into 32 bins corresponding to their frame, which we use as ground truth observations in the KS test. We find that in all 50/50 cases, the p-value from the test is less than 0.05, which provides evidence that the model does not learn the correct distribution of dropping times. We visualize the misalignment between the empirical CDF of the model's in Figure 11. + +In summary, while our model's trajectories show promising tendencies to ground themselves to plausible 3D world states, the range of possible outputs from the model does not align with the ground truth distribution. + +# 6. Conclusion + +This work studies post-training as an avenue for adapting adapting pre-trained video generator into world models. We introduce a post-training strategy that is highly effective in aligning our model. Our work raises interesting insights into the learned distributions of generative models. Qualitatively, large scale image or video generative models appear to excel at generating likely samples from the data distribution, but this alone does not imply that they match the data distribution well in its entirety. As long as a model is able to generate likely samples, global distributional misalignment is not necessarily a problem for content creation. However, this problem becomes critical for world models, where alignment across the entire distribution is necessary for faithful world simulation. The insights revealed by our study, made possible by our constrained and tractable setting, indicate that although post-training improves per-sample accuracy, general distributional alignment remains unsolved. + +# Acknowledgment + +We thank Boyang Zheng, Srivats Poddar, Ellis Brown, Shengbang Tong, Shusheng Yang, Jihan Yang, Daohan Lu, Anjali Gupta and Ziteng Wang for their help with data collection. We thank Jiraphon Yenphraphai for valuable assistance in setting up our simulation code. We thank Runway and Kling AI for providing API credit. SX also acknowledges support from Intel AI SRS, Korean AI Research Hub, Open Path AI Foundation, Amazon Research Award, Google TRC program, and NSF Award IIS-2443404. + +# References + +Agarwal, N., Ali, A., Bala, M., Balaji, Y., Barker, E., Cai, T., Chattopadhyay, P., Chen, Y., Cui, Y., Ding, Y., et al. Cosmos world foundation model platform for physical AI. arXiv preprint arXiv:2501.03575, 2025. +Baillargeon, R. Infants' physical world. Current directions in psychological science, 13(3):89-94, 2004. +Bansal, H., Lin, Z., Xie, T., Zong, Z., Yarom, M., Bitton, Y., Jiang, C., Sun, Y., Chang, K.-W., and Grover, A. Videophy: Evaluating physical commonsense for video generation. arXiv preprint arXiv:2406.03520, 2024. +Battaglia, P. W., Hamrick, J. B., and Tenenbaum, J. B. Simulation as an engine of physical scene understanding. 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Video as the new language for real-world decision making. arXiv preprint arXiv:2402.17139, 2024b. +Yang, Z., Teng, J., Zheng, W., Ding, M., Huang, S., Xu, J., Yang, Y., Hong, W., Zhang, X., Feng, G., et al. Cogvideox: Text-to-video diffusion models with an expert transformer. arXiv preprint arXiv:2408.06072, 2024c. +Zheng, Z., Peng, X., Yang, T., Shen, C., Li, S., Liu, H., Zhou, Y., Li, T., and You, Y. Open-sora: Democratizing efficient video production for all, March 2024. URL https://github.com/hpcaitech/Open-Sora. + +# A. Discussion of Image-to-Video setting. + +We note that our choice of single-image input, as opposed to multi-frame input, comes with some trade-offs. We choose the image-to-video setting because it is widely supported among many different models, allowing us to make effective comparisons across the current state-of-the-art. However, only conditioning on a single frame introduces significant ambiguity. Due to the loss of information caused by projecting the 3D world through perspective, it may not be possible to directly infer the size of the object or its height. In practice, we find our metrics are still reliable signals of task success, but we still study the problem of ambiguity more extensively in Section 5.2. + +# B. Metric details. + +We propose three metrics to assess the accuracy of trajectories, shape fidelity, and object permanence. Each of our metrics compare frames from the ground-truth video with the generated video. Because different models can operate at different fps, we perform fps alignment as part of our evaluation process. To perform fps alignment, we map each frame index of the generated videos to the ground truth using $f_{\mathrm{gen}}$ and $f_{\mathrm{gt}}$ , where $f_{\mathrm{gen}}$ and $f_{\mathrm{gt}}$ are the fps of generated video and ground truth respectively. For $i$ -th frame in the generated video, we find the corresponding aligned frame index $j$ in the ground truth video: + +$$ +j = \operatorname {r o u n d} \left(i \cdot \frac {f _ {\text {g e n}}}{f _ {\mathrm {g t}}}\right) \tag {4} +$$ + +Through fps alignment, we downsample the ground truth video to match the frame number of the generated video. We denote the downsampled ground truth as $\{I_i^{\mathrm{gt}}\}_{i = 1}^N$ and the generated video as $\{I_i^{\mathrm{gen}}\}_{i = 1}^N$ , where $N$ is the number of frames in the generated video. + +Trajectory L2. For each frame in both the generated video and ground truth, we calculate the centroid of the masked region. We then compute $L_{2}$ distance between the centroids of corresponding frames: + +$$ +L _ {2} = \frac {1}{N} \sum_ {i = 1} ^ {N} \| C _ {i} ^ {\text {g e n}} - C _ {i} ^ {\mathrm {g t}} \| _ {2} \tag {5} +$$ + +where $C_i^{\mathrm{gen}}, C_i^{\mathrm{gt}} \in \mathbb{R}^2$ are the centroids of the dropping object in the $i$ -th frame of generated video and the ground truth respectively. + +Chamfer Distance (CD). To assess the shape fidelity of objects, we calculate the Chamfer Distance (CD) between the mask regions of the generated video and ground truth: + +$$ +\mathrm {C D} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left(\frac {1}{| P _ {i} |} \sum_ {p \in P _ {i}} \min _ {q \in Q _ {i}} \| p - q \| _ {2} + \frac {1}{| Q _ {i} |} \sum_ {q \in Q _ {i}} \min _ {p \in P _ {i}} \| q - p \| _ {2}\right) +$$ + +where $P_{i} = \{p_{j}\}_{j = 1}^{|P_{i}|}$ and $Q_{i} = \{q_{j}\}_{j = 1}^{|Q_{i}|}$ are the sets of mask points in the $i$ -th frame of the generated video and ground truth respectively. + +Intersection over Union (IoU). We use the Intersection over Union (IoU) metric to evaluate object permanence. IoU measures objects' degree of overlap between the generated video and ground truth. This is formulated as follows: + +$$ +\mathrm {I o U} = \frac {1}{| N |} \sum_ {i = 1} ^ {N} \frac {\left| M _ {i} ^ {\text {g e n}} \cap M _ {i} ^ {\mathrm {g t}} \right|}{\left| M _ {i} ^ {\text {g e n}} \cup M _ {i} ^ {\mathrm {g t}} \right|} \tag {6} +$$ + +where $M_{i}^{\mathrm{gen}}$ , $M_{i}^{\mathrm{gt}} \in \{0,1\}^{H\times W}$ are binary segmentation masks of the falling object in the $i$ -th frame of the generated and ground truth videos respectively. + +Time error. When testing on videos generated in simulation, we can provide a timing error. From the dropping height $Y_{0}$ of the ground truth video, which we have access to from the simulator, we can derive $t_{\mathrm{drop}} = \sqrt{Y_0\frac{2}{g}}$ . We then obtain a dropping time from the model's output by estimating the frame of impact as the first frame $F$ whose centroid velocity in the $y$ direction is negative. If $t_{\mathrm{drop}}$ occurs in between $F$ and $F - 1$ , then we define the time error $E_{\mathrm{time}}$ as zero. Otherwise, we define the time error as + +$$ +E _ {\text {t i m e}} = \min \left(\left| \frac {F - 1}{\mathrm {f p s}} - t _ {\text {d r o p}} \right|, \left| \frac {F}{\mathrm {f p s}} - t _ {\text {d r o p}} \right|\right). \tag {7} +$$ + +# C. ORO implementation details. + +In our setting, we do not cut the gradient after step $k$ like VADER. The gradient $\nabla_{\theta}R(x_0',x_0)$ backpropagates through all diffusion timesteps and update the model weights $\theta$ : + +$$ +\nabla_ {\theta} \left(R \left(x _ {0} ^ {\prime}, x _ {0}\right)\right) = \sum_ {t = 0} ^ {T} \frac {\partial R \left(x _ {0} ^ {\prime} , x _ {0}\right)}{\partial x _ {t}} \cdot \frac {\partial x _ {t}}{\partial \theta} \tag {8} +$$ + +where $T$ is the total diffusion timesteps. + +Segmentation Reward. We utilize SAM 2 (Ravi et al., 2024) to generate segmentation masks across frames for generated video: + +$$ +M ^ {\text {g e n}} = \operatorname {S A M} - 2 \left(x _ {0}\right) \tag {9} +$$ + +where $M^{\mathrm{gen}}$ denotes the masks of the falling object in the generated video. We obtain ground truth masks $M^{\mathrm{gt}}$ using Kubric (Greff et al., 2022). To avoid non-differentiable reward, we use Sigmoid to normalize mask logits of generated video instead of converting them to binary masks. We use IoU between $M^{\mathrm{gen}}$ and $M^{\mathrm{gt}}$ as reward function: + +$$ +R \left(x _ {0} ^ {\prime}, x _ {0}\right) = \operatorname {I o U} \left(M ^ {\text {g e n}}, M ^ {\text {g t}}\right) \tag {10} +$$ + +Maximizing objective 1 is equivalent to minimizing the following objective: + +$$ +J (\theta) = \mathbb {E} _ {\left(x _ {0}, c\right) \sim \mathcal {D}, x _ {0} ^ {\prime} \sim p _ {\theta} \left(x _ {0} ^ {\prime} \mid c\right)} \left[ 1 - \operatorname {I o U} \left(M ^ {\text {g e n}}, M ^ {\text {g t}}\right) \right] \tag {11} +$$ + +This objective constrains the position and shape of the generated object in the video, encouraging a greater intersection with the object region in the ground truth video. The model learns to generate more accurate object positions and shapes through training with this objective. + +Optical Flow Reward. We utilize RAFT (Teed & Deng, 2020) to generate optical flow for both generated videos and ground truth: + +$$ +V ^ {\text {g e n}} = \operatorname {R A F T} \left(x _ {0} ^ {\prime}\right) \tag {12} +$$ + +$$ +V ^ {\mathrm {g t}} = \operatorname {R A F T} (x _ {0}) +$$ + +where $V^{\mathrm{gen}}$ , $V^{\mathrm{gt}}$ denote the optical flows of generated videos and ground truth. We define the reward as follows: + +$$ +R \left(x _ {0} ^ {\prime}, x _ {0}\right) = - \left| V ^ {\text {g e n}} - V ^ {\text {g t}} \right| \tag {13} +$$ + +Maximizing objective 1 is equivalent to minimizing the following objective: + +$$ +J (\theta) = \mathbb {E} _ {\left(x _ {0}, c\right) \sim \mathcal {D}, x _ {0} ^ {\prime} \sim p _ {\theta} \left(x _ {0} ^ {\prime} \mid c\right)} \left[ \left| V ^ {\text {g e n}} - V ^ {\text {g t}} \right| \right] \tag {14} +$$ + +This objective constrains the motion of the generated object in the video. The model learns to generate more accurate physical motion through training with this objective. + +Depth Reward. We utilize Depth-Anything-V2 (Yang et al., 2024a) to generate optical depth maps for both generated videos and ground truth: + +$$ +D ^ {\text {g e n}} = \text {D e p t h - A n y t h i n g - V 2} \left(x _ {0} ^ {\prime}\right) \tag {15} +$$ + +$$ +D ^ {\mathrm {g t}} = \text {D e p t h - A n y t h i n g - V 2} (x _ {0}) +$$ + +where $D^{\mathrm{gen}}$ , $D^{\mathrm{gt}}$ denote the depth maps of generated videos and ground truth. We define the reward as follows: + +$$ +R \left(x _ {0} ^ {\prime}, x _ {0}\right) = - \left| D ^ {\text {g e n}} - D ^ {\mathrm {g t}} \right| \tag {16} +$$ + +Maximizing objective 1 is equivalent to minimizing the following objective: + +$$ +J (\theta) = \mathbb {E} _ {\left(x _ {0}, c\right) \sim \mathcal {D}, x _ {0} ^ {\prime} \sim p _ {\theta} \left(x _ {0} ^ {\prime} \mid c\right)} \left[ \left| D ^ {\mathrm {g e n}} - D ^ {\mathrm {g t}} \right| \right] \tag {17} +$$ + +This objective constrains the 3d motion of the generated object in the video. The model learns to generate more accurate 3d physical motion through training with this objective. + +# D. Coordinate system + +We give a visualization of the coordinate system used in this paper in Figure 12. To compute $y$ , we first leverage a segmentation map and find pixel row index that is just below the object. Once this row index is found, $y$ can easily be computed from the camera position, camera sensor size, and image resolution. We note that because our camera is assumed to be in perspective with the $XY$ plane, we can ignore $X$ and $x$ (not shown in figure) in our analyses in Section 5.1 and Section 5.2. + +![](images/afd6a41eb9e3a6bfc87ee7d008d6fc6d00d3b71c75ccf91adf12e6a11f200f01.jpg) +Figure 12. A visualization of the coordinate system used in this paper (not to scale). The image plane height of the object is denoted as $y$ , its actual height in 3D as $Y$ , and its depth as $Z$ . The camera focal length is denoted as $f$ . + +![](images/0492c7160061c2167d23b2371de275bf324606389678afb1b4fcc06512b614c9.jpg) + +# E. Derivation of $p(t|y)$ + +In our dataset construction, we assume a uniform distribution for $Z$ , where $Z \sim \mathcal{U}(Z_{\min}, Z_{\max})$ , where $Z_{\min} = 2$ and $Z_{\max} = 18$ . As shown in Figure 12, the dropping height $Y$ is a linear function of $Z$ , i.e. $Y = y + \beta Z$ for the slope $\beta$ that can be computed from $y, f$ , the sensor size, and the camera height. This means we can solve for dropping time as $t = \sqrt{\frac{2}{g}Y} = \sqrt{\frac{2}{g}(y + \beta Z)}$ . Applying the transformation rule for probability density yields + +$$ +p (t | y) = \left\{ \begin{array}{l l} \frac {g t}{\left(Z _ {\max } - Z _ {\min }\right) \beta}, & t _ {\min } \leq t \leq t _ {\max } \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {18} +$$ + +where $t_{\mathrm{min}} = \sqrt{\frac{2}{g} (y + \beta Z_{\mathrm{min}})}$ and $t_{\mathrm{max}} = \sqrt{\frac{2}{g} (y + \beta Z_{\mathrm{max}})}$ . Plugging in $Z_{\mathrm{min}} = 2$ and $Z_{\mathrm{max}} = 18$ yields Equation (3). + +# F. Ambiguous dataset + +We introduce a new dataset for distributional analysis that broadens $p(t|y)$ , in contrast to the PSFT dataset, which prioritizes realism and has a narrower distribution due to limited object depth variability. To create a dataset with $p(t|y)$ that is sufficiently diverse for meaningful analysis, we first set up the initial scenes as before, but then apply an augmentation where a new depth values is sampled uniformly from [2, 18] and the object is scaled and translated such that it appears the same in the original image, as shown in Figure 9. For simplicity, we limit our scenes to a single dropping object with no other objects on the ground. We also disable shadows, preventing the model from using them as cues to infer depth and height. Our dataset contains 5k samples consisting of 1k unique initial scenes each containing 5 different trajectories produced by the augmentation. + +# G. Lifting trajectories to 3D + +To lift trajectories to 3D, we first estimate $t_{\mathrm{drop}}$ as described in Section 5.1. Using SAM2 to estimate object masks in the generated video, we can obtain a trajectory of the bottom of the object which we denote as $y_0, y_1, \ldots, y_N$ where + +$N = t_{\mathrm{drop}} \times \mathrm{fps}$ . From $t_{\mathrm{drop}}$ , we can solve for an implied depth $Z = \frac{\frac{1}{2}gt^2 - y}{\beta}$ . We then compute the lifted 3D trajectory as $y_i \mapsto y_i + \beta Z$ + +# H. PisaBench Details + +In this section, we discuss the details of our data collection pipeline and annotations. We present more examples of real-world videos and corresponding annotations in Figure 13. + +# H.1. Data Collection Pipeline + +Collecting Real World Videos. We enlist approximately 15 volunteers to participate in the data collection process. We hand out a tripod, tape, and invisible wire for each volunteer. To ensure the quality, diversity, and minimize the ambiguity introduced by the environments, volunteers are provided with detailed guidelines. The key points of the data collection guidelines are shown in Table 3. + +Raw videos processing. For the collected raw videos, we cut each video into multiple clips and crop their sizes. For each video clip, we annotate its starting position in the original long video and ensure that the duration of each segment does not exceed 12 seconds. Regarding the sizes of the videos, we manually crop each video to an aspect ratio of $1:1$ , ensuring that the falling objects remain fully visible within the frame during the cropping process. The processing interface is shown in Figure 14. + +# H.2. Annotation Details + +We present our annotation details in Figure 15. For video captions, we present the word cloud figure in (a). For segmentation masks, we annotate all objects in the first frame using positive and negative points, which are then propagated across frames using the SAM 2 (Ravi et al., 2024) model to produce segmentation masks for all objects throughout the video. The annotation interface is shown in (b). + +In addition to providing the annotated caption " {object description} falls," we also add information to inform off-the-shelf models of the task's context as much as possible. To further enhance task comprehension, we append an additional description "A video that conforms to the laws of physics." We also employ negative prompts "no camera motion" and "no slow-motion" to ensure environmental stability and impose constraints on the generated videos. These prompts explicitly instruct the models to avoid including camera motion or any non-real-time object motion, thereby maintaining consistency with real-world physics. + +# I. Inference Details + +We present the inference configurations of each closed or open model we evaluate in Table 4. For models that do not support generating videos with 1:1 aspect ratio, we pad initial frames with black borders to the resolution supported by these models, and finally remove the black borders from the generated videos. + +# J. More Qualitative Examples + +We present more qualitative examples in Figure 16 - Figure 22. Although in some showcases, models can roughly predict the downward trend, models still struggle to predict plausible shape and motion. The defects in the models can be mainly attributed to the following aspects: + +- Trajectory correctness: in most videos, models fail to predict even the basic falling trajectory of objects, as shown in Figure 19 (a), despite this being highly intuitive for humans. Even in cases where the falling trajectory is roughly correctly predicted, the models still struggle to accurately predict subsequent events, such as collisions, as illustrated in Figure 16 (f). +- Object consistency: in many generated videos, object consistency is poor. Models struggle to infer the appearance of objects from multiple viewpoints in a physically plausible manner, resulting in unnatural appearances, as shown in Figure 16 (a). Additionally, models perform poorly in maintaining object permanence, causing objects to appear blurry, as illustrated in Figure 20 (f). Furthermore, models sometimes introduce new objects into the video, as depicted in + +Figure 20 (e). + +- Scene consistency: models struggle to maintain scene consistency, leading to abrupt transitions in many videos. These sudden changes make videos appear unnatural, as shown in Figure 18 (f). + +# K. Simulated Adaption Details + +We use the Kubric (Greff et al., 2022) simulation and rendering engine for creating our simulated videos. Kubric uses PyBullet (Coumans et al., 2010) for running physics simulations and Blender (Community, 2018) for rendering. We set the simulation rate to 240 steps per second and render 2-second videos at 16 fps, resulting in 32 frames per video. Each scene consists of objects from the Google Scanned Objects (GSO) dataset (Downs et al., 2022) and uses environmental lighting from HDRI maps provided by Kubric. We use 930 objects and 458 HDRI maps for training and 103 objects and 51 HDRI maps for testing. + +For each video, we randomly choose 1-6 objects to drop. These objects are placed at a height uniformly sampled from $0.5\mathrm{m}$ to $1.5\mathrm{m}$ . Below each of these objects, a possibly empty pile of up to 4 objects spawns beneath to create collisions. The objects are placed in a spawn region of size $2\mathrm{m} \times 2\mathrm{m}$ . + +The camera is initially positioned $1\mathrm{m}$ behind this region, with its height varying uniformly between $0.4\mathrm{m}$ and $0.6\mathrm{m}$ . Once all objects are placed, the camera moves back in random increments until all objects are visible within the camera frame. The camera uses a focal length of $35\mathrm{mm}$ , a sensor width of $32\mathrm{mm}$ , and an aspect ratio of $1\times 1$ . + +# L. Limitations + +In this work, we collect and manually annotate a dataset of 361 real-world videos and design three spatial metrics to evaluate the performance of state-of-the-art image-to-video (I2V) models in a fundamental physical scenario: free fall. Our metrics focus solely on spatial positional relationships, excluding object appearance attributes such as color. To enable more fine-grained evaluations of appearance characteristics, we aim to develop metrics based on Multimodal Large Language Models (MLLMs) or pixel-level analysis in future work. + +Furthermore, we propose the PSFT and ORO methods to fine-tune the Open-Sora model (Zheng et al., 2024), improving its ability to generate physically plausible videos. Despite these improvements, certain limitations remain, specifically, the generation of blurry objects in some videos. We hope to address these challenges in future research by refining both the dataset and the fine-tuning strategies, aiming to produce videos that better maintain object visuals. + +![](images/2c3255e61507df64f2fe2b8fc33da6df4f8074be9bf5d02291a3cf3bb8a8a94a.jpg) +(a) A white paper roll falls. + +![](images/76661e958af011fe7f1f7ab37c8d6b11f4f98a6f04af442101dbe8308c1127ee.jpg) +(c) A black bottle falls. + +![](images/f96ae24b9af0730f8094994e180d7d5a6e32804e7b580a5dadd002836de5fced.jpg) +(b) A transparent bottle falls. + +![](images/14aef21ca7858494c097f6f67d50528c4b5917b1b19db5da86d4a491cd5a520f.jpg) +(d) A white bottle falls. +Figure 13. Examples of real world videos and annotations. We present video frames in the first row and mask annotations in the second row. + +
AspectRequirements
Camera·The camera must be stabilized using a tripod. +·The dropping object should remain visible throughout the entire fall. +·The trajectory of the object should be sufficiently centered in the frame. +·Ensure the slow-motion setting is configured to 120 fps. +·Avoid a completely top-down perspective; the frame should include both the floor and the wall for spatial context. +·It is acceptable to record one long video containing multiple drops at the same location.
Objects·Most objects should be rigid and non-deformable. +·A limited number of flexible or deformable objects may be included, as such data is also valuable.
Dropping Procedure·Secure the object with a wire using tape, ensuring stability. Multiple tapings may be necessary for proper stabilization. +·Visibility of the wire in the video is acceptable. +·No body parts should appear in the frame. If this is challenging, consider having a partner monitor the camera or use screen-sharing software to view the camera feed on a laptop for uninterrupted framing. +·Record videos in a horizontal orientation to simplify cropping and to help keep the frame free of unnecessary elements. +·Use a short wire to enhance object stability. +·The object should remain stationary before being dropped.
Scene Composition·Make the scenes dynamic and engaging. Include interactions with other objects, such as collisions or objects tipping over. Static objects should serve as active elements rather than mere background props. +·Avoid filming in classroom or laboratory environments. +·Include a variety of dropping heights. +·Film in different environments, ensuring at least one setting is outside your apartment. +·Minimize human shadows in the frame whenever possible. +·Ensure good lighting and maintain strong contrast between the objects and the back-ground.
+ +Table 3. Key points of real world videos collection guideline. We have detailed requirements for camera, objects, dropping procedure and scene composition to ensure the quality, diversity and minimize ambiguity introduced by environments. + +![](images/945c3d2b2e7ba5dd24811fc027b02c812dd3fdb62673324359a47eefccc06ed5.jpg) +(a) + +![](images/4d595693598e6f902081fbae2160c14f17629bf42e1282931e980a4273a07e54.jpg) +(b) + +![](images/8f522784783a329f5017e6371582ae27e84586d17a8f7bcd9025f339933400e5.jpg) +(a) + +![](images/733aaf4a714c7ec870de8f5e762d4a545653a15ef5ea24677ad5c2400309aed0.jpg) +Figure 14. Video processing interface. (a) we annotate starting positions in the original long videos and clip them into multiple clips less than 12 seconds. (b) We drag the cropping box to crop the video size to an aspect ratio of 1:1. +(b) +Figure 15. Annotation details of real world videos. (a) Word cloud of objects in video captions. Our videos contain a variety of daily life objects. (b) Interface for annotating positive and negative points in the first frame. Red and blue dots indicate positive and negative points respectively. We annotate all objects in the midair and ground. + +
ModelResolutionNumber of FramesFPSGuidance ScaleSampling StepsNoise Scheduler
ClosedSora720 × 72015030---
Kling-V1.5960 × 960150301.0--
Kling-V1960 × 960150301.0--
Runway Gen31280 × 76815630---
OpenCogVideoX-5B-I2V720 × 4804886.050DDIM
DynamiCrafter512 × 32090300.750DDIM
Pyramid-Flow1280 × 768120244.010EulerDiscrete
Open-Sora512 × 51290307.030RFLOW
+ +Table 4. Inference details for models we evaluate, where “-” indicates the information is not available. + +![](images/c26bfecf28ebcde71af6d60da63253f75d02e0c5503f1425cbff24859ab09444.jpg) +(a) A brown bottle falls. + +![](images/5f5749c22b33d6469cf285b89aba3d78b780ffbd4338568515ee93f4e1fa544d.jpg) +(b) A grey bottle falls. + +![](images/1f5a8409a2aefddb489c74e7deb33bffefdf80fdb5c072687ddd0946e16f3e00.jpg) +(c) A grey paper cup falls. + +![](images/19fe4f4ece7488446d3a1550236f6f8bf176f70d2615cfa7db7c28a0720cf550.jpg) +(d) A paper cup falls. + +![](images/7ecc93d403dcb06758ac993647a892395af1264eeca956ba139d2929c18192ba.jpg) +(e) A white bottle falls. + +![](images/c8f534dc359b0c6486ea7d10444e18fb31e91a7d173e50458a7fb898ac132de4.jpg) +(f) A white box falls. +Figure 16. Qualitative examples of Kling-V1 (Kuaishou, 2024). In (a) (b) (c) (f), objects have a tendency to fall. (b) (c) are roughly consistent with the laws of physics. In (a) (f), the shape of the object does not match the first frame. In (d), the paper cup is suspended in midair. In (e), new object is introduced. In (e), the model fails to correctly predict the collision that occurs after the white box falls and the chain of events that follows. + +![](images/d24e9d610f63859bf566728e5b51c496af6f6f54f828b2cc2aae2a5186055f4c.jpg) +(a) A black and grey glove falls. + +![](images/936b8ee3ceeca5f82d0050ae068b79e918e73267eaa429a43c2317f1f2323c25.jpg) +(b) A black bottle falls. + +![](images/2d23c7b2c224aa44ab3a8eed9dfe17398040ed64c31737411568651ceb6dcf15.jpg) +(c) A blue and white box falls. + +![](images/20194bd551fbcc50f5676b0a019e1d10041918fadd0264051f4f9a7540545bac.jpg) +(d) A brown bottle falls. + +![](images/baf79faae3094c985d469cccd5f8af1aef1f088b8c03e4b23c119ec86aebd807.jpg) +(e) A Coca-Cola can falls. + +![](images/8cb3aa9d253fc5e51c44a557e5629610fa5ad282a6ce25364e557518e7b8d6c7.jpg) +(f) A pink box falls. +Figure 17. Qualitative examples of Runway Gen3 (Runway, 2024). In (b) (e), objects have a tendency to fall. In (a) (e) (f), new objects are introduced. In (b) (d), the shape of the object does not match the first frame. In (c), the box is suspended in midair. + +![](images/a79a3d2c12bca59c6526e7216d60bb7580bc8c63576be8552b2f29dfd5c346d2.jpg) +(a) A black bottle falls. + +![](images/498fa6c0164db5fd88370c112e6dd2c5829dbe74624f6e825ac28219d5f5aa3d.jpg) +(b) A black helmet falls. + +![](images/8317550ad7aa20a11f3bf97aa716e1da5f6f471ce296a6b0a5da5eba39db5c52.jpg) +(c) A paper box falls. + +![](images/5259adbc56734c97b69c0f5ac5a0debfc574cf0ee9fab5cae058c157503ada7b.jpg) +(d) A white bottle falls. + +![](images/fb0eb57bfd7df70674700e7d467e475c936b995b0451b6a6746c321bb30fd4dc.jpg) +(e) A grey paper cup falls. + +![](images/dad22c2ccf02d28f88996ada3f6458c8f7ba92408c341e39e6da0ed00ee05fbb.jpg) +(f) A white box falls. +Figure 18. Qualitative examples of CogVideoX-5B-I2V (Yang et al., 2024c). In (a) - (f), objects have a tendency to fall. However, in all the videos, there are violations of physics. In (a) (b), the objects are divided into two parts. In (c) (d) (e), the shape of the object does not match the first frame. In (c), the trajectory is not a vertical fall. In (f), scene changes suddenly, which does not match the first frame. + +![](images/e39efd16222ce5ec5787e1ab30db7573f7cb53089f14019eb71cfee5130fa917.jpg) +(a) A black box falls. + +![](images/a17478f38168df434239dbbc27ca455093b6c1e40467cd5487d213bb5d83095d.jpg) +(b) A card holder falls. + +![](images/f5955939eff061d366f9461ca64daddccce438bc7cf26e0ca0177e4bea14e76c.jpg) +(c) A white bottle falls. + +![](images/3064ab2bd099f6c34a0b0143af9b37cafbc9b07d4aff556a41357fd47bdbe8d3.jpg) +(d) A white box falls. + +![](images/f9b6d84ca868eb7b320e5bf66a6830342a093523d4a8c01e2b0d2c6c9b32e833.jpg) +(e) An orange and white box falls. + +![](images/b68b172758804959f5687238c0b53d284f904543618dda06d81c04419d71a2ce.jpg) +(f) A shoe falls. +Figure 19. Qualitative examples of DynamiCrafter (?). In all the videos, objects do not have a tendency to fall, suspended in the midair. + +![](images/b39f635b4b2874364c63137dcdc9fc15f4eb68ba57cc4f852a463fac4a5c56f0.jpg) +(a) A black bottle falls. + +![](images/c3078aa13d861c89ebf70c3db430662cdcd8c83d8880aa9a934a258e5c3598e5.jpg) +(b) A green and white box falls. + +![](images/47bbef5b7ad9b2e303cbcdd98429261eea928bc17ba376000894eba09e78ab5b.jpg) +(c) A grey bottle falls. + +![](images/d20954189b98d66653a95abacce5f2c333474ea3a756f9e105766842d1c52aaf.jpg) +(d) An orange tube falls. + +![](images/52a4ded90059019d5599737a9ccf91373f0a89472a4470044d57fa2d382b574c.jpg) +(e) A white bottle falls. + +![](images/1bfe20845da001136df0ce41999f5d2267a843826b8f310807bc262f0f0570d5.jpg) +(f) A plastic box falls. +Figure 20. Qualitative examples of Pyramid-Flow (Jin et al., 2024). In (b) (d) (e), objects have a tendency to fall. In (a) (b) (e) (f), new objects are introduced. In (c), scene changes, which does not match the first frame.. In (d), the tube becomes blurry. + +![](images/161db114927f1a531685c756c1a59ca048d49f95035d117b63e02913d1aeda55.jpg) +(a) A bottle full of water falls. + +![](images/00dd072f248c8d96ba525c8f9026f6dbe513577c2833c0a39bcc58836058a3ae.jpg) +(b) A brown bottle falls. + +![](images/20691688d65a9c34668843431f6da68506d385837a8adf32d934a8338cfbb623.jpg) +(c) A grey paper cup falls. + +![](images/20dc724f7197dd626747f2db293d23a957a1d7672a436a2fd07469a0a937b08a.jpg) +(d) A paper box falls. + +![](images/5f2dbd497dd96b551059198818fd41a1cc13a1d01d40d7814fd8343102c994a3.jpg) +(e) A white bottle falls. + +![](images/5794ff6b8e6a1c23e1b350538a38f18063fb742919db3216ae76aa58e6f391f5.jpg) +(f) A white box falls. +Figure 21. Qualitative examples of Open-Sora (Zheng et al., 2024). In all the videos, objects do not have a tendency to fall, suspended in the midair. In (b) (d), scene changes suddenly, which does not match the first frame. In (e), new object is introduced. + +![](images/0cc35a21a9c1a24bb99fd5ae428c1b943237dcc4bf44654420f09f88cbbe622f.jpg) +(a) A brown bottle falls. + +![](images/20453f58b53c0dbbefd7d26b5854ca263406b127771a6983ee453bcedd34a9b8.jpg) +(b) A grey eraser falls. + +![](images/d0de139686427ffdf841921b45e326470ebe6a127e77cc98801376148a86c3b4.jpg) +(c) A grey paper cup falls. + +![](images/2c9f209b0aeac72570d8c4fde360b1cf6b4dfcb2b6a0e8d4e853f7b3a78fa4d6.jpg) +(d) A transparent bottle falls. + +![](images/f52bf9a1a1b538e95d70fbf8e8072fe5c66e0fb960e1c0adc65706d6253840a0.jpg) +(e) A red wrapping paper falls. + +![](images/a00eb2f6afd73e7890435740d404820471ec3c29a424ac89fa8f08f0f78a9a90.jpg) +(f) A white bottle falls. +Figure 22. Qualitative examples of our method (Open-Sora + PSFT + ORO). In all the videos, objects have a tendency to fall. However, the consistency of objects is still insufficient. In some frames, objects become blurry. 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"text", + "content": " Oscar Michel " + }, + { + "bbox": [ + 105, + 157, + 488, + 171 + ], + "type": "inline_equation", + "content": "^{*1}" + }, + { + "bbox": [ + 105, + 157, + 488, + 171 + ], + "type": "text", + "content": " Xichen Pan " + }, + { + "bbox": [ + 105, + 157, + 488, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 105, + 157, + 488, + 171 + ], + "type": "text", + "content": " Sainan Liu " + }, + { + "bbox": [ + 105, + 157, + 488, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 105, + 157, + 488, + 171 + ], + "type": "text", + "content": " Mike Roberts " + }, + { + "bbox": [ + 105, + 157, + 488, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 105, + 157, + 488, + 171 + ], + "type": "text", + "content": " Saining Xie" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 148, + 192, + 196, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 192, + 196, + 205 + ], + "spans": [ + { + "bbox": [ + 148, + 192, + 196, + 205 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 72, + 214, + 272, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 214, + 272, + 489 + ], + "spans": [ + { + "bbox": [ + 72, + 214, + 272, + 489 + ], + "type": "text", + "content": "Large-scale pre-trained video generation models excel in content creation but are not reliable as physically accurate world simulators out of the box. This work studies the process of posttraining these models for accurate world modeling through the lens of the simple, yet fundamental, physics task of modeling object freefall. We show state-of-the-art video generation models struggle with this basic task, despite their visually impressive outputs. To remedy this problem, we find that fine-tuning on a relatively small amount of simulated videos is effective in inducing the dropping behavior in the model, and we can further improve results through a novel reward modeling procedure we introduce. Our study also reveals key limitations of post-training in generalization and distribution modeling. Additionally, we release a benchmark for this task that may serve as a useful diagnostic tool for tracking physical accuracy in large-scale video generative model development. Code is available at this repository: https://github.com/vision-x-nyu/pisa-experiments." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 517, + 133, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 517, + 133, + 529 + ], + "spans": [ + { + "bbox": [ + 53, + 517, + 133, + 529 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 536, + 291, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 536, + 291, + 669 + ], + "spans": [ + { + "bbox": [ + 52, + 536, + 291, + 669 + ], + "type": "text", + "content": "Over the past year, video generation models have advanced significantly, inspiring visions of a future where these models could serve as realistic world models (Craik, 1967; LeCun, 2022; Hafner et al., 2019; 2023; Ha & Schmidhuber, 2018). State-of-the-art video generation models models exhibit impressive results in content creation (OpenAI, 2024; Kuaishou, 2024; Luma, 2024; Runway, 2024) and are already being used in advertising and filmmaking (Runway, 2025; NBC, 2025). These advancements have sparked a line of research that seeks to evolve these models from content creators to world simulators for embodied agents (Yang" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 675, + 290, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 675, + 290, + 696 + ], + "spans": [ + { + "bbox": [ + 52, + 675, + 290, + 696 + ], + "type": "text", + "content": "*Equal contribution, alphabetical order. 1New York University 2Intel Labs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 193, + 543, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 543, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 543, + 266 + ], + "type": "text", + "content": "et al., 2023; 2024b; Agarwal et al., 2025). However, accurate world modeling is considerably more challenging than creative content creation because looking \"good enough\" is not sufficient: generated pixels must faithfully represent a world state evolving in accordance with the laws of physics and visual perspective." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 303, + 270, + 544, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 270, + 544, + 428 + ], + "spans": [ + { + "bbox": [ + 303, + 270, + 544, + 428 + ], + "type": "text", + "content": "We find that although the generations of state-of-the-art models are impressive visually, these models still struggle to generate results that are accurate physically, even though these models are pretrained on internet-scale video data demonstrating a wide variety of complex physical interactions. The failure to ground and align visual generations to the laws of physics suggests that pretraining is not enough and a post-training stage is needed. Much like how pretrained Large Language Models (LLMs) need to be adapted through post-training before they can be useful conversational assistants, pretrained video generative models ought to be adapted through post-training before they can be deployed as physically accurate world simulators." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 303, + 433, + 544, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 433, + 544, + 672 + ], + "spans": [ + { + "bbox": [ + 303, + 433, + 544, + 672 + ], + "type": "text", + "content": "In this work, we rigorously examine the post-training process of video generation models by focusing on the simple yet fundamental physics task of modeling object freefall, which we find is highly challenging for state-of-the-art models. Specifically, we study an image-to-video" + }, + { + "bbox": [ + 303, + 433, + 544, + 672 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 303, + 433, + 544, + 672 + ], + "type": "text", + "content": " (I2V) scenario where the goal is to generate a video of an object falling and potentially colliding with other objects on the ground, starting from an initial image of the object suspended in midair. We chose to study this single task, rather than general physics ability as a whole, because its simplicity allows us to conduct controlled experiments that yield insights into the strengths and limitations of the post-training process, which we believe will become an increasingly important component of research in generative world modeling. Additionally, the simplicity of the dropping task allows it to be implemented in simulation which is desirable because it allows us to easily test the properties of dataset scaling, gives us access to ground truth annotations for evaluation, and gives us the ability to precisely manipulate the simulation environment for controlled experimentation." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 304, + 679, + 543, + 700 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 679, + 543, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 679, + 543, + 700 + ], + "type": "text", + "content": "1We discuss our decision to formulate this task in the image-to-video setting instead of the video-to-video setting in Appendix A." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 14, + 205, + 35, + 559 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 14, + 205, + 35, + 559 + ], + "spans": [ + { + "bbox": [ + 14, + 205, + 35, + 559 + ], + "type": "text", + "content": "arXiv:2503.09595v1 [cs.CV] 12 Mar 2025" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "spans": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "text", + "content": "1" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 64, + 293, + 245 + ], + "blocks": [ + { + "bbox": [ + 53, + 64, + 293, + 245 + ], + "lines": [ + { + "bbox": [ + 53, + 64, + 293, + 245 + ], + "spans": [ + { + "bbox": [ + 53, + 64, + 293, + 245 + ], + "type": "image", + "image_path": "19a56cf5e00b438278d859ed1f2a1e950888d74b178b001eab56b1dd9862790e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 51, + 256, + 543, + 301 + ], + "lines": [ + { + "bbox": [ + 51, + 256, + 543, + 301 + ], + "spans": [ + { + "bbox": [ + 51, + 256, + 543, + 301 + ], + "type": "text", + "content": "Figure 1. Our PISA (Physics-Informed Simulation and Alignment) evaluation framework includes a new video dataset, where objects are dropped in a variety of real-world (left) and synthetic (right) scenes. For visualization purposes, we depict object motion by overlaying multiple video frames in each image shown above. Our real-world videos enable us to evaluate the physical accuracy of generated video output, and our synthetic videos enable us to improve accuracy through the use of post-training alignment methods." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 302, + 64, + 542, + 245 + ], + "blocks": [ + { + "bbox": [ + 302, + 64, + 542, + 245 + ], + "lines": [ + { + "bbox": [ + 302, + 64, + 542, + 245 + ], + "spans": [ + { + "bbox": [ + 302, + 64, + 542, + 245 + ], + "type": "image", + "image_path": "00bcbfd531744498cbd9c4457e5710d02b6c2db7bb28bac2414f98156285e998.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 51, + 320, + 291, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 320, + 291, + 452 + ], + "spans": [ + { + "bbox": [ + 51, + 320, + 291, + 452 + ], + "type": "text", + "content": "Named after Galileo's famous dropping experiment, we introduce the PISA (Physics-Informed Simulation and Alignment) framework for studying physics post-training in the context of the dropping task. PISA includes new real and simulated video datasets, as shown in Figure 1, containing a diverse set of dropping scenarios. PISA also includes a set of task-specific metrics that focus on measuring physical accuracy. Our real-world videos and metrics enable us to evaluate the physical accuracy of generated video output, and our synthetic videos enable us to improve accuracy through a post-training process we introduce." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 458, + 292, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 458, + 292, + 662 + ], + "spans": [ + { + "bbox": [ + 51, + 458, + 292, + 662 + ], + "type": "text", + "content": "Our study reveals that current state-of-the-art video generative models struggle significantly with the task of physically accurate object dropping. Generated objects frequently exhibit impossible behaviors, such as floating midair, defying gravity, or failing to preserve realistic trajectories during freefall. However, we find that simple fine-tuning can be remarkably effective: fine-tuning an open-source model on a small dataset of just a few thousand samples enables it to vastly outperform state-of-the-art models in physical accuracy. We further observe that pretrained models are critical for success; models initialized randomly, without leveraging pretraining on large-scale video datasets, fail to achieve comparable results. We also introduce a novel framework for reward modeling that yields further improvement. We demonstrate that our reward learning system is highly flexible in that different reward functions can be chosen to target different axes of physical improvement." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 667, + 293, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 667, + 293, + 717 + ], + "spans": [ + { + "bbox": [ + 51, + 667, + 293, + 717 + ], + "type": "text", + "content": "Our analysis also reveals key limitations. First, we see that model performance degrades when tasked with scenarios outside the training distribution, such as objects dropping from unseen depths or heights. Additionally, while our post" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 302, + 320, + 542, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 320, + 542, + 357 + ], + "spans": [ + { + "bbox": [ + 302, + 320, + 542, + 357 + ], + "type": "text", + "content": "trained model generates object motion that is 3D-consistent and physically accurate, we observe misalignment between the generated and ground truth dropping time distribution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 302, + 361, + 544, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 361, + 544, + 483 + ], + "spans": [ + { + "bbox": [ + 302, + 361, + 544, + 483 + ], + "type": "text", + "content": "These findings indicate that post-training is likely to be an essential component of future world modeling systems. The challenges we identify in this relatively simple task are likely to persist when modeling more sophisticated physical phenomena. By introducing the PISA framework and benchmark, we provide a useful diagnostic tool for researchers to test whether models are on the path to acquiring general physical abilities, as well as identify key limitations that researchers should be aware of when integrating new capabilities into their models through post-training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 498, + 391, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 391, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 391, + 510 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 302, + 517, + 544, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 517, + 544, + 710 + ], + "spans": [ + { + "bbox": [ + 302, + 517, + 544, + 710 + ], + "type": "text", + "content": "Modeling Intuitive Physics. Intuitive physics refers to the innate or learned human capacity to make quick and accurate judgments about the physical properties and behaviors of objects in the world, such as their motion, stability, or interactions. This ability, present even in infancy (Spelke et al., 1992; Baillargeon, 2004; Battaglia et al., 2013), is crucial for navigating and understanding everyday life. Replicating intuitive physics is a foundational step toward creating systems that can interact effectively and safely in dynamic, real-world environments (Lake et al., 2017). Gravity, as a core component of intuitive physics, plays a pivotal role in both domains. It is one of the most universal and observable physical forces, shaping our expectations about object motion, stability, and interaction (Hamrick et al., 2016; Ullman et al., 2017). Many studies in cognitive science (Battaglia et al., 2013) and AI (Wu et al., 2015; Bear et al., 2021) have" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "spans": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "text", + "content": "2" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 52, + 68, + 291, + 104 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 68, + 291, + 104 + ], + "spans": [ + { + "bbox": [ + 52, + 68, + 291, + 104 + ], + "type": "text", + "content": "relied on physics engines to evaluate and model intuitive physics. Our work uses the Kubric engine (Greff et al., 2022) to generate training videos." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 109, + 292, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 109, + 292, + 337 + ], + "spans": [ + { + "bbox": [ + 53, + 109, + 292, + 337 + ], + "type": "text", + "content": "Video Generation Models as World Simulators. Video generation has long been an intriguing topic in computer vision, particularly in the context of predicting future frames (Srivastava et al., 2015; Xue et al., 2016). More recently, as large-scale generative models have become prominent, Yang et al. explored how a wide range of real-world dynamics and decision-making processes can be expressed in terms of video modeling (Yang et al., 2024b; 2023). The introduction of the Sora model (OpenAI, 2024) marked a leap in the quality of generated videos and ignited interest in leveraging such models as \"world simulators.\" Over the past year, numerous video generation models have emerged, some open-source (Zheng et al., 2024; Yang et al., 2024c; Jin et al., 2024; Agarwal et al., 2025) and others commercially available (Kuaishou, 2024; Luma, 2024; Runway, 2024; OpenAI, 2024). Related to our work, Kang et al. (Kang et al., 2024) study the extent to which video generation models learn generalizable laws of physics when trained on 2D data from a synthetic environment." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 342, + 292, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 342, + 292, + 582 + ], + "spans": [ + { + "bbox": [ + 53, + 342, + 292, + 582 + ], + "type": "text", + "content": "Evaluating Video Generation Models. Traditional image-based metrics for generative modeling, such Fréchet inception distance (FID) (Heusel et al., 2017) or inception score (IS) (Salimans et al., 2016), can be incorporated into the video domain, either by applying them on a frame-by-frame basis or by developing video-specific versions, such as Fréchet video distance (FVD) (Unterthiner et al., 2018). Going beyond distribution matching measures, several benchmarks have developed suites of metrics that aim to better evaluate the semantic or visual quality of generated videos. For example, V-Bench (Huang et al., 2024) offers a more granular evaluation by measuring video quality across multiple dimensions, such as with respect to subject consistency or spatial relationships. In physics, some works, such as VideoPhy (Bansal et al., 2024) and PhyGenBench (Meng et al., 2024), evaluate in the T2V setting by utilizing multimodal large language models (MLLM) to generate a VQA-based score. More recently, Cosmos (Agarwal et al., 2025) and Physics-IQ (Motamed et al., 2025), evaluate physics in the image-to-video and video-to-video settings." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 597, + 121, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 597, + 121, + 609 + ], + "spans": [ + { + "bbox": [ + 52, + 597, + 121, + 609 + ], + "type": "text", + "content": "3. PisaBench" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 617, + 290, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 617, + 290, + 654 + ], + "spans": [ + { + "bbox": [ + 52, + 617, + 290, + 654 + ], + "type": "text", + "content": "Our benchmark, PisaBench, examines the ability of video generative models to produce accurate physical phenomena by focusing on a straightforward dropping task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 666, + 206, + 679 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 666, + 206, + 679 + ], + "spans": [ + { + "bbox": [ + 52, + 666, + 206, + 679 + ], + "type": "text", + "content": "3.1. Task Definition & Assumptions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 685, + 291, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 685, + 291, + 710 + ], + "spans": [ + { + "bbox": [ + 52, + 685, + 291, + 710 + ], + "type": "text", + "content": "Our task can be summarized as follows: given an image of an object suspended in midair, generate a video of the object" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 318, + 67, + 526, + 266 + ], + "blocks": [ + { + "bbox": [ + 318, + 67, + 526, + 266 + ], + "lines": [ + { + "bbox": [ + 318, + 67, + 526, + 266 + ], + "spans": [ + { + "bbox": [ + 318, + 67, + 526, + 266 + ], + "type": "image", + "image_path": "1ac3de96698eccbe7ffd3f2cdeee9e6722a7a59125ffbd3af395c8b98701c5c7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 327, + 272, + 518, + 283 + ], + "lines": [ + { + "bbox": [ + 327, + 272, + 518, + 283 + ], + "spans": [ + { + "bbox": [ + 327, + 272, + 518, + 283 + ], + "type": "text", + "content": "Figure 2. The setup for collecting real-world videos." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 303, + 542, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 542, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 542, + 388 + ], + "type": "text", + "content": "falling and colliding with the ground and potentially other objects. Since a video is an incomplete partial observation of the 4D world, we make a number of assumptions to constrain the task space. These assumptions are crucial for ensuring that our metrics are reliable signals for physical accuracy, since they are only approximations of task success computed from a single ground truth and generated video." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 393, + 544, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 544, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 544, + 513 + ], + "type": "text", + "content": "Specifically, we assume that the falling object is completely still in the initial frame, that only the force of gravity is acting on the object while it falls, and that the camera does not move. The first two assumptions are necessary for the image-to-video setting. Since we do not provide multiple frames as input, it is otherwise impossible to establish the initial velocity or acceleration of the falling object without these assumptions. The last assumption is necessary as our metrics derive from the motion of segmentation masks, which would be affected in the presence of camera motion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 526, + 398, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 526, + 398, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 398, + 537 + ], + "type": "text", + "content": "3.2. Real World Data" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 551, + 426, + 647 + ], + "blocks": [ + { + "bbox": [ + 310, + 551, + 426, + 647 + ], + "lines": [ + { + "bbox": [ + 310, + 551, + 426, + 647 + ], + "spans": [ + { + "bbox": [ + 310, + 551, + 426, + 647 + ], + "type": "image", + "image_path": "75bc9f270274a876e0f2d9bb2c4307c38aafd436f796800aeee64fbd5f2d9b29.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 655, + 542, + 677 + ], + "lines": [ + { + "bbox": [ + 304, + 655, + 542, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 655, + 542, + 677 + ], + "type": "text", + "content": "Figure 3. Statistics of the real-world data: (a) number of objects in each video, (b) the proportions of different scenes in the videos." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 439, + 551, + 539, + 647 + ], + "blocks": [ + { + "bbox": [ + 439, + 551, + 539, + 647 + ], + "lines": [ + { + "bbox": [ + 439, + 551, + 539, + 647 + ], + "spans": [ + { + "bbox": [ + 439, + 551, + 539, + 647 + ], + "type": "image", + "image_path": "2a038e4df7899a3c6a7af3f168c48dd30504eb434167e140afe024da4ee58ef5.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 681, + 542, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 681, + 542, + 717 + ], + "spans": [ + { + "bbox": [ + 304, + 681, + 542, + 717 + ], + "type": "text", + "content": "Real World Videos. We collect a set of 361 real-world videos demonstrating the dropping task for evaluation. As is shown in Figure 4, the dataset includes a diverse set" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "spans": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "text", + "content": "3" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 68, + 289, + 231 + ], + "blocks": [ + { + "bbox": [ + 56, + 68, + 289, + 231 + ], + "lines": [ + { + "bbox": [ + 56, + 68, + 289, + 231 + ], + "spans": [ + { + "bbox": [ + 56, + 68, + 289, + 231 + ], + "type": "image", + "image_path": "7d4ceaab34fce33596b3dd1e9d4ba7a5b2fc93095d7bd082617fa0ffe00a3c57.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 52, + 245, + 291, + 289 + ], + "lines": [ + { + "bbox": [ + 52, + 245, + 291, + 289 + ], + "spans": [ + { + "bbox": [ + 52, + 245, + 291, + 289 + ], + "type": "text", + "content": "Figure 4. Examples of various objects included in our dataset. For simulation, we utilize the GSO dataset (Downs et al., 2022), while for the real-world dataset, we curate our own set of common household objects." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 315, + 291, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 315, + 291, + 471 + ], + "spans": [ + { + "bbox": [ + 52, + 315, + 291, + 471 + ], + "type": "text", + "content": "of objects with different shapes and sizes, captured across various settings such as offices, kitchens, parks, and more (see Figure 3). Each video begins with an object suspended by an invisible wire in the first frame, which is necessary to enforce the assumption that objects are stationary at the start of the video. This assumption is required in our imaged-to-video setting; otherwise, the initial velocity of an object is ambiguous. We cut the video clips to begin as soon as the wire is released. We record the videos in slow-motion at 120 frames per second (fps) with cellphone cameras mounted on tripods to eliminate camera motion. An example of our video collection setup is shown in Figure 2. Additional details on our collection system are provided in Appendix H." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 476, + 291, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 476, + 291, + 559 + ], + "spans": [ + { + "bbox": [ + 52, + 476, + 291, + 559 + ], + "type": "text", + "content": "Simulated Test Videos. Since our post-training process uses a dataset of simulated videos, we also create a simulation test-set of 60 videos for understanding sim2real transfer. We create two splits of 30 videos each: one featuring objects and backgrounds seen during training, and the other featuring unseen objects and backgrounds. See Section 4.1 for details on how our simulated data is created." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 566, + 290, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 566, + 290, + 639 + ], + "spans": [ + { + "bbox": [ + 52, + 566, + 290, + 639 + ], + "type": "text", + "content": "Annotations. As is shown in Figure 5, we annotate each video with a caption and segmentation masks estimated from the SAM 2 (Ravi et al., 2024) video segmentation model. We create a descriptive caption for each object in the format of “{object description} falls.” This caption is used to provide context to the task when text input is supported." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 651, + 106, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 651, + 106, + 662 + ], + "spans": [ + { + "bbox": [ + 52, + 651, + 106, + 662 + ], + "type": "text", + "content": "3.3. Metrics" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 670, + 291, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 670, + 291, + 718 + ], + "spans": [ + { + "bbox": [ + 52, + 670, + 291, + 718 + ], + "type": "text", + "content": "We propose three metrics to assess the accuracy of trajectories, shape fidelity, and object permanence. Each of our metrics compare frames from the ground-truth video with the generated video. Further details about the metrics, including" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 305, + 64, + 543, + 248 + ], + "blocks": [ + { + "bbox": [ + 305, + 64, + 543, + 248 + ], + "lines": [ + { + "bbox": [ + 305, + 64, + 543, + 248 + ], + "spans": [ + { + "bbox": [ + 305, + 64, + 543, + 248 + ], + "type": "image", + "image_path": "fdf0c1240713a0f765f0563462d434ced74c2fc826cdce4f827d1a1a50939cc7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 259, + 543, + 304 + ], + "lines": [ + { + "bbox": [ + 304, + 259, + 543, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 543, + 304 + ], + "type": "text", + "content": "Figure 5. Example of annotations in real-world data. For segmentation masks, we manually annotate first frame and utilize SAM 2 to produce segmentation masks across frames. For captions, we annotate “{object description} falls.” for all video segments." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 327, + 542, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 542, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 542, + 351 + ], + "type": "text", + "content": "their formulas and our resampling procedure for accounting for differences in fps, is described in Appendix B." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 357, + 543, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 543, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 543, + 405 + ], + "type": "text", + "content": "Trajectory L2. For each frame in both the generated video and ground truth, we calculate the centroid of the masked region. After doing this, we compute the average " + }, + { + "bbox": [ + 304, + 357, + 543, + 405 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 357, + 543, + 405 + ], + "type": "text", + "content": " distance between the centroids of corresponding frames." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 411, + 543, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 543, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 543, + 447 + ], + "type": "text", + "content": "Chamfer Distance (CD). To assess the shape fidelity of objects, we calculate the Chamfer Distance (CD) between the mask regions of the generated video and ground truth." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 453, + 543, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 543, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 543, + 501 + ], + "type": "text", + "content": "Intersection over Union (IoU). We use the Intersection over Union (IoU) metric to evaluate object permanence. The IoU measures objects' degree of overlap between the generated video and ground truth." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 514, + 405, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 405, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 405, + 525 + ], + "type": "text", + "content": "3.4. Evaluation Results" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 303, + 532, + 543, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 532, + 543, + 640 + ], + "spans": [ + { + "bbox": [ + 303, + 532, + 543, + 640 + ], + "type": "text", + "content": "We evaluate 4 open models including CogVideoX-5B-I2V(Yang et al., 2024c), DynamiCrafter(Xing et al., 2023), Pyramid-Flow(Jin et al., 2024), and Open-Sora-V1.2(Zheng et al., 2024), as well as 4 proprietary models including Sora (OpenAI, 2024), Kling-V1(Kuaishou, 2024), Kling-V1.5(Kuaishou, 2024), and Runway Gen3 (Runway, 2024). We also evaluate OpenSora post-trained through the processes of Supervised Fine-Tuning (PSFT) and Object Reward Optimization (ORO); see Section 4 for details." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 303, + 645, + 544, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 645, + 544, + 718 + ], + "spans": [ + { + "bbox": [ + 303, + 645, + 544, + 718 + ], + "type": "text", + "content": "The results of running the baseline models on the benchmark indicate a consistent failure to generate physically accurate dropping behavior, despite the visual realism of their generated frames. Qualitatively, we see common failure cases in Figure 6, such as implausible object deformations, floating, hallucination of new objects, and unrealistic special" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "spans": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "text", + "content": "4" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 68, + 542, + 241 + ], + "blocks": [ + { + "bbox": [ + 53, + 68, + 542, + 241 + ], + "lines": [ + { + "bbox": [ + 53, + 68, + 542, + 241 + ], + "spans": [ + { + "bbox": [ + 53, + 68, + 542, + 241 + ], + "type": "image", + "image_path": "342a3b4296640d6e8ed1d72350bfb1237311d4fb53b1dc49759aa08ed93e6617.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 51, + 244, + 544, + 289 + ], + "lines": [ + { + "bbox": [ + 51, + 244, + 544, + 289 + ], + "spans": [ + { + "bbox": [ + 51, + 244, + 544, + 289 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison of results on real test set (row 1-2), simulated seen test set (row 3-4) and simulated unseen test set (row 5-6). We present the results of popular open-source and commercially available models alongside those of models fine-tuned through our method. Existing models often struggle to generate videos depicting objects falling, whereas our PSFT method effectively introduces knowledge of free-fall into the model. ORO enables the model to more accurately learn object motion and shape." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 299, + 290, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 299, + 290, + 358 + ], + "spans": [ + { + "bbox": [ + 52, + 299, + 290, + 358 + ], + "type": "text", + "content": "effects. We further visualize a random subset of generated trajectories on the left of Figure 8. In many cases, the object remains completely static, and sometimes the object even moves upward. When downward motion is present, it is often slow or contains unrealistic horizontal movement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 373, + 179, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 373, + 179, + 388 + ], + "spans": [ + { + "bbox": [ + 52, + 373, + 179, + 388 + ], + "type": "text", + "content": "4. Physics Post-Training" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 395, + 291, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 395, + 291, + 515 + ], + "spans": [ + { + "bbox": [ + 52, + 395, + 291, + 515 + ], + "type": "text", + "content": "We present a post-training process to address the limitations of current models described in Section 3.4. We utilize simulated videos that demonstrate realistic dropping behavior. Our approach for post-training is inspired by the two-stage pipeline consisting of supervised fine-tuning followed by reward modeling commonly used in LLMs. We find that our pipeline improves performance on both real and simulated evaluations, with greater gains observed in simulation. This is due to the sim-to-real gap, though our approach still shows substantial gains in transferring to real-world data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 527, + 190, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 527, + 190, + 540 + ], + "spans": [ + { + "bbox": [ + 52, + 527, + 190, + 540 + ], + "type": "text", + "content": "4.1. Simulated Adaptation Data" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 546, + 291, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 546, + 291, + 713 + ], + "spans": [ + { + "bbox": [ + 52, + 546, + 291, + 713 + ], + "type": "text", + "content": "The first stage of our approach involves supervised fine-tuning. We use Kubric (Greff et al., 2022), a simulation and rendering engine designed for scalable video generation, to create simulated videos of objects dropping and colliding with other objects on the ground. Each video consists of 1-6 dropping objects onto a (possibly empty) pile of up to 4 objects underneath them. The videos are 2 seconds long, consisting of 32 frames at 16 fps. The objects are sourced from the Google Scanned Objects (GSO) dataset (Downs et al., 2022), which provides true-to-scale 3D models created from real-world scans across diverse categories (examples shown in Figure 4). The camera remains stationary in each video and is oriented parallel to the ground plane. To introduce variability, we randomly sample the camera height" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 299, + 542, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 542, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 542, + 347 + ], + "type": "text", + "content": "between 0.4 and 0.6 meters and position objects between 1 and 3 meters away from the camera, which corresponds to the distributions observed in the real-world dataset. More information about the dataset can be found in Appendix K." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 360, + 497, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 497, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 497, + 372 + ], + "type": "text", + "content": "4.2. Physics Supervised Fine-Tuning (PSFT)." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 306, + 384, + 419, + 465 + ], + "blocks": [ + { + "bbox": [ + 306, + 384, + 419, + 465 + ], + "lines": [ + { + "bbox": [ + 306, + 384, + 419, + 465 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 419, + 465 + ], + "type": "image", + "image_path": "9cb6168eacd785e4f741b3dbc66836cc1b13221d84cacac490669a7f161086a6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 429, + 384, + 541, + 464 + ], + "blocks": [ + { + "bbox": [ + 429, + 384, + 541, + 464 + ], + "lines": [ + { + "bbox": [ + 429, + 384, + 541, + 464 + ], + "spans": [ + { + "bbox": [ + 429, + 384, + 541, + 464 + ], + "type": "image", + "image_path": "6adf02f646ee4da228177a9bb3d6b9810b033aeaac6c9f68056cd271eb9c47c2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 306, + 466, + 418, + 545 + ], + "blocks": [ + { + "bbox": [ + 306, + 466, + 418, + 545 + ], + "lines": [ + { + "bbox": [ + 306, + 466, + 418, + 545 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 418, + 545 + ], + "type": "image", + "image_path": "91f342955c4abb85297c05b6fbf080e1ae798b04587e39e4104a2985d585e4d7.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 303, + 554, + 542, + 620 + ], + "lines": [ + { + "bbox": [ + 303, + 554, + 542, + 620 + ], + "spans": [ + { + "bbox": [ + 303, + 554, + 542, + 620 + ], + "type": "text", + "content": "Figure 7. Plots (a), (b), and (c) demonstrate that our metrics tend to improve with further training and that leveraging a pre-trained video diffusion model enhances performance compared to random initialization. In plot (d), the size of the training dataset varies in each training run (each consisting of 5k steps). With only 5k samples, we can achieve optimal results." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 429, + 465, + 541, + 545 + ], + "blocks": [ + { + "bbox": [ + 429, + 465, + 541, + 545 + ], + "lines": [ + { + "bbox": [ + 429, + 465, + 541, + 545 + ], + "spans": [ + { + "bbox": [ + 429, + 465, + 541, + 545 + ], + "type": "image", + "image_path": "a7f340f4c1bc1798d01d2bcfa3aac741d7c979c6b80afc4910bba5d647c78286.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 303, + 633, + 542, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 633, + 542, + 717 + ], + "spans": [ + { + "bbox": [ + 303, + 633, + 542, + 717 + ], + "type": "text", + "content": "We use the pretrained Open-Sora v1.2 (Zheng et al., 2024) model as our base model and fine-tune it on our simulated video dataset. We employ Open-Sora v1.2's rectified flow training objective without modification (Liu et al., 2022). Each fine-tuning experiment is conducted with a batch size of 128 and a learning rate of " + }, + { + "bbox": [ + 303, + 633, + 542, + 717 + ], + "type": "inline_equation", + "content": "1\\mathrm{e} - 4" + }, + { + "bbox": [ + 303, + 633, + 542, + 717 + ], + "type": "text", + "content": " on two 80GB NVIDIA A100 GPUs. As shown in Figure 6, fine-tuning with this" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "spans": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "text", + "content": "5" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 57, + 542, + 275 + ], + "blocks": [ + { + "bbox": [ + 53, + 57, + 542, + 275 + ], + "lines": [ + { + "bbox": [ + 53, + 57, + 542, + 275 + ], + "spans": [ + { + "bbox": [ + 53, + 57, + 542, + 275 + ], + "type": "table", + "html": "
MethodRealSim (Seen)Sim (Unseen)
L2 (↓)CD (↓)IoU (↑)L2 (↓)CD (↓)IoU (↑)L2 (↓)CD (↓)IoU (↑)
ProprietarySora (OpenAI, 2024)0.1740.4880.0650.1490.4460.0400.1400.4190.031
Kling-V1 (Kuaishou, 2024)0.1570.4250.0560.1420.4150.0320.1450.4370.028
Kling-V1.5 (Kuaishou, 2024)0.1550.4240.0580.1370.3960.0330.1320.4050.029
Runway Gen3 (Runway, 2024)0.1870.5260.0420.1700.5090.0400.1490.4600.038
OpenCogVideoX-5B-I2V (Yang et al., 2024c)0.1380.3660.0800.1120.3150.0200.1010.2900.020
DynamiCrafter (Xing et al., 2023)0.1870.5040.0210.1570.4850.0390.1360.4300.033
Pyramid-Flow (Jin et al., 2024)0.1750.4850.0620.1260.3520.0590.1300.3810.048
Open-Sora (Zheng et al., 2024)0.1750.5020.0690.1390.4090.0360.1300.3680.034
OursOpen-Sora + PSFT (base)0.0760.1880.1390.0360.0880.1650.0280.0580.129
base + ORO (Seg)0.0750.1830.1420.0330.0760.1700.0320.0630.145
base + ORO (Flow)0.0670.1640.1360.0260.0620.1220.0220.0450.071
base + ORO (Depth)0.0670.1590.1290.0310.0720.1240.0220.0460.096
", + "image_path": "19982fa17713845a5d804164e55f0ffa9571cbf7063e297859e10dcd17cb35ca.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 51, + 282, + 544, + 339 + ], + "lines": [ + { + "bbox": [ + 51, + 282, + 544, + 339 + ], + "spans": [ + { + "bbox": [ + 51, + 282, + 544, + 339 + ], + "type": "text", + "content": "Table 1. PisaBench Evaluation Results. This table compares the performance of four proprietary models, four open models, and the models fine-tuned with PSFT and " + }, + { + "bbox": [ + 51, + 282, + 544, + 339 + ], + "type": "inline_equation", + "content": "\\mathrm{PSFT + ORO}" + }, + { + "bbox": [ + 51, + 282, + 544, + 339 + ], + "type": "text", + "content": " on our real-world and simulated test set which is decomposed into seen and unseen object splits. Across all metrics, our PSFT models outperform all other baselines, including proprietary models like Sora. Reward modeling further enhances results, with segmentation rewards improving the shape-based IoU metric and optical rewards and depth rewards enhancing the motion-based L2 and CD metrics. This suggests that rewards can be flexibly adjusted to target specific aspects of performance." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 51, + 357, + 291, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 357, + 291, + 561 + ], + "spans": [ + { + "bbox": [ + 51, + 357, + 291, + 561 + ], + "type": "text", + "content": "data alone is sufficient to induce realistic dropping behavior in the model. Quantitatively, our PSFT model substantially improves on both our simulated and real-world benchmark, as shown in Table 1. Dataset size. We conduct an ablation study on the number of training samples to understand the amount of data required for optimal performance on our benchmark. We create random subsets from 500 to 20,000 samples and train our model for 5,000 gradient steps on each subset. Notably, as shown in Figure 7, only 5,000 samples are needed to achieve optimal results. Effect of pretraining. Additionally, we investigate the impact of Open-Sora's pre-training on adaptation. We randomly initialize the Open-Sora's denoising network while keeping the pre-trained initialization of the compressor network and train the model on a dataset of 5k training samples. As shown in Figure 8, the learned knowledge from Open-Sora's pretraining plays a critical role in our task." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 51, + 567, + 290, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 567, + 290, + 627 + ], + "spans": [ + { + "bbox": [ + 51, + 567, + 290, + 627 + ], + "type": "text", + "content": "Overall, using PSFT on only 5k samples is sufficient to push Open-Sora's performance past all other evaluated models, including state-of-the-art commercial video generators, by a wide margin. This is made possible by leveraging the knowledge from the sufficiently pre-trained base model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 639, + 230, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 639, + 230, + 651 + ], + "spans": [ + { + "bbox": [ + 52, + 639, + 230, + 651 + ], + "type": "text", + "content": "4.3. Object Reward Optimization (ORO)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 658, + 291, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 658, + 291, + 706 + ], + "spans": [ + { + "bbox": [ + 52, + 658, + 291, + 706 + ], + "type": "text", + "content": "In the second stage, we propose Object Reward Optimization (ORO) to use reward gradients to guide the video generation model toward generating videos where the object's motion and shape more closely align with the ground truth." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 358, + 541, + 461 + ], + "blocks": [ + { + "bbox": [ + 310, + 358, + 541, + 461 + ], + "lines": [ + { + "bbox": [ + 310, + 358, + 541, + 461 + ], + "spans": [ + { + "bbox": [ + 310, + 358, + 541, + 461 + ], + "type": "image", + "image_path": "2b0b1b1edbe72353a808756a9abec58b083266dae8f49a22cf820119f4e51b9d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 303, + 473, + 542, + 540 + ], + "lines": [ + { + "bbox": [ + 303, + 473, + 542, + 540 + ], + "spans": [ + { + "bbox": [ + 303, + 473, + 542, + 540 + ], + "type": "text", + "content": "Figure 8. On the left, we plot random trajectories from the baseline models in Table 1. On the right, we show random trajectories from our fine-tuned model. The baseline trajectories exhibit unrealistic behavior, and most of them stay completely static. On the right, we see the trajectories consistently falling downward with collision and rolling behavior being modeled after the point of contact." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 303, + 548, + 544, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 548, + 544, + 633 + ], + "spans": [ + { + "bbox": [ + 303, + 548, + 544, + 633 + ], + "type": "text", + "content": "We follow the VADER framework from (Prabhudesai et al., 2024) and introduce three reward models. The differences between our approach and VADER include: (1) our reward model utilizes both generated videos and ground truth instead of generated videos and conditioning. (2) gradients propagate through all denoising time steps in fine-tuning. Consequently, the VADER objective is modified as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 339, + 641, + 542, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 641, + 542, + 657 + ], + "spans": [ + { + "bbox": [ + 339, + 641, + 542, + 657 + ], + "type": "interline_equation", + "content": "J (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) \\right] \\tag {1}", + "image_path": "b87ce2810e76a242273a09ac0b48625aaea5cdd89ebf4f8ad8f5727f690a705a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "spans": [ + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "text", + "content": " is the ground truth dataset, " + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "inline_equation", + "content": "p_{\\theta}(.)" + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "text", + "content": " is a given video diffusion model, " + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "inline_equation", + "content": "x_0^{\\prime}, x_0 \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "text", + "content": " are generated video and ground truth, and " + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "inline_equation", + "content": "c \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 303, + 663, + 542, + 700 + ], + "type": "text", + "content": " is the initial image." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 705, + 542, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 705, + 542, + 717 + ], + "spans": [ + { + "bbox": [ + 304, + 705, + 542, + 717 + ], + "type": "text", + "content": "Segmentation Reward. We utilize SAM 2 (Ravi et al.," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "spans": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "text", + "content": "6" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 52, + 67, + 290, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 67, + 290, + 117 + ], + "spans": [ + { + "bbox": [ + 52, + 67, + 290, + 117 + ], + "type": "text", + "content": "2024) to generate segmentation masks across frames for generated videos. We define segmentation reward as the IoU between the dropping object's mask in generated video and the mask from the ground truth simulated segmentation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "spans": [ + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "type": "text", + "content": "Optical Flow Reward. We utilize RAFT (Teed & Deng, 2020) to generate generated video's optical flow " + }, + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "type": "text", + "content": " and ground truth's optical flow " + }, + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{gt}}" + }, + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "type": "text", + "content": ". We define the optical flow reward as " + }, + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "type": "inline_equation", + "content": "R(x_0', x_0) = -|V^{\\mathrm{gen}} - V^{\\mathrm{gt}}|" + }, + { + "bbox": [ + 52, + 121, + 291, + 170 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "spans": [ + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "type": "text", + "content": "Depth Reward. We utilize Depth-Anything-V2 (Yang et al., 2024a) to generate generated video's depth map " + }, + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "type": "text", + "content": " and ground truth's depth map " + }, + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{gt}}" + }, + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "type": "text", + "content": ". We define the optical flow reward as " + }, + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "type": "inline_equation", + "content": "R(x_0', x_0) = -|D^{\\mathrm{gen}} - D^{\\mathrm{gt}}|" + }, + { + "bbox": [ + 52, + 175, + 291, + 223 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 228, + 279, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 228, + 279, + 241 + ], + "spans": [ + { + "bbox": [ + 52, + 228, + 279, + 241 + ], + "type": "text", + "content": "Details on implementation can be found in Appendix C." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 247, + 291, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 247, + 291, + 331 + ], + "spans": [ + { + "bbox": [ + 52, + 247, + 291, + 331 + ], + "type": "text", + "content": "We begin from the checkpoint of the first stage, which is trained on 5,000 samples trained over 5,000 gradient steps. We then fine-tune the model with ORO on the simulated dataset, using a batch size of 1 and two 80GB NVIDIA A100 GPUs for each fine-tuning experiment. We set a learning rate of " + }, + { + "bbox": [ + 52, + 247, + 291, + 331 + ], + "type": "inline_equation", + "content": "1\\mathrm{e} - 6" + }, + { + "bbox": [ + 52, + 247, + 291, + 331 + ], + "type": "text", + "content": " for segmentation reward and depth reward and " + }, + { + "bbox": [ + 52, + 247, + 291, + 331 + ], + "type": "inline_equation", + "content": "1\\mathrm{e} - 5" + }, + { + "bbox": [ + 52, + 247, + 291, + 331 + ], + "type": "text", + "content": " for optical flow." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 336, + 291, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 336, + 291, + 420 + ], + "spans": [ + { + "bbox": [ + 51, + 336, + 291, + 420 + ], + "type": "text", + "content": "As shown in Table 1, incorporating ORO in reward modeling further improves performance. Additionally, each reward function enhances the aspect of physicality that aligns with its intended purpose—segmentation rewards improve shape accuracy, while flow rewards and depth rewards improve motion accuracy. This demonstrates the process is both modular and interpretable." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 435, + 257, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 435, + 257, + 449 + ], + "spans": [ + { + "bbox": [ + 52, + 435, + 257, + 449 + ], + "type": "text", + "content": "5. Assessing Learned Physical Behavior" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 456, + 291, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 456, + 291, + 552 + ], + "spans": [ + { + "bbox": [ + 52, + 456, + 291, + 552 + ], + "type": "text", + "content": "Having introduced our post-training approaches in Section 4, we probe into the model's understanding of the interaction between gravity and perspective—the two laws that determine the dynamics of our videos. We first test if the learned physical behavior of our model can generalize to dropping heights and depths beyond its training distribution. Then, we study the ability of the model to learn the probability distribution induced by the uncertainty of perspective." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 565, + 267, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 565, + 267, + 578 + ], + "spans": [ + { + "bbox": [ + 52, + 565, + 267, + 578 + ], + "type": "text", + "content": "5.1. Generalization to Unseen Depths and Heights" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 52, + 583, + 291, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 583, + 291, + 656 + ], + "spans": [ + { + "bbox": [ + 52, + 583, + 291, + 656 + ], + "type": "text", + "content": "Depth and height are the main factors that affect the dynamics of a falling object in our videos. We can see this by combining the laws of gravity with perspective under our camera assumptions to model the object's image " + }, + { + "bbox": [ + 52, + 583, + 291, + 656 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 52, + 583, + 291, + 656 + ], + "type": "text", + "content": " coordinate as a function of time (further details on our coordinate system are described in Appendix G):" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 117, + 664, + 291, + 691 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 664, + 291, + 691 + ], + "spans": [ + { + "bbox": [ + 117, + 664, + 291, + 691 + ], + "type": "interline_equation", + "content": "y (t) = \\frac {f}{Z} \\left(Y _ {0} - \\frac {1}{2} g t ^ {2}\\right). \\tag {2}", + "image_path": "2af4f4a51a21c94069dd0ccc494f71591672a4c22044b52818a3462e358900fd.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 52, + 705, + 291, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 705, + 291, + 717 + ], + "spans": [ + { + "bbox": [ + 52, + 705, + 291, + 717 + ], + "type": "text", + "content": "From Equation (2), we see that the random variables that af" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "spans": [ + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "text", + "content": "fect object motion are " + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "text", + "content": " (depth) and " + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "text", + "content": " (height) (the camera focal length " + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "text", + "content": " is fixed). Thus, we are interested in testing generalization on unseen values of " + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 67, + 541, + 103 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 303, + 109, + 542, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 109, + 542, + 217 + ], + "spans": [ + { + "bbox": [ + 303, + 109, + 542, + 217 + ], + "type": "text", + "content": "We create a simulated test set in which a single object is dropped from varying depths and heights, using objects and backgrounds unseen during training. We uniformly sample depth and height values (in meters) from the Cartesian product of the ranges [1, 5] and [0.5, 2.5], respectively. The camera height is fixed at " + }, + { + "bbox": [ + 303, + 109, + 542, + 217 + ], + "type": "inline_equation", + "content": "0.5m" + }, + { + "bbox": [ + 303, + 109, + 542, + 217 + ], + "type": "text", + "content": ", and depth-height pairs outside the camera viewing frustum are discarded. A sample is in-distribution (ID) if its dropping depth and height both fall in the range [1, 3] and [0.5, 1.5]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 303, + 223, + 542, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 223, + 542, + 271 + ], + "spans": [ + { + "bbox": [ + 303, + 223, + 542, + 271 + ], + "type": "text", + "content": "Since we have access to the ground truth dropping time in simulation, we also employ a dropping time error, a metric we describe in Appendix B. Our analysis in Table 2 shows that performance degrades for out-of-distribution scenarios." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 303, + 277, + 542, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 277, + 542, + 325 + ], + "spans": [ + { + "bbox": [ + 303, + 277, + 542, + 325 + ], + "type": "text", + "content": "Since depth and height are the main physical quantities that affect falling dynamics, this finding indicates that our model may struggle to learn a fully generalizable law that accounts for the interaction of perspective and gravity." + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 305, + 335, + 542, + 381 + ], + "blocks": [ + { + "bbox": [ + 305, + 335, + 542, + 381 + ], + "lines": [ + { + "bbox": [ + 305, + 335, + 542, + 381 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 542, + 381 + ], + "type": "table", + "html": "
SettingL2 (↓)Chamfer (↓)IOU (↑)Time Error (↓)
ID0.0360.0880.1550.091
OOD0.0440.1430.0490.187
", + "image_path": "88670abb85fb73081ca571f4fc556131bc94f22fa766b8d2ff19594c1ac79e8b.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 388, + 542, + 434 + ], + "lines": [ + { + "bbox": [ + 304, + 388, + 542, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 542, + 434 + ], + "type": "text", + "content": "Table 2. Results of our metrics on in-distribution (ID) and out-of-distribution (OOD) depth-height combinations. The values used for depth range from " + }, + { + "bbox": [ + 304, + 388, + 542, + 434 + ], + "type": "inline_equation", + "content": "1 - 5\\mathrm{m}" + }, + { + "bbox": [ + 304, + 388, + 542, + 434 + ], + "type": "text", + "content": " (ID range [1,3]) and height values range from 0.5-2.5 (ID range [0.5, 1.5])." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 453, + 424, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 424, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 424, + 464 + ], + "type": "text", + "content": "5.2. Distributional Analysis" + } + ] + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 305, + 478, + 399, + 565 + ], + "blocks": [ + { + "bbox": [ + 305, + 478, + 399, + 565 + ], + "lines": [ + { + "bbox": [ + 305, + 478, + 399, + 565 + ], + "spans": [ + { + "bbox": [ + 305, + 478, + 399, + 565 + ], + "type": "image", + "image_path": "173d344ac811372831211d71e1f089dcd0ee90fa7170fbcfc6b6036661f678d4.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 303, + 577, + 542, + 622 + ], + "lines": [ + { + "bbox": [ + 303, + 577, + 542, + 622 + ], + "spans": [ + { + "bbox": [ + 303, + 577, + 542, + 622 + ], + "type": "text", + "content": "Figure 9. Demonstration of ambiguity in 2D perspective projections. Each of the three clouds appears the exact same in the camera's image. The right side shows how we perform a scale and translation augmentation to generate deliberately ambiguous data." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 403, + 477, + 541, + 565 + ], + "blocks": [ + { + "bbox": [ + 403, + 477, + 541, + 565 + ], + "lines": [ + { + "bbox": [ + 403, + 477, + 541, + 565 + ], + "spans": [ + { + "bbox": [ + 403, + 477, + 541, + 565 + ], + "type": "image", + "image_path": "dcf5758aab2710279523e38fe46165467a3e180eeef0ed0b3050233202412b9e.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 303, + 633, + 542, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 633, + 542, + 717 + ], + "spans": [ + { + "bbox": [ + 303, + 633, + 542, + 717 + ], + "type": "text", + "content": "The evolution of a physical system is not uniquely determined by a single initial image, since the lossy uncertainty of perspective induces a distribution of possible outcomes as shown in Figure 9. An ideal video world model should (1) output videos that are faithful to the evolution of some plausible world state and (2) provide accurate coverage across the entire distribution of the world that is possible from" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "spans": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "text", + "content": "7" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "spans": [ + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "type": "text", + "content": "its conditioning signal. In this section, we examine these two facets by studying " + }, + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "type": "inline_equation", + "content": "p(t|y)" + }, + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "type": "text", + "content": ": the distribution of dropping times possible from an object at coordinate " + }, + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "type": "text", + "content": " in the image plane. To do this, we create a simulated dataset that has a much wider distribution " + }, + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "type": "inline_equation", + "content": "p(t|y)" + }, + { + "bbox": [ + 52, + 68, + 291, + 139 + ], + "type": "text", + "content": " than our PSFT dataset. See Appendix F for more details on its construction." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 148, + 290, + 228 + ], + "blocks": [ + { + "bbox": [ + 53, + 148, + 290, + 228 + ], + "lines": [ + { + "bbox": [ + 53, + 148, + 290, + 228 + ], + "spans": [ + { + "bbox": [ + 53, + 148, + 290, + 228 + ], + "type": "image", + "image_path": "73a89a0c5b340af83339e7bdee6111a2850a250f52d7a51435656c3c43642fe2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 52, + 239, + 291, + 295 + ], + "lines": [ + { + "bbox": [ + 52, + 239, + 291, + 295 + ], + "spans": [ + { + "bbox": [ + 52, + 239, + 291, + 295 + ], + "type": "text", + "content": "Figure 10. Examples of model trajectories lifted to 3D. The blue line represents the height of the camera ray passing through the bottom of the dropping object as a function of depth. The set of possible dropping trajectories at a given depth are depicted in gray. The lifted trajectory of the model is depicted in green." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 53, + 308, + 289, + 420 + ], + "blocks": [ + { + "bbox": [ + 53, + 308, + 289, + 420 + ], + "lines": [ + { + "bbox": [ + 53, + 308, + 289, + 420 + ], + "spans": [ + { + "bbox": [ + 53, + 308, + 289, + 420 + ], + "type": "image", + "image_path": "8862d09f5523d53e73a41fca13423e9ac96d265eb77cc7788176d5f31c7abc8a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 52, + 434, + 291, + 479 + ], + "lines": [ + { + "bbox": [ + 52, + 434, + 291, + 479 + ], + "spans": [ + { + "bbox": [ + 52, + 434, + 291, + 479 + ], + "type": "text", + "content": "Figure 11. Visualizing " + }, + { + "bbox": [ + 52, + 434, + 291, + 479 + ], + "type": "inline_equation", + "content": "p(t|y)" + }, + { + "bbox": [ + 52, + 434, + 291, + 479 + ], + "type": "text", + "content": " misalignment for different images. Green shows the ground-truth CDF, orange is the 32-frame quantized version, and blue is the empirical CDF of 128 different samples of dropping times from the model." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 484, + 235, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 484, + 235, + 496 + ], + "spans": [ + { + "bbox": [ + 52, + 484, + 235, + 496 + ], + "type": "text", + "content": "Testing (1): 3D faithfulness of trajectories." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 502, + 291, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 502, + 291, + 670 + ], + "spans": [ + { + "bbox": [ + 52, + 502, + 291, + 670 + ], + "type": "text", + "content": "After training our model on this new dataset, we test whether its trajectories are consistent with a valid 3D world state. We first obtain an estimated dropping time from generated videos using the procedure described in Section 5.1. Using knowledge of the camera position, focal length, sensor width, and " + }, + { + "bbox": [ + 52, + 502, + 291, + 670 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 52, + 502, + 291, + 670 + ], + "type": "text", + "content": ", we can obtain an implied depth and height of the trajectory. We can then back-project the video trajectory to 3D and analyze whether they constitute physically accurate trajectories. We give further details about this process in Appendix G. As show in Figure 10, we find that our model's lifted trajectories consistently align with the 3D trajectory at the height and depth implied by its dropping time, giving evidence that the model's visual outputs are faithful to some plausible real-world state." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 675, + 212, + 688 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 675, + 212, + 688 + ], + "spans": [ + { + "bbox": [ + 52, + 675, + 212, + 688 + ], + "type": "text", + "content": "Testing (2): distributional alignment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 693, + 290, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 693, + 290, + 718 + ], + "spans": [ + { + "bbox": [ + 52, + 693, + 290, + 718 + ], + "type": "text", + "content": "Going beyond the level of individual trajectories, we study the model's learned conditional distribution " + }, + { + "bbox": [ + 52, + 693, + 290, + 718 + ], + "type": "inline_equation", + "content": "p(t|y)" + }, + { + "bbox": [ + 52, + 693, + 290, + 718 + ], + "type": "text", + "content": ". We" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 67, + 542, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 67, + 542, + 139 + ], + "spans": [ + { + "bbox": [ + 304, + 67, + 542, + 139 + ], + "type": "text", + "content": "create 50 different initial images with differing values of " + }, + { + "bbox": [ + 304, + 67, + 542, + 139 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 67, + 542, + 139 + ], + "type": "text", + "content": ", generate 128 different videos from each, and estimate the dropping time in each video. Using the laws of gravity, the laws of perspective, and the assumption of uniform depth sampling in our dataset, we can analytically derive the probability " + }, + { + "bbox": [ + 304, + 67, + 542, + 139 + ], + "type": "inline_equation", + "content": "p(t|y)" + }, + { + "bbox": [ + 304, + 67, + 542, + 139 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 330, + 156, + 542, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 156, + 542, + 188 + ], + "spans": [ + { + "bbox": [ + 330, + 156, + 542, + 188 + ], + "type": "interline_equation", + "content": "p (t | y) = \\left\\{ \\begin{array}{l l} \\frac {g t}{\\left(Z _ {\\max } - Z _ {\\min }\\right) \\beta}, & t _ {\\min } \\leq t \\leq t _ {\\max } \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}", + "image_path": "ec04a35a42939e0e06b8bc1b07070b0c0c90ff460116ede97d74c46464f397b5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "type": "text", + "content": " is a constant that depends on " + }, + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 203, + 542, + 228 + ], + "type": "text", + "content": " and the camera height. The derivation is given in Appendix E." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 233, + 542, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 542, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 542, + 424 + ], + "type": "text", + "content": "We then measure goodness-of-fit for each of the 50 experiments using the Kolmogorov-Smirnov (KS) test (Massey Jr, 1951). The null hypothesis of the KS test is that the two distributions being compared are equal, and we consider p-values less than 0.05 as evidence of misalignment. Since our measured times have limited precision and can only take 32 distinct values—due to estimating the contact frame—we approximate the ground truth " + }, + { + "bbox": [ + 304, + 233, + 542, + 424 + ], + "type": "inline_equation", + "content": "p(t|y)" + }, + { + "bbox": [ + 304, + 233, + 542, + 424 + ], + "type": "text", + "content": " using a Monte Carlo method. We sample 1000 values from the ground truth distribution and then quantized them into 32 bins corresponding to their frame, which we use as ground truth observations in the KS test. We find that in all 50/50 cases, the p-value from the test is less than 0.05, which provides evidence that the model does not learn the correct distribution of dropping times. We visualize the misalignment between the empirical CDF of the model's in Figure 11." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 430, + 542, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 542, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 542, + 478 + ], + "type": "text", + "content": "In summary, while our model's trajectories show promising tendencies to ground themselves to plausible 3D world states, the range of possible outputs from the model does not align with the ground truth distribution." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 494, + 376, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 376, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 376, + 506 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 303, + 514, + 542, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 514, + 542, + 717 + ], + "spans": [ + { + "bbox": [ + 303, + 514, + 542, + 717 + ], + "type": "text", + "content": "This work studies post-training as an avenue for adapting adapting pre-trained video generator into world models. We introduce a post-training strategy that is highly effective in aligning our model. Our work raises interesting insights into the learned distributions of generative models. Qualitatively, large scale image or video generative models appear to excel at generating likely samples from the data distribution, but this alone does not imply that they match the data distribution well in its entirety. As long as a model is able to generate likely samples, global distributional misalignment is not necessarily a problem for content creation. However, this problem becomes critical for world models, where alignment across the entire distribution is necessary for faithful world simulation. The insights revealed by our study, made possible by our constrained and tractable setting, indicate that although post-training improves per-sample accuracy, general distributional alignment remains unsolved." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "spans": [ + { + "bbox": [ + 294, + 731, + 301, + 740 + ], + "type": "text", + "content": "8" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 53, + 66, + 145, + 79 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 66, + 145, + 79 + ], + "spans": [ + { + "bbox": [ + 53, + 66, + 145, + 79 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 87, + 291, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 87, + 291, + 194 + ], + "spans": [ + { + "bbox": [ + 52, + 87, + 291, + 194 + ], + "type": "text", + "content": "We thank Boyang Zheng, Srivats Poddar, Ellis Brown, Shengbang Tong, Shusheng Yang, Jihan Yang, Daohan Lu, Anjali Gupta and Ziteng Wang for their help with data collection. We thank Jiraphon Yenphraphai for valuable assistance in setting up our simulation code. We thank Runway and Kling AI for providing API credit. 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Mind games: Game engines as an architecture for" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 306, + 67, + 542, + 582 + ], + "type": "list", + "angle": 0, + "index": 25, + "blocks": [ + { + "bbox": [ + 315, + 67, + 542, + 91 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 67, + 542, + 91 + ], + "spans": [ + { + "bbox": [ + 315, + 67, + 542, + 91 + ], + "type": "text", + "content": "intuitive physics. Trends in cognitive sciences, 21(9): 649-665, 2017." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 99, + 542, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 99, + 542, + 147 + ], + "spans": [ + { + "bbox": [ + 306, + 99, + 542, + 147 + ], + "type": "text", + "content": "Unterthiner, T., Van Steenkiste, S., Kurach, K., Marinier, R., Michalski, M., and Gelly, S. Towards accurate generative models of video: A new metric & challenges. arXiv preprint arXiv:1812.01717, 2018." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 155, + 542, + 203 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 155, + 542, + 203 + ], + "spans": [ + { + "bbox": [ + 306, + 155, + 542, + 203 + ], + "type": "text", + "content": "Wu, J., Yildirim, I., Lim, J. J., Freeman, B., and Tenenbaum, J. Galileo: Perceiving physical object properties by integrating a physics engine with deep learning. Advances in neural information processing systems, 28, 2015." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 210, + 542, + 258 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 210, + 542, + 258 + ], + "spans": [ + { + "bbox": [ + 306, + 210, + 542, + 258 + ], + "type": "text", + "content": "Xing, J., Xia, M., Zhang, Y., Chen, H., Yu, W., Liu, H., Wang, X., Wong, T.-T., and Shan, Y. Dynamiccafter: Animating open-domain images with video diffusion priors. arXiv preprint arXiv:2310.12190, 2023." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 266, + 542, + 315 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 266, + 542, + 315 + ], + "spans": [ + { + "bbox": [ + 306, + 266, + 542, + 315 + ], + "type": "text", + "content": "Xue, T., Wu, J., Bouman, K., and Freeman, B. Visual dynamics: Probabilistic future frame synthesis via cross convolutional networks. Advances in neural information processing systems, 29, 2016." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 322, + 542, + 357 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 322, + 542, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 322, + 542, + 357 + ], + "type": "text", + "content": "Yang, L., Kang, B., Huang, Z., Zhao, Z., Xu, X., Feng, J., and Zhao, H. Depth anything v2. arXiv:2406.09414, 2024a." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 365, + 542, + 403 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 542, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 542, + 403 + ], + "type": "text", + "content": "Yang, M., Du, Y., Ghasemipour, K., Tompson, J., Schuurmans, D., and Abbeel, P. Learning interactive real-world simulators. arXiv preprint arXiv:2310.06114, 2023." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 410, + 542, + 458 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 410, + 542, + 458 + ], + "spans": [ + { + "bbox": [ + 306, + 410, + 542, + 458 + ], + "type": "text", + "content": "Yang, S., Walker, J., Parker-Holder, J., Du, Y., Bruce, J., Barreto, A., Abbeel, P., and Schuurmans, D. Video as the new language for real-world decision making. arXiv preprint arXiv:2402.17139, 2024b." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 466, + 542, + 525 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 542, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 542, + 525 + ], + "type": "text", + "content": "Yang, Z., Teng, J., Zheng, W., Ding, M., Huang, S., Xu, J., Yang, Y., Hong, W., Zhang, X., Feng, G., et al. Cogvideox: Text-to-video diffusion models with an expert transformer. arXiv preprint arXiv:2408.06072, 2024c." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 533, + 542, + 582 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 542, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 542, + 582 + ], + "type": "text", + "content": "Zheng, Z., Peng, X., Yang, T., Shen, C., Li, S., Liu, H., Zhou, Y., Li, T., and You, Y. Open-sora: Democratizing efficient video production for all, March 2024. URL https://github.com/hpcaitech/Open-Sora." + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "spans": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "text", + "content": "10" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + }, + { + "para_blocks": [ + { + "bbox": [ + 52, + 66, + 258, + 79 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 66, + 258, + 79 + ], + "spans": [ + { + "bbox": [ + 52, + 66, + 258, + 79 + ], + "type": "text", + "content": "A. Discussion of Image-to-Video setting." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 87, + 541, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 87, + 541, + 159 + ], + "spans": [ + { + "bbox": [ + 52, + 87, + 541, + 159 + ], + "type": "text", + "content": "We note that our choice of single-image input, as opposed to multi-frame input, comes with some trade-offs. We choose the image-to-video setting because it is widely supported among many different models, allowing us to make effective comparisons across the current state-of-the-art. However, only conditioning on a single frame introduces significant ambiguity. Due to the loss of information caused by projecting the 3D world through perspective, it may not be possible to directly infer the size of the object or its height. In practice, we find our metrics are still reliable signals of task success, but we still study the problem of ambiguity more extensively in Section 5.2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 174, + 143, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 174, + 143, + 186 + ], + "spans": [ + { + "bbox": [ + 52, + 174, + 143, + 186 + ], + "type": "text", + "content": "B. Metric details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "spans": [ + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "text", + "content": "We propose three metrics to assess the accuracy of trajectories, shape fidelity, and object permanence. Each of our metrics compare frames from the ground-truth video with the generated video. Because different models can operate at different fps, we perform fps alignment as part of our evaluation process. To perform fps alignment, we map each frame index of the generated videos to the ground truth using " + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{gt}}" + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{gt}}" + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "text", + "content": " are the fps of generated video and ground truth respectively. For " + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "text", + "content": "-th frame in the generated video, we find the corresponding aligned frame index " + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 52, + 194, + 541, + 263 + ], + "type": "text", + "content": " in the ground truth video:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 255, + 263, + 542, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 255, + 263, + 542, + 289 + ], + "spans": [ + { + "bbox": [ + 255, + 263, + 542, + 289 + ], + "type": "interline_equation", + "content": "j = \\operatorname {r o u n d} \\left(i \\cdot \\frac {f _ {\\text {g e n}}}{f _ {\\mathrm {g t}}}\\right) \\tag {4}", + "image_path": "ebac98ec4b7c4b91f83432d9328234ee0cb2346246756bf3c6ef6bf977273ad0.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "spans": [ + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "type": "text", + "content": "Through fps alignment, we downsample the ground truth video to match the frame number of the generated video. We denote the downsampled ground truth as " + }, + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "type": "inline_equation", + "content": "\\{I_i^{\\mathrm{gt}}\\}_{i = 1}^N" + }, + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "type": "text", + "content": " and the generated video as " + }, + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "type": "inline_equation", + "content": "\\{I_i^{\\mathrm{gen}}\\}_{i = 1}^N" + }, + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 52, + 293, + 542, + 327 + ], + "type": "text", + "content": " is the number of frames in the generated video." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 328, + 542, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 328, + 542, + 353 + ], + "spans": [ + { + "bbox": [ + 52, + 328, + 542, + 353 + ], + "type": "text", + "content": "Trajectory L2. For each frame in both the generated video and ground truth, we calculate the centroid of the masked region. We then compute " + }, + { + "bbox": [ + 52, + 328, + 542, + 353 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 52, + 328, + 542, + 353 + ], + "type": "text", + "content": " distance between the centroids of corresponding frames:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 238, + 360, + 542, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 238, + 360, + 542, + 393 + ], + "spans": [ + { + "bbox": [ + 238, + 360, + 542, + 393 + ], + "type": "interline_equation", + "content": "L _ {2} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| C _ {i} ^ {\\text {g e n}} - C _ {i} ^ {\\mathrm {g t}} \\| _ {2} \\tag {5}", + "image_path": "74d2a95e99fc2fd73ad4d1df3a6192e0a7054af3d825efca106428f50d84a7b8.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 402, + 541, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 402, + 541, + 426 + ], + "spans": [ + { + "bbox": [ + 52, + 402, + 541, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 52, + 402, + 541, + 426 + ], + "type": "inline_equation", + "content": "C_i^{\\mathrm{gen}}, C_i^{\\mathrm{gt}} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 52, + 402, + 541, + 426 + ], + "type": "text", + "content": " are the centroids of the dropping object in the " + }, + { + "bbox": [ + 52, + 402, + 541, + 426 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 52, + 402, + 541, + 426 + ], + "type": "text", + "content": "-th frame of generated video and the ground truth respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 52, + 426, + 541, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 426, + 541, + 451 + ], + "spans": [ + { + "bbox": [ + 52, + 426, + 541, + 451 + ], + "type": "text", + "content": "Chamfer Distance (CD). To assess the shape fidelity of objects, we calculate the Chamfer Distance (CD) between the mask regions of the generated video and ground truth:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 156, + 459, + 436, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 156, + 459, + 436, + 493 + ], + "spans": [ + { + "bbox": [ + 156, + 459, + 436, + 493 + ], + "type": "interline_equation", + "content": "\\mathrm {C D} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\frac {1}{| P _ {i} |} \\sum_ {p \\in P _ {i}} \\min _ {q \\in Q _ {i}} \\| p - q \\| _ {2} + \\frac {1}{| Q _ {i} |} \\sum_ {q \\in Q _ {i}} \\min _ {p \\in P _ {i}} \\| q - p \\| _ {2}\\right)", + "image_path": "7e1e125b014d5443ce72b21ee8652e2160e81fcf0acf07a108129a1ed596ddf4.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "spans": [ + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "type": "inline_equation", + "content": "P_{i} = \\{p_{j}\\}_{j = 1}^{|P_{i}|}" + }, + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "type": "inline_equation", + "content": "Q_{i} = \\{q_{j}\\}_{j = 1}^{|Q_{i}|}" + }, + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "type": "text", + "content": " are the sets of mask points in the " + }, + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 52, + 502, + 541, + 528 + ], + "type": "text", + "content": "-th frame of the generated video and ground truth respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 52, + 528, + 541, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 528, + 541, + 552 + ], + "spans": [ + { + "bbox": [ + 52, + 528, + 541, + 552 + ], + "type": "text", + "content": "Intersection over Union (IoU). We use the Intersection over Union (IoU) metric to evaluate object permanence. IoU measures objects' degree of overlap between the generated video and ground truth. This is formulated as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 233, + 560, + 542, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 233, + 560, + 542, + 594 + ], + "spans": [ + { + "bbox": [ + 233, + 560, + 542, + 594 + ], + "type": "interline_equation", + "content": "\\mathrm {I o U} = \\frac {1}{| N |} \\sum_ {i = 1} ^ {N} \\frac {\\left| M _ {i} ^ {\\text {g e n}} \\cap M _ {i} ^ {\\mathrm {g t}} \\right|}{\\left| M _ {i} ^ {\\text {g e n}} \\cup M _ {i} ^ {\\mathrm {g t}} \\right|} \\tag {6}", + "image_path": "76e15cbc4824d4b47dfc7cac69adb8b782eaf0ac238e42bf738fa8fe88e04090.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "spans": [ + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "type": "inline_equation", + "content": "M_{i}^{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "type": "inline_equation", + "content": "M_{i}^{\\mathrm{gt}} \\in \\{0,1\\}^{H\\times W}" + }, + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "type": "text", + "content": " are binary segmentation masks of the falling object in the " + }, + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 52, + 601, + 541, + 628 + ], + "type": "text", + "content": "-th frame of the generated and ground truth videos respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "spans": [ + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": "Time error. When testing on videos generated in simulation, we can provide a timing error. From the dropping height " + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "inline_equation", + "content": "Y_{0}" + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": " of the ground truth video, which we have access to from the simulator, we can derive " + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{drop}} = \\sqrt{Y_0\\frac{2}{g}}" + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": ". We then obtain a dropping time from the model's output by estimating the frame of impact as the first frame " + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": " whose centroid velocity in the " + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": " direction is negative. If " + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{drop}}" + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": " occurs in between " + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "inline_equation", + "content": "F - 1" + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": ", then we define the time error " + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{time}}" + }, + { + "bbox": [ + 52, + 632, + 541, + 694 + ], + "type": "text", + "content": " as zero. Otherwise, we define the time error as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 200, + 694, + 542, + 721 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 200, + 694, + 542, + 721 + ], + "spans": [ + { + "bbox": [ + 200, + 694, + 542, + 721 + ], + "type": "interline_equation", + "content": "E _ {\\text {t i m e}} = \\min \\left(\\left| \\frac {F - 1}{\\mathrm {f p s}} - t _ {\\text {d r o p}} \\right|, \\left| \\frac {F}{\\mathrm {f p s}} - t _ {\\text {d r o p}} \\right|\\right). \\tag {7}", + "image_path": "dbfaf034811ce5459e629284804f36c7a1d8b92410b0042ff3289fca3e7293e2.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 292, + 731, + 302, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 292, + 731, + 302, + 740 + ], + "spans": [ + { + "bbox": [ + 292, + 731, + 302, + 740 + ], + "type": "text", + "content": "11" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + }, + { + "para_blocks": [ + { + "bbox": [ + 52, + 66, + 220, + 79 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 66, + 220, + 79 + ], + "spans": [ + { + "bbox": [ + 52, + 66, + 220, + 79 + ], + "type": "text", + "content": "C. ORO implementation details." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "spans": [ + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "type": "text", + "content": "In our setting, we do not cut the gradient after step " + }, + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "type": "text", + "content": " like VADER. The gradient " + }, + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "type": "inline_equation", + "content": "\\nabla_{\\theta}R(x_0',x_0)" + }, + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "type": "text", + "content": " backpropagates through all diffusion timesteps and update the model weights " + }, + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 52, + 87, + 542, + 111 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 213, + 118, + 542, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 213, + 118, + 542, + 152 + ], + "spans": [ + { + "bbox": [ + 213, + 118, + 542, + 152 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\theta} \\left(R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right)\\right) = \\sum_ {t = 0} ^ {T} \\frac {\\partial R \\left(x _ {0} ^ {\\prime} , x _ {0}\\right)}{\\partial x _ {t}} \\cdot \\frac {\\partial x _ {t}}{\\partial \\theta} \\tag {8}", + "image_path": "18f6ca9a4d35a17aace73c8956747dc9f04f552c0b87a2dd86040242c6bd19e8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 159, + 212, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 159, + 212, + 171 + ], + "spans": [ + { + "bbox": [ + 52, + 159, + 212, + 171 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 52, + 159, + 212, + 171 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 52, + 159, + 212, + 171 + ], + "type": "text", + "content": " is the total diffusion timesteps." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 176, + 542, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 176, + 542, + 199 + ], + "spans": [ + { + "bbox": [ + 52, + 176, + 542, + 199 + ], + "type": "text", + "content": "Segmentation Reward. We utilize SAM 2 (Ravi et al., 2024) to generate segmentation masks across frames for generated video:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 254, + 210, + 542, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 254, + 210, + 542, + 224 + ], + "spans": [ + { + "bbox": [ + 254, + 210, + 542, + 224 + ], + "type": "interline_equation", + "content": "M ^ {\\text {g e n}} = \\operatorname {S A M} - 2 \\left(x _ {0}\\right) \\tag {9}", + "image_path": "6e609a608080271c51e72d3bb004d998e6ef365863e6486c69de7a14c67bf666.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "spans": [ + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "inline_equation", + "content": "M^{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "text", + "content": " denotes the masks of the falling object in the generated video. We obtain ground truth masks " + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "inline_equation", + "content": "M^{\\mathrm{gt}}" + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "text", + "content": " using Kubric (Greff et al., 2022). To avoid non-differentiable reward, we use Sigmoid to normalize mask logits of generated video instead of converting them to binary masks. We use IoU between " + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "inline_equation", + "content": "M^{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "inline_equation", + "content": "M^{\\mathrm{gt}}" + }, + { + "bbox": [ + 52, + 233, + 542, + 269 + ], + "type": "text", + "content": " as reward function:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 235, + 277, + 542, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 235, + 277, + 542, + 291 + ], + "spans": [ + { + "bbox": [ + 235, + 277, + 542, + 291 + ], + "type": "interline_equation", + "content": "R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = \\operatorname {I o U} \\left(M ^ {\\text {g e n}}, M ^ {\\text {g t}}\\right) \\tag {10}", + "image_path": "cd46345119bb9f763ede3215ff65c6a675244fe939c3245326654a7eb9c2c6b0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 300, + 362, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 300, + 362, + 312 + ], + "spans": [ + { + "bbox": [ + 52, + 300, + 362, + 312 + ], + "type": "text", + "content": "Maximizing objective 1 is equivalent to minimizing the following objective:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 192, + 319, + 542, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 192, + 319, + 542, + 335 + ], + "spans": [ + { + "bbox": [ + 192, + 319, + 542, + 335 + ], + "type": "interline_equation", + "content": "J (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ 1 - \\operatorname {I o U} \\left(M ^ {\\text {g e n}}, M ^ {\\text {g t}}\\right) \\right] \\tag {11}", + "image_path": "dad12d0b6072d76092e95ba4d3424ea053c4dfb1ed2ec31c20542fc94215138d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 52, + 342, + 542, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 342, + 542, + 378 + ], + "spans": [ + { + "bbox": [ + 52, + 342, + 542, + 378 + ], + "type": "text", + "content": "This objective constrains the position and shape of the generated object in the video, encouraging a greater intersection with the object region in the ground truth video. The model learns to generate more accurate object positions and shapes through training with this objective." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 52, + 384, + 542, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 384, + 542, + 407 + ], + "spans": [ + { + "bbox": [ + 52, + 384, + 542, + 407 + ], + "type": "text", + "content": "Optical Flow Reward. We utilize RAFT (Teed & Deng, 2020) to generate optical flow for both generated videos and ground truth:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 257, + 407, + 542, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 257, + 407, + 542, + 425 + ], + "spans": [ + { + "bbox": [ + 257, + 407, + 542, + 425 + ], + "type": "interline_equation", + "content": "V ^ {\\text {g e n}} = \\operatorname {R A F T} \\left(x _ {0} ^ {\\prime}\\right) \\tag {12}", + "image_path": "afb3cd5801f3ce6384f1620771da148f5537afbdc9f1890db3bb151e6321637a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 262, + 422, + 337, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 262, + 422, + 337, + 434 + ], + "spans": [ + { + "bbox": [ + 262, + 422, + 337, + 434 + ], + "type": "interline_equation", + "content": "V ^ {\\mathrm {g t}} = \\operatorname {R A F T} (x _ {0})", + "image_path": "75ae96615ee2cc27de037c2571b7e943cd4557143b31224230f453e92e8ee6c4.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 52, + 439, + 501, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 439, + 501, + 452 + ], + "spans": [ + { + "bbox": [ + 52, + 439, + 501, + 452 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 52, + 439, + 501, + 452 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 439, + 501, + 452 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 52, + 439, + 501, + 452 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{gt}}" + }, + { + "bbox": [ + 52, + 439, + 501, + 452 + ], + "type": "text", + "content": " denote the optical flows of generated videos and ground truth. We define the reward as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 239, + 460, + 542, + 474 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 239, + 460, + 542, + 474 + ], + "spans": [ + { + "bbox": [ + 239, + 460, + 542, + 474 + ], + "type": "interline_equation", + "content": "R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = - \\left| V ^ {\\text {g e n}} - V ^ {\\text {g t}} \\right| \\tag {13}", + "image_path": "9a02ea6f114914c7d76f049a88a46de99ef271b776da7080f7929a05b2d82157.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 52, + 481, + 362, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 481, + 362, + 494 + ], + "spans": [ + { + "bbox": [ + 52, + 481, + 362, + 494 + ], + "type": "text", + "content": "Maximizing objective 1 is equivalent to minimizing the following objective:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 208, + 502, + 542, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 208, + 502, + 542, + 517 + ], + "spans": [ + { + "bbox": [ + 208, + 502, + 542, + 517 + ], + "type": "interline_equation", + "content": "J (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ \\left| V ^ {\\text {g e n}} - V ^ {\\text {g t}} \\right| \\right] \\tag {14}", + "image_path": "6e1f9e94954a2f07537b844ab77f7db174e9dbc07feff0f2ba04ac58b383fd0c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 52, + 524, + 542, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 524, + 542, + 548 + ], + "spans": [ + { + "bbox": [ + 52, + 524, + 542, + 548 + ], + "type": "text", + "content": "This objective constrains the motion of the generated object in the video. The model learns to generate more accurate physical motion through training with this objective." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 52, + 553, + 542, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 553, + 542, + 577 + ], + "spans": [ + { + "bbox": [ + 52, + 553, + 542, + 577 + ], + "type": "text", + "content": "Depth Reward. We utilize Depth-Anything-V2 (Yang et al., 2024a) to generate optical depth maps for both generated videos and ground truth:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 227, + 577, + 542, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 227, + 577, + 542, + 594 + ], + "spans": [ + { + "bbox": [ + 227, + 577, + 542, + 594 + ], + "type": "interline_equation", + "content": "D ^ {\\text {g e n}} = \\text {D e p t h - A n y t h i n g - V 2} \\left(x _ {0} ^ {\\prime}\\right) \\tag {15}", + "image_path": "eceaeaf5277e4ba1350d29f94dfc4847af28e5a6642caf910ffe300f4e298d7c.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 233, + 592, + 366, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 233, + 592, + 366, + 604 + ], + "spans": [ + { + "bbox": [ + 233, + 592, + 366, + 604 + ], + "type": "interline_equation", + "content": "D ^ {\\mathrm {g t}} = \\text {D e p t h - A n y t h i n g - V 2} (x _ {0})", + "image_path": "fa39dd5c194a70cc51e8058e5369a1cc529a139d485f223e0720f97bfeb118d8.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 52, + 609, + 497, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 609, + 497, + 622 + ], + "spans": [ + { + "bbox": [ + 52, + 609, + 497, + 622 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 52, + 609, + 497, + 622 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{gen}}" + }, + { + "bbox": [ + 52, + 609, + 497, + 622 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 52, + 609, + 497, + 622 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{gt}}" + }, + { + "bbox": [ + 52, + 609, + 497, + 622 + ], + "type": "text", + "content": " denote the depth maps of generated videos and ground truth. We define the reward as follows:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 239, + 630, + 542, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 239, + 630, + 542, + 643 + ], + "spans": [ + { + "bbox": [ + 239, + 630, + 542, + 643 + ], + "type": "interline_equation", + "content": "R \\left(x _ {0} ^ {\\prime}, x _ {0}\\right) = - \\left| D ^ {\\text {g e n}} - D ^ {\\mathrm {g t}} \\right| \\tag {16}", + "image_path": "8ae69436605c27369e44a6c3f836bbf91b30b4935fa8dcf15a6d4b282938dfee.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 52, + 651, + 362, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 651, + 362, + 663 + ], + "spans": [ + { + "bbox": [ + 52, + 651, + 362, + 663 + ], + "type": "text", + "content": "Maximizing objective 1 is equivalent to minimizing the following objective:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 208, + 672, + 542, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 208, + 672, + 542, + 687 + ], + "spans": [ + { + "bbox": [ + 208, + 672, + 542, + 687 + ], + "type": "interline_equation", + "content": "J (\\theta) = \\mathbb {E} _ {\\left(x _ {0}, c\\right) \\sim \\mathcal {D}, x _ {0} ^ {\\prime} \\sim p _ {\\theta} \\left(x _ {0} ^ {\\prime} \\mid c\\right)} \\left[ \\left| D ^ {\\mathrm {g e n}} - D ^ {\\mathrm {g t}} \\right| \\right] \\tag {17}", + "image_path": "99e34ae6711da1dd7f954b4f89af1eb173f91e59afdf52dfd382ee502dbf0eb6.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 52, + 693, + 542, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 693, + 542, + 718 + ], + "spans": [ + { + "bbox": [ + 52, + 693, + 542, + 718 + ], + "type": "text", + "content": "This objective constrains the 3d motion of the generated object in the video. The model learns to generate more accurate 3d physical motion through training with this objective." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "spans": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "text", + "content": "12" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + }, + { + "para_blocks": [ + { + "bbox": [ + 52, + 66, + 167, + 80 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 66, + 167, + 80 + ], + "spans": [ + { + "bbox": [ + 52, + 66, + 167, + 80 + ], + "type": "text", + "content": "D. Coordinate system" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "spans": [ + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "text", + "content": "We give a visualization of the coordinate system used in this paper in Figure 12. To compute " + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "text", + "content": ", we first leverage a segmentation map and find pixel row index that is just below the object. Once this row index is found, " + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "text", + "content": " can easily be computed from the camera position, camera sensor size, and image resolution. We note that because our camera is assumed to be in perspective with the " + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "inline_equation", + "content": "XY" + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "text", + "content": " plane, we can ignore " + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 51, + 87, + 543, + 148 + ], + "type": "text", + "content": " (not shown in figure) in our analyses in Section 5.1 and Section 5.2." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 53, + 158, + 203, + 323 + ], + "blocks": [ + { + "bbox": [ + 53, + 158, + 203, + 323 + ], + "lines": [ + { + "bbox": [ + 53, + 158, + 203, + 323 + ], + "spans": [ + { + "bbox": [ + 53, + 158, + 203, + 323 + ], + "type": "image", + "image_path": "afd6a41eb9e3a6bfc87ee7d008d6fc6d00d3b71c75ccf91adf12e6a11f200f01.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "lines": [ + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "spans": [ + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "text", + "content": "Figure 12. A visualization of the coordinate system used in this paper (not to scale). The image plane height of the object is denoted as " + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "text", + "content": ", its actual height in 3D as " + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "text", + "content": ", and its depth as " + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "text", + "content": ". The camera focal length is denoted as " + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 51, + 340, + 544, + 365 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 230, + 157, + 538, + 326 + ], + "blocks": [ + { + "bbox": [ + 230, + 157, + 538, + 326 + ], + "lines": [ + { + "bbox": [ + 230, + 157, + 538, + 326 + ], + "spans": [ + { + "bbox": [ + 230, + 157, + 538, + 326 + ], + "type": "image", + "image_path": "0492c7160061c2167d23b2371de275bf324606389678afb1b4fcc06512b614c9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 390, + 168, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 390, + 168, + 404 + ], + "spans": [ + { + "bbox": [ + 52, + 390, + 168, + 404 + ], + "type": "text", + "content": "E. Derivation of " + }, + { + "bbox": [ + 52, + 390, + 168, + 404 + ], + "type": "inline_equation", + "content": "p(t|y)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "spans": [ + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": "In our dataset construction, we assume a uniform distribution for " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "Z \\sim \\mathcal{U}(Z_{\\min}, Z_{\\max})" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "Z_{\\min} = 2" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "Z_{\\max} = 18" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": ". As shown in Figure 12, the dropping height " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": " is a linear function of " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": ", i.e. " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "Y = y + \\beta Z" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": " for the slope " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": " that can be computed from " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "y, f" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": ", the sensor size, and the camera height. This means we can solve for dropping time as " + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "inline_equation", + "content": "t = \\sqrt{\\frac{2}{g}Y} = \\sqrt{\\frac{2}{g}(y + \\beta Z)}" + }, + { + "bbox": [ + 52, + 411, + 543, + 467 + ], + "type": "text", + "content": ". Applying the transformation rule for probability density yields" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 203, + 471, + 542, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 203, + 471, + 542, + 502 + ], + "spans": [ + { + "bbox": [ + 203, + 471, + 542, + 502 + ], + "type": "interline_equation", + "content": "p (t | y) = \\left\\{ \\begin{array}{l l} \\frac {g t}{\\left(Z _ {\\max } - Z _ {\\min }\\right) \\beta}, & t _ {\\min } \\leq t \\leq t _ {\\max } \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {18}", + "image_path": "305b266d41310514e36020946f50f0d4e84d78dde1d04ab214ef5e367fadf418.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "spans": [ + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{min}} = \\sqrt{\\frac{2}{g} (y + \\beta Z_{\\mathrm{min}})}" + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{max}} = \\sqrt{\\frac{2}{g} (y + \\beta Z_{\\mathrm{max}})}" + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "text", + "content": ". Plugging in " + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{min}} = 2" + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{max}} = 18" + }, + { + "bbox": [ + 51, + 508, + 541, + 529 + ], + "type": "text", + "content": " yields Equation (3)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 52, + 541, + 167, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 541, + 167, + 555 + ], + "spans": [ + { + "bbox": [ + 52, + 541, + 167, + 555 + ], + "type": "text", + "content": "F. Ambiguous dataset" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 51, + 561, + 543, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 561, + 543, + 658 + ], + "spans": [ + { + "bbox": [ + 51, + 561, + 543, + 658 + ], + "type": "text", + "content": "We introduce a new dataset for distributional analysis that broadens " + }, + { + "bbox": [ + 51, + 561, + 543, + 658 + ], + "type": "inline_equation", + "content": "p(t|y)" + }, + { + "bbox": [ + 51, + 561, + 543, + 658 + ], + "type": "text", + "content": ", in contrast to the PSFT dataset, which prioritizes realism and has a narrower distribution due to limited object depth variability. To create a dataset with " + }, + { + "bbox": [ + 51, + 561, + 543, + 658 + ], + "type": "inline_equation", + "content": "p(t|y)" + }, + { + "bbox": [ + 51, + 561, + 543, + 658 + ], + "type": "text", + "content": " that is sufficiently diverse for meaningful analysis, we first set up the initial scenes as before, but then apply an augmentation where a new depth values is sampled uniformly from [2, 18] and the object is scaled and translated such that it appears the same in the original image, as shown in Figure 9. For simplicity, we limit our scenes to a single dropping object with no other objects on the ground. We also disable shadows, preventing the model from using them as cues to infer depth and height. Our dataset contains 5k samples consisting of 1k unique initial scenes each containing 5 different trajectories produced by the augmentation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 52, + 673, + 200, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 673, + 200, + 687 + ], + "spans": [ + { + "bbox": [ + 52, + 673, + 200, + 687 + ], + "type": "text", + "content": "G. Lifting trajectories to 3D" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 51, + 693, + 543, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 693, + 543, + 718 + ], + "spans": [ + { + "bbox": [ + 51, + 693, + 543, + 718 + ], + "type": "text", + "content": "To lift trajectories to 3D, we first estimate " + }, + { + "bbox": [ + 51, + 693, + 543, + 718 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{drop}}" + }, + { + "bbox": [ + 51, + 693, + 543, + 718 + ], + "type": "text", + "content": " as described in Section 5.1. Using SAM2 to estimate object masks in the generated video, we can obtain a trajectory of the bottom of the object which we denote as " + }, + { + "bbox": [ + 51, + 693, + 543, + 718 + ], + "type": "inline_equation", + "content": "y_0, y_1, \\ldots, y_N" + }, + { + "bbox": [ + 51, + 693, + 543, + 718 + ], + "type": "text", + "content": " where" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "spans": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "text", + "content": "13" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + }, + { + "para_blocks": [ + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "spans": [ + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "type": "inline_equation", + "content": "N = t_{\\mathrm{drop}} \\times \\mathrm{fps}" + }, + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "type": "text", + "content": ". From " + }, + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{drop}}" + }, + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "type": "text", + "content": ", we can solve for an implied depth " + }, + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "type": "inline_equation", + "content": "Z = \\frac{\\frac{1}{2}gt^2 - y}{\\beta}" + }, + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "type": "text", + "content": ". We then compute the lifted 3D trajectory as " + }, + { + "bbox": [ + 52, + 67, + 543, + 95 + ], + "type": "inline_equation", + "content": "y_i \\mapsto y_i + \\beta Z" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 108, + 162, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 108, + 162, + 121 + ], + "spans": [ + { + "bbox": [ + 53, + 108, + 162, + 121 + ], + "type": "text", + "content": "H. PisaBench Details" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 129, + 543, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 129, + 543, + 153 + ], + "spans": [ + { + "bbox": [ + 52, + 129, + 543, + 153 + ], + "type": "text", + "content": "In this section, we discuss the details of our data collection pipeline and annotations. We present more examples of real-world videos and corresponding annotations in Figure 13." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 166, + 180, + 178 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 166, + 180, + 178 + ], + "spans": [ + { + "bbox": [ + 52, + 166, + 180, + 178 + ], + "type": "text", + "content": "H.1. Data Collection Pipeline" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 184, + 543, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 184, + 543, + 233 + ], + "spans": [ + { + "bbox": [ + 52, + 184, + 543, + 233 + ], + "type": "text", + "content": "Collecting Real World Videos. We enlist approximately 15 volunteers to participate in the data collection process. We hand out a tripod, tape, and invisible wire for each volunteer. To ensure the quality, diversity, and minimize the ambiguity introduced by the environments, volunteers are provided with detailed guidelines. The key points of the data collection guidelines are shown in Table 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 238, + 543, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 238, + 543, + 299 + ], + "spans": [ + { + "bbox": [ + 52, + 238, + 543, + 299 + ], + "type": "text", + "content": "Raw videos processing. For the collected raw videos, we cut each video into multiple clips and crop their sizes. For each video clip, we annotate its starting position in the original long video and ensure that the duration of each segment does not exceed 12 seconds. Regarding the sizes of the videos, we manually crop each video to an aspect ratio of " + }, + { + "bbox": [ + 52, + 238, + 543, + 299 + ], + "type": "inline_equation", + "content": "1:1" + }, + { + "bbox": [ + 52, + 238, + 543, + 299 + ], + "type": "text", + "content": ", ensuring that the falling objects remain fully visible within the frame during the cropping process. The processing interface is shown in Figure 14." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 312, + 157, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 312, + 157, + 323 + ], + "spans": [ + { + "bbox": [ + 53, + 312, + 157, + 323 + ], + "type": "text", + "content": "H.2. Annotation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 330, + 543, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 330, + 543, + 378 + ], + "spans": [ + { + "bbox": [ + 52, + 330, + 543, + 378 + ], + "type": "text", + "content": "We present our annotation details in Figure 15. For video captions, we present the word cloud figure in (a). For segmentation masks, we annotate all objects in the first frame using positive and negative points, which are then propagated across frames using the SAM 2 (Ravi et al., 2024) model to produce segmentation masks for all objects throughout the video. The annotation interface is shown in (b)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 384, + 543, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 384, + 543, + 456 + ], + "spans": [ + { + "bbox": [ + 52, + 384, + 543, + 456 + ], + "type": "text", + "content": "In addition to providing the annotated caption \" {object description} falls,\" we also add information to inform off-the-shelf models of the task's context as much as possible. To further enhance task comprehension, we append an additional description \"A video that conforms to the laws of physics.\" We also employ negative prompts \"no camera motion\" and \"no slow-motion\" to ensure environmental stability and impose constraints on the generated videos. These prompts explicitly instruct the models to avoid including camera motion or any non-real-time object motion, thereby maintaining consistency with real-world physics." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 53, + 471, + 154, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 471, + 154, + 483 + ], + "spans": [ + { + "bbox": [ + 53, + 471, + 154, + 483 + ], + "type": "text", + "content": "I. Inference Details" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 52, + 491, + 543, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 491, + 543, + 529 + ], + "spans": [ + { + "bbox": [ + 52, + 491, + 543, + 529 + ], + "type": "text", + "content": "We present the inference configurations of each closed or open model we evaluate in Table 4. For models that do not support generating videos with 1:1 aspect ratio, we pad initial frames with black borders to the resolution supported by these models, and finally remove the black borders from the generated videos." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 53, + 543, + 208, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 543, + 208, + 556 + ], + "spans": [ + { + "bbox": [ + 53, + 543, + 208, + 556 + ], + "type": "text", + "content": "J. More Qualitative Examples" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 52, + 563, + 543, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 563, + 543, + 600 + ], + "spans": [ + { + "bbox": [ + 52, + 563, + 543, + 600 + ], + "type": "text", + "content": "We present more qualitative examples in Figure 16 - Figure 22. Although in some showcases, models can roughly predict the downward trend, models still struggle to predict plausible shape and motion. The defects in the models can be mainly attributed to the following aspects:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 63, + 613, + 541, + 715 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 63, + 613, + 541, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 613, + 541, + 659 + ], + "spans": [ + { + "bbox": [ + 63, + 613, + 541, + 659 + ], + "type": "text", + "content": "- Trajectory correctness: in most videos, models fail to predict even the basic falling trajectory of objects, as shown in Figure 19 (a), despite this being highly intuitive for humans. Even in cases where the falling trajectory is roughly correctly predicted, the models still struggle to accurately predict subsequent events, such as collisions, as illustrated in Figure 16 (f)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 63, + 670, + 541, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 670, + 541, + 715 + ], + "spans": [ + { + "bbox": [ + 63, + 670, + 541, + 715 + ], + "type": "text", + "content": "- Object consistency: in many generated videos, object consistency is poor. Models struggle to infer the appearance of objects from multiple viewpoints in a physically plausible manner, resulting in unnatural appearances, as shown in Figure 16 (a). Additionally, models perform poorly in maintaining object permanence, causing objects to appear blurry, as illustrated in Figure 20 (f). Furthermore, models sometimes introduce new objects into the video, as depicted in" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 95, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "spans": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "text", + "content": "14" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 13 + }, + { + "para_blocks": [ + { + "bbox": [ + 74, + 68, + 129, + 79 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 68, + 129, + 79 + ], + "spans": [ + { + "bbox": [ + 74, + 68, + 129, + 79 + ], + "type": "text", + "content": "Figure 20 (e)." + } + ] + } + ], + "index": 1, + "type": "text" + }, + { + "bbox": [ + 66, + 87, + 543, + 112 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 87, + 543, + 112 + ], + "spans": [ + { + "bbox": [ + 66, + 87, + 543, + 112 + ], + "type": "text", + "content": "- Scene consistency: models struggle to maintain scene consistency, leading to abrupt transitions in many videos. These sudden changes make videos appear unnatural, as shown in Figure 18 (f)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 126, + 211, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 126, + 211, + 140 + ], + "spans": [ + { + "bbox": [ + 54, + 126, + 211, + 140 + ], + "type": "text", + "content": "K. Simulated Adaption Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 147, + 543, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 147, + 543, + 220 + ], + "spans": [ + { + "bbox": [ + 54, + 147, + 543, + 220 + ], + "type": "text", + "content": "We use the Kubric (Greff et al., 2022) simulation and rendering engine for creating our simulated videos. Kubric uses PyBullet (Coumans et al., 2010) for running physics simulations and Blender (Community, 2018) for rendering. We set the simulation rate to 240 steps per second and render 2-second videos at 16 fps, resulting in 32 frames per video. Each scene consists of objects from the Google Scanned Objects (GSO) dataset (Downs et al., 2022) and uses environmental lighting from HDRI maps provided by Kubric. We use 930 objects and 458 HDRI maps for training and 103 objects and 51 HDRI maps for testing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "spans": [ + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "type": "text", + "content": "For each video, we randomly choose 1-6 objects to drop. These objects are placed at a height uniformly sampled from " + }, + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{m}" + }, + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "type": "inline_equation", + "content": "1.5\\mathrm{m}" + }, + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "type": "text", + "content": ". Below each of these objects, a possibly empty pile of up to 4 objects spawns beneath to create collisions. The objects are placed in a spawn region of size " + }, + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "type": "inline_equation", + "content": "2\\mathrm{m} \\times 2\\mathrm{m}" + }, + { + "bbox": [ + 54, + 224, + 543, + 261 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "spans": [ + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "text", + "content": "The camera is initially positioned " + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "inline_equation", + "content": "1\\mathrm{m}" + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "text", + "content": " behind this region, with its height varying uniformly between " + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "inline_equation", + "content": "0.4\\mathrm{m}" + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "inline_equation", + "content": "0.6\\mathrm{m}" + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "text", + "content": ". Once all objects are placed, the camera moves back in random increments until all objects are visible within the camera frame. The camera uses a focal length of " + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "inline_equation", + "content": "35\\mathrm{mm}" + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "text", + "content": ", a sensor width of " + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "inline_equation", + "content": "32\\mathrm{mm}" + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "text", + "content": ", and an aspect ratio of " + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 54, + 266, + 543, + 303 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 318, + 129, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 318, + 129, + 331 + ], + "spans": [ + { + "bbox": [ + 54, + 318, + 129, + 331 + ], + "type": "text", + "content": "L. Limitations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 338, + 543, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 338, + 543, + 398 + ], + "spans": [ + { + "bbox": [ + 54, + 338, + 543, + 398 + ], + "type": "text", + "content": "In this work, we collect and manually annotate a dataset of 361 real-world videos and design three spatial metrics to evaluate the performance of state-of-the-art image-to-video (I2V) models in a fundamental physical scenario: free fall. Our metrics focus solely on spatial positional relationships, excluding object appearance attributes such as color. To enable more fine-grained evaluations of appearance characteristics, we aim to develop metrics based on Multimodal Large Language Models (MLLMs) or pixel-level analysis in future work." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 403, + 543, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 403, + 543, + 453 + ], + "spans": [ + { + "bbox": [ + 54, + 403, + 543, + 453 + ], + "type": "text", + "content": "Furthermore, we propose the PSFT and ORO methods to fine-tune the Open-Sora model (Zheng et al., 2024), improving its ability to generate physically plausible videos. Despite these improvements, certain limitations remain, specifically, the generation of blurry objects in some videos. We hope to address these challenges in future research by refining both the dataset and the fine-tuning strategies, aiming to produce videos that better maintain object visuals." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 95, + 45, + 499, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 45, + 499, + 56 + ], + "spans": [ + { + "bbox": [ + 95, + 45, + 499, + 56 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 293, + 731, + 302, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 731, + 302, + 740 + ], + "spans": [ + { + "bbox": [ + 293, + 731, + 302, + 740 + ], + "type": "text", + "content": "15" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 14 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 95, + 541, + 218 + ], + "blocks": [ + { + "bbox": [ + 53, + 95, + 541, + 218 + ], + "lines": [ + { + "bbox": [ + 53, + 95, + 541, + 218 + ], + "spans": [ + { + "bbox": [ + 53, + 95, + 541, + 218 + ], + "type": "image", + "image_path": "2c3255e61507df64f2fe2b8fc33da6df4f8074be9bf5d02291a3cf3bb8a8a94a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 222, + 220, + 373, + 234 + ], + "lines": [ + { + "bbox": [ + 222, + 220, + 373, + 234 + ], + "spans": [ + { + "bbox": [ + 222, + 220, + 373, + 234 + ], + "type": "text", + "content": "(a) A white paper roll falls." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 236, + 541, + 358 + ], + "blocks": [ + { + "bbox": [ + 53, + 236, + 541, + 358 + ], + "lines": [ + { + "bbox": [ + 53, + 236, + 541, + 358 + ], + "spans": [ + { + "bbox": [ + 53, + 236, + 541, + 358 + ], + "type": "image", + "image_path": "76661e958af011fe7f1f7ab37c8d6b11f4f98a6f04af442101dbe8308c1127ee.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 222, + 361, + 351, + 374 + ], + "lines": [ + { + "bbox": [ + 222, + 361, + 351, + 374 + ], + "spans": [ + { + "bbox": [ + 222, + 361, + 351, + 374 + ], + "type": "text", + "content": "(c) A black bottle falls." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 53, + 377, + 541, + 499 + ], + "blocks": [ + { + "bbox": [ + 53, + 377, + 541, + 499 + ], + "lines": [ + { + "bbox": [ + 53, + 377, + 541, + 499 + ], + "spans": [ + { + "bbox": [ + 53, + 377, + 541, + 499 + ], + "type": "image", + "image_path": "f96ae24b9af0730f8094994e180d7d5a6e32804e7b580a5dadd002836de5fced.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 222, + 502, + 386, + 515 + ], + "lines": [ + { + "bbox": [ + 222, + 502, + 386, + 515 + ], + "spans": [ + { + "bbox": [ + 222, + 502, + 386, + 515 + ], + "type": "text", + "content": "(b) A transparent bottle falls." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 53, + 518, + 541, + 640 + ], + "blocks": [ + { + "bbox": [ + 53, + 518, + 541, + 640 + ], + "lines": [ + { + "bbox": [ + 53, + 518, + 541, + 640 + ], + "spans": [ + { + "bbox": [ + 53, + 518, + 541, + 640 + ], + "type": "image", + "image_path": "14aef21ca7858494c097f6f67d50528c4b5917b1b19db5da86d4a491cd5a520f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 222, + 643, + 352, + 656 + ], + "lines": [ + { + "bbox": [ + 222, + 643, + 352, + 656 + ], + "spans": [ + { + "bbox": [ + 222, + 643, + 352, + 656 + ], + "type": "text", + "content": "(d) A white bottle falls." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 674, + 541, + 696 + ], + "lines": [ + { + "bbox": [ + 51, + 674, + 541, + 696 + ], + "spans": [ + { + "bbox": [ + 51, + 674, + 541, + 696 + ], + "type": "text", + "content": "Figure 13. Examples of real world videos and annotations. 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AspectRequirements
Camera·The camera must be stabilized using a tripod.\n·The dropping object should remain visible throughout the entire fall.\n·The trajectory of the object should be sufficiently centered in the frame.\n·Ensure the slow-motion setting is configured to 120 fps.\n·Avoid a completely top-down perspective; the frame should include both the floor and the wall for spatial context.\n·It is acceptable to record one long video containing multiple drops at the same location.
Objects·Most objects should be rigid and non-deformable.\n·A limited number of flexible or deformable objects may be included, as such data is also valuable.
Dropping Procedure·Secure the object with a wire using tape, ensuring stability. Multiple tapings may be necessary for proper stabilization.\n·Visibility of the wire in the video is acceptable.\n·No body parts should appear in the frame. If this is challenging, consider having a partner monitor the camera or use screen-sharing software to view the camera feed on a laptop for uninterrupted framing.\n·Record videos in a horizontal orientation to simplify cropping and to help keep the frame free of unnecessary elements.\n·Use a short wire to enhance object stability.\n·The object should remain stationary before being dropped.
Scene Composition·Make the scenes dynamic and engaging. Include interactions with other objects, such as collisions or objects tipping over. Static objects should serve as active elements rather than mere background props.\n·Avoid filming in classroom or laboratory environments.\n·Include a variety of dropping heights.\n·Film in different environments, ensuring at least one setting is outside your apartment.\n·Minimize human shadows in the frame whenever possible.\n·Ensure good lighting and maintain strong contrast between the objects and the back-ground.
", + "image_path": "1211a8336c5089da8a8c3424e1cc2df81e4f22b093cc82bb6236a03de951a3b1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 684, + 541, + 707 + ], + "lines": [ + { + "bbox": [ + 52, + 684, + 541, + 707 + ], + "spans": [ + { + "bbox": [ + 52, + 684, + 541, + 707 + ], + "type": "text", + "content": "Table 3. Key points of real world videos collection guideline. We have detailed requirements for camera, objects, dropping procedure and scene composition to ensure the quality, diversity and minimize ambiguity introduced by environments." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 499, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "spans": [ + { + "bbox": [ + 292, + 731, + 303, + 740 + ], + "type": "text", + "content": "17" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 16 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 282, + 223 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 282, + 223 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 282, + 223 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 282, + 223 + ], + "type": "image", + "image_path": "945c3d2b2e7ba5dd24811fc027b02c812dd3fdb62673324359a47eefccc06ed5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 160, + 224, + 170, + 233 + ], + "lines": [ + { + "bbox": [ + 160, + 224, + 170, + 233 + ], + "spans": [ + { + "bbox": [ + 160, + 224, + 170, + 233 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 301, + 69, + 543, + 223 + ], + "blocks": [ + { + "bbox": [ + 301, + 69, + 543, + 223 + ], + "lines": [ + { + "bbox": [ + 301, + 69, + 543, + 223 + ], + "spans": [ + { + "bbox": [ + 301, + 69, + 543, + 223 + ], + "type": "image", + "image_path": "4d595693598e6f902081fbae2160c14f17629bf42e1282931e980a4273a07e54.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 416, + 224, + 427, + 233 + ], + "lines": [ + { + "bbox": [ + 416, + 224, + 427, + 233 + ], + "spans": [ + { + "bbox": [ + 416, + 224, + 427, + 233 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 55, + 276, + 260, + 480 + ], + "blocks": [ + { + "bbox": [ + 55, + 276, + 260, + 480 + ], + "lines": [ + { + "bbox": [ + 55, + 276, + 260, + 480 + ], + "spans": [ + { + "bbox": [ + 55, + 276, + 260, + 480 + ], + "type": "image", + "image_path": "8f522784783a329f5017e6371582ae27e84586d17a8f7bcd9025f339933400e5.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 149, + 492, + 161, + 502 + ], + "lines": [ + { + "bbox": [ + 149, + 492, + 161, + 502 + ], + "spans": [ + { + "bbox": [ + 149, + 492, + 161, + 502 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 290, + 274, + 542, + 483 + ], + "blocks": [ + { + "bbox": [ + 51, + 244, + 542, + 268 + ], + "lines": [ + { + "bbox": [ + 51, + 244, + 542, + 268 + ], + "spans": [ + { + "bbox": [ + 51, + 244, + 542, + 268 + ], + "type": "text", + "content": "Figure 14. Video processing interface. (a) we annotate starting positions in the original long videos and clip them into multiple clips less than 12 seconds. (b) We drag the cropping box to crop the video size to an aspect ratio of 1:1." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 290, + 274, + 542, + 483 + ], + "lines": [ + { + "bbox": [ + 290, + 274, + 542, + 483 + ], + "spans": [ + { + "bbox": [ + 290, + 274, + 542, + 483 + ], + "type": "image", + "image_path": "733aaf4a714c7ec870de8f5e762d4a545653a15ef5ea24677ad5c2400309aed0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 408, + 492, + 421, + 502 + ], + "lines": [ + { + "bbox": [ + 408, + 492, + 421, + 502 + ], + "spans": [ + { + "bbox": [ + 408, + 492, + 421, + 502 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 516, + 543, + 550 + ], + "lines": [ + { + "bbox": [ + 51, + 516, + 543, + 550 + ], + "spans": [ + { + "bbox": [ + 51, + 516, + 543, + 550 + ], + "type": "text", + "content": "Figure 15. Annotation details of real world videos. (a) Word cloud of objects in video captions. Our videos contain a variety of daily life objects. (b) Interface for annotating positive and negative points in the first frame. Red and blue dots indicate positive and negative points respectively. We annotate all objects in the midair and ground." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 53, + 556, + 542, + 692 + ], + "blocks": [ + { + "bbox": [ + 53, + 556, + 542, + 692 + ], + "lines": [ + { + "bbox": [ + 53, + 556, + 542, + 692 + ], + "spans": [ + { + "bbox": [ + 53, + 556, + 542, + 692 + ], + "type": "table", + "html": "
ModelResolutionNumber of FramesFPSGuidance ScaleSampling StepsNoise Scheduler
ClosedSora720 × 72015030---
Kling-V1.5960 × 960150301.0--
Kling-V1960 × 960150301.0--
Runway Gen31280 × 76815630---
OpenCogVideoX-5B-I2V720 × 4804886.050DDIM
DynamiCrafter512 × 32090300.750DDIM
Pyramid-Flow1280 × 768120244.010EulerDiscrete
Open-Sora512 × 51290307.030RFLOW
", + "image_path": "5ff8dcc1fc52105fef32fc975178bc49046b998c818452290cac625a89916132.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 112, + 699, + 482, + 710 + ], + "lines": [ + { + "bbox": [ + 112, + 699, + 482, + 710 + ], + "spans": [ + { + "bbox": [ + 112, + 699, + 482, + 710 + ], + "type": "text", + "content": "Table 4. Inference details for models we evaluate, where “-” indicates the information is not available." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 499, + 56 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 292, + 731, + 302, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 292, + 731, + 302, + 740 + ], + "spans": [ + { + "bbox": [ + 292, + 731, + 302, + 740 + ], + "type": "text", + "content": "18" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 17 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 105, + 541, + 167 + ], + "blocks": [ 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"image_path": "c8f534dc359b0c6486ea7d10444e18fb31e91a7d173e50458a7fb898ac132de4.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 216, + 612, + 329, + 625 + ], + "lines": [ + { + "bbox": [ + 216, + 612, + 329, + 625 + ], + "spans": [ + { + "bbox": [ + 216, + 612, + 329, + 625 + ], + "type": "text", + "content": "(f) A white box falls." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 643, + 542, + 687 + ], + "lines": [ + { + "bbox": [ + 51, + 643, + 542, + 687 + ], + "spans": [ + { + "bbox": [ + 51, + 643, + 542, + 687 + ], + "type": "text", + "content": "Figure 16. Qualitative examples of Kling-V1 (Kuaishou, 2024). In (a) (b) (c) (f), objects have a tendency to fall. (b) (c) are roughly consistent with the laws of physics. In (a) (f), the shape of the object does not match the first frame. In (d), the paper cup is suspended in midair. In (e), new object is introduced. 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Qualitative examples of Runway Gen3 (Runway, 2024). In (b) (e), objects have a tendency to fall. In (a) (e) (f), new objects are introduced. In (b) (d), the shape of the object does not match the first frame. 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"image_path": "dad22c2ccf02d28f88996ada3f6458c8f7ba92408c341e39e6da0ed00ee05fbb.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 615, + 330, + 629 + ], + "lines": [ + { + "bbox": [ + 214, + 615, + 330, + 629 + ], + "spans": [ + { + "bbox": [ + 214, + 615, + 330, + 629 + ], + "type": "text", + "content": "(f) A white box falls." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 647, + 543, + 681 + ], + "lines": [ + { + "bbox": [ + 51, + 647, + 543, + 681 + ], + "spans": [ + { + "bbox": [ + 51, + 647, + 543, + 681 + ], + "type": "text", + "content": "Figure 18. Qualitative examples of CogVideoX-5B-I2V (Yang et al., 2024c). In (a) - (f), objects have a tendency to fall. However, in all the videos, there are violations of physics. In (a) (b), the objects are divided into two parts. In (c) (d) (e), the shape of the object does not match the first frame. In (c), the trajectory is not a vertical fall. 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"image", + "image_path": "b68b172758804959f5687238c0b53d284f904543618dda06d81c04419d71a2ce.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 627, + 301, + 640 + ], + "lines": [ + { + "bbox": [ + 214, + 627, + 301, + 640 + ], + "spans": [ + { + "bbox": [ + 214, + 627, + 301, + 640 + ], + "type": "text", + "content": "(f) A shoe falls." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 52, + 658, + 541, + 670 + ], + "lines": [ + { + "bbox": [ + 52, + 658, + 541, + 670 + ], + "spans": [ + { + "bbox": [ + 52, + 658, + 541, + 670 + ], + "type": "text", + "content": "Figure 19. Qualitative examples of DynamiCrafter (?). 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Qualitative examples of Pyramid-Flow (Jin et al., 2024). In (b) (d) (e), objects have a tendency to fall. In (a) (b) (e) (f), new objects are introduced. In (c), scene changes, which does not match the first frame.. 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Qualitative examples of Open-Sora (Zheng et al., 2024). In all the videos, objects do not have a tendency to fall, suspended in the midair. In (b) (d), scene changes suddenly, which does not match the first frame. In (e), new object is introduced." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 500, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 500, + 57 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 500, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 291, + 731, + 303, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 291, + 731, + 303, + 740 + ], + "spans": [ + { + "bbox": [ + 291, + 731, + 303, + 740 + ], + "type": "text", + "content": "24" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 23 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 114, + 542, + 178 + ], + "blocks": [ + { + "bbox": [ + 53, + 114, 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"text", + "content": "(c) A grey paper cup falls." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 53, + 378, + 542, + 441 + ], + "blocks": [ + { + "bbox": [ + 53, + 378, + 542, + 441 + ], + "lines": [ + { + "bbox": [ + 53, + 378, + 542, + 441 + ], + "spans": [ + { + "bbox": [ + 53, + 378, + 542, + 441 + ], + "type": "image", + "image_path": "2c9f209b0aeac72570d8c4fde360b1cf6b4dfcb2b6a0e8d4e853f7b3a78fa4d6.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 446, + 379, + 460 + ], + "lines": [ + { + "bbox": [ + 214, + 446, + 379, + 460 + ], + "spans": [ + { + "bbox": [ + 214, + 446, + 379, + 460 + ], + "type": "text", + "content": "(d) A transparent bottle falls." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 53, + 465, + 542, + 529 + ], + "blocks": [ + { + 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"a00eb2f6afd73e7890435740d404820471ec3c29a424ac89fa8f08f0f78a9a90.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 621, + 342, + 635 + ], + "lines": [ + { + "bbox": [ + 214, + 621, + 342, + 635 + ], + "spans": [ + { + "bbox": [ + 214, + 621, + 342, + 635 + ], + "type": "text", + "content": "(f) A white bottle falls." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 653, + 543, + 677 + ], + "lines": [ + { + "bbox": [ + 51, + 653, + 543, + 677 + ], + "spans": [ + { + "bbox": [ + 51, + 653, + 543, + 677 + ], + "type": "text", + "content": "Figure 22. Qualitative examples of our method (Open-Sora + PSFT + ORO). In all the videos, objects have a tendency to fall. However, the consistency of objects is still insufficient. In some frames, objects become blurry. Objects sometimes disappear after collision." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 96, + 45, + 500, + 57 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 45, + 500, + 57 + ], + "spans": [ + { + "bbox": [ + 96, + 45, + 500, + 57 + ], + "type": "text", + "content": "PISA Experiments: Exploring Physics Post-Training for Video Diffusion Models by Watching Stuff Drop" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 291, + 731, + 303, + 740 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 291, + 731, + 303, + 740 + ], + "spans": [ + { + "bbox": [ + 291, + 731, + 303, + 740 + ], + "type": "text", + "content": "25" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 24 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_content_list.json b/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..229b85d006535ca8c03ef9d2df0ffe148fd0dd43 --- /dev/null +++ b/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_content_list.json @@ -0,0 +1,2781 @@ +[ + { + "type": "text", + "text": "A Survey of Direct Preference Optimization", + "text_level": 1, + "bbox": [ + 122, + 66, + 872, + 101 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shunyu Liu, Wenkai Fang, Zetian Hu, Junjie Zhang, Yang Zhou, Kongcheng Zhang, Rongcheng Tu, Ting-En Lin, Fei Huang, Mingli Song, Yongbin Li, and Dacheng Tao, Fellow, IEEE", + "bbox": [ + 102, + 114, + 893, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract—Large Language Models (LLMs) have demonstrated unprecedented generative capabilities, yet their alignment with human values remains critical for ensuring helpful and harmless deployments. While Reinforcement Learning from Human Feedback (RLHF) has emerged as a powerful paradigm for aligning LLMs with human preferences, its reliance on complex reward modeling introduces inherent trade-offs in computational efficiency and training stability. In this context, Direct Preference Optimization (DPO) has recently gained prominence as a streamlined alternative that directly optimizes LLMs using human preferences, thereby circumventing the need for explicit reward modeling. Owing to its theoretical elegance and computational efficiency, DPO has rapidly attracted substantial research efforts exploring its various implementations and applications. However, this field currently lacks systematic organization and comparative analysis. In this survey, we conduct a comprehensive overview of DPO and introduce a novel taxonomy, categorizing previous works into four key dimensions: data strategy, learning framework, constraint mechanism, and model property. We further present a rigorous empirical analysis of DPO variants across standardized benchmarks. Additionally, we discuss real-world applications, open challenges, and future directions for DPO. This work delivers both a conceptual framework for understanding DPO and practical guidance for practitioners, aiming to advance robust and generalizable alignment paradigms. All collected resources are available and will be continuously updated at https://github.com/liushunyu/awesome-direct-preference-optimization.", + "bbox": [ + 104, + 172, + 892, + 345 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Index Terms—Alignment, Direct Preference Optimization, Large Language Models, Reinforcement Learning from Human Feedback.", + "bbox": [ + 104, + 356, + 877, + 369 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION", + "text_level": 1, + "bbox": [ + 73, + 430, + 228, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The rapid advancement of Large Language Models (LLMs) has revolutionized artificial intelligence [1, 2, 3, 4, 5, 6, 7, 8], enabling unprecedented generative capabilities across diverse applications, such as dialogue systems [9, 10], code generation [11, 12, 13], and medical diagnosis [14, 15, 16, 17]. Models like OpenAI-o1 [18] and DeepSeekR1 [19] have demonstrated remarkable proficiency in understanding and generating human-like text, outperforming traditional language processing techniques [20]. However, their immense power also introduces significant risks: LLMs may inadvertently produce harmful content (e.g., jailbreak suggestion) [21], exhibit hallucination behaviors (e.g., misinformation) [22], or propagate sociocultural stereotypes (e.g., biased recommendations) [23]. Ensuring that these models align with human values (producing outputs that are helpful, harmless, and honest) has thus become a cornerstone of responsible AI development [24].", + "bbox": [ + 71, + 454, + 491, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The critical challenge of aligning LLMs with human values stems from the inherent complexity of encoding abstract", + "bbox": [ + 73, + 702, + 491, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A\\*STAR, as well as supported by Alibaba Group and NTU Singapore through Alibaba-NTU Global e-Sustainability CorpLab (ANGEL). (Corresponding author: Dacheng Tao.) Shunyu Liu, Junjie Zhang, Rongcheng Tu and Dacheng Tao are with Nanyang Technological University, Singapore (e-mail: shunyu.liu@ntu.edu.sg; junjie.zhang@ntu.edu.sg; turongcheng@gmail.com; dacheng.tao@ntu.edu.sg). Wenkai Fang, Yang Zhou, Kongcheng Zhang, and Mingli Song are with the College of Computer Science and Technology, Zhejiang University, China (e-mail: wenkfang@zju.edu.cn; imzhouyang@zju.edu.cn; zhangkc@zju.edu.cn; brooksong@zju.edu.cn). Zetian Hu is with the School of Aerospace Engineering, Tsinghua University, China (e-mail: huzt22@mails.tsinghua.edu.cn). Ting-En Lin, Fei Huang, and Yongbin Li are with the Tongyi Lab, Alibaba Group, China (e-mail: ting-en.lte@alibaba-inc.com; f.huang@alibaba-inc.com; shuide.lyb@alibaba-inc.com).", + "bbox": [ + 71, + 746, + 491, + 941 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ethical principles into concrete model behaviors [25, 26, 27]. Traditional approaches, such as rule-based filtering or supervised learning on curated datasets, often prove inadequate due to their inability to generalize across diverse contexts and adapt to evolving societal norms [28]. The emergence of preference-based alignment paradigms addresses these limitations by framing the problem as optimizing for human feedback rather than inflexible heuristics [29, 30, 31, 32]. This shift recognizes that LLM decision-making often involves nuanced trade-offs between competing values, requiring flexible frameworks capable of incorporating subjective human preferences [33].", + "bbox": [ + 501, + 431, + 924, + 606 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Building upon these insights, Reinforcement Learning from Human Feedback (RLHF) [34, 35] has emerged as the predominant alignment paradigm, leveraging human preferences to guide model optimization. In the RLHF pipeline, human annotators first rank the outputs generated by the language model, and these comparisons are used to train a reward model that quantifies human preferences. The language model is then fine-tuned using RL guided by this reward model, enabling the language model to align with human values by maximizing the predicted rewards. The success of RLHF in aligning models like ChatGPT [36, 37] and Claude [38, 39] underscores its practical utility. By translating subjective human preferences into an objective reward signal, RLHF facilitates the optimization of model behavior for value alignment. However, this RLHF paradigm suffers from critical limitations of computational complexity and training instability. Training a separate reward model demands substantial computational resources and high-quality human preference data, which scales poorly across different domains. Moreover, the RL phase often struggles with optimization challenges, such as reward hacking [40] and mode collapse [41].", + "bbox": [ + 503, + 607, + 923, + 926 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "These limitations have spurred interest in alternative", + "bbox": [ + 527, + 926, + 923, + 941 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1", + "bbox": [ + 911, + 32, + 919, + 42 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2503.11701v1 [cs.LG] 12 Mar 2025", + "bbox": [ + 22, + 260, + 57, + 705 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eec766babe90c18e92b263abf2f3723da32c85a958aae6f3eb98f4722ac37fa7.jpg", + "image_caption": [ + "Fig. 1: A taxonomy of DPO. We categorize existing DPO works into four branches: data strategy, learning framework, constraint mechanism, and model property. Different colored boxes indicate different categories and their corresponding representative references." + ], + "image_footnote": [], + "bbox": [ + 81, + 54, + 919, + 597 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "alignment methods that bypass reward modeling while preserving the benefits of preference-based learning. Direct Preference Optimization (DPO) [74, 210] represents a groundbreaking shift in this direction. Unlike RLHF, DPO reframes alignment as a supervised learning problem, directly optimizing the LLM policy using preference data without explicit reward modeling. By leveraging a closed-form mapping between reward functions and optimal policies, DPO eliminates the need for iterative RL training, reducing computational overhead and improving stability. Due to its inherent advantages, DPO has rapidly gained increasing attention from research communities. Existing studies vary widely in data strategies (e.g., point-wise v.s. pair-wise feedback) [67, 211], learning frameworks (e.g., offline v.s. online learning) [121, 122, 126], constraint mechanisms (e.g., different divergence constraints) [169, 171], and model properties (e.g., length bias) [191, 195]. Recent advancements in DPO variants have demonstrated remarkable efficacy in enhancing model alignment with human preferences, achieving unprecedented success across diverse domains [32].", + "bbox": [ + 71, + 641, + 495, + 933 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These developments position DPO-based approaches as a compelling alternative to conventional RLHF paradigms for preference alignment tasks. However, despite its promise, the DPO research landscape remains fragmented.", + "bbox": [ + 503, + 641, + 924, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Several surveys related to DPO have been published in recent years, yet they exhibit notable limitations in their scope and analysis of DPO. (1) Scope limitations. While an early survey of [212] presents a comprehensive overview of preference-based RL methods, it predates the advent of DPO and does not address its applications to modern LLMs. Recent surveys on alignment [24, 26, 213, 214] provide broad overviews of LLM alignment techniques but only offer cursory summaries of DPO-related approaches without in-depth analysis. Similarly, surveys on learning from human feedback [30, 215, 216, 217] also only briefly mention DPO as a potential alternative. (2) Taxonomy deficiencies. Gao et al. [29] and Winata et al. [32] introduce a simplified taxonomy for preference learning, while overlooking technical distinctions within its broad categorization. In contrast, Wang et al. [31] attempt to classify preference learning across dimensions", + "bbox": [ + 503, + 708, + 923, + 941 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 911, + 32, + 921, + 42 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "such as reinforcement learning, reward modeling, feedback, and optimization. However, this taxonomy suffers from significant conceptual overlaps (e.g. reinforcement learning inherently involves optimization). A recent work by Xiao et al. [210] categorizes DPO studies through isolated research questions, which, while useful for problem identification, fragments the methodological connections. Our survey addresses these gaps by presenting the first comprehensive analysis specifically focused on DPO. The main contributions of this survey are summarized as follows:", + "bbox": [ + 71, + 53, + 491, + 198 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- In this survey, we introduce a novel taxonomy that categorizes existing DPO works into four key dimensions based on different components of the DPO loss: data strategy, learning framework, constraint mechanism, and model property, as shown in Fig. 1. This taxonomy provides a systematic framework for understanding the methodological evolution of DPO and highlights the key distinctions between different variations.", + "- We conduct a rigorous empirical analysis of DPO variants across standardized benchmarks, revealing critical insights into their performance in diverse scenarios. This analysis offers a comprehensive evaluation of DPO variants and provides practical guidance for practitioners.", + "- We discuss real-world applications of DPO and highlight its potential to democratize alignment research by enabling efficient and scalable preference learning across diverse domains. We also outline open challenges and future directions for DPO research, emphasizing the need for robust and generalizable alignment paradigms." + ], + "bbox": [ + 83, + 202, + 491, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The remainder of this survey is organized as follows. Section 2 introduces the background and formulation of DPO. Section 3 presents a taxonomy of DPO, categorizing existing works based on key dimensions. Section 4 describes standardized benchmarks for evaluating DPO methods and presents empirical results. Section 5 discusses real-world applications of DPO and highlights its potential. Section 6 outlines open challenges and future directions for DPO research. Finally, Section 7 concludes the survey.", + "bbox": [ + 71, + 483, + 491, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2 BACKGROUND AND FORMULATION", + "text_level": 1, + "bbox": [ + 73, + 641, + 383, + 655 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preference learning aims to train language model policies to generate responses that better align with human preferences. Specifically, we denote the language model policy as $\\pi(y|x)$ , where $x$ represents the input prompt and $y$ is a candidate response (completion). A language model can be viewed as an autoregressive function that sequentially predicts tokens based on prior context. Mathematically, this is expressed as: $\\pi(y|x) = \\prod_{t=1}^{T} \\pi(y_t | y_{ 0$ is a hyperparameter that controls the strength of the Kullback-Leibler (KL) divergence penalty. Here, the term $\\log \\pi_{\\theta}(\\cdot |x) / \\pi_{\\mathrm{ref}}(\\cdot |x)$ represents the KL divergence between the current policy $\\pi_{\\theta}$ and a reference policy $\\pi_{\\mathrm{ref}}$ . In practice, the reference policy $\\pi_{\\mathrm{ref}}$ is set to the SFT model $\\pi_{\\mathrm{sft}}$ , ensuring that the updated policy remains close to the initial model.", + "bbox": [ + 501, + 781, + 923, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To optimize the above objective, Proximal Policy Optimization (PPO) [219] has emerged as a promising RL algorithm for LLMs. PPO stabilizes training by constraining policy updates within a trust region via a clipped objective, which prevents significant deviations from the previous", + "bbox": [ + 501, + 869, + 924, + 944 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 911, + 32, + 921, + 42 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "policy. However, PPO requires an additional critic model to estimate value functions for advantage calculation, thereby introducing extra computational and memory overhead. To address this, recent methods, such as RLOO [220], ReMax [221], GRPO [222], and Reinforce++ [223], introduce critic-free advantage estimation to reduce resource demands while maintaining stable optimization, making them more scalable for large-scale LLM training.", + "bbox": [ + 71, + 53, + 491, + 170 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2 Direct Preference Optimization", + "text_level": 1, + "bbox": [ + 73, + 185, + 341, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "DPO offers an alternative that streamlines the training process by directly optimizing the policy with preference data [74, 224, 225, 226, 227, 228, 229], thereby eliminating the need for explicit reward modeling in RLHF. The key idea of DPO is a closed-form solution of Eq. 3 that connects reward with the optimal policies. Specifically, the optimal policy corresponding to a given $r$ is defined as follows:", + "bbox": [ + 71, + 203, + 490, + 306 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\pi^ {*} (y | x) = \\frac {1}{Z (x)} \\pi_ {\\mathrm {r e f}} (y | x) \\exp \\left(\\frac {1}{\\beta} r (x, y)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 311, + 491, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the partition function $Z(x)$ is defined as:", + "bbox": [ + 71, + 348, + 406, + 363 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nZ (x) = \\sum_ {y} \\pi_ {\\mathrm {r e f}} (y | x) \\exp \\left(\\frac {1}{\\beta} r (x, y)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 368, + 491, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By rearranging the above equation, the reward $r$ can be recovered from the optimal policy $\\pi^{*}$ :", + "bbox": [ + 71, + 409, + 491, + 439 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr (x, y) = \\beta \\log \\frac {\\pi^ {*} (y | x)}{\\pi_ {\\operatorname {r e f}} (y | x)} + \\beta \\log Z (x). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 444, + 491, + 476 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Notice that the partition function $Z(x)$ depends only on the prompt $x$ . By substituting this expression into the preference model of Eq. 1, the preference probability model that $y_{w}$ is preferred over $y_{l}$ becomes:", + "bbox": [ + 71, + 479, + 491, + 540 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(y _ {w} \\succ y _ {l} | x\\right) = \\sigma \\left(\\beta \\log \\frac {\\pi^ {*} \\left(y _ {w} \\mid x\\right)}{\\pi_ {\\text {r e f}} \\left(y _ {w} \\mid x\\right)} - \\beta \\log \\frac {\\pi^ {*} \\left(y _ {l} \\mid x\\right)}{\\pi_ {\\text {r e f}} \\left(y _ {l} \\mid x\\right)}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 544, + 491, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the above preference probability model, DPO directly optimizes the language mode policy $\\pi_{\\theta}$ by minimizing the following negative log-likelihood loss function:", + "bbox": [ + 71, + 588, + 491, + 633 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {D P O}} (\\theta) = \\\\ - \\mathbb {E} _ {(x, y _ {w}, y _ {l}) \\sim \\mathcal {D}} \\left[ \\log \\sigma \\left(\\beta \\log \\frac {\\pi_ {\\theta} (y _ {w} | x)}{\\pi_ {\\text {r e f}} (y _ {w} | x)} - \\beta \\log \\frac {\\pi_ {\\theta} (y _ {l} | x)}{\\pi_ {\\text {r e f}} (y _ {l} | x)}\\right) \\right], \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 643, + 491, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the KL constraint is implicitly integrated through the use of the reference model $\\pi_{\\mathrm{ref}}$ . By minimizing this DPO loss, we directly train the policy to satisfy human preferences without resorting to a separate reward modeling stage or using reinforcement learning optimization as in RLHF, significantly reducing implementation complexity while improving training stability.", + "bbox": [ + 71, + 717, + 491, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.3 Other Preference Optimization", + "text_level": 1, + "bbox": [ + 71, + 835, + 339, + 851 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition to DPO, several concurrent preference optimization methods [190, 230, 231] have been proposed that offer alternative approaches to RLHF. These methods explore different strategies for optimizing LLMs to align with human preference without RL. Below, we provide a brief introduction to these approaches.", + "bbox": [ + 71, + 854, + 491, + 944 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.3.1 Sequence Likelihood Calibration", + "text_level": 1, + "bbox": [ + 504, + 53, + 784, + 66 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Zhao et al. [230] propose Sequence Likelihood Calibration with Human Feedback (SLiC-HF) to directly align LLMs with human preferences. Specifically, the loss function of SLiC-HF is defined as follows:", + "bbox": [ + 503, + 69, + 921, + 127 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {S L i C - H F}} (\\theta) = \\max (0, \\delta - \\log \\pi_ {\\theta} (y _ {w} | x) + \\log \\pi_ {\\theta} (y _ {l} | x)) \\\\ - \\lambda \\log \\pi_ {\\theta} (y ^ {*} | x), \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 137, + 921, + 172 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the first term is the rank calibration loss with $\\delta$ as a margin hyperparameter, and the second term is the cross-entropy regularization loss with $\\lambda$ as a regularization weight. $y^{*}$ is obtained from either high-quality supervised responses in the SFT dataset or the top-ranked candidate response generated by the SFT model.", + "bbox": [ + 503, + 176, + 923, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.3.2 Rank Responses to Align Human Feedback", + "text_level": 1, + "bbox": [ + 504, + 272, + 862, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Yuan et al. [190] introduce Rank Responses to align Human Feedback (RRHF) for LLMs. RRHF extends pair-wise ranking by considering the list-wise ranking order of multiple responses, thus better utilizing the preference information. For an input prompt $x$ and $N$ candidate responses $\\{y_i\\}_{i=1}^N$ , it optimizes the model to assign higher probabilities to higher-ranked responses via a ranking loss and directly supervises the best response using cross-entropy as follows:", + "bbox": [ + 501, + 287, + 923, + 406 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R R H F}} (\\theta) = \\sum_ {r _ {i} < r _ {j}} \\max \\left(0, \\frac {\\log \\pi_ {\\theta} (y _ {i} | x)}{| | y _ {i} | |} - \\frac {\\log \\pi_ {\\theta} (y _ {j} | x)}{| | y _ {j} | |}\\right) \\\\ - \\lambda \\log \\pi_ {\\theta} \\left(y ^ {*} \\mid x\\right), \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 412, + 921, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $r_i = r_\\phi(x, y_i)$ represents the reward of the response $y_i$ and $y^* = \\arg \\max_{y_i} r_i$ is the response with the highest reward. Although RRHF avoids the need for reinforcement learning in RLHF, it still utilizes a reward model $r_\\phi$ to rank candidate responses based on human preferences.", + "bbox": [ + 503, + 473, + 921, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.3.3 Preference Ranking Optimization", + "text_level": 1, + "bbox": [ + 504, + 554, + 790, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similarly, Song et al. [231] propose Preference Ranking Optimization (PRO) to align LLMs with human preferences by leveraging multiple responses $\\{y_{i}\\}_{i = 1}^{N}$ with the human-annotated order $y_{1} > y_{2} > \\dots >y_{N}$ . The loss function of PRO is defined as follows:", + "bbox": [ + 503, + 571, + 923, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {P R O}} (\\theta) = - \\sum_ {i = 1} ^ {N - 1} \\log \\frac {\\exp \\left(\\frac {1}{\\| y _ {i} \\|} \\log \\pi_ {\\theta} \\left(y _ {i} | x\\right) / \\mathcal {T} _ {i} ^ {i}\\right)}{\\sum_ {j = i} ^ {N} \\exp \\left(\\frac {1}{\\| y _ {j} \\|} \\log \\pi_ {\\theta} \\left(y _ {j} | x\\right) / \\mathcal {T} _ {i} ^ {j}\\right)}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 646, + 923, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the dynamic penalty temperature is defined as $\\mathcal{T}_i^j = 1 / (r_\\phi (x,y^j) - r_\\phi (x,y^i))$ and $\\mathcal{T}_i^i = \\min_{i < j}\\mathcal{T}_i^j$ . This temperature ensures that the probability gap between higher-ranked and lower-ranked responses is adaptively scaled according to their reward differences, thereby stabilizing the optimization process.", + "bbox": [ + 503, + 705, + 921, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 A TAXONOMY OF DPO", + "text_level": 1, + "bbox": [ + 504, + 805, + 720, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce a novel taxonomy that categorizes existing DPO works based on four key dimensions: data strategy, learning framework, constraint mechanism, and model property. As illustrated in Fig. 1, these four dimensions are derived from different components of the DPO loss, providing a systematic framework for understanding the methodological evolution of DPO and highlighting the key distinctions between different variations.", + "bbox": [ + 501, + 825, + 923, + 941 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 911, + 32, + 921, + 42 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1 Data Strategy of DPO", + "text_level": 1, + "bbox": [ + 73, + 51, + 272, + 68 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The data strategy constitutes the foundational pillar of DPO, focusing on how to leverage diverse types of preference data for training LLMs. As shown in Fig. 2, our taxonomy identifies three principal axes of data strategy: quality, feedback, and granularity.", + "bbox": [ + 71, + 73, + 491, + 148 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.1.1 Data Quality", + "text_level": 1, + "bbox": [ + 73, + 162, + 215, + 178 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The quality of preference data is a critical factor in determining the effectiveness of DPO training. High-quality data ensures that LLMs effectively learn to align with human preferences, while low-quality data may introduce noise and bias, leading to suboptimal model performance. We categorize data quality considerations into three key aspects: heterogeneity, distinguishability, and noise.", + "bbox": [ + 71, + 181, + 491, + 285 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(a) Data Heterogeneity. Conventional DPO methods assume uniform human preferences when annotating data, thereby overlooking the diversity among annotators. This assumption often skews the model toward the preferences of the majority while neglecting minority viewpoints, potentially leading to biases and unfair treatment of underrepresented groups. To address this issue, Chidambaram et al. [42] propose EM-DPO, which learns the distribution of different preference types and their corresponding response strategies. Building on this, they introduce the MinMax-DPO algorithm, which selects a strategy by minimizing the maximum regret across subgroups, ensuring a more balanced representation of preferences among all groups. MallowsPO [43] decomposes the implicit rewards in DPO into prompt dispersion and response scaling rewards. It introduces a novel objective function to capture human preferences for diverse responses to the same prompt. GRPO [44] formulates an objective function that minimizes the loss for the worst-case group, thereby ensuring fairness by prioritizing the disadvantaged groups in the optimization process. GDPO [45] models the language generation process as a combination of belief distribution prediction and belief-based response generation. The corresponding GDPO loss function consists of belief calibration loss and belief-conditioned preference alignment loss. The former encourages the model to capture the diversity of beliefs across groups, while the latter ensures that generated responses align with the given belief.", + "bbox": [ + 71, + 286, + 493, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(b) Data Distinguishability. A key limitation of DPO is its inability to account for the distinguishability of preference between responses [46, 50, 51, 56, 57]. In some cases, the preferred response is only marginally better than the dispreferred one, while in others, the dispreferred response contains harmful or misleading content, making it significantly worse. Thus, optimization should focus more on cases with substantial preference differences while reducing the effort spent on minor differences. However, most existing methods treat all samples equally, ignoring this data distinguishability. To address this, ODPO [46] introduces a monotonically increasing offset function, requiring the reward of the preferred response to exceed that of the dispreferred one by a certain margin. This ensures stronger updates for larger preference gaps. Similarly, Ada-DPO [54] introduces an instance-specific nonlinear scaling parameter, assigning larger weights to strong preference pairs and smaller weights to ambiguous ones based on the reward differences, thereby capturing", + "bbox": [ + 71, + 680, + 493, + 944 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7d0b0c1f1f41595c2153dd474b54b2117d70052e28f86633cea08504dba7746a.jpg", + "image_caption": [ + "Fig. 2: An overview of DPO data strategy." + ], + "image_footnote": [], + "bbox": [ + 511, + 55, + 919, + 373 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "different levels of data distinguishability. DPO-rc [48] also incorporates the preference reward difference as a coefficient in the loss function. $\\alpha$ -DPO [49] introduces an adaptive preference distribution to obtain dynamic reward margins based on the distribution difference between the policy and reference models. $\\beta$ -DPO [51] analyzes the optimal $\\beta$ parameter for datasets with different reward margins, which dynamically adjusts $\\beta$ based on batch-level reward differences. They also introduce $\\beta$ -guided data filtering to prioritize valuable training data. Curri-DPO [53] sorts preference pairs by reward differences and trains progressively from large to small differences, enabling curricular learning. Similarly, MPO [47] utilizes a reward model to score responses generated by the SFT model, constructing a preference dataset and partitioning it based on preference differences to learn from simple to complex tasks. sDPO [55] computes reward accuracy for different datasets based on an initial target model and partitions the dataset in descending order of accuracy, allowing the model to first optimize on simpler samples. Ma et al. [58] propose a preference dataset construction method that adjusts update weights based on response accuracy, assigning lower weights when the model demonstrates higher proficiency. Furthermore, fDPO [52] enhances DPO training by filtering out samples where the generated response of the model policy surpasses the preferred dataset response in reward score.", + "bbox": [ + 501, + 412, + 924, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(c) Data Noise. Human-generated preference annotations often contain inconsistencies, errors, or noise, negatively affecting the performance of DPO. Such noisy data can mislead models, impairing their ability to accurately capture true preferences and generalize effectively to unseen data. Im and Li [64] analyze how noisy feedback influences the generalization performance of preference optimization, showing that increased noise results in higher generalization risks. Specifically, standard DPO loss functions can yield biased estimates under noisy conditions. To address this", + "bbox": [ + 503, + 796, + 923, + 941 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 911, + 32, + 921, + 42 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "issue, rDPO [59] proposes to enhance DPO robustness against noisy annotations and improve overall training performance. Zhang et al. [63] introduce a noise-aware strategy leveraging annotator confidence and stability to identify and downweight noisy samples during training. They also propose an adaptive reward margin, emphasizing clean samples to improve learning effectiveness. Complementary to these approaches, PerpCorrect [60] employs a data-driven method to correct noisy annotations directly in the dataset. It trains a proxy language model on both clean and noisy samples, distinguishing noise through perplexity differences to improve dataset quality. To systematically explore noise effects, Gao et al. [65] artificially inject various noise types (e.g., Gaussian noise) into datasets, controlling noise intensity via hyperparameters. Their analysis highlights how noise impacts model alignment, guiding future research towards mitigating such negative effects. To address the vulnerability of DPO in noisy environments, ROPO [61] introduces a regularization term to enhance noise tolerance. Additionally, ROPO employs a robust-guided rejection sampling technique. This technique supplements the dataset with samples that contribute minimally to the loss, thereby improving the overall data quality. Kim et al. [62] propose the SPA framework, using model-generated responses and associated confidence scores to detect noise in annotations. SPA further incorporates smoothing techniques into the loss function to alleviate the noise problem. Finally, Wu et al. [66] categorize noise into two types: point noise (single annotation errors) and pairwise noise (errors between annotated pairs). While DPO naturally handles point noise well, it struggles with pairwise noise. Their proposed Dr. DPO introduces a novel loss function explicitly designed for robustness against both point and pairwise noise.", + "bbox": [ + 76, + 53, + 491, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.1.2 Preference Feedback", + "text_level": 1, + "bbox": [ + 76, + 546, + 274, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Preference feedback refers to the label signals provided by annotators regarding their preferences for different responses. It can be categorized into point-wise, pair-wise, and list-wise feedback. Point-wise feedback evaluates each response independently, assigning a score or labeling it as positive or negative. Pair-wise feedback compares two responses to determine which one is preferred, while list-wise feedback ranks multiple responses.", + "bbox": [ + 76, + 563, + 490, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(a) Point-Wise Feedback. Point-wise feedback is the basic form of feedback. It refers to the type of feedback where individual outputs or samples are evaluated independently, rather than through comparisons with other outputs. This form of feedback is characterized by its simplicity and directness, focusing on the quality or relevance of a single response or item. The predominant methodology in RLHF [35] employs point-wise reward signals generated by reward models to optimize policy models. Similarly, KTO [67] directly maximizes the utility of model generations using loss functions based on prospect theory rather than the log-likelihood of preferences. It requires only a binary signal indicating whether an output is desirable or undesirable for a given input. Furthermore, BCO [68] builds upon the concepts introduced in KTO and explores a new approach to aligning with binary signals. While KTO focuses on optimizing human utility, BCO introduces a binary classifier framework incorporating reward shift and distribution matching that implicitly", + "bbox": [ + 76, + 680, + 491, + 941 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "minimizes the DPO loss. Chen et al. [72] and GPO [73] adopt explicit rewards using Noise Contrastive Alignment (NCA) and General Preference Model (GRM) respectively, and then directly optimize language model policies from point-wise preference data with rewards. However, some methods leverage implicit reward signals to refine model behaviors. To ensure that the learned implicit rewards are comparable to the ground-truth rewards, Cal-DPO [69] introduces a calibration term to the preference optimization objective, which prevents the likelihood of chosen responses from decreasing during training. ULMA [71] unifies human demonstration and point-wise preference data into a single framework and handles positive and negative samples with a hybrid objective function. Unlike them, DRO [211] adopts a simple mean-squared objective to optimize the model policy and value function jointly for a single trajectory. Additionally, AOT [70] casts the distributional preference constraint as an optimal transport problem with a convex cost function. The key idea is to minimize the violation of stochastic dominance using a smooth, convex cost function.", + "bbox": [ + 508, + 53, + 919, + 343 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(b) Pair-Wise Feedback. Pair-wise feedback focuses on comparing pairs of data or actions to determine their relative quality or preference. Building upon the theoretical framework of RLHF, DPO implements this paradigm through the utilization of pair-wise preference data, thereby fitting an implicit reward model. Azar et al. [75] introduces a general theoretical framework to unify existing RLHF and DPO methods. The proposed Identity-Preference Optimization (IPO) directly optimizes policies from preferences without relying on reward modeling or the Bradley-Terry assumption, thereby avoiding overfitting issues observed in DPO. Subsequently, DPO-RK and DPO-R [76] integrate the Rao-Kupper and Davidson models into the DPO training objective respectively, thereby extending the capabilities of DPO by explicitly modeling ties in pairwise comparisons. BMC [77] further addresses a key limitation of the weak correlation between winning and losing responses in pairwise data. Specifically, BMC uses \"Bridging\" to enhance the correlation between winning and losing responses by increasing the consistency and informativeness of pairwise preference signals. However, previous attempts for aligning LLMs primarily focus on optimizing the model's output preferences given an instruction, which struggles to effectively perceive the fine-grained constraints within complex instructions. Thus IOPO [78] extends traditional alignment methods by considering both input and output preferences to better understand the constraints within the instructions. As current methods rely heavily on paired preference data (i.e., explicitly labeled preferred vs. dispreferred examples), they can be limiting in scenarios where such paired data is unavailable or insufficient. SAPO [80] addresses this issue based on the concept of self-play, which enhances data exploration and exploitation by automatically generating negative samples and integrating off-policy learning. Furthermore, PMPO [79] extends the EM algorithm to incorporate both preferred and dispreferred outcomes. By introducing the probability distribution of dis-preferred outcomes, PMPO can optimize using both types of samples, even when only negative feedback is available. Similarly, D2O [81] avoids harmful information by maximizing the discrepancy between the generated responses and the negative samples. NPO [82]", + "bbox": [ + 508, + 345, + 919, + 941 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 911, + 32, + 921, + 42 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and SimNPO [83] achieve the goal of forgetting the negative impact by regulating the model's prediction probabilities on negative datasets to be as minimal as possible, where SimNPO further eliminates the reference model bias issue inherent in NPO.", + "bbox": [ + 76, + 53, + 488, + 125 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(c) List-Wise Feedback. List-wise feedback refers to the type of feedback where multiple outputs or responses generated by the model for a given input are evaluated collectively as a list. This approach considers the relative ranking or ordering among the outputs, rather than focusing on individual outputs in isolation. Panacea [84] reframes alignment as a Multi-Dimensional Preference Optimization (MDPO) problem and introduces a method that aims to learn the entire Pareto front to accommodate diverse user preferences. In short, Panacea is designed to adapt a single model to list-wise preferences in a Pareto-optimal manner. LiPO [85] and LIRE [86] also treat LM alignment as a list-wise ranking problem, drawing on the rich literature of Learning-To-Rank (LTR). Specifically, LiPO introduces a specific method LiPO-λ, which leverages a list-wise ranking objective that weights each preference pair based on the difference in ranking metrics; while LIRE optimizes the response probability by calculating the exponential probability distribution and uses the reward model to directly guide the optimization process. To better capture the relative proximity within ordinal multiple responses, OPO [87] utilizes the Normalized Discounted Cumulative Gain (NDCG), a widely used ranking metric, to optimize the model's generation probability to match the permutation of responses based on these labels. Similarly, DRPO [88] leverages NDCG as a key metric to optimize the ranking of model outputs. However, DRPO incorporates novel elements like diffNDCG and Adaptive Rank Policy Score to dynamically adjust the score margins between preferred and non-preferred responses based on their ranking positions. mDPO [232] extends preference optimization to multi-sample comparisons and introduces a framework that evaluates and optimizes the collective properties of sample groups. It not only addresses the limitations of single pair-wise methods but also provides a more robust optimization framework, especially for characteristics like diversity and bias. Furthermore, RPO [90] introduces a contrastive weighting mechanism that constructs a contrast matrix within each mini-batch to compare preferred and less-preferred responses across prompts. The weights of these comparisons are dynamically adjusted based on the semantic similarity between prompts. Additionally, TODO [91] integrates a tie ranking system into list-wise preference modeling, significantly improving the capture of nuances of human preferences, especially in the presence of noisy or inconsistent labels and frequent ties.", + "bbox": [ + 76, + 125, + 490, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.1.3 Preference Granularity", + "text_level": 1, + "bbox": [ + 76, + 794, + 284, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Preference granularity refers to the granularity of preference labels, which determines the level at which preferences are assigned to data. It can be categorized into token-level, step-level, sentence-level, and turn-level granularity, ranging from fine-grained focus on individual tokens to broader preferences over entire interaction turns.", + "bbox": [ + 76, + 811, + 488, + 897 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(a) Token-Level Granularity. Token-level alignment operates at the character/subword unit of text generation, providing the finest-grained control over model outputs", + "bbox": [ + 76, + 898, + 488, + 941 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Theoretically, Rafailov et al. [92] demonstrate that DPO can represent any dense reward function by reparameterizing it as an optimal advantage function, which allows DPO to optimize policies in the token-level MDP effectively TDPO [93] refines the alignment process from the sentence level to the token level and introduces forward KL divergence constraints. TDPO utilizes the Bradley-Terry model to convert sentence-level preference comparisons into a token-level reward system, which allows the model to dynamically adjust its strategy at each token generation step. Furthermore, TIS-DPO[94] estimates the importance weights of tokens based on the differences in prediction probabilities from contrastive LLMs, performing token-level importance sampling on existing data to approximate optimal distribution by assigning weights to each token based on its reward. Moreover, $\\mathrm{D}^2\\mathrm{PO}$ [99] proposes a temporal decay mechanism that dynamically adjusts the contribution of each token-level reward based on its position in the sequences. Unlike these, SparsePO [95] directly learns sparse masks during the training process and controls which tokens are more important for preferences through the sparsity of the masks, thereby achieving dynamic optimization. RTO [96] and SePO [97] first learn a token-level reward function from preference data using DPO, and then RTO optimizes PPO based on this reward signal, while SePO selects key tokens through the estimated reward function. To tackle the need for large-scale annotated data in training, EPO [98] proposes a hierarchical framework that decomposes complex tasks into manageable subgoals using separate LLMs for subgoal prediction and low-level action generation, leveraging environment feedback to automatically generate reward signals and preference data for aligning LLMs.", + "bbox": [ + 506, + 53, + 919, + 518 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To conclude, token-level granularity optimizes models at individual token positions to maximize expected objectives, preserving semantic precision and capturing local syntactic dependencies. However, it increases computational complexity, as processing numerous tokens extends training time, and its sensitivity to noise means errors in a single token can affect the entire sequence. Thus, careful loss function design and regularization are essential for stability.", + "bbox": [ + 506, + 520, + 921, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(b) Step-level Granularity. Step-level granularity focuses on the intermediate steps or stages in a process, particularly effective for complex problem-solving tasks requiring multiple intermediate steps. Step-DPO [100] and SCDPO [101] treat individual reasoning steps as the basic units for preference optimization, where preference pairs of correct and incorrect steps are generated using LLMs. Furthermore, CPO [102] and MCTS-DPO [103] first utilize more powerful inference structures to generate multiple candidate thoughts at each reasoning step following the Tree-of-Thought (ToT) and Monte Carlo Tree Search (MCTS) respectively, and construct preference pairs based on the selected and unselected intermediate steps. Then they finetune LLMs to generate reasoning steps preferred by ToT during inference using DPO. TPO [104] proposes a preference learning algorithm specifically designed for preference trees that have multiple branches and multi-step responses, and introduces the adaptive step reward mechanism to address the issue of small reward margins caused by shared subtrajectories. It adjusts the reward values for each step based on semantic similarity, helping the model better distinguish", + "bbox": [ + 506, + 636, + 921, + 941 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 911, + 32, + 921, + 42 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "between preference pairs. RDPO [105] extends traditional preference datasets to incorporate a rationale field, which explains why a particular response is preferred. RDPO introduces rationale information into the DPO loss function by maximizing the likelihood of both the preference and the rationale, which allows the model to better understand the logic behind preferences during training. To address the challenges of sparse rewards and training instability, DAPO [106] uses a critic function to generate dense signals for policy optimization and trains the actor and critic independently to avoid instability.", + "bbox": [ + 71, + 53, + 491, + 213 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To conclude, step-level alignment demonstrates unique advantages in multi-step reasoning tasks by decomposing holistic preferences into intermediate decision points. The primary strength of step-level granularity lies in its capacity to decompose complex objectives into verifiable subgoals, enhancing both interpretability and robustness. For instance, in mathematical reasoning, LLMs can receive feedback on equation derivation steps before final answers, reducing error propagation. However, this granularity still have two key challenges: first, the need for precise step segmentation, which may require domain-specific heuristics or auxiliary models to delineate reasoning boundaries; second, the risk of local optima, where over-optimization of individual steps degrades global coherence.", + "bbox": [ + 71, + 214, + 491, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(c) Sentence-level Granularity. Sentence-level granularity aligns preferences at the complete utterance level, balancing fine-grained control and computational efficiency. This granularity, represented by the original DPO framework, operates on full response sequences as atomic units for preference comparison. MAPO [107] uses a well-trained translation model to calculate alignment scores between answers in nondominant and dominant languages and then employs preference optimization methods to enhance reasoning consistency. EURUS [108] structures each instruction as a preference tree, containing pairs of correct and incorrect actions to facilitate preference learning. Similarly, IRPO [109] focuses on improving the reasoning capabilities of LLMs through an iterative preference optimization on constructed preference pairs such that the winning response has a higher reward than the losing response. FACTALIGN [110] proposes a fine-grained, sentence-level alignment algorithm called fKTO, which extends the KTO method to leverage fine-grained factuality assessments at the sentence level.", + "bbox": [ + 71, + 417, + 491, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To conclude, the key strength of sentence-level granularity lies in its capacity to preserve holistic semantics while maintaining tractable optimization complexity. Nevertheless, we must carefully consider task requirements. While suitable for short-form generation and classification tasks, sentence-level methods may insufficiently capture fine-grained stylistic nuances or long-range dependencies critical in generation and reasoning domains.", + "bbox": [ + 71, + 694, + 491, + 811 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(d) Turn-level Granularity. Turn-level granularity focuses on the optimization of model behavior at the level of conversational turns, which is particularly relevant for dialogue systems and interactive agents. This granularity level treats each turn of a conversation as a unit for preference alignment, allowing the LLMs to receive feedback on their responses within the context of a single turn. M-DPO [111] introduces a multi-turn direct preference learning framework to enhance the mathematical reasoning capabilities of LLMs when", + "bbox": [ + 71, + 811, + 491, + 941 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "integrated with external tools. It leverages feedback from code interpreters and optimizes trajectory-level preferences using signals generated by the Bradley-Terry model to improve model performance in multi-turn reasoning tasks. ETO [112] presents a novel trial-and-error learning method that optimizes LLM agents' policies by contrasting successful and failed trajectories that contain multi-turn interaction. To address the challenges of coarse granularity and training noise in previous methods, SDPO [113] optimizes specific key segments within interactions to improve multi-turn dialogues while minimizing training noise. Specifically, it extracts key segments from the positive sessions that contribute to higher goal and relationship scores and pairs them with corresponding segments from the negative sessions to calculate an adapted DPO loss. Similarly, AgentQ [114] combines MCTS with self-critique mechanisms to provide process-level supervision by ranking actions, and then iterative fine-tuning using DPO. This approach enables LLMs to effectively learn from both successful and unsuccessful trajectories, enhancing their generalization and decision-making capabilities in complex, multi-turn reasoning tasks within interactive environments. DMPO [115] enhances the existing DPO method by replacing the policy constraint with a State-Action Occupancy Measure (SAOM) constraint and incorporating length normalization into the Bradley-Terry model, effectively addressing challenges in multi-turn scenarios. Compared to traditional policy constraints, SAOM constraints better guide the agent to select actions that align with expert trajectories, especially in unexplored states, thereby reducing compounding errors.", + "bbox": [ + 501, + 53, + 924, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To conclude, turn-level alignment offers critical advantages for interactive systems by optimizing contextually grounded responses while preserving conversational flow. However, in multi-turn dialogue tasks, the turn-level granularity may introduce additional training noise. For example, some correct turns in negative samples may be mistakenly treated as incorrect turns in the loss calculation. Additionally, since each turn needs to be processed independently, this can lead to reduced training efficiency.", + "bbox": [ + 503, + 489, + 926, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3.2 Learning Framework of DPO", + "text_level": 1, + "bbox": [ + 504, + 642, + 756, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The learning framework of DPO focuses on how the language model policy learns from preference data. In this section, we present an overview of the learning framework in DPO, as shown in Fig. 3, which encompasses the learning paradigm and the learning objectives.", + "bbox": [ + 503, + 661, + 923, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3.2.1 Learning Paradigm", + "text_level": 1, + "bbox": [ + 504, + 750, + 692, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The learning paradigm in DPO determines how preference data is acquired during model training and falls into three distinct categories: offline learning, where the model learns from pre-collected preference datasets; online Learning, where the model updates based on newly generated data; and active Learning, where the model selectively queries annotators obtain preference data.", + "bbox": [ + 501, + 766, + 923, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(a) Offline Learning. The original DPO framework [74] itself is an offline learning paradigm, where the model learns from a static, pre-collected dataset of preference pairs. Recent research has explored different approaches to merging preference optimization and supervised fine-tuning", + "bbox": [ + 503, + 869, + 924, + 944 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 911, + 32, + 921, + 42 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ab1cb06bdd578e7bee29a0deff07d4285154eb2afd39c5194af16ae72fc055ce.jpg", + "image_caption": [ + "Fig. 3: An overview of DPO learning framework." + ], + "image_footnote": [], + "bbox": [ + 81, + 55, + 483, + 349 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "into a single training phase [190]. CPO [116] incorporates a behavior cloning regularizer through KL divergence minimization between the model and preferred data distribution, which effectively combines into adding a negative log-likelihood term on preferred data alongside the contrastive preference loss. Taking a more direct approach, ORPO [117] proposes a monolithic framework that directly augments the standard negative log-likelihood loss with an odds ratio term comparing chosen and rejected responses, eliminating the need for a separate reference policy while preserving SFT's domain adaptation capabilities. ULMA [71] proposes a hybrid method that applies standard SFT loss on positive samples while using a ranking-based DPO loss on negative samples. PAFT [118] introduces a parallel training paradigm where SFT and preference alignment are performed concurrently on the same pre-trained model and then merged using parameter fusion techniques, avoiding the sequential pipeline that can lead to catastrophic forgetting.", + "bbox": [ + 71, + 383, + 491, + 648 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Several advances explore curriculum learning strategies to enhance DPO performance and training efficiency. CurriDPO [53] introduces curriculum learning by ordering multiple preference pairs from easy to hard based on the rating difference between chosen and rejected responses, where pairs with larger rating gaps are presented first, followed by progressively more challenging pairs with smaller rating differences. sDPO [55] implements curriculum learning by partitioning preference datasets into sequential chunks measured by reward accuracy and applying them incrementally.", + "bbox": [ + 71, + 648, + 491, + 796 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To avoid substantial computational and data annotation costs for preference alignment, fine-tuning-free alignment methods have gained popularity. Linear Alignment [119] works by directly estimating the optimal policy through a one-step update to the output distribution during inference without requiring parameter tuning or feedback data. ICDPO [120] reinterprets DPO's reward-policy relationship to create a fine-tuning-free alignment method that harnesses in-context learning, treating models before and after demonstration exposure as amateur and expert policies, respectively,", + "bbox": [ + 71, + 796, + 491, + 944 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "then computing their log probability ratio to score and rank candidate responses.", + "bbox": [ + 503, + 53, + 921, + 82 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "(b) Online Learning. DPO faces significant limitations when relying solely on static, pre-collected preference datasets. These datasets, generated by different models, cause a distribution shift that leads to ineffective off-policy learning as the model evolves [145, 152]. By contrast, online DPO employs an iterative framework that continuously updates the policy with real-time feedback, ensuring on-policy learning and reducing misalignment [143, 144, 233].", + "bbox": [ + 501, + 82, + 923, + 198 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "As online DPO progresses, researchers have introduced more flexible frameworks to tackle key challenges. For instance, Yuan et al. [123] proposed a self-rewarding language model: the model generates prompts and responses, then serves as its own judge via LLM-as-a-Judge prompting, scoring on a 5-point scale. OAIF [121] uses an LLM as an online annotator for real-time feedback, and OFSDPO [122] addresses catastrophic forgetting by using two Low-Rank Adaptive (LoRA) modules with different optimization speeds. BPO [124] constructs a dynamic trust region around the behavior LLM, adjusting it as preference data is collected, unlike methods that rely on fixed reference models. Furthermore, researchers have refined sampling strategies for online DPO. RSO [126] and RS-DPO [125] employ rejection sampling based on reward gaps. ROPO [61] recovers useful information from discarded queries via robustness-guided rejection sampling. Shi et al. [127] introduced DPO-Mix-R and DPO-Mix-P, demonstrating faster convergence by mixing online samplers with uniform samplers. OPTUNE [128] selectively regenerates responses with low reward scores while reusing high-reward responses. Iterative RPO [109] and DPO-ST [129] enhance CoT reasoning by selecting correct and incorrect answers to form preference pairs at each iteration. Xie et al. [103] used MCTS to collect preference data during training. Researchers have also explored advanced optimization techniques. APO [130] incorporates momentum-based acceleration, using an extrapolation step between the current and previous policies to update the policy. Xiong et al. [131] proposed a two-agent, non-symmetric online DPO framework with a main agent for optimal policy learning and an enhancer agent for exploration. COMAL [132] formulates alignment as a two-player zero-sum game, updating its policy toward a regularized Nash equilibrium in each iteration. PCO [133] iteratively trains the model on preference data with pairwise cringe Loss.", + "bbox": [ + 501, + 198, + 923, + 709 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Recent efforts push for greater autonomy by letting models generate their own feedback [62]. SeRA [134] introduces a self-reviewed preference bootstrapping method, using an implicit reward margin to select informative pairs, and employs an ensemble reward approach across iterations. CREAM [135] mitigates self-improving biases by applying a consistency regularization on the preference rankings of consecutive iterations. D2PO [136] combines human-labeled gold data with concurrently updated, discriminator-labeled data. DLMA [137] uses contrastive prompts to compute self-reward scores via log ratio differences, then integrates these scores directly into the DPO objective. Addressing exploration and uncertainty in online DPO has also been a focus [234]. XPO [138] encourages exploration by adding a bonus for responses outside the initial policy's support, and SELM [139] uses an optimism term in reward fitting to", + "bbox": [ + 501, + 709, + 923, + 944 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9", + "bbox": [ + 911, + 32, + 921, + 42 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "actively seek high-reward responses. ETO [112] alternates exploration and training phases to collect failure trajectories, while VPO [140] applies optimism by regularizing the reward model to favor higher-value responses. Xiong et al. [111] extended DPO from single-turn to multi-turn tasks, balancing KL-regularized and non-regularized objectives, and COPO [141] incorporates a count-based bonus to encourage novel responses with low visitation counts.", + "bbox": [ + 71, + 53, + 491, + 167 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Finally, a growing body of work aims to merge online and offline techniques. HyPO [142] uses offline preference data for DPO training while regularizing via online data. MPO [47] combines the strengths of DPO and PPO in a two-stage process: it first trains DPO on an easier dataset, then uses this model as a reference for PPO training on more challenging samples.", + "bbox": [ + 71, + 169, + 491, + 271 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "(c) Active Learning. Active learning in DPO is a strategic approach that aims to reduce the annotation cost and improve sample efficiency by selectively querying annotators for the most informative preference examples. Unlike offline learning that uses a fixed dataset or online learning that generates new data continuously, active learning intelligently selects which data points should be labeled based on model uncertainty or other informativeness criteria.", + "bbox": [ + 71, + 272, + 491, + 387 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Muldrew et al. [146] introduced APL, an iterative data acquisition and fine-tuning loop in which batches of prompt/completion pairs are strategically selected using acquisition functions: a predictive entropy-based approach to measure model uncertainty for prompts and a preference certainty measure based on the implicit Bradley-Terry model for completion pairs in DPO. Unlike two-step selection processes in APL that separately select uncertain input prompts and corresponding completions, divAPO [147] integrates both stages into a single selection phase. divAPO maximizes the preference model certainty by simultaneously evaluating the informativeness of input prompts and completion pairs, while also considering the data distribution of the input prompts. Ji et al. [148] proposed ADPO, which selectively queries human preferences only for responses where the model exhibits high uncertainty while using pseudo-labels for confident cases. Das et al. [149] also employed active learning on RLHF, which actively selects the context-action pairs that maximize exploration and minimize uncertainty in the reward model.", + "bbox": [ + 76, + 388, + 493, + 680 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "3.2.2 Learning Objective", + "text_level": 1, + "bbox": [ + 73, + 691, + 261, + 705 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "In what follows, we present the learning objective in DPO, which determines how the model policy is optimized based on preference data. We first discuss multi-objective learning in DPO, which aims to optimize multiple objectives simultaneously. Then, we introduce self-play learning, which leverages self-generated data for preference alignment.", + "bbox": [ + 71, + 708, + 491, + 796 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "(a) Multi-Objective Learning. Multi-objective learning in DPO addresses the challenge of simultaneously optimizing the language model for multiple, potentially competing preference dimensions, such as helpfulness, harmlessness, and truthfulness. This approach aims to find a balanced policy that satisfies multiple human values rather than optimizing for a single objective, which more closely mirrors the complexity of real-world human preferences.", + "bbox": [ + 71, + 797, + 491, + 912 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "MODPO [150] achieves the sequential optimization of multiple preference objectives by incorporating language", + "bbox": [ + 71, + 912, + 491, + 943 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "modeling directly into reward modeling, using a margin-based loss to maintain performance on previously optimized dimensions. SPO [151] takes a similar iterative constrained optimization approach, optimizing each preference dimension while preventing the degradation of prior alignments through regularization terms. MOSLIM [152] takes a different approach by introducing a multi-head classification reward model that assigns different preference dimensions to separate classification heads, enabling simultaneous optimization of multiple preferences without requiring multiple reward or policy models. HPO [153] incorporates auxiliary objectives through offline RL, where the model uses a weighted maximum likelihood objective that combines a preference alignment term with an advantage-weighted term for maximizing arbitrary auxiliary rewards like readability and safety. CPO [154] introduces explicit preference tokens during training that specify desired scores for different objectives, transforming the multi-objective optimization into a conditional optimization problem. DRDO [155] simultaneously models rewards and preferences through a combination of reward distillation and a contrastive log-unlikelihood term in its loss function.", + "bbox": [ + 501, + 53, + 924, + 372 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "(b) Self-Play Learning. Self-play learning in DPO represents an approach where the language model interacts with itself or its previous iterations to generate its own preference data for training, reducing or eliminating the need for human annotations [139, 164]. This method enables continuous self-improvement by leveraging the model's own judgment capabilities to identify and learn from better responses, creating a form of autonomous preference learning.", + "bbox": [ + 503, + 373, + 926, + 489 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "SPIN [156] involves a self-play mechanism where the LLM generates synthetic data from its prior iterations, then fine-tunes itself to distinguish these self-generated responses from those of human-annotated data. The method resembles a two-player game, where the model's current iteration tries to improve its responses to better match the target distribution, while the previous iteration attempts to generate responses as close to human data as possible. SPPO [157] treats LLM alignment as a constant-sum two-player game and iteratively refines itself by competing against its previous iteration. Instead of maintaining two competing policies or a reward model, SPO [158] uses a single policy to sample multiple trajectories and uses the proportion of wins in pairwise comparisons as the reward signal. BoNBoN [159] Alignment likewise relies on sampling responses from a base model, but it selects the best ones among n candidates and fine-tunes itself to approximate that best-of-n distribution.", + "bbox": [ + 503, + 489, + 924, + 737 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Some works approach the alignment problem by leveraging Nash equilibrium [132]. Nash-MD [160] learns a preference model from pairwise human feedback and then computes a Nash equilibrium policy that consistently produces preferred responses. Its self-play approach updates the policy by having it compete against itself (or a slight variant of itself) under the learned preference model, which measures how often one response is preferred to another. DNO [161] extends this concept by implementing a batched on-policy algorithm where the current policy generates multiple outputs that are compared both against each other and against a teacher model's outputs. IPO-MD [162] combines the strengths of IPO and Nash-MD, where the model generates data using a mixture policy between the online and reference", + "bbox": [ + 503, + 738, + 924, + 941 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10", + "bbox": [ + 906, + 32, + 923, + 42 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "policies, and uses a preference model to annotate pairs of generations, making the optimization equivalent to finding a Nash equilibrium through self-play. SRPO [163] modifies Nash-MD by introducing a self-improvement policy that refines model outputs through iterative revisions, enabling offline optimization without a learned reward function.", + "bbox": [ + 71, + 53, + 491, + 141 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "3.3 Constraint Mechanism of DPO", + "text_level": 1, + "bbox": [ + 73, + 161, + 341, + 175 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "The constraint mechanism of DPO derives from its reformulation of RLHF, which includes a KL divergence constraint between the current policy and a reference policy. As shown in Fig. 4, we re-examine the constraint mechanism of DPO from the perspective of the reference model and different divergence constraints. We also explore various DPO variants with different safety constraints.", + "bbox": [ + 71, + 180, + 491, + 282 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "3.3.1 Reference Model", + "text_level": 1, + "bbox": [ + 73, + 297, + 250, + 311 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "The reference model in DPO functions as an anchor to ensure policy updates remain within a controlled range, preventing excessive deviation from initial behaviors. Typically, the reference model is initialized using the SFT model that serves as the starting point for preference optimization. The choice of reference model significantly impacts optimization dynamics. A static reference model ensures stable training but may limit adaptability. In the following subsections, we introduce two advanced approaches: reference-free DPO eliminates reliance on the reference model, while dynamic-reference DPO employs an evolving reference model.", + "bbox": [ + 71, + 314, + 491, + 474 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) Reference-Free DPO. To reduce the computational and memory costs associated with a reference model, many algorithms have explored training modes that do not require loading the reference model. Xu et al. [116] replaces the reference model with a uniform prior distribution, adding an SFT loss term on preferred data to maintain consistency with the desired behavior. ORPO [117] integrates an odds ratio-based penalty with traditional SFT loss, increasing the probability of preferred responses while decreasing undesirable ones, thereby enabling single-stage training without a separate reference model. SimPO [166] directly uses the average log probability as implicit rewards. This removes the requirement for a separate reference model, significantly improving computational and memory efficiency. SimPER [167] also directly optimizes reverse perplexity for preferred versus rejected responses, creating a preference optimization approach that does not require a separate reference model, thus simplifying training. Despite these advancements, [168] argue that a reference model remains crucial. They compared two reference-free variants using posterior probabilities and likelihood functions as rewards, respectively, and found the original DPO consistently outperformed both. Their results indicate that a strong, well-aligned reference policy can significantly enhance DPO performance.", + "(b) Dynamic-Reference DPO. Offline DPO methods often suffer from reward over-optimization, meaning that as the trained model deviates from the reference model, the quality of generated samples tends to degrade. To address this issue, Gorbatovski et al. [165] proposed dynamically updating the reference model using the current model parameters during training, preventing excessive divergence and maintaining high-quality outputs. Curri-DPO [53] and sDPO [55] adopt" + ], + "bbox": [ + 71, + 476, + 491, + 944 + ], + "page_idx": 10 + }, + { + "type": "image", + "img_path": "images/cddebe4de78a02102cffc5e93cf429138280b5deac316fd35c18e11122d7aa8e.jpg", + "image_caption": [ + "Fig. 4: An overview of DPO constraint mechanism." + ], + "image_footnote": [], + "bbox": [ + 511, + 53, + 916, + 329 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "curriculum learning by sorting data samples from simpler to more complex based on predefined metrics. At each training iteration, the model from the previous step serves as the updated reference model to provide constraints, facilitating progressive learning. Similarly, MPO [47] partitions datasets according to task difficulty, employing a two-stage training procedure. The model trained in the initial stage serves as the reference for the subsequent stage. Additionally, M-DPO [89] compares the performance of a fixed reference model versus a dynamic reference model, finding that the latter yields superior results.", + "bbox": [ + 503, + 357, + 924, + 518 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "3.3.2 Divergence Constraint", + "text_level": 1, + "bbox": [ + 504, + 531, + 718, + 545 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Divergence constraints in DPO play a crucial role in constraining model optimization, balancing alignment performance and model stability. In the following subsections, we introduce two modifications to the divergence constraint: one for enhancing diversity and the other for improving generalization.", + "bbox": [ + 503, + 547, + 924, + 635 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) Diversity. Standard DPO typically uses reverse KL divergence equivalent to RLHF. However, the mode-seeking nature of reverse KL divergence reduces the diversity of the generated outputs. To overcome this limitation, f-DPO [169] explores various divergences, including forward KL divergence, reverse KL divergence, Jensen-Shannon divergence, and $\\alpha$ -divergence, to achieve a better trade-off between alignment performance and diversity. Slocum et al. [170] further proposes splitting the KL divergence term into entropy and cross-entropy terms. This decoupling allows independent control of generation diversity and closeness to the reference model, preserving output diversity without degrading overall model quality.", + "(b) Generalization. Over-optimization in DPO can negatively impact generalization, causing reduced performance on inputs outside the training distribution. To mitigate this, Huang et al. [178] introduce $\\chi^2$ -divergence as a more aggressive form of regularization compared to KL divergence, alleviating the over-optimization problem. DPO-Kernels [171] employs data-driven methods to select optimal kernel-divergence pairs dynamically, improving task adaptability" + ], + "bbox": [ + 503, + 636, + 926, + 944 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11", + "bbox": [ + 906, + 32, + 919, + 42 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "and robustness. FlipGuard [172] introduces a customized reward characterization to monitor model performance. If performance drops relative to earlier versions, FlipGuard constrains the model's updates to ensure alignment with previous stable behavior. FPO [173] leverages the feature-level constraints using Sparse Autoencoders (SAEs) to improve computational efficiency and training stability. SPO [176] integrates a natural preference loss with a KL divergence-based regularization term computed over the entire model output distribution. By adjusting this divergence term, SPO prevents unwanted shifts beyond the preference dataset, ensuring stable alignment. EXO [175] argues that minimizing the forward KL divergence in DPO introduces bias when approximating the optimal policy. They establish a generalized alignment objective and reveal the equivalence between maximizing KL regularization rewards and minimizing the reverse KL divergence relative to the optimal policy. QDPO [177] utilizes divergence between the quantized model and the full-precision model for preference optimization, effectively addressing the token-flipping issue. Token-flipping refers to the phenomenon where quantization errors skew token distributions, leading to incorrect token selection. GPO [174] constructs a framework that unifies different DPO-related algorithms through theoretical derivations, enabling a deeper understanding of the regularization mechanisms in the DPO family of algorithms.", + "bbox": [ + 71, + 53, + 491, + 433 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "3.3.3 Safety Constraint", + "text_level": 1, + "bbox": [ + 73, + 446, + 250, + 460 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Safety constraints in DPO aim to prevent LLMs from generating harmful, biased, or unethical outputs. However, traditional alignment algorithms often fail to address safety concerns. To enhance the safety alignment, recent studies have introduced several specialized mechanisms based on DPO. SafeDPO [179] introduces a streamlined approach for safety alignment by implicitly optimizing safety objectives within a single stage of policy learning. SACPO [180] addresses safety constraints by explicitly formulating language model alignment as a constrained optimization problem, using DPO to optimize the model under safety constraints. Zhang et al. [184] propose creating a backtracking preference dataset that identifies and reverses unsafe outputs, enhancing the safety and robustness of the model. C-DPO [181] integrates dual gradient descent into DPO to balance safety and utility efficiently. This approach achieves a robust trade-off between helpfulness and harmlessness, offering explicit safety guarantees. ADPO [182] introduces adversarial techniques into DPO. It specifically trains models to reduce the probability of unsafe outputs by deliberately generating harmful responses using controlled toxic tokens. Finally, Lee et al. [183] explore the internal mechanisms through which DPO reduces harmful outputs. Their findings suggest that DPO does not remove harmful behaviors learned during pretraining but instead teaches models to bypass or suppress these behaviors. This insight helps explain certain safety vulnerabilities like jailbreaks.", + "bbox": [ + 71, + 465, + 491, + 859 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "3.4 Model Property of DPO", + "text_level": 1, + "bbox": [ + 71, + 878, + 285, + 893 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "DPO has shown great promise in aligning LLMs with human preferences by directly optimizing model outputs based on preference data. During this process, the underlying models", + "bbox": [ + 71, + 898, + 491, + 944 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/e5c5a6a0d780ea4b5c9a8a90db2723f6fdb6c09e14347e19016d55dcced76086.jpg", + "image_caption": [ + "Fig. 5: An overview of DPO model property." + ], + "image_footnote": [], + "bbox": [ + 514, + 55, + 916, + 327 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "exhibit certain properties that are crucial for understanding their behavior and effectiveness. These properties can be broadly categorized into two aspects: the generation property and the optimization property, as shown in Fig. 5. In the following sections, we explore these two properties in more detail, analyzing their implications for model alignment.", + "bbox": [ + 503, + 356, + 923, + 446 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "3.4.1 Generation Property", + "text_level": 1, + "bbox": [ + 504, + 458, + 702, + 473 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "The generation property of DPO primarily concerns issues related to distribution shifts and length biases. DPO is sensitive to distribution shifts between the base model outputs and the preference data, which may reduce diversity and generalization. Additionally, DPO has a tendency to favor longer responses, a phenomenon known as morbidity, which can negatively impact performance and user experience.", + "bbox": [ + 501, + 474, + 923, + 578 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "(a) Distribution Shift. In RLHF, the reward model is trained on a static set of preference data collected offline. During fine-tuning, the generated responses often differ from this original training data, resulting in a distribution shift. This shift can cause inaccurate reward predictions and lead to over-optimization. The implicit reward model in DPO also suffers from this distribution shift issue. Moreover, Lin et al. [188] have shown that the implicit reward model in DPO performs poorly on Out-Of-Distribution (OOD) data compared to explicit reward models. Experimental results indicate that DPO can transfer probability mass to the highreward response regions covered by the preference data, but it may also cause the distribution of responses generated by the model to deviate significantly from that of the reference policy, resulting in responses that do not meet expectations [189]. To address these problems, many researchers are now exploring online DPO approaches [109, 121, 122, 125], aiming to mitigate OOD by continuously updating preference data during training.", + "bbox": [ + 503, + 578, + 923, + 853 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Existing DPO methods also face significant limitations due to their dependence on specific training tasks. Their optimal solutions lack robustness when applied to OOD tasks. Thus, SRPO [163] reframes alignment as a self-improvement process, which optimizes a self-improvement policy and a generative policy using a min-max objective, ensuring", + "bbox": [ + 501, + 854, + 924, + 944 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12", + "bbox": [ + 906, + 32, + 921, + 42 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "robustness by making the solution independent of training tasks. Zhang et al. [139] also identify notable issues in DPO when handling OOD tasks. First, DPO tends to overly favor novel content it has not seen during training. Second, it easily gets stuck in local optima, limiting exploration. To address these problems, they propose Self-Exploring Language Models (SELM), incorporating an optimism term to encourage broader exploration of new responses.", + "bbox": [ + 71, + 53, + 491, + 169 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Another significant challenge of DPO is preference drift, where human preferences evolve, changing data distributions over time. Traditional DPO algorithms typically overlook such temporal shifts, mistakenly interpreting them as noise. To address this, NS-DPO [185] propose to assign higher weights to recent data, allowing models to better adjust to evolving preferences.", + "bbox": [ + 71, + 169, + 491, + 272 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "(b) Length Bias. Length bias in DPO refers to the tendency of model-generated outputs to become excessively long during training. This issue is similar to the length bias observed in RLHF [197] and is particularly pronounced in DPO. Length bias affects response quality and overall model performance. To mitigate this issue, researchers have developed several solutions, which can be categorized into three main approaches: length regularization, length normalization, and length sampling.", + "bbox": [ + 71, + 272, + 491, + 404 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Length regularization is a common approach to controlling length bias in DPO. By introducing regularization terms into the objective function, the model can constrain response length and reduce morbidity, thereby alleviating the length bias problem. R-DPO [191] introduces a length-based penalty term to the DPO objective function, explicitly discouraging morbidity. $\\mathrm{D}^2\\mathrm{PO}$ [99] introduces a dynamic weighting mechanism by incorporating a temporal decay factor. Unlike previous methods that apply uniform reward contributions across sequences, $\\mathrm{D}^2\\mathrm{PO}$ adjusts the influence of each reward based on its position in the response. Higher weights are assigned to rewards associated with earlier tokens, as they are more critical for model alignment, while later rewards gradually receive lower weights. This adaptive approach prevents overfitting to less relevant tokens, thereby addressing length bias in DPO.", + "bbox": [ + 71, + 404, + 491, + 636 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Length normalization aims to eliminate the loss bias caused by response length differences, allowing the model to evaluate texts of varying lengths more fairly. This approach prevents the model from developing an unreasonable preference for either long or short responses [198]. RRHF [190] and SimPO [166] first propose to apply length normalization to responses, ensuring that the loss remains unaffected by response length. LN-DPO [194] further integrates SimPO-like length normalization into DPO, demonstrating that this approach enhances response quality while mitigating morbidity. LD-DPO [195] achieves length desensitization by reparameterizing the likelihood in DPO. Specifically, it decomposes the likelihood of the longer response in a preference pair into the product of the likelihood of the public-length portion and the likelihood of the excessive portion. It then introduces a hyperparameter to mitigate the morbidity preference. This adjustment smooths the relationship between likelihood and response length, reducing its impact on optimization. For multi-turn dialogue tasks, DMPO [115] introduces length normalization for the number of turns in multi-turn preference optimization.", + "bbox": [ + 71, + 636, + 493, + 944 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "An alternative approach to controlling length bias in DPO is through sampling-based methods. SamPO [192] introduces a down-sampling method to compute regularized KL divergences. By balancing token-level probability distributions between preferred and rejected responses, SamPO reduces length bias in DPO training. Yuan et al. [193] propose Length-Instruction Fine-Tuning (LIFT), a method to improve instruction-following models' ability to adhere to length constraints by augmenting existing training data with explicit length instructions and using DPO for training. This enables the model to generalize across prompts requiring different response lengths. For long-context tasks, LongPO [196] enables short-context LLMs to self-evolve for long-context tasks by learning from self-generated short-to-long preference data, which includes paired responses for long-context inputs and their compressed short-context counterparts. LongPO incorporates a short-to-long KL constraint to prevent degradation of short-context performance during long-context alignment, achieving strong performance on both short- and long-context tasks.", + "bbox": [ + 501, + 53, + 924, + 345 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "3.4.2 Optimization Property", + "text_level": 1, + "bbox": [ + 504, + 356, + 714, + 372 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The optimization property of DPO involves likelihood collapse and alignment tax. While DPO aims to increase the likelihood of preferred responses and decrease dispreferred ones, the actual optimization process does not explicitly enforce this balance. Moreover, alignment improvements often come at the cost of the original capabilities of LLMs, known as alignment tax.", + "bbox": [ + 501, + 373, + 924, + 474 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "(a) Likelihood Collapse. Likelihood collapse refers to the unintended reduction in the likelihood of both preferred and dispreferred responses during DPO training [92]. This phenomenon can lead to unintentional unalignment, where the model's outputs deviate from human preferences, potentially producing undesirable or harmful responses. This phenomenon is also referred to as likelihood displacement in prior studies [204]. Additionally, the gradients associated with increasing the likelihood of preferred responses and decreasing that of dispreferred responses can become entangled, hindering effective learning. This entanglement complicates the optimization process, making it challenging to achieve the desired alignment [203]. Theoretical analyses have further elucidated the underlying causes of likelihood collapse. In particular, Feng et al. [202] developed an analytical framework grounded in field theory. Their analysis of the gradient vector field of the DPO loss function revealed that the loss function decreases the probability of generating human-disliked data at a faster rate than it increases the probability of generating human-like data.", + "bbox": [ + 503, + 476, + 924, + 767 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Several strategies have been proposed to address likelihood collapse. Pal et al. [200] introduce DPO-Positive (DPOP), which adds a penalty term to maintain a high log-likelihood for preferred examples. Similarly, LLaMA [235] augments DPO training with a negative log-likelihood term to stabilize training and preserve the log-likelihood of chosen responses [109]. Flex-DPO [201] adaptively adjusts parameters to slow the decline in the likelihood of dispreferred responses and balance gradients for both chosen and rejected outputs. D'Oosterlinck et al. [199] propose Anchored Preference Optimization (APO), which provides fine-grained control over probability updates: APO-zero increases the", + "bbox": [ + 503, + 767, + 924, + 941 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "13", + "bbox": [ + 906, + 32, + 923, + 42 + ], + "page_idx": 12 + }, + { + "type": "table", + "img_path": "images/522902a82b6177e867e4aff6c3488ea5e1a2da6b4a249cebc164f52549476e7d.jpg", + "table_caption": [ + "TABLE 1: An overview of datasets (upper row) and benchmarks (lower row) for DPO." + ], + "table_footnote": [], + "table_body": "
DatasetTask DescriptionData Size (Training & Test)Data SourceData StructureEvaluation Metric
UltraFeedback [237]Instruction-Following, Helpful64K&-AIList-
SafeRLHF [238]Harmless, Helpful73.9K&8.21KHuman&AIPair-
HelpSteer [239]Helpful35.3K&1.8KHumanPoint-
PRM800K [240]Mathematical Reasoning800K&-HumanPoint-
SHP-2 [241]Q&A From Reddit3600K&241KHumanPair-
Nectar [242]Conversations183K&-AIList-
OpenOrca [243]Conversations2940K&-AISample-
Capybara [244]Multi-Turn Conversations16K&-Human&AISample-
Step-DPO [100]Mathematical Reasoning10.8K&-Human&AIPair-
BeaverTails [245]Harmless, Helpful330K&36KHuman&AIPoint-
IMDb [246]Movie Reviews25K&25KHumanSampleAccuracy
Reddit TL;DR [247]Summarization1330K&-HumanSampleWin Rate
Anthropic-HH [248]Harmless, Helpful161K&8.55KAIPairWin Rate
GSM8K [249]Mathematical Reasoning7.47K&1.32KHumanSampleAccuracy
AlpacaEval2 [250]Automatic Evaluation-&0.8KAISampleWin Rate
MT-Bench [251]Multi-Turn Question-&3.3KHumanPairWin Rate
AdvBench [252]Harmful Behaviors-&0.5KHumanSampleAttack Success
Arena-Hard [253]Updating Evaluation-&0.5KAISampleWin Rate
TruthfulQA [254]Truthful-&0.8KHumanPairAccuracy
IFEval [255]Instruction-Following-&0.5KHumanSampleAccuracy
BBH [256]Multistep Reasoning-&23 TasksHumanSampleAccuracy
MATH [257]Mathematical Reasoning7.5K&5KHumanSampleAccuracy
GPQA [258]Biology, Physics, and Chemistry-&0.45KHumanSampleAccuracy
MUSR [259]Multistep Reasoning-&0.76KAISampleAccuracy
MMLU-Pro [260]Language Understanding-&12KHuman&AISampleAccuracy
", + "bbox": [ + 76, + 61, + 919, + 377 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "probability of winning outputs and decreases that of losing outputs, whereas APO-down decreases both, but with a stronger decline for losing outputs.", + "bbox": [ + 71, + 388, + 491, + 434 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Another notable challenge related to likelihood collapse is likelihood over-optimization, where the performance of a model on a proxy metric (such as its own likelihood estimates) improves, while its true performance does not. Zhang and Ranganath [236] show that reductions in the likelihood loss of DPO do not necessarily translate into higher win rates. Similarly, Shi et al. [205] further investigates the problem of likelihood over-optimization in DPO, demonstrating that higher completion likelihoods do not necessarily correlate with better model performance and may even degrade it. This study identifies key indicators of over-optimization and highlights the need to balance likelihood optimization with output diversity. e-DPO [187] also shows that DPO can lead to degenerate policies due to overfitting, and proposes a solution using reward model distillation to regularize the implicit reward of the language model. The method trains the language model to match the probability distribution induced by a reward model and introduces a pessimistic extension to handle uncertainty in the reward model, thereby improving the robustness of DPO.", + "bbox": [ + 71, + 439, + 491, + 733 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "(b) Alignment Tax. Alignment tax refers to the unintended consequence where improving a model's preference alignment degrades its general capabilities acquired during pretraining [206]. Thakkar et al. [207] demonstrate the sensitivity of DPO to training data composition, showing significantly worse performance degradation than SFT when using mixed-preference datasets. Furthermore, Chen et al. [209] identify that DPO struggles with optimizing ranking tasks. While DPO improves ranking accuracy, it disproportionately harms generative capabilities. Pentyala et al. [118] also observes capability forgetting during sequential training, where DPO objectives conflict with previously learned SFT patterns. To address this, researchers propose model merging strategies that balance alignment and performance.", + "bbox": [ + 71, + 737, + 495, + 944 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "PAFT [118] separately trains SFT and DPO objectives on a pretrained model using distinct datasets, then merges the parameters through weighted averaging. Additionally, Lu et al. [208] proposes online merging optimizers, which integrate model merging into each optimization step of DPO to balance human preferences and basic capabilities. By merging gradients with parameter differences between SFT and pretrained models, these optimizers effectively enhance alignment while mitigating alignment tax.", + "bbox": [ + 503, + 388, + 924, + 523 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "4 BENCHMARKS AND ANALYSIS", + "text_level": 1, + "bbox": [ + 504, + 544, + 779, + 559 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "In this section, we provide a comprehensive overview of existing benchmarks and evaluation for DPO methods. We first introduce the key datasets and benchmarks used to train or evaluate DPO models. We then present a comparative analysis of the performance of different DPO methods on these benchmarks, highlighting their strengths and limitations.", + "bbox": [ + 503, + 566, + 924, + 655 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "4.1 Datasets and Benchmarks", + "text_level": 1, + "bbox": [ + 504, + 674, + 741, + 689 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A diverse range of datasets and benchmarks has been specifically curated to facilitate research in DPO. Table 1 summarizes these datasets and benchmarks, highlighting their task descriptions, dataset sizes, data sources, data structures, and evaluation metrics. These datasets and benchmarks span a broad range of tasks, such as harmlessness and helpfulness evaluation and mathematical reasoning. They also exhibit significant diversity in scale, ranging from smaller, specialized datasets to large-scale collections such as SHP-2, which contains over 3.6 million samples. Additionally, datasets differ in their sources: some rely purely on human annotations, others on AI-generated content, and many adopt a hybrid approach combining human and AI-generated data. The data structures employed across these datasets include single-sample without preference label, point-wise annotations, pair-wise comparisons, and list-wise comparisons. Common evaluation metrics include accuracy", + "bbox": [ + 501, + 694, + 924, + 944 + ], + "page_idx": 13 + }, + { + "type": "page_number", + "text": "14", + "bbox": [ + 906, + 32, + 921, + 42 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/6f8f061ab915d05683da8b9488cffb80716ed95531ead04552cb45454c8c4d61.jpg", + "table_caption": [ + "TABLE 2: Experimental results of different DPO variants on Open LLM Leaderboard. The underline indicates the best performance." + ], + "table_footnote": [], + "table_body": "
ModelMistral-7B-BaseLLaMA-3-8B-Base
IFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGEIFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGE
SFT3.441.19.228.842.027.725.429.046.315.328.641.331.031.9
RRHF [190]10.040.61.726.446.326.125.231.046.813.931.436.830.531.7
SLiC-HF [230]11.044.09.929.242.628.127.541.749.517.530.439.731.735.1
DPO [74]11.143.77.128.543.826.726.834.348.217.231.940.131.533.9
IPO [75]9.442.89.729.739.727.826.535.349.015.932.841.431.934.4
CPO [116]8.042.79.628.942.127.326.432.446.916.830.639.131.832.9
KTO [67]12.943.712.028.946.128.328.640.248.318.031.040.131.134.8
ORPO [117]28.446.413.530.241.429.531.640.049.116.830.738.432.034.5
R-DPO [191]10.043.07.628.739.327.226.036.448.817.231.640.631.534.4
SimPO [166]11.143.18.428.939.527.226.440.848.615.831.040.531.834.7
ModelMistral-7B-InstructLLaMA-3-8B-Instruct
IFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGEIFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGE
SFT48.446.210.929.147.627.134.950.749.326.931.037.935.738.6
RRHF [190]45.245.310.128.544.226.233.351.349.327.229.639.535.338.7
SLiC-HF [230]39.446.211.428.749.026.833.641.650.926.331.339.235.337.4
DPO [74]49.045.611.026.946.126.834.248.950.125.829.438.736.038.2
IPO [75]42.645.311.827.849.327.234.050.449.526.329.637.935.738.2
CPO [116]38.846.010.128.548.426.933.150.649.126.831.338.135.838.6
KTO [67]46.245.710.927.846.027.334.043.150.126.331.238.135.037.3
ORPO [117]37.645.111.228.246.926.532.643.050.626.929.339.135.137.3
R-DPO [191]46.845.99.928.746.227.634.250.950.325.329.839.035.738.5
SimPO [166]45.445.910.428.345.027.133.748.849.225.029.339.235.137.8
", + "bbox": [ + 76, + 61, + 919, + 324 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "(for tasks like mathematical reasoning found in GSM8K and MATH), win rates derived from pairwise comparisons (such as MT-Bench and Anthropic-HH), and attack success rates used for assessing adversarial robustness (AdvBench).", + "bbox": [ + 71, + 337, + 491, + 398 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "4.2 Results", + "text_level": 1, + "bbox": [ + 73, + 412, + 171, + 426 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of different DPO variants, we conduct experiments on the Open LLM Leaderboard. We compare different DPO variants using Mistral-7B-Base, Mistral-7B-Instruct [261], LLaMA-3-8B-Base, and LLaMA-3-8B-Instruct [235] as starting points. The overall experimental setup follows Meng et al. [166], ensuring a reproducible evaluation of different DPO variants. For Mistral-7B-Base and LLaMA-3-8B-Base, the SFT models are trained based on the UltraChat-200k dataset [262], and subsequently applied different DPO variants on the SFT models using the UltraFeedback dataset [237]. For Mistral-7B-Instruct and LLaMA-3-8B-Instruct, which have already undergone instruction-tuning, the preference dataset is regenerated by collecting responses from the SFT models using prompts from the UltraFeedback dataset [237].", + "bbox": [ + 71, + 431, + 491, + 648 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "The experimental results, as summarized in Table 2, highlight the performance of different DPO variants across various benchmarks. For the Mistral-7B-Base and LLaMA-3-8B-Base models, ORPO consistently achieves the highest average scores, indicating its effectiveness in aligning models with human preferences. Notably, ORPO outperforms other methods on IFEval, BBH, and MATH, demonstrating its superiority in instruction-following and mathematical reasoning tasks. Meanwhile, SLiC-HF and KTO also achieve competitive results, particularly in BBH and GPQA, suggesting that these methods effectively leverage preference data for enhanced performance. For the Mistral-7B-Instruct and LLaMA-3-8B-Instruct models, the improvements across different DPO variants are more nuanced. While DPO and R-DPO show strong performance in IFEval and MMLU-Pro, IPO and CPO demonstrate robustness in handling complex reasoning tasks like MATH and GPQA. Overall, the results indicate that different DPO variants exhibit varying strengths across benchmarks, with some methods excelling in base models while others are more effective for instruct models.", + "bbox": [ + 71, + 650, + 493, + 941 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "5 APPLICATIONS", + "text_level": 1, + "bbox": [ + 504, + 335, + 658, + 351 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "In this section, we discuss the applications of DPO in various domains, including different LLM-based applications, diffusion models, and multi-modal LLMs. We provide an overview of the key challenges and opportunities in each domain and highlight the potential impact of DPO on real-world applications.", + "bbox": [ + 503, + 354, + 926, + 445 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "5.1 LLM-based Applications", + "text_level": 1, + "bbox": [ + 504, + 462, + 728, + 478 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "DPO has emerged as a powerful paradigm for aligning LLMs with human preferences across diverse applications [116, 235, 263, 264]. In code generation, DPO enhances control over code quality by optimizing based on preferences from automated tests [265, 266, 267]. In mathematical reasoning, DPO reduces errors in complex problem-solving by emphasizing step-level preference optimization [100, 101, 129, 268]. Multilingual applications leverage DPO to synchronize cross-lingual preferences, thereby improving translation accuracy and cultural relevance [107, 269]. Recommendation systems utilize DPO to refine personalization by incorporating user preference data to optimize item rankings, thereby enhancing the model ability to distinguish preferred items from less preferred ones [270, 271]. These examples highlight the adaptability of DPO in achieving human-aligned outputs across diverse tasks.", + "bbox": [ + 501, + 479, + 924, + 715 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "5.2 Diffusion Models", + "text_level": 1, + "bbox": [ + 504, + 733, + 671, + 747 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "In the realm of diffusion models, DPO has been adapted to better align generated content with user expectations [272, 273, 274, 275]. By optimizing preferences over image-text pairs, DPO enhances the semantic accuracy of generated images and mitigates the production of undesirable or biased content. Studies have demonstrated that diffusion models fine-tuned with DPO respond more accurately to complex prompts compared to those trained with traditional techniques. Moreover, the efficiency of DPO allows for the fine-tuning of large-scale models using limited preference data, addressing significant computational challenges in training diffusion models [276, 277, 278]. While scaling DPO for high-resolution and dynamic content generation remains", + "bbox": [ + 501, + 751, + 924, + 944 + ], + "page_idx": 14 + }, + { + "type": "page_number", + "text": "15", + "bbox": [ + 906, + 32, + 921, + 42 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "challenging, its ability to simplify reward modeling makes it a promising method for controlled content creation [279].", + "bbox": [ + 71, + 53, + 491, + 84 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "5.3 Multi-Modal LLMs", + "text_level": 1, + "bbox": [ + 73, + 102, + 246, + 116 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "For multi-modal LLMs, DPO plays a crucial role in aligning preferences across different data types, thereby improving coherence in tasks such as visual question answering and image captioning [89, 280, 281, 282, 283]. By optimizing alignment between textual responses and visual inputs, DPO reduces hallucinations in multi-modal interactions, ensuring outputs remain faithful to the given context. Although reconciling different types of feedback can be challenging, DPO offers a practical framework for lightweight adaptation, making it well-suited to preference-intensive multi-modal applications [280, 284, 285].", + "bbox": [ + 71, + 121, + 491, + 282 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "6 CHALLENGES AND FUTURE DIRECTIONS", + "text_level": 1, + "bbox": [ + 73, + 304, + 433, + 319 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "In this section, we discuss the key challenges and future directions in DPO research. We identify several critical issues that need to be addressed to further advance the field. Moreover, we propose several promising research directions that can help overcome these challenges and accelerate the adoption of DPO in the future.", + "bbox": [ + 71, + 324, + 491, + 412 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "6.1 Efficient Preference Optimization", + "text_level": 1, + "bbox": [ + 73, + 431, + 361, + 446 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Efficient preference optimization remains a pivotal challenge, as current DPO methods hinge on the availability of high-quality preference data, yet the manual collection of human annotations is both time-consuming and labor-intensive while automatically model-generated datasets often suffer from issues such as limited diversity, inherent biases, and insufficient fidelity to human judgment [121, 122, 128, 129]. Moreover, even though DPO circumvents the intricacies of reward model engineering common in RL, it does not fully leverage the exploratory strengths that RL methods offer, as evidenced by recent advances in reasoning approaches where RL-based training has achieved notable successes [18, 19]. This opens up an avenue for future research to not only enhance data efficiency through advanced learning techniques but also to integrate novel exploration mechanisms [138, 141], potentially through hybrid models that amalgamate the direct preference optimization benefits of DPO with the robust exploratory capabilities characteristic of RL.", + "bbox": [ + 71, + 450, + 493, + 715 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "6.2 Multi-Modal Preference Optimization", + "text_level": 1, + "bbox": [ + 73, + 733, + 385, + 748 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Multi-Modal Preference Optimization presents another frontier, given that existing DPO frameworks have primarily targeted text-based modalities while many real-world applications demand the alignment of diverse human preferences across text, images, audio, and even video [280, 284, 285, 286, 287]. In scenarios where cross-modal cues might conflict, such as the need for concise text paired with richly detailed imagery, the challenge lies in constructing a unified preference representation space that can intelligently and automatically recalibrate the priority of different modalities based on the contextual demands of the task at hand [89, 282, 283]. Future directions in this area could involve the development of innovative multi-modal preference encoding architectures,", + "bbox": [ + 71, + 752, + 495, + 944 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "which are capable of disentangling compound preferences into modality-specific and cross-modal components that align conflicting preferences while also adapting dynamically to changing inputs.", + "bbox": [ + 503, + 53, + 924, + 113 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "6.3 Continuous Preference Optimization", + "text_level": 1, + "bbox": [ + 504, + 136, + 816, + 151 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Continuous preference optimization addresses the dynamic nature of human preferences that evolve over time or vary with different phases of a task, a factor that static DPO models often fail to capture [123, 135, 137, 185]. As social norms and individual preferences shift, there is an increasing need for systems that can continuously recalibrate their alignment strategies in real time while simultaneously mitigating the risk of catastrophic forgetting. Future research in this domain may focus on meta-learning approaches that enable models to learn not only from the current state of preferences but also how to efficiently adapt when these preferences change. By integrating online learning frameworks with mechanisms for detecting temporal shifts and contextual variability in user behavior, researchers can pave the way toward systems that remain consistently relevant and effective in the face of evolving societal and individual expectations.", + "bbox": [ + 503, + 157, + 924, + 392 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "6.4 Interpretable Preference Optimization", + "text_level": 1, + "bbox": [ + 504, + 416, + 823, + 431 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "Interpretable preference optimization is critical for building trust in models that implicitly align human values, as the opaque nature of current DPO complicates the ability to audit and control the alignment process. In practice, human preferences are multi-dimensional [150, 151, 154], encompassing aspects such as factual accuracy, fairness, creativity, and beyond, and there is a pressing need to decompose these complex preferences into interpretable components that can be individually examined and fine-tuned. Future research could leverage advances in explainable techniques to develop models that not only achieve fine-grained alignment across diverse values but also provide transparent insights into how different preference dimensions interact to shape final decisions. This level of interpretability would allow stakeholders to balance competing values more effectively, ensuring that the alignment process remains both accountable and adaptable as societal norms continue to evolve.", + "bbox": [ + 503, + 436, + 926, + 686 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "7 CONCLUSION", + "text_level": 1, + "bbox": [ + 504, + 713, + 648, + 728 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "In recent years, DPO has emerged as a promising paradigm for aligning LLMs with human preferences by directly optimizing model policies using preference data. Despite its potential, the DPO research landscape remains fragmented, with a lack of systematic organization and comparative analysis. In this survey, we present a comprehensive overview of DPO and introduce a novel taxonomy that categorizes existing works into four key dimensions: data strategy, learning framework, constraint mechanism, and model property. We have also discussed the key benchmarks, evaluation results, and applications of DPO, highlighting the challenges and future directions in this field. By providing a systematic analysis of the existing DPO methods, we aim to facilitate further research and development in this area.", + "bbox": [ + 503, + 737, + 924, + 944 + ], + "page_idx": 15 + }, + { + "type": "page_number", + "text": "16", + "bbox": [ + 906, + 32, + 923, + 42 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "REFERENCES", + "text_level": 1, + "bbox": [ + 75, + 51, + 187, + 66 + ], + "page_idx": 16 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Wayne Xin Zhao et al. A survey of large language models. arXiv, 2023.", + "[2] Humza Naveed et al. A comprehensive overview of large language models. arXiv, 2023.", + "[3] Yupeng Chang et al. A survey on evaluation of large language models. TIIS, 2024.", + "[4] Shervin Minaee et al. 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TPAMI, 2025." + ], + "bbox": [ + 506, + 55, + 921, + 929 + ], + "page_idx": 19 + }, + { + "type": "page_number", + "text": "20", + "bbox": [ + 906, + 32, + 921, + 42 + ], + "page_idx": 19 + } +] \ No newline at end of file diff --git a/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_model.json b/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..38ef40e9ed04d6163cf226786a81a491a51f0548 --- /dev/null +++ b/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_model.json @@ -0,0 +1,5795 @@ +[ + [ + { + "type": "page_number", + "bbox": [ + 0.913, + 0.034, + 0.921, + 0.043 + ], + "angle": 0, + "content": "1" + }, + { + "type": "title", + "bbox": [ + 0.123, + 0.067, + 0.873, + 0.102 + ], + "angle": 0, + "content": "A Survey of Direct Preference Optimization" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.116, + 0.895, + 0.152 + ], + "angle": 0, + "content": "Shunyu Liu, Wenkai Fang, Zetian Hu, Junjie Zhang, Yang Zhou, Kongcheng Zhang, Rongcheng Tu, Ting-En Lin, Fei Huang, Mingli Song, Yongbin Li, and Dacheng Tao, Fellow, IEEE" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.173, + 0.893, + 0.346 + ], + "angle": 0, + "content": "Abstract—Large Language Models (LLMs) have demonstrated unprecedented generative capabilities, yet their alignment with human values remains critical for ensuring helpful and harmless deployments. While Reinforcement Learning from Human Feedback (RLHF) has emerged as a powerful paradigm for aligning LLMs with human preferences, its reliance on complex reward modeling introduces inherent trade-offs in computational efficiency and training stability. In this context, Direct Preference Optimization (DPO) has recently gained prominence as a streamlined alternative that directly optimizes LLMs using human preferences, thereby circumventing the need for explicit reward modeling. Owing to its theoretical elegance and computational efficiency, DPO has rapidly attracted substantial research efforts exploring its various implementations and applications. However, this field currently lacks systematic organization and comparative analysis. In this survey, we conduct a comprehensive overview of DPO and introduce a novel taxonomy, categorizing previous works into four key dimensions: data strategy, learning framework, constraint mechanism, and model property. We further present a rigorous empirical analysis of DPO variants across standardized benchmarks. Additionally, we discuss real-world applications, open challenges, and future directions for DPO. This work delivers both a conceptual framework for understanding DPO and practical guidance for practitioners, aiming to advance robust and generalizable alignment paradigms. All collected resources are available and will be continuously updated at https://github.com/liushunyu/awesome-direct-preference-optimization." + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.357, + 0.878, + 0.371 + ], + "angle": 0, + "content": "Index Terms—Alignment, Direct Preference Optimization, Large Language Models, Reinforcement Learning from Human Feedback." + }, + { + "type": "aside_text", + "bbox": [ + 0.023, + 0.261, + 0.058, + 0.707 + ], + "angle": 270, + "content": "arXiv:2503.11701v1 [cs.LG] 12 Mar 2025" + }, + { + "type": "title", + "bbox": [ + 0.075, + 0.431, + 0.23, + 0.446 + ], + "angle": 0, + "content": "1 INTRODUCTION" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.455, + 0.493, + 0.703 + ], + "angle": 0, + "content": "The rapid advancement of Large Language Models (LLMs) has revolutionized artificial intelligence [1, 2, 3, 4, 5, 6, 7, 8], enabling unprecedented generative capabilities across diverse applications, such as dialogue systems [9, 10], code generation [11, 12, 13], and medical diagnosis [14, 15, 16, 17]. Models like OpenAI-o1 [18] and DeepSeekR1 [19] have demonstrated remarkable proficiency in understanding and generating human-like text, outperforming traditional language processing techniques [20]. However, their immense power also introduces significant risks: LLMs may inadvertently produce harmful content (e.g., jailbreak suggestion) [21], exhibit hallucination behaviors (e.g., misinformation) [22], or propagate sociocultural stereotypes (e.g., biased recommendations) [23]. Ensuring that these models align with human values (producing outputs that are helpful, harmless, and honest) has thus become a cornerstone of responsible AI development [24]." + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.703, + 0.493, + 0.734 + ], + "angle": 0, + "content": "The critical challenge of aligning LLMs with human values stems from the inherent complexity of encoding abstract" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.747, + 0.492, + 0.943 + ], + "angle": 0, + "content": "This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A\\*STAR, as well as supported by Alibaba Group and NTU Singapore through Alibaba-NTU Global e-Sustainability CorpLab (ANGEL). (Corresponding author: Dacheng Tao.) Shunyu Liu, Junjie Zhang, Rongcheng Tu and Dacheng Tao are with Nanyang Technological University, Singapore (e-mail: shunyu.liu@ntu.edu.sg; junjie.zhang@ntu.edu.sg; turongcheng@gmail.com; dacheng.tao@ntu.edu.sg). Wenkai Fang, Yang Zhou, Kongcheng Zhang, and Mingli Song are with the College of Computer Science and Technology, Zhejiang University, China (e-mail: wenkfang@zju.edu.cn; imzhouyang@zju.edu.cn; zhangkc@zju.edu.cn; brooksong@zju.edu.cn). Zetian Hu is with the School of Aerospace Engineering, Tsinghua University, China (e-mail: huzt22@mails.tsinghua.edu.cn). Ting-En Lin, Fei Huang, and Yongbin Li are with the Tongyi Lab, Alibaba Group, China (e-mail: ting-en.lte@alibaba-inc.com; f.huang@alibaba-inc.com; shuide.lyb@alibaba-inc.com)." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.432, + 0.925, + 0.607 + ], + "angle": 0, + "content": "ethical principles into concrete model behaviors [25, 26, 27]. Traditional approaches, such as rule-based filtering or supervised learning on curated datasets, often prove inadequate due to their inability to generalize across diverse contexts and adapt to evolving societal norms [28]. The emergence of preference-based alignment paradigms addresses these limitations by framing the problem as optimizing for human feedback rather than inflexible heuristics [29, 30, 31, 32]. This shift recognizes that LLM decision-making often involves nuanced trade-offs between competing values, requiring flexible frameworks capable of incorporating subjective human preferences [33]." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.608, + 0.924, + 0.928 + ], + "angle": 0, + "content": "Building upon these insights, Reinforcement Learning from Human Feedback (RLHF) [34, 35] has emerged as the predominant alignment paradigm, leveraging human preferences to guide model optimization. In the RLHF pipeline, human annotators first rank the outputs generated by the language model, and these comparisons are used to train a reward model that quantifies human preferences. The language model is then fine-tuned using RL guided by this reward model, enabling the language model to align with human values by maximizing the predicted rewards. The success of RLHF in aligning models like ChatGPT [36, 37] and Claude [38, 39] underscores its practical utility. By translating subjective human preferences into an objective reward signal, RLHF facilitates the optimization of model behavior for value alignment. However, this RLHF paradigm suffers from critical limitations of computational complexity and training instability. Training a separate reward model demands substantial computational resources and high-quality human preference data, which scales poorly across different domains. Moreover, the RL phase often struggles with optimization challenges, such as reward hacking [40] and mode collapse [41]." + }, + { + "type": "text", + "bbox": [ + 0.529, + 0.928, + 0.924, + 0.943 + ], + "angle": 0, + "content": "These limitations have spurred interest in alternative" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.912, + 0.034, + 0.922, + 0.043 + ], + "angle": 0, + "content": "2" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.055, + 0.92, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.072, + 0.606, + 0.924, + 0.631 + ], + "angle": 0, + "content": "Fig. 1: A taxonomy of DPO. We categorize existing DPO works into four branches: data strategy, learning framework, constraint mechanism, and model property. Different colored boxes indicate different categories and their corresponding representative references." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.642, + 0.496, + 0.934 + ], + "angle": 0, + "content": "alignment methods that bypass reward modeling while preserving the benefits of preference-based learning. Direct Preference Optimization (DPO) [74, 210] represents a groundbreaking shift in this direction. Unlike RLHF, DPO reframes alignment as a supervised learning problem, directly optimizing the LLM policy using preference data without explicit reward modeling. By leveraging a closed-form mapping between reward functions and optimal policies, DPO eliminates the need for iterative RL training, reducing computational overhead and improving stability. Due to its inherent advantages, DPO has rapidly gained increasing attention from research communities. Existing studies vary widely in data strategies (e.g., point-wise v.s. pair-wise feedback) [67, 211], learning frameworks (e.g., offline v.s. online learning) [121, 122, 126], constraint mechanisms (e.g., different divergence constraints) [169, 171], and model properties (e.g., length bias) [191, 195]. Recent advancements in DPO variants have demonstrated remarkable efficacy in enhancing model alignment with human preferences, achieving unprecedented success across diverse domains [32]." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.642, + 0.925, + 0.701 + ], + "angle": 0, + "content": "These developments position DPO-based approaches as a compelling alternative to conventional RLHF paradigms for preference alignment tasks. However, despite its promise, the DPO research landscape remains fragmented." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.709, + 0.924, + 0.943 + ], + "angle": 0, + "content": "Several surveys related to DPO have been published in recent years, yet they exhibit notable limitations in their scope and analysis of DPO. (1) Scope limitations. While an early survey of [212] presents a comprehensive overview of preference-based RL methods, it predates the advent of DPO and does not address its applications to modern LLMs. Recent surveys on alignment [24, 26, 213, 214] provide broad overviews of LLM alignment techniques but only offer cursory summaries of DPO-related approaches without in-depth analysis. Similarly, surveys on learning from human feedback [30, 215, 216, 217] also only briefly mention DPO as a potential alternative. (2) Taxonomy deficiencies. Gao et al. [29] and Winata et al. [32] introduce a simplified taxonomy for preference learning, while overlooking technical distinctions within its broad categorization. In contrast, Wang et al. [31] attempt to classify preference learning across dimensions" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.913, + 0.034, + 0.922, + 0.043 + ], + "angle": 0, + "content": "3" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.054, + 0.493, + 0.199 + ], + "angle": 0, + "content": "such as reinforcement learning, reward modeling, feedback, and optimization. However, this taxonomy suffers from significant conceptual overlaps (e.g. reinforcement learning inherently involves optimization). A recent work by Xiao et al. [210] categorizes DPO studies through isolated research questions, which, while useful for problem identification, fragments the methodological connections. Our survey addresses these gaps by presenting the first comprehensive analysis specifically focused on DPO. The main contributions of this survey are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.203, + 0.493, + 0.319 + ], + "angle": 0, + "content": "- In this survey, we introduce a novel taxonomy that categorizes existing DPO works into four key dimensions based on different components of the DPO loss: data strategy, learning framework, constraint mechanism, and model property, as shown in Fig. 1. This taxonomy provides a systematic framework for understanding the methodological evolution of DPO and highlights the key distinctions between different variations." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.32, + 0.493, + 0.393 + ], + "angle": 0, + "content": "- We conduct a rigorous empirical analysis of DPO variants across standardized benchmarks, revealing critical insights into their performance in diverse scenarios. This analysis offers a comprehensive evaluation of DPO variants and provides practical guidance for practitioners." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.393, + 0.493, + 0.481 + ], + "angle": 0, + "content": "- We discuss real-world applications of DPO and highlight its potential to democratize alignment research by enabling efficient and scalable preference learning across diverse domains. We also outline open challenges and future directions for DPO research, emphasizing the need for robust and generalizable alignment paradigms." + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.203, + 0.493, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.484, + 0.493, + 0.616 + ], + "angle": 0, + "content": "The remainder of this survey is organized as follows. Section 2 introduces the background and formulation of DPO. Section 3 presents a taxonomy of DPO, categorizing existing works based on key dimensions. Section 4 describes standardized benchmarks for evaluating DPO methods and presents empirical results. Section 5 discusses real-world applications of DPO and highlights its potential. Section 6 outlines open challenges and future directions for DPO research. Finally, Section 7 concludes the survey." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.642, + 0.385, + 0.656 + ], + "angle": 0, + "content": "2 BACKGROUND AND FORMULATION" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.664, + 0.495, + 0.945 + ], + "angle": 0, + "content": "Preference learning aims to train language model policies to generate responses that better align with human preferences. Specifically, we denote the language model policy as \\(\\pi(y|x)\\), where \\(x\\) represents the input prompt and \\(y\\) is a candidate response (completion). A language model can be viewed as an autoregressive function that sequentially predicts tokens based on prior context. Mathematically, this is expressed as: \\(\\pi(y|x) = \\prod_{t=1}^{T} \\pi(y_t | y_{ 0\\) is a hyperparameter that controls the strength of the Kullback-Leibler (KL) divergence penalty. Here, the term \\(\\log \\pi_{\\theta}(\\cdot |x) / \\pi_{\\mathrm{ref}}(\\cdot |x)\\) represents the KL divergence between the current policy \\(\\pi_{\\theta}\\) and a reference policy \\(\\pi_{\\mathrm{ref}}\\). In practice, the reference policy \\(\\pi_{\\mathrm{ref}}\\) is set to the SFT model \\(\\pi_{\\mathrm{sft}}\\), ensuring that the updated policy remains close to the initial model." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.87, + 0.925, + 0.945 + ], + "angle": 0, + "content": "To optimize the above objective, Proximal Policy Optimization (PPO) [219] has emerged as a promising RL algorithm for LLMs. PPO stabilizes training by constraining policy updates within a trust region via a clipped objective, which prevents significant deviations from the previous" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.913, + 0.034, + 0.922, + 0.043 + ], + "angle": 0, + "content": "4" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.054, + 0.493, + 0.171 + ], + "angle": 0, + "content": "policy. However, PPO requires an additional critic model to estimate value functions for advantage calculation, thereby introducing extra computational and memory overhead. To address this, recent methods, such as RLOO [220], ReMax [221], GRPO [222], and Reinforce++ [223], introduce critic-free advantage estimation to reduce resource demands while maintaining stable optimization, making them more scalable for large-scale LLM training." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.186, + 0.343, + 0.201 + ], + "angle": 0, + "content": "2.2 Direct Preference Optimization" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.204, + 0.491, + 0.307 + ], + "angle": 0, + "content": "DPO offers an alternative that streamlines the training process by directly optimizing the policy with preference data [74, 224, 225, 226, 227, 228, 229], thereby eliminating the need for explicit reward modeling in RLHF. The key idea of DPO is a closed-form solution of Eq. 3 that connects reward with the optimal policies. Specifically, the optimal policy corresponding to a given \\( r \\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.312, + 0.493, + 0.345 + ], + "angle": 0, + "content": "\\[\n\\pi^ {*} (y | x) = \\frac {1}{Z (x)} \\pi_ {\\mathrm {r e f}} (y | x) \\exp \\left(\\frac {1}{\\beta} r (x, y)\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.349, + 0.408, + 0.364 + ], + "angle": 0, + "content": "where the partition function \\( Z(x) \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.369, + 0.493, + 0.405 + ], + "angle": 0, + "content": "\\[\nZ (x) = \\sum_ {y} \\pi_ {\\mathrm {r e f}} (y | x) \\exp \\left(\\frac {1}{\\beta} r (x, y)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.41, + 0.492, + 0.44 + ], + "angle": 0, + "content": "By rearranging the above equation, the reward \\( r \\) can be recovered from the optimal policy \\( \\pi^{*} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.445, + 0.493, + 0.477 + ], + "angle": 0, + "content": "\\[\nr (x, y) = \\beta \\log \\frac {\\pi^ {*} (y | x)}{\\pi_ {\\operatorname {r e f}} (y | x)} + \\beta \\log Z (x). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.481, + 0.492, + 0.541 + ], + "angle": 0, + "content": "Notice that the partition function \\( Z(x) \\) depends only on the prompt \\( x \\). By substituting this expression into the preference model of Eq. 1, the preference probability model that \\( y_{w} \\) is preferred over \\( y_{l} \\) becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.545, + 0.493, + 0.589 + ], + "angle": 0, + "content": "\\[\nP \\left(y _ {w} \\succ y _ {l} | x\\right) = \\sigma \\left(\\beta \\log \\frac {\\pi^ {*} \\left(y _ {w} \\mid x\\right)}{\\pi_ {\\text {r e f}} \\left(y _ {w} \\mid x\\right)} - \\beta \\log \\frac {\\pi^ {*} \\left(y _ {l} \\mid x\\right)}{\\pi_ {\\text {r e f}} \\left(y _ {l} \\mid x\\right)}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.589, + 0.493, + 0.634 + ], + "angle": 0, + "content": "Based on the above preference probability model, DPO directly optimizes the language mode policy \\(\\pi_{\\theta}\\) by minimizing the following negative log-likelihood loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.645, + 0.493, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {D P O}} (\\theta) = \\\\ - \\mathbb {E} _ {(x, y _ {w}, y _ {l}) \\sim \\mathcal {D}} \\left[ \\log \\sigma \\left(\\beta \\log \\frac {\\pi_ {\\theta} (y _ {w} | x)}{\\pi_ {\\text {r e f}} (y _ {w} | x)} - \\beta \\log \\frac {\\pi_ {\\theta} (y _ {l} | x)}{\\pi_ {\\text {r e f}} (y _ {l} | x)}\\right) \\right], \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.718, + 0.493, + 0.822 + ], + "angle": 0, + "content": "where the KL constraint is implicitly integrated through the use of the reference model \\(\\pi_{\\mathrm{ref}}\\). By minimizing this DPO loss, we directly train the policy to satisfy human preferences without resorting to a separate reward modeling stage or using reinforcement learning optimization as in RLHF, significantly reducing implementation complexity while improving training stability." + }, + { + "type": "title", + "bbox": [ + 0.073, + 0.837, + 0.341, + 0.852 + ], + "angle": 0, + "content": "2.3 Other Preference Optimization" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.855, + 0.493, + 0.945 + ], + "angle": 0, + "content": "In addition to DPO, several concurrent preference optimization methods [190, 230, 231] have been proposed that offer alternative approaches to RLHF. These methods explore different strategies for optimizing LLMs to align with human preference without RL. Below, we provide a brief introduction to these approaches." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.054, + 0.785, + 0.068 + ], + "angle": 0, + "content": "2.3.1 Sequence Likelihood Calibration" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.07, + 0.923, + 0.128 + ], + "angle": 0, + "content": "Zhao et al. [230] propose Sequence Likelihood Calibration with Human Feedback (SLiC-HF) to directly align LLMs with human preferences. Specifically, the loss function of SLiC-HF is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.138, + 0.923, + 0.173 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {S L i C - H F}} (\\theta) = \\max (0, \\delta - \\log \\pi_ {\\theta} (y _ {w} | x) + \\log \\pi_ {\\theta} (y _ {l} | x)) \\\\ - \\lambda \\log \\pi_ {\\theta} (y ^ {*} | x), \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.177, + 0.924, + 0.266 + ], + "angle": 0, + "content": "where the first term is the rank calibration loss with \\(\\delta\\) as a margin hyperparameter, and the second term is the cross-entropy regularization loss with \\(\\lambda\\) as a regularization weight. \\(y^{*}\\) is obtained from either high-quality supervised responses in the SFT dataset or the top-ranked candidate response generated by the SFT model." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.273, + 0.863, + 0.287 + ], + "angle": 0, + "content": "2.3.2 Rank Responses to Align Human Feedback" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.289, + 0.924, + 0.407 + ], + "angle": 0, + "content": "Yuan et al. [190] introduce Rank Responses to align Human Feedback (RRHF) for LLMs. RRHF extends pair-wise ranking by considering the list-wise ranking order of multiple responses, thus better utilizing the preference information. For an input prompt \\( x \\) and \\( N \\) candidate responses \\( \\{y_i\\}_{i=1}^N \\), it optimizes the model to assign higher probabilities to higher-ranked responses via a ranking loss and directly supervises the best response using cross-entropy as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.414, + 0.923, + 0.469 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R R H F}} (\\theta) = \\sum_ {r _ {i} < r _ {j}} \\max \\left(0, \\frac {\\log \\pi_ {\\theta} (y _ {i} | x)}{| | y _ {i} | |} - \\frac {\\log \\pi_ {\\theta} (y _ {j} | x)}{| | y _ {j} | |}\\right) \\\\ - \\lambda \\log \\pi_ {\\theta} \\left(y ^ {*} \\mid x\\right), \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.474, + 0.923, + 0.548 + ], + "angle": 0, + "content": "where \\( r_i = r_\\phi(x, y_i) \\) represents the reward of the response \\( y_i \\) and \\( y^* = \\arg \\max_{y_i} r_i \\) is the response with the highest reward. Although RRHF avoids the need for reinforcement learning in RLHF, it still utilizes a reward model \\( r_\\phi \\) to rank candidate responses based on human preferences." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.555, + 0.791, + 0.57 + ], + "angle": 0, + "content": "2.3.3 Preference Ranking Optimization" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.572, + 0.924, + 0.644 + ], + "angle": 0, + "content": "Similarly, Song et al. [231] propose Preference Ranking Optimization (PRO) to align LLMs with human preferences by leveraging multiple responses \\(\\{y_{i}\\}_{i = 1}^{N}\\) with the human-annotated order \\(y_{1} > y_{2} > \\dots >y_{N}\\). The loss function of PRO is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.647, + 0.924, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {P R O}} (\\theta) = - \\sum_ {i = 1} ^ {N - 1} \\log \\frac {\\exp \\left(\\frac {1}{\\| y _ {i} \\|} \\log \\pi_ {\\theta} \\left(y _ {i} | x\\right) / \\mathcal {T} _ {i} ^ {i}\\right)}{\\sum_ {j = i} ^ {N} \\exp \\left(\\frac {1}{\\| y _ {j} \\|} \\log \\pi_ {\\theta} \\left(y _ {j} | x\\right) / \\mathcal {T} _ {i} ^ {j}\\right)}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.707, + 0.923, + 0.796 + ], + "angle": 0, + "content": "where the dynamic penalty temperature is defined as \\(\\mathcal{T}_i^j = 1 / (r_\\phi (x,y^j) - r_\\phi (x,y^i))\\) and \\(\\mathcal{T}_i^i = \\min_{i < j}\\mathcal{T}_i^j\\). This temperature ensures that the probability gap between higher-ranked and lower-ranked responses is adaptively scaled according to their reward differences, thereby stabilizing the optimization process." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.806, + 0.722, + 0.821 + ], + "angle": 0, + "content": "3 A TAXONOMY OF DPO" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.826, + 0.924, + 0.942 + ], + "angle": 0, + "content": "In this section, we introduce a novel taxonomy that categorizes existing DPO works based on four key dimensions: data strategy, learning framework, constraint mechanism, and model property. As illustrated in Fig. 1, these four dimensions are derived from different components of the DPO loss, providing a systematic framework for understanding the methodological evolution of DPO and highlighting the key distinctions between different variations." + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.913, + 0.034, + 0.922, + 0.043 + ], + "angle": 0, + "content": "5" + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.053, + 0.274, + 0.069 + ], + "angle": 0, + "content": "3.1 Data Strategy of DPO" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.074, + 0.493, + 0.149 + ], + "angle": 0, + "content": "The data strategy constitutes the foundational pillar of DPO, focusing on how to leverage diverse types of preference data for training LLMs. As shown in Fig. 2, our taxonomy identifies three principal axes of data strategy: quality, feedback, and granularity." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.164, + 0.217, + 0.179 + ], + "angle": 0, + "content": "3.1.1 Data Quality" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.183, + 0.493, + 0.286 + ], + "angle": 0, + "content": "The quality of preference data is a critical factor in determining the effectiveness of DPO training. High-quality data ensures that LLMs effectively learn to align with human preferences, while low-quality data may introduce noise and bias, leading to suboptimal model performance. We categorize data quality considerations into three key aspects: heterogeneity, distinguishability, and noise." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.287, + 0.495, + 0.681 + ], + "angle": 0, + "content": "(a) Data Heterogeneity. Conventional DPO methods assume uniform human preferences when annotating data, thereby overlooking the diversity among annotators. This assumption often skews the model toward the preferences of the majority while neglecting minority viewpoints, potentially leading to biases and unfair treatment of underrepresented groups. To address this issue, Chidambaram et al. [42] propose EM-DPO, which learns the distribution of different preference types and their corresponding response strategies. Building on this, they introduce the MinMax-DPO algorithm, which selects a strategy by minimizing the maximum regret across subgroups, ensuring a more balanced representation of preferences among all groups. MallowsPO [43] decomposes the implicit rewards in DPO into prompt dispersion and response scaling rewards. It introduces a novel objective function to capture human preferences for diverse responses to the same prompt. GRPO [44] formulates an objective function that minimizes the loss for the worst-case group, thereby ensuring fairness by prioritizing the disadvantaged groups in the optimization process. GDPO [45] models the language generation process as a combination of belief distribution prediction and belief-based response generation. The corresponding GDPO loss function consists of belief calibration loss and belief-conditioned preference alignment loss. The former encourages the model to capture the diversity of beliefs across groups, while the latter ensures that generated responses align with the given belief." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.681, + 0.495, + 0.945 + ], + "angle": 0, + "content": "(b) Data Distinguishability. A key limitation of DPO is its inability to account for the distinguishability of preference between responses [46, 50, 51, 56, 57]. In some cases, the preferred response is only marginally better than the dispreferred one, while in others, the dispreferred response contains harmful or misleading content, making it significantly worse. Thus, optimization should focus more on cases with substantial preference differences while reducing the effort spent on minor differences. However, most existing methods treat all samples equally, ignoring this data distinguishability. To address this, ODPO [46] introduces a monotonically increasing offset function, requiring the reward of the preferred response to exceed that of the dispreferred one by a certain margin. This ensures stronger updates for larger preference gaps. Similarly, Ada-DPO [54] introduces an instance-specific nonlinear scaling parameter, assigning larger weights to strong preference pairs and smaller weights to ambiguous ones based on the reward differences, thereby capturing" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.056, + 0.92, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.59, + 0.385, + 0.838, + 0.399 + ], + "angle": 0, + "content": "Fig. 2: An overview of DPO data strategy." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.414, + 0.925, + 0.793 + ], + "angle": 0, + "content": "different levels of data distinguishability. DPO-rc [48] also incorporates the preference reward difference as a coefficient in the loss function. \\(\\alpha\\)-DPO [49] introduces an adaptive preference distribution to obtain dynamic reward margins based on the distribution difference between the policy and reference models. \\(\\beta\\)-DPO [51] analyzes the optimal \\(\\beta\\) parameter for datasets with different reward margins, which dynamically adjusts \\(\\beta\\) based on batch-level reward differences. They also introduce \\(\\beta\\)-guided data filtering to prioritize valuable training data. Curri-DPO [53] sorts preference pairs by reward differences and trains progressively from large to small differences, enabling curricular learning. Similarly, MPO [47] utilizes a reward model to score responses generated by the SFT model, constructing a preference dataset and partitioning it based on preference differences to learn from simple to complex tasks. sDPO [55] computes reward accuracy for different datasets based on an initial target model and partitions the dataset in descending order of accuracy, allowing the model to first optimize on simpler samples. Ma et al. [58] propose a preference dataset construction method that adjusts update weights based on response accuracy, assigning lower weights when the model demonstrates higher proficiency. Furthermore, fDPO [52] enhances DPO training by filtering out samples where the generated response of the model policy surpasses the preferred dataset response in reward score." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.797, + 0.924, + 0.943 + ], + "angle": 0, + "content": "(c) Data Noise. Human-generated preference annotations often contain inconsistencies, errors, or noise, negatively affecting the performance of DPO. Such noisy data can mislead models, impairing their ability to accurately capture true preferences and generalize effectively to unseen data. Im and Li [64] analyze how noisy feedback influences the generalization performance of preference optimization, showing that increased noise results in higher generalization risks. Specifically, standard DPO loss functions can yield biased estimates under noisy conditions. To address this" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.913, + 0.034, + 0.923, + 0.043 + ], + "angle": 0, + "content": "6" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.054, + 0.492, + 0.535 + ], + "angle": 0, + "content": "issue, rDPO [59] proposes to enhance DPO robustness against noisy annotations and improve overall training performance. Zhang et al. [63] introduce a noise-aware strategy leveraging annotator confidence and stability to identify and downweight noisy samples during training. They also propose an adaptive reward margin, emphasizing clean samples to improve learning effectiveness. Complementary to these approaches, PerpCorrect [60] employs a data-driven method to correct noisy annotations directly in the dataset. It trains a proxy language model on both clean and noisy samples, distinguishing noise through perplexity differences to improve dataset quality. To systematically explore noise effects, Gao et al. [65] artificially inject various noise types (e.g., Gaussian noise) into datasets, controlling noise intensity via hyperparameters. Their analysis highlights how noise impacts model alignment, guiding future research towards mitigating such negative effects. To address the vulnerability of DPO in noisy environments, ROPO [61] introduces a regularization term to enhance noise tolerance. Additionally, ROPO employs a robust-guided rejection sampling technique. This technique supplements the dataset with samples that contribute minimally to the loss, thereby improving the overall data quality. Kim et al. [62] propose the SPA framework, using model-generated responses and associated confidence scores to detect noise in annotations. SPA further incorporates smoothing techniques into the loss function to alleviate the noise problem. Finally, Wu et al. [66] categorize noise into two types: point noise (single annotation errors) and pairwise noise (errors between annotated pairs). While DPO naturally handles point noise well, it struggles with pairwise noise. Their proposed Dr. DPO introduces a novel loss function explicitly designed for robustness against both point and pairwise noise." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.547, + 0.276, + 0.56 + ], + "angle": 0, + "content": "3.1.2 Preference Feedback" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.564, + 0.491, + 0.68 + ], + "angle": 0, + "content": "Preference feedback refers to the label signals provided by annotators regarding their preferences for different responses. It can be categorized into point-wise, pair-wise, and list-wise feedback. Point-wise feedback evaluates each response independently, assigning a score or labeling it as positive or negative. Pair-wise feedback compares two responses to determine which one is preferred, while list-wise feedback ranks multiple responses." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.681, + 0.492, + 0.943 + ], + "angle": 0, + "content": "(a) Point-Wise Feedback. Point-wise feedback is the basic form of feedback. It refers to the type of feedback where individual outputs or samples are evaluated independently, rather than through comparisons with other outputs. This form of feedback is characterized by its simplicity and directness, focusing on the quality or relevance of a single response or item. The predominant methodology in RLHF [35] employs point-wise reward signals generated by reward models to optimize policy models. Similarly, KTO [67] directly maximizes the utility of model generations using loss functions based on prospect theory rather than the log-likelihood of preferences. It requires only a binary signal indicating whether an output is desirable or undesirable for a given input. Furthermore, BCO [68] builds upon the concepts introduced in KTO and explores a new approach to aligning with binary signals. While KTO focuses on optimizing human utility, BCO introduces a binary classifier framework incorporating reward shift and distribution matching that implicitly" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.054, + 0.921, + 0.344 + ], + "angle": 0, + "content": "minimizes the DPO loss. Chen et al. [72] and GPO [73] adopt explicit rewards using Noise Contrastive Alignment (NCA) and General Preference Model (GRM) respectively, and then directly optimize language model policies from point-wise preference data with rewards. However, some methods leverage implicit reward signals to refine model behaviors. To ensure that the learned implicit rewards are comparable to the ground-truth rewards, Cal-DPO [69] introduces a calibration term to the preference optimization objective, which prevents the likelihood of chosen responses from decreasing during training. ULMA [71] unifies human demonstration and point-wise preference data into a single framework and handles positive and negative samples with a hybrid objective function. Unlike them, DRO [211] adopts a simple mean-squared objective to optimize the model policy and value function jointly for a single trajectory. Additionally, AOT [70] casts the distributional preference constraint as an optimal transport problem with a convex cost function. The key idea is to minimize the violation of stochastic dominance using a smooth, convex cost function." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.346, + 0.921, + 0.943 + ], + "angle": 0, + "content": "(b) Pair-Wise Feedback. Pair-wise feedback focuses on comparing pairs of data or actions to determine their relative quality or preference. Building upon the theoretical framework of RLHF, DPO implements this paradigm through the utilization of pair-wise preference data, thereby fitting an implicit reward model. Azar et al. [75] introduces a general theoretical framework to unify existing RLHF and DPO methods. The proposed Identity-Preference Optimization (IPO) directly optimizes policies from preferences without relying on reward modeling or the Bradley-Terry assumption, thereby avoiding overfitting issues observed in DPO. Subsequently, DPO-RK and DPO-R [76] integrate the Rao-Kupper and Davidson models into the DPO training objective respectively, thereby extending the capabilities of DPO by explicitly modeling ties in pairwise comparisons. BMC [77] further addresses a key limitation of the weak correlation between winning and losing responses in pairwise data. Specifically, BMC uses \"Bridging\" to enhance the correlation between winning and losing responses by increasing the consistency and informativeness of pairwise preference signals. However, previous attempts for aligning LLMs primarily focus on optimizing the model's output preferences given an instruction, which struggles to effectively perceive the fine-grained constraints within complex instructions. Thus IOPO [78] extends traditional alignment methods by considering both input and output preferences to better understand the constraints within the instructions. As current methods rely heavily on paired preference data (i.e., explicitly labeled preferred vs. dispreferred examples), they can be limiting in scenarios where such paired data is unavailable or insufficient. SAPO [80] addresses this issue based on the concept of self-play, which enhances data exploration and exploitation by automatically generating negative samples and integrating off-policy learning. Furthermore, PMPO [79] extends the EM algorithm to incorporate both preferred and dispreferred outcomes. By introducing the probability distribution of dis-preferred outcomes, PMPO can optimize using both types of samples, even when only negative feedback is available. Similarly, D2O [81] avoids harmful information by maximizing the discrepancy between the generated responses and the negative samples. NPO [82]" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.913, + 0.034, + 0.922, + 0.043 + ], + "angle": 0, + "content": "7" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.054, + 0.49, + 0.126 + ], + "angle": 0, + "content": "and SimNPO [83] achieve the goal of forgetting the negative impact by regulating the model's prediction probabilities on negative datasets to be as minimal as possible, where SimNPO further eliminates the reference model bias issue inherent in NPO." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.126, + 0.491, + 0.784 + ], + "angle": 0, + "content": "(c) List-Wise Feedback. List-wise feedback refers to the type of feedback where multiple outputs or responses generated by the model for a given input are evaluated collectively as a list. This approach considers the relative ranking or ordering among the outputs, rather than focusing on individual outputs in isolation. Panacea [84] reframes alignment as a Multi-Dimensional Preference Optimization (MDPO) problem and introduces a method that aims to learn the entire Pareto front to accommodate diverse user preferences. In short, Panacea is designed to adapt a single model to list-wise preferences in a Pareto-optimal manner. LiPO [85] and LIRE [86] also treat LM alignment as a list-wise ranking problem, drawing on the rich literature of Learning-To-Rank (LTR). Specifically, LiPO introduces a specific method LiPO-λ, which leverages a list-wise ranking objective that weights each preference pair based on the difference in ranking metrics; while LIRE optimizes the response probability by calculating the exponential probability distribution and uses the reward model to directly guide the optimization process. To better capture the relative proximity within ordinal multiple responses, OPO [87] utilizes the Normalized Discounted Cumulative Gain (NDCG), a widely used ranking metric, to optimize the model's generation probability to match the permutation of responses based on these labels. Similarly, DRPO [88] leverages NDCG as a key metric to optimize the ranking of model outputs. However, DRPO incorporates novel elements like diffNDCG and Adaptive Rank Policy Score to dynamically adjust the score margins between preferred and non-preferred responses based on their ranking positions. mDPO [232] extends preference optimization to multi-sample comparisons and introduces a framework that evaluates and optimizes the collective properties of sample groups. It not only addresses the limitations of single pair-wise methods but also provides a more robust optimization framework, especially for characteristics like diversity and bias. Furthermore, RPO [90] introduces a contrastive weighting mechanism that constructs a contrast matrix within each mini-batch to compare preferred and less-preferred responses across prompts. The weights of these comparisons are dynamically adjusted based on the semantic similarity between prompts. Additionally, TODO [91] integrates a tie ranking system into list-wise preference modeling, significantly improving the capture of nuances of human preferences, especially in the presence of noisy or inconsistent labels and frequent ties." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.795, + 0.285, + 0.809 + ], + "angle": 0, + "content": "3.1.3 Preference Granularity" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.812, + 0.49, + 0.898 + ], + "angle": 0, + "content": "Preference granularity refers to the granularity of preference labels, which determines the level at which preferences are assigned to data. It can be categorized into token-level, step-level, sentence-level, and turn-level granularity, ranging from fine-grained focus on individual tokens to broader preferences over entire interaction turns." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.9, + 0.49, + 0.943 + ], + "angle": 0, + "content": "(a) Token-Level Granularity. Token-level alignment operates at the character/subword unit of text generation, providing the finest-grained control over model outputs" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.054, + 0.921, + 0.519 + ], + "angle": 0, + "content": "Theoretically, Rafailov et al. [92] demonstrate that DPO can represent any dense reward function by reparameterizing it as an optimal advantage function, which allows DPO to optimize policies in the token-level MDP effectively TDPO [93] refines the alignment process from the sentence level to the token level and introduces forward KL divergence constraints. TDPO utilizes the Bradley-Terry model to convert sentence-level preference comparisons into a token-level reward system, which allows the model to dynamically adjust its strategy at each token generation step. Furthermore, TIS-DPO[94] estimates the importance weights of tokens based on the differences in prediction probabilities from contrastive LLMs, performing token-level importance sampling on existing data to approximate optimal distribution by assigning weights to each token based on its reward. Moreover, \\(\\mathrm{D}^2\\mathrm{PO}\\) [99] proposes a temporal decay mechanism that dynamically adjusts the contribution of each token-level reward based on its position in the sequences. Unlike these, SparsePO [95] directly learns sparse masks during the training process and controls which tokens are more important for preferences through the sparsity of the masks, thereby achieving dynamic optimization. RTO [96] and SePO [97] first learn a token-level reward function from preference data using DPO, and then RTO optimizes PPO based on this reward signal, while SePO selects key tokens through the estimated reward function. To tackle the need for large-scale annotated data in training, EPO [98] proposes a hierarchical framework that decomposes complex tasks into manageable subgoals using separate LLMs for subgoal prediction and low-level action generation, leveraging environment feedback to automatically generate reward signals and preference data for aligning LLMs." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.521, + 0.922, + 0.636 + ], + "angle": 0, + "content": "To conclude, token-level granularity optimizes models at individual token positions to maximize expected objectives, preserving semantic precision and capturing local syntactic dependencies. However, it increases computational complexity, as processing numerous tokens extends training time, and its sensitivity to noise means errors in a single token can affect the entire sequence. Thus, careful loss function design and regularization are essential for stability." + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.637, + 0.922, + 0.942 + ], + "angle": 0, + "content": "(b) Step-level Granularity. Step-level granularity focuses on the intermediate steps or stages in a process, particularly effective for complex problem-solving tasks requiring multiple intermediate steps. Step-DPO [100] and SCDPO [101] treat individual reasoning steps as the basic units for preference optimization, where preference pairs of correct and incorrect steps are generated using LLMs. Furthermore, CPO [102] and MCTS-DPO [103] first utilize more powerful inference structures to generate multiple candidate thoughts at each reasoning step following the Tree-of-Thought (ToT) and Monte Carlo Tree Search (MCTS) respectively, and construct preference pairs based on the selected and unselected intermediate steps. Then they finetune LLMs to generate reasoning steps preferred by ToT during inference using DPO. TPO [104] proposes a preference learning algorithm specifically designed for preference trees that have multiple branches and multi-step responses, and introduces the adaptive step reward mechanism to address the issue of small reward margins caused by shared subtrajectories. It adjusts the reward values for each step based on semantic similarity, helping the model better distinguish" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.913, + 0.034, + 0.923, + 0.043 + ], + "angle": 0, + "content": "8" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.054, + 0.493, + 0.214 + ], + "angle": 0, + "content": "between preference pairs. RDPO [105] extends traditional preference datasets to incorporate a rationale field, which explains why a particular response is preferred. RDPO introduces rationale information into the DPO loss function by maximizing the likelihood of both the preference and the rationale, which allows the model to better understand the logic behind preferences during training. To address the challenges of sparse rewards and training instability, DAPO [106] uses a critic function to generate dense signals for policy optimization and trains the actor and critic independently to avoid instability." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.215, + 0.493, + 0.418 + ], + "angle": 0, + "content": "To conclude, step-level alignment demonstrates unique advantages in multi-step reasoning tasks by decomposing holistic preferences into intermediate decision points. The primary strength of step-level granularity lies in its capacity to decompose complex objectives into verifiable subgoals, enhancing both interpretability and robustness. For instance, in mathematical reasoning, LLMs can receive feedback on equation derivation steps before final answers, reducing error propagation. However, this granularity still have two key challenges: first, the need for precise step segmentation, which may require domain-specific heuristics or auxiliary models to delineate reasoning boundaries; second, the risk of local optima, where over-optimization of individual steps degrades global coherence." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.418, + 0.493, + 0.695 + ], + "angle": 0, + "content": "(c) Sentence-level Granularity. Sentence-level granularity aligns preferences at the complete utterance level, balancing fine-grained control and computational efficiency. This granularity, represented by the original DPO framework, operates on full response sequences as atomic units for preference comparison. MAPO [107] uses a well-trained translation model to calculate alignment scores between answers in nondominant and dominant languages and then employs preference optimization methods to enhance reasoning consistency. EURUS [108] structures each instruction as a preference tree, containing pairs of correct and incorrect actions to facilitate preference learning. Similarly, IRPO [109] focuses on improving the reasoning capabilities of LLMs through an iterative preference optimization on constructed preference pairs such that the winning response has a higher reward than the losing response. FACTALIGN [110] proposes a fine-grained, sentence-level alignment algorithm called fKTO, which extends the KTO method to leverage fine-grained factuality assessments at the sentence level." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.695, + 0.493, + 0.812 + ], + "angle": 0, + "content": "To conclude, the key strength of sentence-level granularity lies in its capacity to preserve holistic semantics while maintaining tractable optimization complexity. Nevertheless, we must carefully consider task requirements. While suitable for short-form generation and classification tasks, sentence-level methods may insufficiently capture fine-grained stylistic nuances or long-range dependencies critical in generation and reasoning domains." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.812, + 0.493, + 0.943 + ], + "angle": 0, + "content": "(d) Turn-level Granularity. Turn-level granularity focuses on the optimization of model behavior at the level of conversational turns, which is particularly relevant for dialogue systems and interactive agents. This granularity level treats each turn of a conversation as a unit for preference alignment, allowing the LLMs to receive feedback on their responses within the context of a single turn. M-DPO [111] introduces a multi-turn direct preference learning framework to enhance the mathematical reasoning capabilities of LLMs when" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.054, + 0.925, + 0.491 + ], + "angle": 0, + "content": "integrated with external tools. It leverages feedback from code interpreters and optimizes trajectory-level preferences using signals generated by the Bradley-Terry model to improve model performance in multi-turn reasoning tasks. ETO [112] presents a novel trial-and-error learning method that optimizes LLM agents' policies by contrasting successful and failed trajectories that contain multi-turn interaction. To address the challenges of coarse granularity and training noise in previous methods, SDPO [113] optimizes specific key segments within interactions to improve multi-turn dialogues while minimizing training noise. Specifically, it extracts key segments from the positive sessions that contribute to higher goal and relationship scores and pairs them with corresponding segments from the negative sessions to calculate an adapted DPO loss. Similarly, AgentQ [114] combines MCTS with self-critique mechanisms to provide process-level supervision by ranking actions, and then iterative fine-tuning using DPO. This approach enables LLMs to effectively learn from both successful and unsuccessful trajectories, enhancing their generalization and decision-making capabilities in complex, multi-turn reasoning tasks within interactive environments. DMPO [115] enhances the existing DPO method by replacing the policy constraint with a State-Action Occupancy Measure (SAOM) constraint and incorporating length normalization into the Bradley-Terry model, effectively addressing challenges in multi-turn scenarios. Compared to traditional policy constraints, SAOM constraints better guide the agent to select actions that align with expert trajectories, especially in unexplored states, thereby reducing compounding errors." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.491, + 0.927, + 0.624 + ], + "angle": 0, + "content": "To conclude, turn-level alignment offers critical advantages for interactive systems by optimizing contextually grounded responses while preserving conversational flow. However, in multi-turn dialogue tasks, the turn-level granularity may introduce additional training noise. For example, some correct turns in negative samples may be mistakenly treated as incorrect turns in the loss calculation. Additionally, since each turn needs to be processed independently, this can lead to reduced training efficiency." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.643, + 0.757, + 0.658 + ], + "angle": 0, + "content": "3.2 Learning Framework of DPO" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.662, + 0.924, + 0.737 + ], + "angle": 0, + "content": "The learning framework of DPO focuses on how the language model policy learns from preference data. In this section, we present an overview of the learning framework in DPO, as shown in Fig. 3, which encompasses the learning paradigm and the learning objectives." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.75, + 0.693, + 0.765 + ], + "angle": 0, + "content": "3.2.1 Learning Paradigm" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.767, + 0.924, + 0.87 + ], + "angle": 0, + "content": "The learning paradigm in DPO determines how preference data is acquired during model training and falls into three distinct categories: offline learning, where the model learns from pre-collected preference datasets; online Learning, where the model updates based on newly generated data; and active Learning, where the model selectively queries annotators obtain preference data." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.87, + 0.925, + 0.945 + ], + "angle": 0, + "content": "(a) Offline Learning. The original DPO framework [74] itself is an offline learning paradigm, where the model learns from a static, pre-collected dataset of preference pairs. Recent research has explored different approaches to merging preference optimization and supervised fine-tuning" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.913, + 0.034, + 0.922, + 0.043 + ], + "angle": 0, + "content": "9" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.056, + 0.484, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.137, + 0.36, + 0.427, + 0.373 + ], + "angle": 0, + "content": "Fig. 3: An overview of DPO learning framework." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.385, + 0.493, + 0.649 + ], + "angle": 0, + "content": "into a single training phase [190]. CPO [116] incorporates a behavior cloning regularizer through KL divergence minimization between the model and preferred data distribution, which effectively combines into adding a negative log-likelihood term on preferred data alongside the contrastive preference loss. Taking a more direct approach, ORPO [117] proposes a monolithic framework that directly augments the standard negative log-likelihood loss with an odds ratio term comparing chosen and rejected responses, eliminating the need for a separate reference policy while preserving SFT's domain adaptation capabilities. ULMA [71] proposes a hybrid method that applies standard SFT loss on positive samples while using a ranking-based DPO loss on negative samples. PAFT [118] introduces a parallel training paradigm where SFT and preference alignment are performed concurrently on the same pre-trained model and then merged using parameter fusion techniques, avoiding the sequential pipeline that can lead to catastrophic forgetting." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.65, + 0.493, + 0.797 + ], + "angle": 0, + "content": "Several advances explore curriculum learning strategies to enhance DPO performance and training efficiency. CurriDPO [53] introduces curriculum learning by ordering multiple preference pairs from easy to hard based on the rating difference between chosen and rejected responses, where pairs with larger rating gaps are presented first, followed by progressively more challenging pairs with smaller rating differences. sDPO [55] implements curriculum learning by partitioning preference datasets into sequential chunks measured by reward accuracy and applying them incrementally." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.797, + 0.493, + 0.945 + ], + "angle": 0, + "content": "To avoid substantial computational and data annotation costs for preference alignment, fine-tuning-free alignment methods have gained popularity. Linear Alignment [119] works by directly estimating the optimal policy through a one-step update to the output distribution during inference without requiring parameter tuning or feedback data. ICDPO [120] reinterprets DPO's reward-policy relationship to create a fine-tuning-free alignment method that harnesses in-context learning, treating models before and after demonstration exposure as amateur and expert policies, respectively," + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.054, + 0.923, + 0.083 + ], + "angle": 0, + "content": "then computing their log probability ratio to score and rank candidate responses." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.083, + 0.924, + 0.199 + ], + "angle": 0, + "content": "(b) Online Learning. DPO faces significant limitations when relying solely on static, pre-collected preference datasets. These datasets, generated by different models, cause a distribution shift that leads to ineffective off-policy learning as the model evolves [145, 152]. By contrast, online DPO employs an iterative framework that continuously updates the policy with real-time feedback, ensuring on-policy learning and reducing misalignment [143, 144, 233]." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.199, + 0.924, + 0.71 + ], + "angle": 0, + "content": "As online DPO progresses, researchers have introduced more flexible frameworks to tackle key challenges. For instance, Yuan et al. [123] proposed a self-rewarding language model: the model generates prompts and responses, then serves as its own judge via LLM-as-a-Judge prompting, scoring on a 5-point scale. OAIF [121] uses an LLM as an online annotator for real-time feedback, and OFSDPO [122] addresses catastrophic forgetting by using two Low-Rank Adaptive (LoRA) modules with different optimization speeds. BPO [124] constructs a dynamic trust region around the behavior LLM, adjusting it as preference data is collected, unlike methods that rely on fixed reference models. Furthermore, researchers have refined sampling strategies for online DPO. RSO [126] and RS-DPO [125] employ rejection sampling based on reward gaps. ROPO [61] recovers useful information from discarded queries via robustness-guided rejection sampling. Shi et al. [127] introduced DPO-Mix-R and DPO-Mix-P, demonstrating faster convergence by mixing online samplers with uniform samplers. OPTUNE [128] selectively regenerates responses with low reward scores while reusing high-reward responses. Iterative RPO [109] and DPO-ST [129] enhance CoT reasoning by selecting correct and incorrect answers to form preference pairs at each iteration. Xie et al. [103] used MCTS to collect preference data during training. Researchers have also explored advanced optimization techniques. APO [130] incorporates momentum-based acceleration, using an extrapolation step between the current and previous policies to update the policy. Xiong et al. [131] proposed a two-agent, non-symmetric online DPO framework with a main agent for optimal policy learning and an enhancer agent for exploration. COMAL [132] formulates alignment as a two-player zero-sum game, updating its policy toward a regularized Nash equilibrium in each iteration. PCO [133] iteratively trains the model on preference data with pairwise cringe Loss." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.71, + 0.924, + 0.945 + ], + "angle": 0, + "content": "Recent efforts push for greater autonomy by letting models generate their own feedback [62]. SeRA [134] introduces a self-reviewed preference bootstrapping method, using an implicit reward margin to select informative pairs, and employs an ensemble reward approach across iterations. CREAM [135] mitigates self-improving biases by applying a consistency regularization on the preference rankings of consecutive iterations. D2PO [136] combines human-labeled gold data with concurrently updated, discriminator-labeled data. DLMA [137] uses contrastive prompts to compute self-reward scores via log ratio differences, then integrates these scores directly into the DPO objective. Addressing exploration and uncertainty in online DPO has also been a focus [234]. XPO [138] encourages exploration by adding a bonus for responses outside the initial policy's support, and SELM [139] uses an optimism term in reward fitting to" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.908, + 0.034, + 0.924, + 0.044 + ], + "angle": 0, + "content": "10" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.054, + 0.493, + 0.169 + ], + "angle": 0, + "content": "actively seek high-reward responses. ETO [112] alternates exploration and training phases to collect failure trajectories, while VPO [140] applies optimism by regularizing the reward model to favor higher-value responses. Xiong et al. [111] extended DPO from single-turn to multi-turn tasks, balancing KL-regularized and non-regularized objectives, and COPO [141] incorporates a count-based bonus to encourage novel responses with low visitation counts." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.17, + 0.493, + 0.272 + ], + "angle": 0, + "content": "Finally, a growing body of work aims to merge online and offline techniques. HyPO [142] uses offline preference data for DPO training while regularizing via online data. MPO [47] combines the strengths of DPO and PPO in a two-stage process: it first trains DPO on an easier dataset, then uses this model as a reference for PPO training on more challenging samples." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.273, + 0.493, + 0.388 + ], + "angle": 0, + "content": "(c) Active Learning. Active learning in DPO is a strategic approach that aims to reduce the annotation cost and improve sample efficiency by selectively querying annotators for the most informative preference examples. Unlike offline learning that uses a fixed dataset or online learning that generates new data continuously, active learning intelligently selects which data points should be labeled based on model uncertainty or other informativeness criteria." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.389, + 0.495, + 0.681 + ], + "angle": 0, + "content": "Muldrew et al. [146] introduced APL, an iterative data acquisition and fine-tuning loop in which batches of prompt/completion pairs are strategically selected using acquisition functions: a predictive entropy-based approach to measure model uncertainty for prompts and a preference certainty measure based on the implicit Bradley-Terry model for completion pairs in DPO. Unlike two-step selection processes in APL that separately select uncertain input prompts and corresponding completions, divAPO [147] integrates both stages into a single selection phase. divAPO maximizes the preference model certainty by simultaneously evaluating the informativeness of input prompts and completion pairs, while also considering the data distribution of the input prompts. Ji et al. [148] proposed ADPO, which selectively queries human preferences only for responses where the model exhibits high uncertainty while using pseudo-labels for confident cases. Das et al. [149] also employed active learning on RLHF, which actively selects the context-action pairs that maximize exploration and minimize uncertainty in the reward model." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.692, + 0.262, + 0.707 + ], + "angle": 0, + "content": "3.2.2 Learning Objective" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.709, + 0.493, + 0.797 + ], + "angle": 0, + "content": "In what follows, we present the learning objective in DPO, which determines how the model policy is optimized based on preference data. We first discuss multi-objective learning in DPO, which aims to optimize multiple objectives simultaneously. Then, we introduce self-play learning, which leverages self-generated data for preference alignment." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.798, + 0.493, + 0.913 + ], + "angle": 0, + "content": "(a) Multi-Objective Learning. Multi-objective learning in DPO addresses the challenge of simultaneously optimizing the language model for multiple, potentially competing preference dimensions, such as helpfulness, harmlessness, and truthfulness. This approach aims to find a balanced policy that satisfies multiple human values rather than optimizing for a single objective, which more closely mirrors the complexity of real-world human preferences." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.913, + 0.493, + 0.944 + ], + "angle": 0, + "content": "MODPO [150] achieves the sequential optimization of multiple preference objectives by incorporating language" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.054, + 0.925, + 0.373 + ], + "angle": 0, + "content": "modeling directly into reward modeling, using a margin-based loss to maintain performance on previously optimized dimensions. SPO [151] takes a similar iterative constrained optimization approach, optimizing each preference dimension while preventing the degradation of prior alignments through regularization terms. MOSLIM [152] takes a different approach by introducing a multi-head classification reward model that assigns different preference dimensions to separate classification heads, enabling simultaneous optimization of multiple preferences without requiring multiple reward or policy models. HPO [153] incorporates auxiliary objectives through offline RL, where the model uses a weighted maximum likelihood objective that combines a preference alignment term with an advantage-weighted term for maximizing arbitrary auxiliary rewards like readability and safety. CPO [154] introduces explicit preference tokens during training that specify desired scores for different objectives, transforming the multi-objective optimization into a conditional optimization problem. DRDO [155] simultaneously models rewards and preferences through a combination of reward distillation and a contrastive log-unlikelihood term in its loss function." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.374, + 0.927, + 0.491 + ], + "angle": 0, + "content": "(b) Self-Play Learning. Self-play learning in DPO represents an approach where the language model interacts with itself or its previous iterations to generate its own preference data for training, reducing or eliminating the need for human annotations [139, 164]. This method enables continuous self-improvement by leveraging the model's own judgment capabilities to identify and learn from better responses, creating a form of autonomous preference learning." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.491, + 0.925, + 0.738 + ], + "angle": 0, + "content": "SPIN [156] involves a self-play mechanism where the LLM generates synthetic data from its prior iterations, then fine-tunes itself to distinguish these self-generated responses from those of human-annotated data. The method resembles a two-player game, where the model's current iteration tries to improve its responses to better match the target distribution, while the previous iteration attempts to generate responses as close to human data as possible. SPPO [157] treats LLM alignment as a constant-sum two-player game and iteratively refines itself by competing against its previous iteration. Instead of maintaining two competing policies or a reward model, SPO [158] uses a single policy to sample multiple trajectories and uses the proportion of wins in pairwise comparisons as the reward signal. BoNBoN [159] Alignment likewise relies on sampling responses from a base model, but it selects the best ones among n candidates and fine-tunes itself to approximate that best-of-n distribution." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.739, + 0.925, + 0.943 + ], + "angle": 0, + "content": "Some works approach the alignment problem by leveraging Nash equilibrium [132]. Nash-MD [160] learns a preference model from pairwise human feedback and then computes a Nash equilibrium policy that consistently produces preferred responses. Its self-play approach updates the policy by having it compete against itself (or a slight variant of itself) under the learned preference model, which measures how often one response is preferred to another. DNO [161] extends this concept by implementing a batched on-policy algorithm where the current policy generates multiple outputs that are compared both against each other and against a teacher model's outputs. IPO-MD [162] combines the strengths of IPO and Nash-MD, where the model generates data using a mixture policy between the online and reference" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.907, + 0.034, + 0.921, + 0.043 + ], + "angle": 0, + "content": "11" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.054, + 0.493, + 0.142 + ], + "angle": 0, + "content": "policies, and uses a preference model to annotate pairs of generations, making the optimization equivalent to finding a Nash equilibrium through self-play. SRPO [163] modifies Nash-MD by introducing a self-improvement policy that refines model outputs through iterative revisions, enabling offline optimization without a learned reward function." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.162, + 0.342, + 0.176 + ], + "angle": 0, + "content": "3.3 Constraint Mechanism of DPO" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.181, + 0.492, + 0.284 + ], + "angle": 0, + "content": "The constraint mechanism of DPO derives from its reformulation of RLHF, which includes a KL divergence constraint between the current policy and a reference policy. As shown in Fig. 4, we re-examine the constraint mechanism of DPO from the perspective of the reference model and different divergence constraints. We also explore various DPO variants with different safety constraints." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.298, + 0.25, + 0.312 + ], + "angle": 0, + "content": "3.3.1 Reference Model" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.315, + 0.493, + 0.476 + ], + "angle": 0, + "content": "The reference model in DPO functions as an anchor to ensure policy updates remain within a controlled range, preventing excessive deviation from initial behaviors. Typically, the reference model is initialized using the SFT model that serves as the starting point for preference optimization. The choice of reference model significantly impacts optimization dynamics. A static reference model ensures stable training but may limit adaptability. In the following subsections, we introduce two advanced approaches: reference-free DPO eliminates reliance on the reference model, while dynamic-reference DPO employs an evolving reference model." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.477, + 0.493, + 0.826 + ], + "angle": 0, + "content": "(a) Reference-Free DPO. To reduce the computational and memory costs associated with a reference model, many algorithms have explored training modes that do not require loading the reference model. Xu et al. [116] replaces the reference model with a uniform prior distribution, adding an SFT loss term on preferred data to maintain consistency with the desired behavior. ORPO [117] integrates an odds ratio-based penalty with traditional SFT loss, increasing the probability of preferred responses while decreasing undesirable ones, thereby enabling single-stage training without a separate reference model. SimPO [166] directly uses the average log probability as implicit rewards. This removes the requirement for a separate reference model, significantly improving computational and memory efficiency. SimPER [167] also directly optimizes reverse perplexity for preferred versus rejected responses, creating a preference optimization approach that does not require a separate reference model, thus simplifying training. Despite these advancements, [168] argue that a reference model remains crucial. They compared two reference-free variants using posterior probabilities and likelihood functions as rewards, respectively, and found the original DPO consistently outperformed both. Their results indicate that a strong, well-aligned reference policy can significantly enhance DPO performance." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.826, + 0.493, + 0.945 + ], + "angle": 0, + "content": "(b) Dynamic-Reference DPO. Offline DPO methods often suffer from reward over-optimization, meaning that as the trained model deviates from the reference model, the quality of generated samples tends to degrade. To address this issue, Gorbatovski et al. [165] proposed dynamically updating the reference model using the current model parameters during training, preventing excessive divergence and maintaining high-quality outputs. Curri-DPO [53] and sDPO [55] adopt" + }, + { + "type": "list", + "bbox": [ + 0.073, + 0.477, + 0.493, + 0.945 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.054, + 0.918, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.563, + 0.338, + 0.866, + 0.351 + ], + "angle": 0, + "content": "Fig. 4: An overview of DPO constraint mechanism." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.358, + 0.925, + 0.52 + ], + "angle": 0, + "content": "curriculum learning by sorting data samples from simpler to more complex based on predefined metrics. At each training iteration, the model from the previous step serves as the updated reference model to provide constraints, facilitating progressive learning. Similarly, MPO [47] partitions datasets according to task difficulty, employing a two-stage training procedure. The model trained in the initial stage serves as the reference for the subsequent stage. Additionally, M-DPO [89] compares the performance of a fixed reference model versus a dynamic reference model, finding that the latter yields superior results." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.532, + 0.719, + 0.546 + ], + "angle": 0, + "content": "3.3.2 Divergence Constraint" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.549, + 0.925, + 0.636 + ], + "angle": 0, + "content": "Divergence constraints in DPO play a crucial role in constraining model optimization, balancing alignment performance and model stability. In the following subsections, we introduce two modifications to the divergence constraint: one for enhancing diversity and the other for improving generalization." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.637, + 0.925, + 0.827 + ], + "angle": 0, + "content": "(a) Diversity. Standard DPO typically uses reverse KL divergence equivalent to RLHF. However, the mode-seeking nature of reverse KL divergence reduces the diversity of the generated outputs. To overcome this limitation, f-DPO [169] explores various divergences, including forward KL divergence, reverse KL divergence, Jensen-Shannon divergence, and \\(\\alpha\\)-divergence, to achieve a better trade-off between alignment performance and diversity. Slocum et al. [170] further proposes splitting the KL divergence term into entropy and cross-entropy terms. This decoupling allows independent control of generation diversity and closeness to the reference model, preserving output diversity without degrading overall model quality." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.827, + 0.927, + 0.945 + ], + "angle": 0, + "content": "(b) Generalization. Over-optimization in DPO can negatively impact generalization, causing reduced performance on inputs outside the training distribution. To mitigate this, Huang et al. [178] introduce \\(\\chi^2\\)-divergence as a more aggressive form of regularization compared to KL divergence, alleviating the over-optimization problem. DPO-Kernels [171] employs data-driven methods to select optimal kernel-divergence pairs dynamically, improving task adaptability" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.637, + 0.927, + 0.945 + ], + "angle": 0, + "content": null + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.908, + 0.034, + 0.923, + 0.043 + ], + "angle": 0, + "content": "12" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.054, + 0.493, + 0.434 + ], + "angle": 0, + "content": "and robustness. FlipGuard [172] introduces a customized reward characterization to monitor model performance. If performance drops relative to earlier versions, FlipGuard constrains the model's updates to ensure alignment with previous stable behavior. FPO [173] leverages the feature-level constraints using Sparse Autoencoders (SAEs) to improve computational efficiency and training stability. SPO [176] integrates a natural preference loss with a KL divergence-based regularization term computed over the entire model output distribution. By adjusting this divergence term, SPO prevents unwanted shifts beyond the preference dataset, ensuring stable alignment. EXO [175] argues that minimizing the forward KL divergence in DPO introduces bias when approximating the optimal policy. They establish a generalized alignment objective and reveal the equivalence between maximizing KL regularization rewards and minimizing the reverse KL divergence relative to the optimal policy. QDPO [177] utilizes divergence between the quantized model and the full-precision model for preference optimization, effectively addressing the token-flipping issue. Token-flipping refers to the phenomenon where quantization errors skew token distributions, leading to incorrect token selection. GPO [174] constructs a framework that unifies different DPO-related algorithms through theoretical derivations, enabling a deeper understanding of the regularization mechanisms in the DPO family of algorithms." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.447, + 0.25, + 0.461 + ], + "angle": 0, + "content": "3.3.3 Safety Constraint" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.466, + 0.493, + 0.86 + ], + "angle": 0, + "content": "Safety constraints in DPO aim to prevent LLMs from generating harmful, biased, or unethical outputs. However, traditional alignment algorithms often fail to address safety concerns. To enhance the safety alignment, recent studies have introduced several specialized mechanisms based on DPO. SafeDPO [179] introduces a streamlined approach for safety alignment by implicitly optimizing safety objectives within a single stage of policy learning. SACPO [180] addresses safety constraints by explicitly formulating language model alignment as a constrained optimization problem, using DPO to optimize the model under safety constraints. Zhang et al. [184] propose creating a backtracking preference dataset that identifies and reverses unsafe outputs, enhancing the safety and robustness of the model. C-DPO [181] integrates dual gradient descent into DPO to balance safety and utility efficiently. This approach achieves a robust trade-off between helpfulness and harmlessness, offering explicit safety guarantees. ADPO [182] introduces adversarial techniques into DPO. It specifically trains models to reduce the probability of unsafe outputs by deliberately generating harmful responses using controlled toxic tokens. Finally, Lee et al. [183] explore the internal mechanisms through which DPO reduces harmful outputs. Their findings suggest that DPO does not remove harmful behaviors learned during pretraining but instead teaches models to bypass or suppress these behaviors. This insight helps explain certain safety vulnerabilities like jailbreaks." + }, + { + "type": "title", + "bbox": [ + 0.073, + 0.879, + 0.287, + 0.894 + ], + "angle": 0, + "content": "3.4 Model Property of DPO" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.899, + 0.492, + 0.945 + ], + "angle": 0, + "content": "DPO has shown great promise in aligning LLMs with human preferences by directly optimizing model outputs based on preference data. During this process, the underlying models" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.056, + 0.917, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.337, + 0.846, + 0.351 + ], + "angle": 0, + "content": "Fig. 5: An overview of DPO model property." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.357, + 0.924, + 0.447 + ], + "angle": 0, + "content": "exhibit certain properties that are crucial for understanding their behavior and effectiveness. These properties can be broadly categorized into two aspects: the generation property and the optimization property, as shown in Fig. 5. In the following sections, we explore these two properties in more detail, analyzing their implications for model alignment." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.459, + 0.704, + 0.474 + ], + "angle": 0, + "content": "3.4.1 Generation Property" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.476, + 0.924, + 0.579 + ], + "angle": 0, + "content": "The generation property of DPO primarily concerns issues related to distribution shifts and length biases. DPO is sensitive to distribution shifts between the base model outputs and the preference data, which may reduce diversity and generalization. Additionally, DPO has a tendency to favor longer responses, a phenomenon known as morbidity, which can negatively impact performance and user experience." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.579, + 0.924, + 0.854 + ], + "angle": 0, + "content": "(a) Distribution Shift. In RLHF, the reward model is trained on a static set of preference data collected offline. During fine-tuning, the generated responses often differ from this original training data, resulting in a distribution shift. This shift can cause inaccurate reward predictions and lead to over-optimization. The implicit reward model in DPO also suffers from this distribution shift issue. Moreover, Lin et al. [188] have shown that the implicit reward model in DPO performs poorly on Out-Of-Distribution (OOD) data compared to explicit reward models. Experimental results indicate that DPO can transfer probability mass to the highreward response regions covered by the preference data, but it may also cause the distribution of responses generated by the model to deviate significantly from that of the reference policy, resulting in responses that do not meet expectations [189]. To address these problems, many researchers are now exploring online DPO approaches [109, 121, 122, 125], aiming to mitigate OOD by continuously updating preference data during training." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.855, + 0.925, + 0.945 + ], + "angle": 0, + "content": "Existing DPO methods also face significant limitations due to their dependence on specific training tasks. Their optimal solutions lack robustness when applied to OOD tasks. Thus, SRPO [163] reframes alignment as a self-improvement process, which optimizes a self-improvement policy and a generative policy using a min-max objective, ensuring" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.908, + 0.034, + 0.924, + 0.044 + ], + "angle": 0, + "content": "13" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.054, + 0.493, + 0.17 + ], + "angle": 0, + "content": "robustness by making the solution independent of training tasks. Zhang et al. [139] also identify notable issues in DPO when handling OOD tasks. First, DPO tends to overly favor novel content it has not seen during training. Second, it easily gets stuck in local optima, limiting exploration. To address these problems, they propose Self-Exploring Language Models (SELM), incorporating an optimism term to encourage broader exploration of new responses." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.17, + 0.493, + 0.273 + ], + "angle": 0, + "content": "Another significant challenge of DPO is preference drift, where human preferences evolve, changing data distributions over time. Traditional DPO algorithms typically overlook such temporal shifts, mistakenly interpreting them as noise. To address this, NS-DPO [185] propose to assign higher weights to recent data, allowing models to better adjust to evolving preferences." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.273, + 0.493, + 0.405 + ], + "angle": 0, + "content": "(b) Length Bias. Length bias in DPO refers to the tendency of model-generated outputs to become excessively long during training. This issue is similar to the length bias observed in RLHF [197] and is particularly pronounced in DPO. Length bias affects response quality and overall model performance. To mitigate this issue, researchers have developed several solutions, which can be categorized into three main approaches: length regularization, length normalization, and length sampling." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.405, + 0.493, + 0.637 + ], + "angle": 0, + "content": "Length regularization is a common approach to controlling length bias in DPO. By introducing regularization terms into the objective function, the model can constrain response length and reduce morbidity, thereby alleviating the length bias problem. R-DPO [191] introduces a length-based penalty term to the DPO objective function, explicitly discouraging morbidity. \\(\\mathrm{D}^2\\mathrm{PO}\\) [99] introduces a dynamic weighting mechanism by incorporating a temporal decay factor. Unlike previous methods that apply uniform reward contributions across sequences, \\(\\mathrm{D}^2\\mathrm{PO}\\) adjusts the influence of each reward based on its position in the response. Higher weights are assigned to rewards associated with earlier tokens, as they are more critical for model alignment, while later rewards gradually receive lower weights. This adaptive approach prevents overfitting to less relevant tokens, thereby addressing length bias in DPO." + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.637, + 0.495, + 0.945 + ], + "angle": 0, + "content": "Length normalization aims to eliminate the loss bias caused by response length differences, allowing the model to evaluate texts of varying lengths more fairly. This approach prevents the model from developing an unreasonable preference for either long or short responses [198]. RRHF [190] and SimPO [166] first propose to apply length normalization to responses, ensuring that the loss remains unaffected by response length. LN-DPO [194] further integrates SimPO-like length normalization into DPO, demonstrating that this approach enhances response quality while mitigating morbidity. LD-DPO [195] achieves length desensitization by reparameterizing the likelihood in DPO. Specifically, it decomposes the likelihood of the longer response in a preference pair into the product of the likelihood of the public-length portion and the likelihood of the excessive portion. It then introduces a hyperparameter to mitigate the morbidity preference. This adjustment smooths the relationship between likelihood and response length, reducing its impact on optimization. For multi-turn dialogue tasks, DMPO [115] introduces length normalization for the number of turns in multi-turn preference optimization." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.054, + 0.925, + 0.346 + ], + "angle": 0, + "content": "An alternative approach to controlling length bias in DPO is through sampling-based methods. SamPO [192] introduces a down-sampling method to compute regularized KL divergences. By balancing token-level probability distributions between preferred and rejected responses, SamPO reduces length bias in DPO training. Yuan et al. [193] propose Length-Instruction Fine-Tuning (LIFT), a method to improve instruction-following models' ability to adhere to length constraints by augmenting existing training data with explicit length instructions and using DPO for training. This enables the model to generalize across prompts requiring different response lengths. For long-context tasks, LongPO [196] enables short-context LLMs to self-evolve for long-context tasks by learning from self-generated short-to-long preference data, which includes paired responses for long-context inputs and their compressed short-context counterparts. LongPO incorporates a short-to-long KL constraint to prevent degradation of short-context performance during long-context alignment, achieving strong performance on both short- and long-context tasks." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.357, + 0.715, + 0.373 + ], + "angle": 0, + "content": "3.4.2 Optimization Property" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.374, + 0.925, + 0.476 + ], + "angle": 0, + "content": "The optimization property of DPO involves likelihood collapse and alignment tax. While DPO aims to increase the likelihood of preferred responses and decrease dispreferred ones, the actual optimization process does not explicitly enforce this balance. Moreover, alignment improvements often come at the cost of the original capabilities of LLMs, known as alignment tax." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.477, + 0.925, + 0.768 + ], + "angle": 0, + "content": "(a) Likelihood Collapse. Likelihood collapse refers to the unintended reduction in the likelihood of both preferred and dispreferred responses during DPO training [92]. This phenomenon can lead to unintentional unalignment, where the model's outputs deviate from human preferences, potentially producing undesirable or harmful responses. This phenomenon is also referred to as likelihood displacement in prior studies [204]. Additionally, the gradients associated with increasing the likelihood of preferred responses and decreasing that of dispreferred responses can become entangled, hindering effective learning. This entanglement complicates the optimization process, making it challenging to achieve the desired alignment [203]. Theoretical analyses have further elucidated the underlying causes of likelihood collapse. In particular, Feng et al. [202] developed an analytical framework grounded in field theory. Their analysis of the gradient vector field of the DPO loss function revealed that the loss function decreases the probability of generating human-disliked data at a faster rate than it increases the probability of generating human-like data." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.768, + 0.925, + 0.943 + ], + "angle": 0, + "content": "Several strategies have been proposed to address likelihood collapse. Pal et al. [200] introduce DPO-Positive (DPOP), which adds a penalty term to maintain a high log-likelihood for preferred examples. Similarly, LLaMA [235] augments DPO training with a negative log-likelihood term to stabilize training and preserve the log-likelihood of chosen responses [109]. Flex-DPO [201] adaptively adjusts parameters to slow the decline in the likelihood of dispreferred responses and balance gradients for both chosen and rejected outputs. D'Oosterlinck et al. [199] propose Anchored Preference Optimization (APO), which provides fine-grained control over probability updates: APO-zero increases the" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.908, + 0.034, + 0.923, + 0.043 + ], + "angle": 0, + "content": "14" + }, + { + "type": "table_caption", + "bbox": [ + 0.245, + 0.048, + 0.751, + 0.062 + ], + "angle": 0, + "content": "TABLE 1: An overview of datasets (upper row) and benchmarks (lower row) for DPO." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.063, + 0.921, + 0.378 + ], + "angle": 0, + "content": "
DatasetTask DescriptionData Size (Training & Test)Data SourceData StructureEvaluation Metric
UltraFeedback [237]Instruction-Following, Helpful64K&-AIList-
SafeRLHF [238]Harmless, Helpful73.9K&8.21KHuman&AIPair-
HelpSteer [239]Helpful35.3K&1.8KHumanPoint-
PRM800K [240]Mathematical Reasoning800K&-HumanPoint-
SHP-2 [241]Q&A From Reddit3600K&241KHumanPair-
Nectar [242]Conversations183K&-AIList-
OpenOrca [243]Conversations2940K&-AISample-
Capybara [244]Multi-Turn Conversations16K&-Human&AISample-
Step-DPO [100]Mathematical Reasoning10.8K&-Human&AIPair-
BeaverTails [245]Harmless, Helpful330K&36KHuman&AIPoint-
IMDb [246]Movie Reviews25K&25KHumanSampleAccuracy
Reddit TL;DR [247]Summarization1330K&-HumanSampleWin Rate
Anthropic-HH [248]Harmless, Helpful161K&8.55KAIPairWin Rate
GSM8K [249]Mathematical Reasoning7.47K&1.32KHumanSampleAccuracy
AlpacaEval2 [250]Automatic Evaluation-&0.8KAISampleWin Rate
MT-Bench [251]Multi-Turn Question-&3.3KHumanPairWin Rate
AdvBench [252]Harmful Behaviors-&0.5KHumanSampleAttack Success
Arena-Hard [253]Updating Evaluation-&0.5KAISampleWin Rate
TruthfulQA [254]Truthful-&0.8KHumanPairAccuracy
IFEval [255]Instruction-Following-&0.5KHumanSampleAccuracy
BBH [256]Multistep Reasoning-&23 TasksHumanSampleAccuracy
MATH [257]Mathematical Reasoning7.5K&5KHumanSampleAccuracy
GPQA [258]Biology, Physics, and Chemistry-&0.45KHumanSampleAccuracy
MUSR [259]Multistep Reasoning-&0.76KAISampleAccuracy
MMLU-Pro [260]Language Understanding-&12KHuman&AISampleAccuracy
" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.39, + 0.492, + 0.435 + ], + "angle": 0, + "content": "probability of winning outputs and decreases that of losing outputs, whereas APO-down decreases both, but with a stronger decline for losing outputs." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.44, + 0.493, + 0.734 + ], + "angle": 0, + "content": "Another notable challenge related to likelihood collapse is likelihood over-optimization, where the performance of a model on a proxy metric (such as its own likelihood estimates) improves, while its true performance does not. Zhang and Ranganath [236] show that reductions in the likelihood loss of DPO do not necessarily translate into higher win rates. Similarly, Shi et al. [205] further investigates the problem of likelihood over-optimization in DPO, demonstrating that higher completion likelihoods do not necessarily correlate with better model performance and may even degrade it. This study identifies key indicators of over-optimization and highlights the need to balance likelihood optimization with output diversity. e-DPO [187] also shows that DPO can lead to degenerate policies due to overfitting, and proposes a solution using reward model distillation to regularize the implicit reward of the language model. The method trains the language model to match the probability distribution induced by a reward model and introduces a pessimistic extension to handle uncertainty in the reward model, thereby improving the robustness of DPO." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.738, + 0.496, + 0.945 + ], + "angle": 0, + "content": "(b) Alignment Tax. Alignment tax refers to the unintended consequence where improving a model's preference alignment degrades its general capabilities acquired during pretraining [206]. Thakkar et al. [207] demonstrate the sensitivity of DPO to training data composition, showing significantly worse performance degradation than SFT when using mixed-preference datasets. Furthermore, Chen et al. [209] identify that DPO struggles with optimizing ranking tasks. While DPO improves ranking accuracy, it disproportionately harms generative capabilities. Pentyala et al. [118] also observes capability forgetting during sequential training, where DPO objectives conflict with previously learned SFT patterns. To address this, researchers propose model merging strategies that balance alignment and performance." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.39, + 0.926, + 0.524 + ], + "angle": 0, + "content": "PAFT [118] separately trains SFT and DPO objectives on a pretrained model using distinct datasets, then merges the parameters through weighted averaging. Additionally, Lu et al. [208] proposes online merging optimizers, which integrate model merging into each optimization step of DPO to balance human preferences and basic capabilities. By merging gradients with parameter differences between SFT and pretrained models, these optimizers effectively enhance alignment while mitigating alignment tax." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.545, + 0.78, + 0.56 + ], + "angle": 0, + "content": "4 BENCHMARKS AND ANALYSIS" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.567, + 0.925, + 0.656 + ], + "angle": 0, + "content": "In this section, we provide a comprehensive overview of existing benchmarks and evaluation for DPO methods. We first introduce the key datasets and benchmarks used to train or evaluate DPO models. We then present a comparative analysis of the performance of different DPO methods on these benchmarks, highlighting their strengths and limitations." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.675, + 0.742, + 0.69 + ], + "angle": 0, + "content": "4.1 Datasets and Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.695, + 0.925, + 0.945 + ], + "angle": 0, + "content": "A diverse range of datasets and benchmarks has been specifically curated to facilitate research in DPO. Table 1 summarizes these datasets and benchmarks, highlighting their task descriptions, dataset sizes, data sources, data structures, and evaluation metrics. These datasets and benchmarks span a broad range of tasks, such as harmlessness and helpfulness evaluation and mathematical reasoning. They also exhibit significant diversity in scale, ranging from smaller, specialized datasets to large-scale collections such as SHP-2, which contains over 3.6 million samples. Additionally, datasets differ in their sources: some rely purely on human annotations, others on AI-generated content, and many adopt a hybrid approach combining human and AI-generated data. The data structures employed across these datasets include single-sample without preference label, point-wise annotations, pair-wise comparisons, and list-wise comparisons. Common evaluation metrics include accuracy" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.908, + 0.034, + 0.923, + 0.043 + ], + "angle": 0, + "content": "15" + }, + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.048, + 0.884, + 0.062 + ], + "angle": 0, + "content": "TABLE 2: Experimental results of different DPO variants on Open LLM Leaderboard. The underline indicates the best performance." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.063, + 0.921, + 0.325 + ], + "angle": 0, + "content": "
ModelMistral-7B-BaseLLaMA-3-8B-Base
IFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGEIFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGE
SFT3.441.19.228.842.027.725.429.046.315.328.641.331.031.9
RRHF [190]10.040.61.726.446.326.125.231.046.813.931.436.830.531.7
SLiC-HF [230]11.044.09.929.242.628.127.541.749.517.530.439.731.735.1
DPO [74]11.143.77.128.543.826.726.834.348.217.231.940.131.533.9
IPO [75]9.442.89.729.739.727.826.535.349.015.932.841.431.934.4
CPO [116]8.042.79.628.942.127.326.432.446.916.830.639.131.832.9
KTO [67]12.943.712.028.946.128.328.640.248.318.031.040.131.134.8
ORPO [117]28.446.413.530.241.429.531.640.049.116.830.738.432.034.5
R-DPO [191]10.043.07.628.739.327.226.036.448.817.231.640.631.534.4
SimPO [166]11.143.18.428.939.527.226.440.848.615.831.040.531.834.7
ModelMistral-7B-InstructLLaMA-3-8B-Instruct
IFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGEIFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGE
SFT48.446.210.929.147.627.134.950.749.326.931.037.935.738.6
RRHF [190]45.245.310.128.544.226.233.351.349.327.229.639.535.338.7
SLiC-HF [230]39.446.211.428.749.026.833.641.650.926.331.339.235.337.4
DPO [74]49.045.611.026.946.126.834.248.950.125.829.438.736.038.2
IPO [75]42.645.311.827.849.327.234.050.449.526.329.637.935.738.2
CPO [116]38.846.010.128.548.426.933.150.649.126.831.338.135.838.6
KTO [67]46.245.710.927.846.027.334.043.150.126.331.238.135.037.3
ORPO [117]37.645.111.228.246.926.532.643.050.626.929.339.135.137.3
R-DPO [191]46.845.99.928.746.227.634.250.950.325.329.839.035.738.5
SimPO [166]45.445.910.428.345.027.133.748.849.225.029.339.235.137.8
" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.338, + 0.493, + 0.399 + ], + "angle": 0, + "content": "(for tasks like mathematical reasoning found in GSM8K and MATH), win rates derived from pairwise comparisons (such as MT-Bench and Anthropic-HH), and attack success rates used for assessing adversarial robustness (AdvBench)." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.414, + 0.173, + 0.428 + ], + "angle": 0, + "content": "4.2 Results" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.432, + 0.493, + 0.65 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of different DPO variants, we conduct experiments on the Open LLM Leaderboard. We compare different DPO variants using Mistral-7B-Base, Mistral-7B-Instruct [261], LLaMA-3-8B-Base, and LLaMA-3-8B-Instruct [235] as starting points. The overall experimental setup follows Meng et al. [166], ensuring a reproducible evaluation of different DPO variants. For Mistral-7B-Base and LLaMA-3-8B-Base, the SFT models are trained based on the UltraChat-200k dataset [262], and subsequently applied different DPO variants on the SFT models using the UltraFeedback dataset [237]. For Mistral-7B-Instruct and LLaMA-3-8B-Instruct, which have already undergone instruction-tuning, the preference dataset is regenerated by collecting responses from the SFT models using prompts from the UltraFeedback dataset [237]." + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.651, + 0.495, + 0.943 + ], + "angle": 0, + "content": "The experimental results, as summarized in Table 2, highlight the performance of different DPO variants across various benchmarks. For the Mistral-7B-Base and LLaMA-3-8B-Base models, ORPO consistently achieves the highest average scores, indicating its effectiveness in aligning models with human preferences. Notably, ORPO outperforms other methods on IFEval, BBH, and MATH, demonstrating its superiority in instruction-following and mathematical reasoning tasks. Meanwhile, SLiC-HF and KTO also achieve competitive results, particularly in BBH and GPQA, suggesting that these methods effectively leverage preference data for enhanced performance. For the Mistral-7B-Instruct and LLaMA-3-8B-Instruct models, the improvements across different DPO variants are more nuanced. While DPO and R-DPO show strong performance in IFEval and MMLU-Pro, IPO and CPO demonstrate robustness in handling complex reasoning tasks like MATH and GPQA. Overall, the results indicate that different DPO variants exhibit varying strengths across benchmarks, with some methods excelling in base models while others are more effective for instruct models." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.337, + 0.66, + 0.352 + ], + "angle": 0, + "content": "5 APPLICATIONS" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.356, + 0.927, + 0.446 + ], + "angle": 0, + "content": "In this section, we discuss the applications of DPO in various domains, including different LLM-based applications, diffusion models, and multi-modal LLMs. We provide an overview of the key challenges and opportunities in each domain and highlight the potential impact of DPO on real-world applications." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.463, + 0.729, + 0.479 + ], + "angle": 0, + "content": "5.1 LLM-based Applications" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.481, + 0.925, + 0.716 + ], + "angle": 0, + "content": "DPO has emerged as a powerful paradigm for aligning LLMs with human preferences across diverse applications [116, 235, 263, 264]. In code generation, DPO enhances control over code quality by optimizing based on preferences from automated tests [265, 266, 267]. In mathematical reasoning, DPO reduces errors in complex problem-solving by emphasizing step-level preference optimization [100, 101, 129, 268]. Multilingual applications leverage DPO to synchronize cross-lingual preferences, thereby improving translation accuracy and cultural relevance [107, 269]. Recommendation systems utilize DPO to refine personalization by incorporating user preference data to optimize item rankings, thereby enhancing the model ability to distinguish preferred items from less preferred ones [270, 271]. These examples highlight the adaptability of DPO in achieving human-aligned outputs across diverse tasks." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.734, + 0.673, + 0.748 + ], + "angle": 0, + "content": "5.2 Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.752, + 0.925, + 0.945 + ], + "angle": 0, + "content": "In the realm of diffusion models, DPO has been adapted to better align generated content with user expectations [272, 273, 274, 275]. By optimizing preferences over image-text pairs, DPO enhances the semantic accuracy of generated images and mitigates the production of undesirable or biased content. Studies have demonstrated that diffusion models fine-tuned with DPO respond more accurately to complex prompts compared to those trained with traditional techniques. Moreover, the efficiency of DPO allows for the fine-tuning of large-scale models using limited preference data, addressing significant computational challenges in training diffusion models [276, 277, 278]. While scaling DPO for high-resolution and dynamic content generation remains" + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.908, + 0.034, + 0.924, + 0.044 + ], + "angle": 0, + "content": "16" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.054, + 0.493, + 0.085 + ], + "angle": 0, + "content": "challenging, its ability to simplify reward modeling makes it a promising method for controlled content creation [279]." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.103, + 0.248, + 0.117 + ], + "angle": 0, + "content": "5.3 Multi-Modal LLMs" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.122, + 0.493, + 0.284 + ], + "angle": 0, + "content": "For multi-modal LLMs, DPO plays a crucial role in aligning preferences across different data types, thereby improving coherence in tasks such as visual question answering and image captioning [89, 280, 281, 282, 283]. By optimizing alignment between textual responses and visual inputs, DPO reduces hallucinations in multi-modal interactions, ensuring outputs remain faithful to the given context. Although reconciling different types of feedback can be challenging, DPO offers a practical framework for lightweight adaptation, making it well-suited to preference-intensive multi-modal applications [280, 284, 285]." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.305, + 0.434, + 0.32 + ], + "angle": 0, + "content": "6 CHALLENGES AND FUTURE DIRECTIONS" + }, + { + "type": "text", + "bbox": [ + 0.073, + 0.325, + 0.492, + 0.414 + ], + "angle": 0, + "content": "In this section, we discuss the key challenges and future directions in DPO research. We identify several critical issues that need to be addressed to further advance the field. Moreover, we propose several promising research directions that can help overcome these challenges and accelerate the adoption of DPO in the future." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.433, + 0.362, + 0.448 + ], + "angle": 0, + "content": "6.1 Efficient Preference Optimization" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.451, + 0.495, + 0.716 + ], + "angle": 0, + "content": "Efficient preference optimization remains a pivotal challenge, as current DPO methods hinge on the availability of high-quality preference data, yet the manual collection of human annotations is both time-consuming and labor-intensive while automatically model-generated datasets often suffer from issues such as limited diversity, inherent biases, and insufficient fidelity to human judgment [121, 122, 128, 129]. Moreover, even though DPO circumvents the intricacies of reward model engineering common in RL, it does not fully leverage the exploratory strengths that RL methods offer, as evidenced by recent advances in reasoning approaches where RL-based training has achieved notable successes [18, 19]. This opens up an avenue for future research to not only enhance data efficiency through advanced learning techniques but also to integrate novel exploration mechanisms [138, 141], potentially through hybrid models that amalgamate the direct preference optimization benefits of DPO with the robust exploratory capabilities characteristic of RL." + }, + { + "type": "title", + "bbox": [ + 0.074, + 0.734, + 0.387, + 0.749 + ], + "angle": 0, + "content": "6.2 Multi-Modal Preference Optimization" + }, + { + "type": "text", + "bbox": [ + 0.072, + 0.753, + 0.496, + 0.945 + ], + "angle": 0, + "content": "Multi-Modal Preference Optimization presents another frontier, given that existing DPO frameworks have primarily targeted text-based modalities while many real-world applications demand the alignment of diverse human preferences across text, images, audio, and even video [280, 284, 285, 286, 287]. In scenarios where cross-modal cues might conflict, such as the need for concise text paired with richly detailed imagery, the challenge lies in constructing a unified preference representation space that can intelligently and automatically recalibrate the priority of different modalities based on the contextual demands of the task at hand [89, 282, 283]. Future directions in this area could involve the development of innovative multi-modal preference encoding architectures," + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.054, + 0.925, + 0.114 + ], + "angle": 0, + "content": "which are capable of disentangling compound preferences into modality-specific and cross-modal components that align conflicting preferences while also adapting dynamically to changing inputs." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.137, + 0.817, + 0.152 + ], + "angle": 0, + "content": "6.3 Continuous Preference Optimization" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.159, + 0.925, + 0.393 + ], + "angle": 0, + "content": "Continuous preference optimization addresses the dynamic nature of human preferences that evolve over time or vary with different phases of a task, a factor that static DPO models often fail to capture [123, 135, 137, 185]. As social norms and individual preferences shift, there is an increasing need for systems that can continuously recalibrate their alignment strategies in real time while simultaneously mitigating the risk of catastrophic forgetting. Future research in this domain may focus on meta-learning approaches that enable models to learn not only from the current state of preferences but also how to efficiently adapt when these preferences change. By integrating online learning frameworks with mechanisms for detecting temporal shifts and contextual variability in user behavior, researchers can pave the way toward systems that remain consistently relevant and effective in the face of evolving societal and individual expectations." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.417, + 0.825, + 0.433 + ], + "angle": 0, + "content": "6.4 Interpretable Preference Optimization" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.438, + 0.927, + 0.688 + ], + "angle": 0, + "content": "Interpretable preference optimization is critical for building trust in models that implicitly align human values, as the opaque nature of current DPO complicates the ability to audit and control the alignment process. In practice, human preferences are multi-dimensional [150, 151, 154], encompassing aspects such as factual accuracy, fairness, creativity, and beyond, and there is a pressing need to decompose these complex preferences into interpretable components that can be individually examined and fine-tuned. Future research could leverage advances in explainable techniques to develop models that not only achieve fine-grained alignment across diverse values but also provide transparent insights into how different preference dimensions interact to shape final decisions. This level of interpretability would allow stakeholders to balance competing values more effectively, ensuring that the alignment process remains both accountable and adaptable as societal norms continue to evolve." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.714, + 0.649, + 0.729 + ], + "angle": 0, + "content": "7 CONCLUSION" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.738, + 0.925, + 0.945 + ], + "angle": 0, + "content": "In recent years, DPO has emerged as a promising paradigm for aligning LLMs with human preferences by directly optimizing model policies using preference data. Despite its potential, the DPO research landscape remains fragmented, with a lack of systematic organization and comparative analysis. In this survey, we present a comprehensive overview of DPO and introduce a novel taxonomy that categorizes existing works into four key dimensions: data strategy, learning framework, constraint mechanism, and model property. We have also discussed the key benchmarks, evaluation results, and applications of DPO, highlighting the challenges and future directions in this field. By providing a systematic analysis of the existing DPO methods, we aim to facilitate further research and development in this area." + } + ], + [ + { + "type": "page_number", + "bbox": [ + 0.908, + 0.034, + 0.922, + 0.043 + ], + "angle": 0, + "content": "17" + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.053, + 0.188, + 0.067 + ], + "angle": 0, + "content": "REFERENCES" + }, + { + "type": "ref_text", + "bbox": [ + 0.077, + 0.077, + 0.492, + 0.099 + ], + "angle": 0, + "content": "[1] Wayne Xin Zhao et al. A survey of large language models. arXiv, 2023." + }, + { + "type": "ref_text", + "bbox": [ + 0.077, + 0.101, + 0.492, + 0.123 + ], + "angle": 0, + "content": "[2] Humza Naveed et al. 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TPAMI, 2025." + }, + { + "type": "list", + "bbox": [ + 0.508, + 0.056, + 0.922, + 0.93 + ], + "angle": 0, + "content": null + } + ] +] \ No newline at end of file diff --git a/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_origin.pdf b/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bc35b2196f2cc55d5afcb7fe0b91739d68f939f5 --- /dev/null +++ b/data/2025/2503_11xxx/2503.11701/f561bad2-8e9b-4fb7-9083-b32d2bfd8f1f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:33d9968dce449e0efc3a3bb1450fe7ea34dcec36ed6d534a445ab4dd321f41f8 +size 1136222 diff --git a/data/2025/2503_11xxx/2503.11701/full.md b/data/2025/2503_11xxx/2503.11701/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d760d6a043a7a4100634ab7679c1e67ed77f281e --- /dev/null +++ b/data/2025/2503_11xxx/2503.11701/full.md @@ -0,0 +1,709 @@ +# A Survey of Direct Preference Optimization + +Shunyu Liu, Wenkai Fang, Zetian Hu, Junjie Zhang, Yang Zhou, Kongcheng Zhang, Rongcheng Tu, Ting-En Lin, Fei Huang, Mingli Song, Yongbin Li, and Dacheng Tao, Fellow, IEEE + +Abstract—Large Language Models (LLMs) have demonstrated unprecedented generative capabilities, yet their alignment with human values remains critical for ensuring helpful and harmless deployments. While Reinforcement Learning from Human Feedback (RLHF) has emerged as a powerful paradigm for aligning LLMs with human preferences, its reliance on complex reward modeling introduces inherent trade-offs in computational efficiency and training stability. In this context, Direct Preference Optimization (DPO) has recently gained prominence as a streamlined alternative that directly optimizes LLMs using human preferences, thereby circumventing the need for explicit reward modeling. Owing to its theoretical elegance and computational efficiency, DPO has rapidly attracted substantial research efforts exploring its various implementations and applications. However, this field currently lacks systematic organization and comparative analysis. In this survey, we conduct a comprehensive overview of DPO and introduce a novel taxonomy, categorizing previous works into four key dimensions: data strategy, learning framework, constraint mechanism, and model property. We further present a rigorous empirical analysis of DPO variants across standardized benchmarks. Additionally, we discuss real-world applications, open challenges, and future directions for DPO. This work delivers both a conceptual framework for understanding DPO and practical guidance for practitioners, aiming to advance robust and generalizable alignment paradigms. All collected resources are available and will be continuously updated at https://github.com/liushunyu/awesome-direct-preference-optimization. + +Index Terms—Alignment, Direct Preference Optimization, Large Language Models, Reinforcement Learning from Human Feedback. + +# 1 INTRODUCTION + +The rapid advancement of Large Language Models (LLMs) has revolutionized artificial intelligence [1, 2, 3, 4, 5, 6, 7, 8], enabling unprecedented generative capabilities across diverse applications, such as dialogue systems [9, 10], code generation [11, 12, 13], and medical diagnosis [14, 15, 16, 17]. Models like OpenAI-o1 [18] and DeepSeekR1 [19] have demonstrated remarkable proficiency in understanding and generating human-like text, outperforming traditional language processing techniques [20]. However, their immense power also introduces significant risks: LLMs may inadvertently produce harmful content (e.g., jailbreak suggestion) [21], exhibit hallucination behaviors (e.g., misinformation) [22], or propagate sociocultural stereotypes (e.g., biased recommendations) [23]. Ensuring that these models align with human values (producing outputs that are helpful, harmless, and honest) has thus become a cornerstone of responsible AI development [24]. + +The critical challenge of aligning LLMs with human values stems from the inherent complexity of encoding abstract + +This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A\*STAR, as well as supported by Alibaba Group and NTU Singapore through Alibaba-NTU Global e-Sustainability CorpLab (ANGEL). (Corresponding author: Dacheng Tao.) Shunyu Liu, Junjie Zhang, Rongcheng Tu and Dacheng Tao are with Nanyang Technological University, Singapore (e-mail: shunyu.liu@ntu.edu.sg; junjie.zhang@ntu.edu.sg; turongcheng@gmail.com; dacheng.tao@ntu.edu.sg). Wenkai Fang, Yang Zhou, Kongcheng Zhang, and Mingli Song are with the College of Computer Science and Technology, Zhejiang University, China (e-mail: wenkfang@zju.edu.cn; imzhouyang@zju.edu.cn; zhangkc@zju.edu.cn; brooksong@zju.edu.cn). Zetian Hu is with the School of Aerospace Engineering, Tsinghua University, China (e-mail: huzt22@mails.tsinghua.edu.cn). Ting-En Lin, Fei Huang, and Yongbin Li are with the Tongyi Lab, Alibaba Group, China (e-mail: ting-en.lte@alibaba-inc.com; f.huang@alibaba-inc.com; shuide.lyb@alibaba-inc.com). + +ethical principles into concrete model behaviors [25, 26, 27]. Traditional approaches, such as rule-based filtering or supervised learning on curated datasets, often prove inadequate due to their inability to generalize across diverse contexts and adapt to evolving societal norms [28]. The emergence of preference-based alignment paradigms addresses these limitations by framing the problem as optimizing for human feedback rather than inflexible heuristics [29, 30, 31, 32]. This shift recognizes that LLM decision-making often involves nuanced trade-offs between competing values, requiring flexible frameworks capable of incorporating subjective human preferences [33]. + +Building upon these insights, Reinforcement Learning from Human Feedback (RLHF) [34, 35] has emerged as the predominant alignment paradigm, leveraging human preferences to guide model optimization. In the RLHF pipeline, human annotators first rank the outputs generated by the language model, and these comparisons are used to train a reward model that quantifies human preferences. The language model is then fine-tuned using RL guided by this reward model, enabling the language model to align with human values by maximizing the predicted rewards. The success of RLHF in aligning models like ChatGPT [36, 37] and Claude [38, 39] underscores its practical utility. By translating subjective human preferences into an objective reward signal, RLHF facilitates the optimization of model behavior for value alignment. However, this RLHF paradigm suffers from critical limitations of computational complexity and training instability. Training a separate reward model demands substantial computational resources and high-quality human preference data, which scales poorly across different domains. Moreover, the RL phase often struggles with optimization challenges, such as reward hacking [40] and mode collapse [41]. + +These limitations have spurred interest in alternative + +![](images/eec766babe90c18e92b263abf2f3723da32c85a958aae6f3eb98f4722ac37fa7.jpg) +Fig. 1: A taxonomy of DPO. We categorize existing DPO works into four branches: data strategy, learning framework, constraint mechanism, and model property. Different colored boxes indicate different categories and their corresponding representative references. + +alignment methods that bypass reward modeling while preserving the benefits of preference-based learning. Direct Preference Optimization (DPO) [74, 210] represents a groundbreaking shift in this direction. Unlike RLHF, DPO reframes alignment as a supervised learning problem, directly optimizing the LLM policy using preference data without explicit reward modeling. By leveraging a closed-form mapping between reward functions and optimal policies, DPO eliminates the need for iterative RL training, reducing computational overhead and improving stability. Due to its inherent advantages, DPO has rapidly gained increasing attention from research communities. Existing studies vary widely in data strategies (e.g., point-wise v.s. pair-wise feedback) [67, 211], learning frameworks (e.g., offline v.s. online learning) [121, 122, 126], constraint mechanisms (e.g., different divergence constraints) [169, 171], and model properties (e.g., length bias) [191, 195]. Recent advancements in DPO variants have demonstrated remarkable efficacy in enhancing model alignment with human preferences, achieving unprecedented success across diverse domains [32]. + +These developments position DPO-based approaches as a compelling alternative to conventional RLHF paradigms for preference alignment tasks. However, despite its promise, the DPO research landscape remains fragmented. + +Several surveys related to DPO have been published in recent years, yet they exhibit notable limitations in their scope and analysis of DPO. (1) Scope limitations. While an early survey of [212] presents a comprehensive overview of preference-based RL methods, it predates the advent of DPO and does not address its applications to modern LLMs. Recent surveys on alignment [24, 26, 213, 214] provide broad overviews of LLM alignment techniques but only offer cursory summaries of DPO-related approaches without in-depth analysis. Similarly, surveys on learning from human feedback [30, 215, 216, 217] also only briefly mention DPO as a potential alternative. (2) Taxonomy deficiencies. Gao et al. [29] and Winata et al. [32] introduce a simplified taxonomy for preference learning, while overlooking technical distinctions within its broad categorization. In contrast, Wang et al. [31] attempt to classify preference learning across dimensions + +such as reinforcement learning, reward modeling, feedback, and optimization. However, this taxonomy suffers from significant conceptual overlaps (e.g. reinforcement learning inherently involves optimization). A recent work by Xiao et al. [210] categorizes DPO studies through isolated research questions, which, while useful for problem identification, fragments the methodological connections. Our survey addresses these gaps by presenting the first comprehensive analysis specifically focused on DPO. The main contributions of this survey are summarized as follows: + +- In this survey, we introduce a novel taxonomy that categorizes existing DPO works into four key dimensions based on different components of the DPO loss: data strategy, learning framework, constraint mechanism, and model property, as shown in Fig. 1. This taxonomy provides a systematic framework for understanding the methodological evolution of DPO and highlights the key distinctions between different variations. +- We conduct a rigorous empirical analysis of DPO variants across standardized benchmarks, revealing critical insights into their performance in diverse scenarios. This analysis offers a comprehensive evaluation of DPO variants and provides practical guidance for practitioners. +- We discuss real-world applications of DPO and highlight its potential to democratize alignment research by enabling efficient and scalable preference learning across diverse domains. We also outline open challenges and future directions for DPO research, emphasizing the need for robust and generalizable alignment paradigms. + +The remainder of this survey is organized as follows. Section 2 introduces the background and formulation of DPO. Section 3 presents a taxonomy of DPO, categorizing existing works based on key dimensions. Section 4 describes standardized benchmarks for evaluating DPO methods and presents empirical results. Section 5 discusses real-world applications of DPO and highlights its potential. Section 6 outlines open challenges and future directions for DPO research. Finally, Section 7 concludes the survey. + +# 2 BACKGROUND AND FORMULATION + +Preference learning aims to train language model policies to generate responses that better align with human preferences. Specifically, we denote the language model policy as $\pi(y|x)$ , where $x$ represents the input prompt and $y$ is a candidate response (completion). A language model can be viewed as an autoregressive function that sequentially predicts tokens based on prior context. Mathematically, this is expressed as: $\pi(y|x) = \prod_{t=1}^{T} \pi(y_t | y_{ 0$ is a hyperparameter that controls the strength of the Kullback-Leibler (KL) divergence penalty. Here, the term $\log \pi_{\theta}(\cdot |x) / \pi_{\mathrm{ref}}(\cdot |x)$ represents the KL divergence between the current policy $\pi_{\theta}$ and a reference policy $\pi_{\mathrm{ref}}$ . In practice, the reference policy $\pi_{\mathrm{ref}}$ is set to the SFT model $\pi_{\mathrm{sft}}$ , ensuring that the updated policy remains close to the initial model. + +To optimize the above objective, Proximal Policy Optimization (PPO) [219] has emerged as a promising RL algorithm for LLMs. PPO stabilizes training by constraining policy updates within a trust region via a clipped objective, which prevents significant deviations from the previous + +policy. However, PPO requires an additional critic model to estimate value functions for advantage calculation, thereby introducing extra computational and memory overhead. To address this, recent methods, such as RLOO [220], ReMax [221], GRPO [222], and Reinforce++ [223], introduce critic-free advantage estimation to reduce resource demands while maintaining stable optimization, making them more scalable for large-scale LLM training. + +# 2.2 Direct Preference Optimization + +DPO offers an alternative that streamlines the training process by directly optimizing the policy with preference data [74, 224, 225, 226, 227, 228, 229], thereby eliminating the need for explicit reward modeling in RLHF. The key idea of DPO is a closed-form solution of Eq. 3 that connects reward with the optimal policies. Specifically, the optimal policy corresponding to a given $r$ is defined as follows: + +$$ +\pi^ {*} (y | x) = \frac {1}{Z (x)} \pi_ {\mathrm {r e f}} (y | x) \exp \left(\frac {1}{\beta} r (x, y)\right), \tag {4} +$$ + +where the partition function $Z(x)$ is defined as: + +$$ +Z (x) = \sum_ {y} \pi_ {\mathrm {r e f}} (y | x) \exp \left(\frac {1}{\beta} r (x, y)\right). \tag {5} +$$ + +By rearranging the above equation, the reward $r$ can be recovered from the optimal policy $\pi^{*}$ : + +$$ +r (x, y) = \beta \log \frac {\pi^ {*} (y | x)}{\pi_ {\operatorname {r e f}} (y | x)} + \beta \log Z (x). \tag {6} +$$ + +Notice that the partition function $Z(x)$ depends only on the prompt $x$ . By substituting this expression into the preference model of Eq. 1, the preference probability model that $y_{w}$ is preferred over $y_{l}$ becomes: + +$$ +P \left(y _ {w} \succ y _ {l} | x\right) = \sigma \left(\beta \log \frac {\pi^ {*} \left(y _ {w} \mid x\right)}{\pi_ {\text {r e f}} \left(y _ {w} \mid x\right)} - \beta \log \frac {\pi^ {*} \left(y _ {l} \mid x\right)}{\pi_ {\text {r e f}} \left(y _ {l} \mid x\right)}\right). \tag {7} +$$ + +Based on the above preference probability model, DPO directly optimizes the language mode policy $\pi_{\theta}$ by minimizing the following negative log-likelihood loss function: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {D P O}} (\theta) = \\ - \mathbb {E} _ {(x, y _ {w}, y _ {l}) \sim \mathcal {D}} \left[ \log \sigma \left(\beta \log \frac {\pi_ {\theta} (y _ {w} | x)}{\pi_ {\text {r e f}} (y _ {w} | x)} - \beta \log \frac {\pi_ {\theta} (y _ {l} | x)}{\pi_ {\text {r e f}} (y _ {l} | x)}\right) \right], \tag {8} \\ \end{array} +$$ + +where the KL constraint is implicitly integrated through the use of the reference model $\pi_{\mathrm{ref}}$ . By minimizing this DPO loss, we directly train the policy to satisfy human preferences without resorting to a separate reward modeling stage or using reinforcement learning optimization as in RLHF, significantly reducing implementation complexity while improving training stability. + +# 2.3 Other Preference Optimization + +In addition to DPO, several concurrent preference optimization methods [190, 230, 231] have been proposed that offer alternative approaches to RLHF. These methods explore different strategies for optimizing LLMs to align with human preference without RL. Below, we provide a brief introduction to these approaches. + +# 2.3.1 Sequence Likelihood Calibration + +Zhao et al. [230] propose Sequence Likelihood Calibration with Human Feedback (SLiC-HF) to directly align LLMs with human preferences. Specifically, the loss function of SLiC-HF is defined as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {S L i C - H F}} (\theta) = \max (0, \delta - \log \pi_ {\theta} (y _ {w} | x) + \log \pi_ {\theta} (y _ {l} | x)) \\ - \lambda \log \pi_ {\theta} (y ^ {*} | x), \tag {9} \\ \end{array} +$$ + +where the first term is the rank calibration loss with $\delta$ as a margin hyperparameter, and the second term is the cross-entropy regularization loss with $\lambda$ as a regularization weight. $y^{*}$ is obtained from either high-quality supervised responses in the SFT dataset or the top-ranked candidate response generated by the SFT model. + +# 2.3.2 Rank Responses to Align Human Feedback + +Yuan et al. [190] introduce Rank Responses to align Human Feedback (RRHF) for LLMs. RRHF extends pair-wise ranking by considering the list-wise ranking order of multiple responses, thus better utilizing the preference information. For an input prompt $x$ and $N$ candidate responses $\{y_i\}_{i=1}^N$ , it optimizes the model to assign higher probabilities to higher-ranked responses via a ranking loss and directly supervises the best response using cross-entropy as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {R R H F}} (\theta) = \sum_ {r _ {i} < r _ {j}} \max \left(0, \frac {\log \pi_ {\theta} (y _ {i} | x)}{| | y _ {i} | |} - \frac {\log \pi_ {\theta} (y _ {j} | x)}{| | y _ {j} | |}\right) \\ - \lambda \log \pi_ {\theta} \left(y ^ {*} \mid x\right), \tag {10} \\ \end{array} +$$ + +where $r_i = r_\phi(x, y_i)$ represents the reward of the response $y_i$ and $y^* = \arg \max_{y_i} r_i$ is the response with the highest reward. Although RRHF avoids the need for reinforcement learning in RLHF, it still utilizes a reward model $r_\phi$ to rank candidate responses based on human preferences. + +# 2.3.3 Preference Ranking Optimization + +Similarly, Song et al. [231] propose Preference Ranking Optimization (PRO) to align LLMs with human preferences by leveraging multiple responses $\{y_{i}\}_{i = 1}^{N}$ with the human-annotated order $y_{1} > y_{2} > \dots >y_{N}$ . The loss function of PRO is defined as follows: + +$$ +\mathcal {L} _ {\mathrm {P R O}} (\theta) = - \sum_ {i = 1} ^ {N - 1} \log \frac {\exp \left(\frac {1}{\| y _ {i} \|} \log \pi_ {\theta} \left(y _ {i} | x\right) / \mathcal {T} _ {i} ^ {i}\right)}{\sum_ {j = i} ^ {N} \exp \left(\frac {1}{\| y _ {j} \|} \log \pi_ {\theta} \left(y _ {j} | x\right) / \mathcal {T} _ {i} ^ {j}\right)}, \tag {11} +$$ + +where the dynamic penalty temperature is defined as $\mathcal{T}_i^j = 1 / (r_\phi (x,y^j) - r_\phi (x,y^i))$ and $\mathcal{T}_i^i = \min_{i < j}\mathcal{T}_i^j$ . This temperature ensures that the probability gap between higher-ranked and lower-ranked responses is adaptively scaled according to their reward differences, thereby stabilizing the optimization process. + +# 3 A TAXONOMY OF DPO + +In this section, we introduce a novel taxonomy that categorizes existing DPO works based on four key dimensions: data strategy, learning framework, constraint mechanism, and model property. As illustrated in Fig. 1, these four dimensions are derived from different components of the DPO loss, providing a systematic framework for understanding the methodological evolution of DPO and highlighting the key distinctions between different variations. + +# 3.1 Data Strategy of DPO + +The data strategy constitutes the foundational pillar of DPO, focusing on how to leverage diverse types of preference data for training LLMs. As shown in Fig. 2, our taxonomy identifies three principal axes of data strategy: quality, feedback, and granularity. + +# 3.1.1 Data Quality + +The quality of preference data is a critical factor in determining the effectiveness of DPO training. High-quality data ensures that LLMs effectively learn to align with human preferences, while low-quality data may introduce noise and bias, leading to suboptimal model performance. We categorize data quality considerations into three key aspects: heterogeneity, distinguishability, and noise. + +(a) Data Heterogeneity. Conventional DPO methods assume uniform human preferences when annotating data, thereby overlooking the diversity among annotators. This assumption often skews the model toward the preferences of the majority while neglecting minority viewpoints, potentially leading to biases and unfair treatment of underrepresented groups. To address this issue, Chidambaram et al. [42] propose EM-DPO, which learns the distribution of different preference types and their corresponding response strategies. Building on this, they introduce the MinMax-DPO algorithm, which selects a strategy by minimizing the maximum regret across subgroups, ensuring a more balanced representation of preferences among all groups. MallowsPO [43] decomposes the implicit rewards in DPO into prompt dispersion and response scaling rewards. It introduces a novel objective function to capture human preferences for diverse responses to the same prompt. GRPO [44] formulates an objective function that minimizes the loss for the worst-case group, thereby ensuring fairness by prioritizing the disadvantaged groups in the optimization process. GDPO [45] models the language generation process as a combination of belief distribution prediction and belief-based response generation. The corresponding GDPO loss function consists of belief calibration loss and belief-conditioned preference alignment loss. The former encourages the model to capture the diversity of beliefs across groups, while the latter ensures that generated responses align with the given belief. + +(b) Data Distinguishability. A key limitation of DPO is its inability to account for the distinguishability of preference between responses [46, 50, 51, 56, 57]. In some cases, the preferred response is only marginally better than the dispreferred one, while in others, the dispreferred response contains harmful or misleading content, making it significantly worse. Thus, optimization should focus more on cases with substantial preference differences while reducing the effort spent on minor differences. However, most existing methods treat all samples equally, ignoring this data distinguishability. To address this, ODPO [46] introduces a monotonically increasing offset function, requiring the reward of the preferred response to exceed that of the dispreferred one by a certain margin. This ensures stronger updates for larger preference gaps. Similarly, Ada-DPO [54] introduces an instance-specific nonlinear scaling parameter, assigning larger weights to strong preference pairs and smaller weights to ambiguous ones based on the reward differences, thereby capturing + +![](images/7d0b0c1f1f41595c2153dd474b54b2117d70052e28f86633cea08504dba7746a.jpg) +Fig. 2: An overview of DPO data strategy. + +different levels of data distinguishability. DPO-rc [48] also incorporates the preference reward difference as a coefficient in the loss function. $\alpha$ -DPO [49] introduces an adaptive preference distribution to obtain dynamic reward margins based on the distribution difference between the policy and reference models. $\beta$ -DPO [51] analyzes the optimal $\beta$ parameter for datasets with different reward margins, which dynamically adjusts $\beta$ based on batch-level reward differences. They also introduce $\beta$ -guided data filtering to prioritize valuable training data. Curri-DPO [53] sorts preference pairs by reward differences and trains progressively from large to small differences, enabling curricular learning. Similarly, MPO [47] utilizes a reward model to score responses generated by the SFT model, constructing a preference dataset and partitioning it based on preference differences to learn from simple to complex tasks. sDPO [55] computes reward accuracy for different datasets based on an initial target model and partitions the dataset in descending order of accuracy, allowing the model to first optimize on simpler samples. Ma et al. [58] propose a preference dataset construction method that adjusts update weights based on response accuracy, assigning lower weights when the model demonstrates higher proficiency. Furthermore, fDPO [52] enhances DPO training by filtering out samples where the generated response of the model policy surpasses the preferred dataset response in reward score. + +(c) Data Noise. Human-generated preference annotations often contain inconsistencies, errors, or noise, negatively affecting the performance of DPO. Such noisy data can mislead models, impairing their ability to accurately capture true preferences and generalize effectively to unseen data. Im and Li [64] analyze how noisy feedback influences the generalization performance of preference optimization, showing that increased noise results in higher generalization risks. Specifically, standard DPO loss functions can yield biased estimates under noisy conditions. To address this + +issue, rDPO [59] proposes to enhance DPO robustness against noisy annotations and improve overall training performance. Zhang et al. [63] introduce a noise-aware strategy leveraging annotator confidence and stability to identify and downweight noisy samples during training. They also propose an adaptive reward margin, emphasizing clean samples to improve learning effectiveness. Complementary to these approaches, PerpCorrect [60] employs a data-driven method to correct noisy annotations directly in the dataset. It trains a proxy language model on both clean and noisy samples, distinguishing noise through perplexity differences to improve dataset quality. To systematically explore noise effects, Gao et al. [65] artificially inject various noise types (e.g., Gaussian noise) into datasets, controlling noise intensity via hyperparameters. Their analysis highlights how noise impacts model alignment, guiding future research towards mitigating such negative effects. To address the vulnerability of DPO in noisy environments, ROPO [61] introduces a regularization term to enhance noise tolerance. Additionally, ROPO employs a robust-guided rejection sampling technique. This technique supplements the dataset with samples that contribute minimally to the loss, thereby improving the overall data quality. Kim et al. [62] propose the SPA framework, using model-generated responses and associated confidence scores to detect noise in annotations. SPA further incorporates smoothing techniques into the loss function to alleviate the noise problem. Finally, Wu et al. [66] categorize noise into two types: point noise (single annotation errors) and pairwise noise (errors between annotated pairs). While DPO naturally handles point noise well, it struggles with pairwise noise. Their proposed Dr. DPO introduces a novel loss function explicitly designed for robustness against both point and pairwise noise. + +# 3.1.2 Preference Feedback + +Preference feedback refers to the label signals provided by annotators regarding their preferences for different responses. It can be categorized into point-wise, pair-wise, and list-wise feedback. Point-wise feedback evaluates each response independently, assigning a score or labeling it as positive or negative. Pair-wise feedback compares two responses to determine which one is preferred, while list-wise feedback ranks multiple responses. + +(a) Point-Wise Feedback. Point-wise feedback is the basic form of feedback. It refers to the type of feedback where individual outputs or samples are evaluated independently, rather than through comparisons with other outputs. This form of feedback is characterized by its simplicity and directness, focusing on the quality or relevance of a single response or item. The predominant methodology in RLHF [35] employs point-wise reward signals generated by reward models to optimize policy models. Similarly, KTO [67] directly maximizes the utility of model generations using loss functions based on prospect theory rather than the log-likelihood of preferences. It requires only a binary signal indicating whether an output is desirable or undesirable for a given input. Furthermore, BCO [68] builds upon the concepts introduced in KTO and explores a new approach to aligning with binary signals. While KTO focuses on optimizing human utility, BCO introduces a binary classifier framework incorporating reward shift and distribution matching that implicitly + +minimizes the DPO loss. Chen et al. [72] and GPO [73] adopt explicit rewards using Noise Contrastive Alignment (NCA) and General Preference Model (GRM) respectively, and then directly optimize language model policies from point-wise preference data with rewards. However, some methods leverage implicit reward signals to refine model behaviors. To ensure that the learned implicit rewards are comparable to the ground-truth rewards, Cal-DPO [69] introduces a calibration term to the preference optimization objective, which prevents the likelihood of chosen responses from decreasing during training. ULMA [71] unifies human demonstration and point-wise preference data into a single framework and handles positive and negative samples with a hybrid objective function. Unlike them, DRO [211] adopts a simple mean-squared objective to optimize the model policy and value function jointly for a single trajectory. Additionally, AOT [70] casts the distributional preference constraint as an optimal transport problem with a convex cost function. The key idea is to minimize the violation of stochastic dominance using a smooth, convex cost function. + +(b) Pair-Wise Feedback. Pair-wise feedback focuses on comparing pairs of data or actions to determine their relative quality or preference. Building upon the theoretical framework of RLHF, DPO implements this paradigm through the utilization of pair-wise preference data, thereby fitting an implicit reward model. Azar et al. [75] introduces a general theoretical framework to unify existing RLHF and DPO methods. The proposed Identity-Preference Optimization (IPO) directly optimizes policies from preferences without relying on reward modeling or the Bradley-Terry assumption, thereby avoiding overfitting issues observed in DPO. Subsequently, DPO-RK and DPO-R [76] integrate the Rao-Kupper and Davidson models into the DPO training objective respectively, thereby extending the capabilities of DPO by explicitly modeling ties in pairwise comparisons. BMC [77] further addresses a key limitation of the weak correlation between winning and losing responses in pairwise data. Specifically, BMC uses "Bridging" to enhance the correlation between winning and losing responses by increasing the consistency and informativeness of pairwise preference signals. However, previous attempts for aligning LLMs primarily focus on optimizing the model's output preferences given an instruction, which struggles to effectively perceive the fine-grained constraints within complex instructions. Thus IOPO [78] extends traditional alignment methods by considering both input and output preferences to better understand the constraints within the instructions. As current methods rely heavily on paired preference data (i.e., explicitly labeled preferred vs. dispreferred examples), they can be limiting in scenarios where such paired data is unavailable or insufficient. SAPO [80] addresses this issue based on the concept of self-play, which enhances data exploration and exploitation by automatically generating negative samples and integrating off-policy learning. Furthermore, PMPO [79] extends the EM algorithm to incorporate both preferred and dispreferred outcomes. By introducing the probability distribution of dis-preferred outcomes, PMPO can optimize using both types of samples, even when only negative feedback is available. Similarly, D2O [81] avoids harmful information by maximizing the discrepancy between the generated responses and the negative samples. NPO [82] + +and SimNPO [83] achieve the goal of forgetting the negative impact by regulating the model's prediction probabilities on negative datasets to be as minimal as possible, where SimNPO further eliminates the reference model bias issue inherent in NPO. + +(c) List-Wise Feedback. List-wise feedback refers to the type of feedback where multiple outputs or responses generated by the model for a given input are evaluated collectively as a list. This approach considers the relative ranking or ordering among the outputs, rather than focusing on individual outputs in isolation. Panacea [84] reframes alignment as a Multi-Dimensional Preference Optimization (MDPO) problem and introduces a method that aims to learn the entire Pareto front to accommodate diverse user preferences. In short, Panacea is designed to adapt a single model to list-wise preferences in a Pareto-optimal manner. LiPO [85] and LIRE [86] also treat LM alignment as a list-wise ranking problem, drawing on the rich literature of Learning-To-Rank (LTR). Specifically, LiPO introduces a specific method LiPO-λ, which leverages a list-wise ranking objective that weights each preference pair based on the difference in ranking metrics; while LIRE optimizes the response probability by calculating the exponential probability distribution and uses the reward model to directly guide the optimization process. To better capture the relative proximity within ordinal multiple responses, OPO [87] utilizes the Normalized Discounted Cumulative Gain (NDCG), a widely used ranking metric, to optimize the model's generation probability to match the permutation of responses based on these labels. Similarly, DRPO [88] leverages NDCG as a key metric to optimize the ranking of model outputs. However, DRPO incorporates novel elements like diffNDCG and Adaptive Rank Policy Score to dynamically adjust the score margins between preferred and non-preferred responses based on their ranking positions. mDPO [232] extends preference optimization to multi-sample comparisons and introduces a framework that evaluates and optimizes the collective properties of sample groups. It not only addresses the limitations of single pair-wise methods but also provides a more robust optimization framework, especially for characteristics like diversity and bias. Furthermore, RPO [90] introduces a contrastive weighting mechanism that constructs a contrast matrix within each mini-batch to compare preferred and less-preferred responses across prompts. The weights of these comparisons are dynamically adjusted based on the semantic similarity between prompts. Additionally, TODO [91] integrates a tie ranking system into list-wise preference modeling, significantly improving the capture of nuances of human preferences, especially in the presence of noisy or inconsistent labels and frequent ties. + +# 3.1.3 Preference Granularity + +Preference granularity refers to the granularity of preference labels, which determines the level at which preferences are assigned to data. It can be categorized into token-level, step-level, sentence-level, and turn-level granularity, ranging from fine-grained focus on individual tokens to broader preferences over entire interaction turns. + +(a) Token-Level Granularity. Token-level alignment operates at the character/subword unit of text generation, providing the finest-grained control over model outputs + +Theoretically, Rafailov et al. [92] demonstrate that DPO can represent any dense reward function by reparameterizing it as an optimal advantage function, which allows DPO to optimize policies in the token-level MDP effectively TDPO [93] refines the alignment process from the sentence level to the token level and introduces forward KL divergence constraints. TDPO utilizes the Bradley-Terry model to convert sentence-level preference comparisons into a token-level reward system, which allows the model to dynamically adjust its strategy at each token generation step. Furthermore, TIS-DPO[94] estimates the importance weights of tokens based on the differences in prediction probabilities from contrastive LLMs, performing token-level importance sampling on existing data to approximate optimal distribution by assigning weights to each token based on its reward. Moreover, $\mathrm{D}^2\mathrm{PO}$ [99] proposes a temporal decay mechanism that dynamically adjusts the contribution of each token-level reward based on its position in the sequences. Unlike these, SparsePO [95] directly learns sparse masks during the training process and controls which tokens are more important for preferences through the sparsity of the masks, thereby achieving dynamic optimization. RTO [96] and SePO [97] first learn a token-level reward function from preference data using DPO, and then RTO optimizes PPO based on this reward signal, while SePO selects key tokens through the estimated reward function. To tackle the need for large-scale annotated data in training, EPO [98] proposes a hierarchical framework that decomposes complex tasks into manageable subgoals using separate LLMs for subgoal prediction and low-level action generation, leveraging environment feedback to automatically generate reward signals and preference data for aligning LLMs. + +To conclude, token-level granularity optimizes models at individual token positions to maximize expected objectives, preserving semantic precision and capturing local syntactic dependencies. However, it increases computational complexity, as processing numerous tokens extends training time, and its sensitivity to noise means errors in a single token can affect the entire sequence. Thus, careful loss function design and regularization are essential for stability. + +(b) Step-level Granularity. Step-level granularity focuses on the intermediate steps or stages in a process, particularly effective for complex problem-solving tasks requiring multiple intermediate steps. Step-DPO [100] and SCDPO [101] treat individual reasoning steps as the basic units for preference optimization, where preference pairs of correct and incorrect steps are generated using LLMs. Furthermore, CPO [102] and MCTS-DPO [103] first utilize more powerful inference structures to generate multiple candidate thoughts at each reasoning step following the Tree-of-Thought (ToT) and Monte Carlo Tree Search (MCTS) respectively, and construct preference pairs based on the selected and unselected intermediate steps. Then they finetune LLMs to generate reasoning steps preferred by ToT during inference using DPO. TPO [104] proposes a preference learning algorithm specifically designed for preference trees that have multiple branches and multi-step responses, and introduces the adaptive step reward mechanism to address the issue of small reward margins caused by shared subtrajectories. It adjusts the reward values for each step based on semantic similarity, helping the model better distinguish + +between preference pairs. RDPO [105] extends traditional preference datasets to incorporate a rationale field, which explains why a particular response is preferred. RDPO introduces rationale information into the DPO loss function by maximizing the likelihood of both the preference and the rationale, which allows the model to better understand the logic behind preferences during training. To address the challenges of sparse rewards and training instability, DAPO [106] uses a critic function to generate dense signals for policy optimization and trains the actor and critic independently to avoid instability. + +To conclude, step-level alignment demonstrates unique advantages in multi-step reasoning tasks by decomposing holistic preferences into intermediate decision points. The primary strength of step-level granularity lies in its capacity to decompose complex objectives into verifiable subgoals, enhancing both interpretability and robustness. For instance, in mathematical reasoning, LLMs can receive feedback on equation derivation steps before final answers, reducing error propagation. However, this granularity still have two key challenges: first, the need for precise step segmentation, which may require domain-specific heuristics or auxiliary models to delineate reasoning boundaries; second, the risk of local optima, where over-optimization of individual steps degrades global coherence. + +(c) Sentence-level Granularity. Sentence-level granularity aligns preferences at the complete utterance level, balancing fine-grained control and computational efficiency. This granularity, represented by the original DPO framework, operates on full response sequences as atomic units for preference comparison. MAPO [107] uses a well-trained translation model to calculate alignment scores between answers in nondominant and dominant languages and then employs preference optimization methods to enhance reasoning consistency. EURUS [108] structures each instruction as a preference tree, containing pairs of correct and incorrect actions to facilitate preference learning. Similarly, IRPO [109] focuses on improving the reasoning capabilities of LLMs through an iterative preference optimization on constructed preference pairs such that the winning response has a higher reward than the losing response. FACTALIGN [110] proposes a fine-grained, sentence-level alignment algorithm called fKTO, which extends the KTO method to leverage fine-grained factuality assessments at the sentence level. + +To conclude, the key strength of sentence-level granularity lies in its capacity to preserve holistic semantics while maintaining tractable optimization complexity. Nevertheless, we must carefully consider task requirements. While suitable for short-form generation and classification tasks, sentence-level methods may insufficiently capture fine-grained stylistic nuances or long-range dependencies critical in generation and reasoning domains. + +(d) Turn-level Granularity. Turn-level granularity focuses on the optimization of model behavior at the level of conversational turns, which is particularly relevant for dialogue systems and interactive agents. This granularity level treats each turn of a conversation as a unit for preference alignment, allowing the LLMs to receive feedback on their responses within the context of a single turn. M-DPO [111] introduces a multi-turn direct preference learning framework to enhance the mathematical reasoning capabilities of LLMs when + +integrated with external tools. It leverages feedback from code interpreters and optimizes trajectory-level preferences using signals generated by the Bradley-Terry model to improve model performance in multi-turn reasoning tasks. ETO [112] presents a novel trial-and-error learning method that optimizes LLM agents' policies by contrasting successful and failed trajectories that contain multi-turn interaction. To address the challenges of coarse granularity and training noise in previous methods, SDPO [113] optimizes specific key segments within interactions to improve multi-turn dialogues while minimizing training noise. Specifically, it extracts key segments from the positive sessions that contribute to higher goal and relationship scores and pairs them with corresponding segments from the negative sessions to calculate an adapted DPO loss. Similarly, AgentQ [114] combines MCTS with self-critique mechanisms to provide process-level supervision by ranking actions, and then iterative fine-tuning using DPO. This approach enables LLMs to effectively learn from both successful and unsuccessful trajectories, enhancing their generalization and decision-making capabilities in complex, multi-turn reasoning tasks within interactive environments. DMPO [115] enhances the existing DPO method by replacing the policy constraint with a State-Action Occupancy Measure (SAOM) constraint and incorporating length normalization into the Bradley-Terry model, effectively addressing challenges in multi-turn scenarios. Compared to traditional policy constraints, SAOM constraints better guide the agent to select actions that align with expert trajectories, especially in unexplored states, thereby reducing compounding errors. + +To conclude, turn-level alignment offers critical advantages for interactive systems by optimizing contextually grounded responses while preserving conversational flow. However, in multi-turn dialogue tasks, the turn-level granularity may introduce additional training noise. For example, some correct turns in negative samples may be mistakenly treated as incorrect turns in the loss calculation. Additionally, since each turn needs to be processed independently, this can lead to reduced training efficiency. + +# 3.2 Learning Framework of DPO + +The learning framework of DPO focuses on how the language model policy learns from preference data. In this section, we present an overview of the learning framework in DPO, as shown in Fig. 3, which encompasses the learning paradigm and the learning objectives. + +# 3.2.1 Learning Paradigm + +The learning paradigm in DPO determines how preference data is acquired during model training and falls into three distinct categories: offline learning, where the model learns from pre-collected preference datasets; online Learning, where the model updates based on newly generated data; and active Learning, where the model selectively queries annotators obtain preference data. + +(a) Offline Learning. The original DPO framework [74] itself is an offline learning paradigm, where the model learns from a static, pre-collected dataset of preference pairs. Recent research has explored different approaches to merging preference optimization and supervised fine-tuning + +![](images/ab1cb06bdd578e7bee29a0deff07d4285154eb2afd39c5194af16ae72fc055ce.jpg) +Fig. 3: An overview of DPO learning framework. + +into a single training phase [190]. CPO [116] incorporates a behavior cloning regularizer through KL divergence minimization between the model and preferred data distribution, which effectively combines into adding a negative log-likelihood term on preferred data alongside the contrastive preference loss. Taking a more direct approach, ORPO [117] proposes a monolithic framework that directly augments the standard negative log-likelihood loss with an odds ratio term comparing chosen and rejected responses, eliminating the need for a separate reference policy while preserving SFT's domain adaptation capabilities. ULMA [71] proposes a hybrid method that applies standard SFT loss on positive samples while using a ranking-based DPO loss on negative samples. PAFT [118] introduces a parallel training paradigm where SFT and preference alignment are performed concurrently on the same pre-trained model and then merged using parameter fusion techniques, avoiding the sequential pipeline that can lead to catastrophic forgetting. + +Several advances explore curriculum learning strategies to enhance DPO performance and training efficiency. CurriDPO [53] introduces curriculum learning by ordering multiple preference pairs from easy to hard based on the rating difference between chosen and rejected responses, where pairs with larger rating gaps are presented first, followed by progressively more challenging pairs with smaller rating differences. sDPO [55] implements curriculum learning by partitioning preference datasets into sequential chunks measured by reward accuracy and applying them incrementally. + +To avoid substantial computational and data annotation costs for preference alignment, fine-tuning-free alignment methods have gained popularity. Linear Alignment [119] works by directly estimating the optimal policy through a one-step update to the output distribution during inference without requiring parameter tuning or feedback data. ICDPO [120] reinterprets DPO's reward-policy relationship to create a fine-tuning-free alignment method that harnesses in-context learning, treating models before and after demonstration exposure as amateur and expert policies, respectively, + +then computing their log probability ratio to score and rank candidate responses. + +(b) Online Learning. DPO faces significant limitations when relying solely on static, pre-collected preference datasets. These datasets, generated by different models, cause a distribution shift that leads to ineffective off-policy learning as the model evolves [145, 152]. By contrast, online DPO employs an iterative framework that continuously updates the policy with real-time feedback, ensuring on-policy learning and reducing misalignment [143, 144, 233]. + +As online DPO progresses, researchers have introduced more flexible frameworks to tackle key challenges. For instance, Yuan et al. [123] proposed a self-rewarding language model: the model generates prompts and responses, then serves as its own judge via LLM-as-a-Judge prompting, scoring on a 5-point scale. OAIF [121] uses an LLM as an online annotator for real-time feedback, and OFSDPO [122] addresses catastrophic forgetting by using two Low-Rank Adaptive (LoRA) modules with different optimization speeds. BPO [124] constructs a dynamic trust region around the behavior LLM, adjusting it as preference data is collected, unlike methods that rely on fixed reference models. Furthermore, researchers have refined sampling strategies for online DPO. RSO [126] and RS-DPO [125] employ rejection sampling based on reward gaps. ROPO [61] recovers useful information from discarded queries via robustness-guided rejection sampling. Shi et al. [127] introduced DPO-Mix-R and DPO-Mix-P, demonstrating faster convergence by mixing online samplers with uniform samplers. OPTUNE [128] selectively regenerates responses with low reward scores while reusing high-reward responses. Iterative RPO [109] and DPO-ST [129] enhance CoT reasoning by selecting correct and incorrect answers to form preference pairs at each iteration. Xie et al. [103] used MCTS to collect preference data during training. Researchers have also explored advanced optimization techniques. APO [130] incorporates momentum-based acceleration, using an extrapolation step between the current and previous policies to update the policy. Xiong et al. [131] proposed a two-agent, non-symmetric online DPO framework with a main agent for optimal policy learning and an enhancer agent for exploration. COMAL [132] formulates alignment as a two-player zero-sum game, updating its policy toward a regularized Nash equilibrium in each iteration. PCO [133] iteratively trains the model on preference data with pairwise cringe Loss. + +Recent efforts push for greater autonomy by letting models generate their own feedback [62]. SeRA [134] introduces a self-reviewed preference bootstrapping method, using an implicit reward margin to select informative pairs, and employs an ensemble reward approach across iterations. CREAM [135] mitigates self-improving biases by applying a consistency regularization on the preference rankings of consecutive iterations. D2PO [136] combines human-labeled gold data with concurrently updated, discriminator-labeled data. DLMA [137] uses contrastive prompts to compute self-reward scores via log ratio differences, then integrates these scores directly into the DPO objective. Addressing exploration and uncertainty in online DPO has also been a focus [234]. XPO [138] encourages exploration by adding a bonus for responses outside the initial policy's support, and SELM [139] uses an optimism term in reward fitting to + +actively seek high-reward responses. ETO [112] alternates exploration and training phases to collect failure trajectories, while VPO [140] applies optimism by regularizing the reward model to favor higher-value responses. Xiong et al. [111] extended DPO from single-turn to multi-turn tasks, balancing KL-regularized and non-regularized objectives, and COPO [141] incorporates a count-based bonus to encourage novel responses with low visitation counts. + +Finally, a growing body of work aims to merge online and offline techniques. HyPO [142] uses offline preference data for DPO training while regularizing via online data. MPO [47] combines the strengths of DPO and PPO in a two-stage process: it first trains DPO on an easier dataset, then uses this model as a reference for PPO training on more challenging samples. + +(c) Active Learning. Active learning in DPO is a strategic approach that aims to reduce the annotation cost and improve sample efficiency by selectively querying annotators for the most informative preference examples. Unlike offline learning that uses a fixed dataset or online learning that generates new data continuously, active learning intelligently selects which data points should be labeled based on model uncertainty or other informativeness criteria. + +Muldrew et al. [146] introduced APL, an iterative data acquisition and fine-tuning loop in which batches of prompt/completion pairs are strategically selected using acquisition functions: a predictive entropy-based approach to measure model uncertainty for prompts and a preference certainty measure based on the implicit Bradley-Terry model for completion pairs in DPO. Unlike two-step selection processes in APL that separately select uncertain input prompts and corresponding completions, divAPO [147] integrates both stages into a single selection phase. divAPO maximizes the preference model certainty by simultaneously evaluating the informativeness of input prompts and completion pairs, while also considering the data distribution of the input prompts. Ji et al. [148] proposed ADPO, which selectively queries human preferences only for responses where the model exhibits high uncertainty while using pseudo-labels for confident cases. Das et al. [149] also employed active learning on RLHF, which actively selects the context-action pairs that maximize exploration and minimize uncertainty in the reward model. + +# 3.2.2 Learning Objective + +In what follows, we present the learning objective in DPO, which determines how the model policy is optimized based on preference data. We first discuss multi-objective learning in DPO, which aims to optimize multiple objectives simultaneously. Then, we introduce self-play learning, which leverages self-generated data for preference alignment. + +(a) Multi-Objective Learning. Multi-objective learning in DPO addresses the challenge of simultaneously optimizing the language model for multiple, potentially competing preference dimensions, such as helpfulness, harmlessness, and truthfulness. This approach aims to find a balanced policy that satisfies multiple human values rather than optimizing for a single objective, which more closely mirrors the complexity of real-world human preferences. + +MODPO [150] achieves the sequential optimization of multiple preference objectives by incorporating language + +modeling directly into reward modeling, using a margin-based loss to maintain performance on previously optimized dimensions. SPO [151] takes a similar iterative constrained optimization approach, optimizing each preference dimension while preventing the degradation of prior alignments through regularization terms. MOSLIM [152] takes a different approach by introducing a multi-head classification reward model that assigns different preference dimensions to separate classification heads, enabling simultaneous optimization of multiple preferences without requiring multiple reward or policy models. HPO [153] incorporates auxiliary objectives through offline RL, where the model uses a weighted maximum likelihood objective that combines a preference alignment term with an advantage-weighted term for maximizing arbitrary auxiliary rewards like readability and safety. CPO [154] introduces explicit preference tokens during training that specify desired scores for different objectives, transforming the multi-objective optimization into a conditional optimization problem. DRDO [155] simultaneously models rewards and preferences through a combination of reward distillation and a contrastive log-unlikelihood term in its loss function. + +(b) Self-Play Learning. Self-play learning in DPO represents an approach where the language model interacts with itself or its previous iterations to generate its own preference data for training, reducing or eliminating the need for human annotations [139, 164]. This method enables continuous self-improvement by leveraging the model's own judgment capabilities to identify and learn from better responses, creating a form of autonomous preference learning. + +SPIN [156] involves a self-play mechanism where the LLM generates synthetic data from its prior iterations, then fine-tunes itself to distinguish these self-generated responses from those of human-annotated data. The method resembles a two-player game, where the model's current iteration tries to improve its responses to better match the target distribution, while the previous iteration attempts to generate responses as close to human data as possible. SPPO [157] treats LLM alignment as a constant-sum two-player game and iteratively refines itself by competing against its previous iteration. Instead of maintaining two competing policies or a reward model, SPO [158] uses a single policy to sample multiple trajectories and uses the proportion of wins in pairwise comparisons as the reward signal. BoNBoN [159] Alignment likewise relies on sampling responses from a base model, but it selects the best ones among n candidates and fine-tunes itself to approximate that best-of-n distribution. + +Some works approach the alignment problem by leveraging Nash equilibrium [132]. Nash-MD [160] learns a preference model from pairwise human feedback and then computes a Nash equilibrium policy that consistently produces preferred responses. Its self-play approach updates the policy by having it compete against itself (or a slight variant of itself) under the learned preference model, which measures how often one response is preferred to another. DNO [161] extends this concept by implementing a batched on-policy algorithm where the current policy generates multiple outputs that are compared both against each other and against a teacher model's outputs. IPO-MD [162] combines the strengths of IPO and Nash-MD, where the model generates data using a mixture policy between the online and reference + +policies, and uses a preference model to annotate pairs of generations, making the optimization equivalent to finding a Nash equilibrium through self-play. SRPO [163] modifies Nash-MD by introducing a self-improvement policy that refines model outputs through iterative revisions, enabling offline optimization without a learned reward function. + +# 3.3 Constraint Mechanism of DPO + +The constraint mechanism of DPO derives from its reformulation of RLHF, which includes a KL divergence constraint between the current policy and a reference policy. As shown in Fig. 4, we re-examine the constraint mechanism of DPO from the perspective of the reference model and different divergence constraints. We also explore various DPO variants with different safety constraints. + +# 3.3.1 Reference Model + +The reference model in DPO functions as an anchor to ensure policy updates remain within a controlled range, preventing excessive deviation from initial behaviors. Typically, the reference model is initialized using the SFT model that serves as the starting point for preference optimization. The choice of reference model significantly impacts optimization dynamics. A static reference model ensures stable training but may limit adaptability. In the following subsections, we introduce two advanced approaches: reference-free DPO eliminates reliance on the reference model, while dynamic-reference DPO employs an evolving reference model. + +(a) Reference-Free DPO. To reduce the computational and memory costs associated with a reference model, many algorithms have explored training modes that do not require loading the reference model. Xu et al. [116] replaces the reference model with a uniform prior distribution, adding an SFT loss term on preferred data to maintain consistency with the desired behavior. ORPO [117] integrates an odds ratio-based penalty with traditional SFT loss, increasing the probability of preferred responses while decreasing undesirable ones, thereby enabling single-stage training without a separate reference model. SimPO [166] directly uses the average log probability as implicit rewards. This removes the requirement for a separate reference model, significantly improving computational and memory efficiency. SimPER [167] also directly optimizes reverse perplexity for preferred versus rejected responses, creating a preference optimization approach that does not require a separate reference model, thus simplifying training. Despite these advancements, [168] argue that a reference model remains crucial. They compared two reference-free variants using posterior probabilities and likelihood functions as rewards, respectively, and found the original DPO consistently outperformed both. Their results indicate that a strong, well-aligned reference policy can significantly enhance DPO performance. +(b) Dynamic-Reference DPO. Offline DPO methods often suffer from reward over-optimization, meaning that as the trained model deviates from the reference model, the quality of generated samples tends to degrade. To address this issue, Gorbatovski et al. [165] proposed dynamically updating the reference model using the current model parameters during training, preventing excessive divergence and maintaining high-quality outputs. Curri-DPO [53] and sDPO [55] adopt + +![](images/cddebe4de78a02102cffc5e93cf429138280b5deac316fd35c18e11122d7aa8e.jpg) +Fig. 4: An overview of DPO constraint mechanism. + +curriculum learning by sorting data samples from simpler to more complex based on predefined metrics. At each training iteration, the model from the previous step serves as the updated reference model to provide constraints, facilitating progressive learning. Similarly, MPO [47] partitions datasets according to task difficulty, employing a two-stage training procedure. The model trained in the initial stage serves as the reference for the subsequent stage. Additionally, M-DPO [89] compares the performance of a fixed reference model versus a dynamic reference model, finding that the latter yields superior results. + +# 3.3.2 Divergence Constraint + +Divergence constraints in DPO play a crucial role in constraining model optimization, balancing alignment performance and model stability. In the following subsections, we introduce two modifications to the divergence constraint: one for enhancing diversity and the other for improving generalization. + +(a) Diversity. Standard DPO typically uses reverse KL divergence equivalent to RLHF. However, the mode-seeking nature of reverse KL divergence reduces the diversity of the generated outputs. To overcome this limitation, f-DPO [169] explores various divergences, including forward KL divergence, reverse KL divergence, Jensen-Shannon divergence, and $\alpha$ -divergence, to achieve a better trade-off between alignment performance and diversity. Slocum et al. [170] further proposes splitting the KL divergence term into entropy and cross-entropy terms. This decoupling allows independent control of generation diversity and closeness to the reference model, preserving output diversity without degrading overall model quality. +(b) Generalization. Over-optimization in DPO can negatively impact generalization, causing reduced performance on inputs outside the training distribution. To mitigate this, Huang et al. [178] introduce $\chi^2$ -divergence as a more aggressive form of regularization compared to KL divergence, alleviating the over-optimization problem. DPO-Kernels [171] employs data-driven methods to select optimal kernel-divergence pairs dynamically, improving task adaptability + +and robustness. FlipGuard [172] introduces a customized reward characterization to monitor model performance. If performance drops relative to earlier versions, FlipGuard constrains the model's updates to ensure alignment with previous stable behavior. FPO [173] leverages the feature-level constraints using Sparse Autoencoders (SAEs) to improve computational efficiency and training stability. SPO [176] integrates a natural preference loss with a KL divergence-based regularization term computed over the entire model output distribution. By adjusting this divergence term, SPO prevents unwanted shifts beyond the preference dataset, ensuring stable alignment. EXO [175] argues that minimizing the forward KL divergence in DPO introduces bias when approximating the optimal policy. They establish a generalized alignment objective and reveal the equivalence between maximizing KL regularization rewards and minimizing the reverse KL divergence relative to the optimal policy. QDPO [177] utilizes divergence between the quantized model and the full-precision model for preference optimization, effectively addressing the token-flipping issue. Token-flipping refers to the phenomenon where quantization errors skew token distributions, leading to incorrect token selection. GPO [174] constructs a framework that unifies different DPO-related algorithms through theoretical derivations, enabling a deeper understanding of the regularization mechanisms in the DPO family of algorithms. + +# 3.3.3 Safety Constraint + +Safety constraints in DPO aim to prevent LLMs from generating harmful, biased, or unethical outputs. However, traditional alignment algorithms often fail to address safety concerns. To enhance the safety alignment, recent studies have introduced several specialized mechanisms based on DPO. SafeDPO [179] introduces a streamlined approach for safety alignment by implicitly optimizing safety objectives within a single stage of policy learning. SACPO [180] addresses safety constraints by explicitly formulating language model alignment as a constrained optimization problem, using DPO to optimize the model under safety constraints. Zhang et al. [184] propose creating a backtracking preference dataset that identifies and reverses unsafe outputs, enhancing the safety and robustness of the model. C-DPO [181] integrates dual gradient descent into DPO to balance safety and utility efficiently. This approach achieves a robust trade-off between helpfulness and harmlessness, offering explicit safety guarantees. ADPO [182] introduces adversarial techniques into DPO. It specifically trains models to reduce the probability of unsafe outputs by deliberately generating harmful responses using controlled toxic tokens. Finally, Lee et al. [183] explore the internal mechanisms through which DPO reduces harmful outputs. Their findings suggest that DPO does not remove harmful behaviors learned during pretraining but instead teaches models to bypass or suppress these behaviors. This insight helps explain certain safety vulnerabilities like jailbreaks. + +# 3.4 Model Property of DPO + +DPO has shown great promise in aligning LLMs with human preferences by directly optimizing model outputs based on preference data. During this process, the underlying models + +![](images/e5c5a6a0d780ea4b5c9a8a90db2723f6fdb6c09e14347e19016d55dcced76086.jpg) +Fig. 5: An overview of DPO model property. + +exhibit certain properties that are crucial for understanding their behavior and effectiveness. These properties can be broadly categorized into two aspects: the generation property and the optimization property, as shown in Fig. 5. In the following sections, we explore these two properties in more detail, analyzing their implications for model alignment. + +# 3.4.1 Generation Property + +The generation property of DPO primarily concerns issues related to distribution shifts and length biases. DPO is sensitive to distribution shifts between the base model outputs and the preference data, which may reduce diversity and generalization. Additionally, DPO has a tendency to favor longer responses, a phenomenon known as morbidity, which can negatively impact performance and user experience. + +(a) Distribution Shift. In RLHF, the reward model is trained on a static set of preference data collected offline. During fine-tuning, the generated responses often differ from this original training data, resulting in a distribution shift. This shift can cause inaccurate reward predictions and lead to over-optimization. The implicit reward model in DPO also suffers from this distribution shift issue. Moreover, Lin et al. [188] have shown that the implicit reward model in DPO performs poorly on Out-Of-Distribution (OOD) data compared to explicit reward models. Experimental results indicate that DPO can transfer probability mass to the highreward response regions covered by the preference data, but it may also cause the distribution of responses generated by the model to deviate significantly from that of the reference policy, resulting in responses that do not meet expectations [189]. To address these problems, many researchers are now exploring online DPO approaches [109, 121, 122, 125], aiming to mitigate OOD by continuously updating preference data during training. + +Existing DPO methods also face significant limitations due to their dependence on specific training tasks. Their optimal solutions lack robustness when applied to OOD tasks. Thus, SRPO [163] reframes alignment as a self-improvement process, which optimizes a self-improvement policy and a generative policy using a min-max objective, ensuring + +robustness by making the solution independent of training tasks. Zhang et al. [139] also identify notable issues in DPO when handling OOD tasks. First, DPO tends to overly favor novel content it has not seen during training. Second, it easily gets stuck in local optima, limiting exploration. To address these problems, they propose Self-Exploring Language Models (SELM), incorporating an optimism term to encourage broader exploration of new responses. + +Another significant challenge of DPO is preference drift, where human preferences evolve, changing data distributions over time. Traditional DPO algorithms typically overlook such temporal shifts, mistakenly interpreting them as noise. To address this, NS-DPO [185] propose to assign higher weights to recent data, allowing models to better adjust to evolving preferences. + +(b) Length Bias. Length bias in DPO refers to the tendency of model-generated outputs to become excessively long during training. This issue is similar to the length bias observed in RLHF [197] and is particularly pronounced in DPO. Length bias affects response quality and overall model performance. To mitigate this issue, researchers have developed several solutions, which can be categorized into three main approaches: length regularization, length normalization, and length sampling. + +Length regularization is a common approach to controlling length bias in DPO. By introducing regularization terms into the objective function, the model can constrain response length and reduce morbidity, thereby alleviating the length bias problem. R-DPO [191] introduces a length-based penalty term to the DPO objective function, explicitly discouraging morbidity. $\mathrm{D}^2\mathrm{PO}$ [99] introduces a dynamic weighting mechanism by incorporating a temporal decay factor. Unlike previous methods that apply uniform reward contributions across sequences, $\mathrm{D}^2\mathrm{PO}$ adjusts the influence of each reward based on its position in the response. Higher weights are assigned to rewards associated with earlier tokens, as they are more critical for model alignment, while later rewards gradually receive lower weights. This adaptive approach prevents overfitting to less relevant tokens, thereby addressing length bias in DPO. + +Length normalization aims to eliminate the loss bias caused by response length differences, allowing the model to evaluate texts of varying lengths more fairly. This approach prevents the model from developing an unreasonable preference for either long or short responses [198]. RRHF [190] and SimPO [166] first propose to apply length normalization to responses, ensuring that the loss remains unaffected by response length. LN-DPO [194] further integrates SimPO-like length normalization into DPO, demonstrating that this approach enhances response quality while mitigating morbidity. LD-DPO [195] achieves length desensitization by reparameterizing the likelihood in DPO. Specifically, it decomposes the likelihood of the longer response in a preference pair into the product of the likelihood of the public-length portion and the likelihood of the excessive portion. It then introduces a hyperparameter to mitigate the morbidity preference. This adjustment smooths the relationship between likelihood and response length, reducing its impact on optimization. For multi-turn dialogue tasks, DMPO [115] introduces length normalization for the number of turns in multi-turn preference optimization. + +An alternative approach to controlling length bias in DPO is through sampling-based methods. SamPO [192] introduces a down-sampling method to compute regularized KL divergences. By balancing token-level probability distributions between preferred and rejected responses, SamPO reduces length bias in DPO training. Yuan et al. [193] propose Length-Instruction Fine-Tuning (LIFT), a method to improve instruction-following models' ability to adhere to length constraints by augmenting existing training data with explicit length instructions and using DPO for training. This enables the model to generalize across prompts requiring different response lengths. For long-context tasks, LongPO [196] enables short-context LLMs to self-evolve for long-context tasks by learning from self-generated short-to-long preference data, which includes paired responses for long-context inputs and their compressed short-context counterparts. LongPO incorporates a short-to-long KL constraint to prevent degradation of short-context performance during long-context alignment, achieving strong performance on both short- and long-context tasks. + +# 3.4.2 Optimization Property + +The optimization property of DPO involves likelihood collapse and alignment tax. While DPO aims to increase the likelihood of preferred responses and decrease dispreferred ones, the actual optimization process does not explicitly enforce this balance. Moreover, alignment improvements often come at the cost of the original capabilities of LLMs, known as alignment tax. + +(a) Likelihood Collapse. Likelihood collapse refers to the unintended reduction in the likelihood of both preferred and dispreferred responses during DPO training [92]. This phenomenon can lead to unintentional unalignment, where the model's outputs deviate from human preferences, potentially producing undesirable or harmful responses. This phenomenon is also referred to as likelihood displacement in prior studies [204]. Additionally, the gradients associated with increasing the likelihood of preferred responses and decreasing that of dispreferred responses can become entangled, hindering effective learning. This entanglement complicates the optimization process, making it challenging to achieve the desired alignment [203]. Theoretical analyses have further elucidated the underlying causes of likelihood collapse. In particular, Feng et al. [202] developed an analytical framework grounded in field theory. Their analysis of the gradient vector field of the DPO loss function revealed that the loss function decreases the probability of generating human-disliked data at a faster rate than it increases the probability of generating human-like data. + +Several strategies have been proposed to address likelihood collapse. Pal et al. [200] introduce DPO-Positive (DPOP), which adds a penalty term to maintain a high log-likelihood for preferred examples. Similarly, LLaMA [235] augments DPO training with a negative log-likelihood term to stabilize training and preserve the log-likelihood of chosen responses [109]. Flex-DPO [201] adaptively adjusts parameters to slow the decline in the likelihood of dispreferred responses and balance gradients for both chosen and rejected outputs. D'Oosterlinck et al. [199] propose Anchored Preference Optimization (APO), which provides fine-grained control over probability updates: APO-zero increases the + +TABLE 1: An overview of datasets (upper row) and benchmarks (lower row) for DPO. + +
DatasetTask DescriptionData Size (Training & Test)Data SourceData StructureEvaluation Metric
UltraFeedback [237]Instruction-Following, Helpful64K&-AIList-
SafeRLHF [238]Harmless, Helpful73.9K&8.21KHuman&AIPair-
HelpSteer [239]Helpful35.3K&1.8KHumanPoint-
PRM800K [240]Mathematical Reasoning800K&-HumanPoint-
SHP-2 [241]Q&A From Reddit3600K&241KHumanPair-
Nectar [242]Conversations183K&-AIList-
OpenOrca [243]Conversations2940K&-AISample-
Capybara [244]Multi-Turn Conversations16K&-Human&AISample-
Step-DPO [100]Mathematical Reasoning10.8K&-Human&AIPair-
BeaverTails [245]Harmless, Helpful330K&36KHuman&AIPoint-
IMDb [246]Movie Reviews25K&25KHumanSampleAccuracy
Reddit TL;DR [247]Summarization1330K&-HumanSampleWin Rate
Anthropic-HH [248]Harmless, Helpful161K&8.55KAIPairWin Rate
GSM8K [249]Mathematical Reasoning7.47K&1.32KHumanSampleAccuracy
AlpacaEval2 [250]Automatic Evaluation-&0.8KAISampleWin Rate
MT-Bench [251]Multi-Turn Question-&3.3KHumanPairWin Rate
AdvBench [252]Harmful Behaviors-&0.5KHumanSampleAttack Success
Arena-Hard [253]Updating Evaluation-&0.5KAISampleWin Rate
TruthfulQA [254]Truthful-&0.8KHumanPairAccuracy
IFEval [255]Instruction-Following-&0.5KHumanSampleAccuracy
BBH [256]Multistep Reasoning-&23 TasksHumanSampleAccuracy
MATH [257]Mathematical Reasoning7.5K&5KHumanSampleAccuracy
GPQA [258]Biology, Physics, and Chemistry-&0.45KHumanSampleAccuracy
MUSR [259]Multistep Reasoning-&0.76KAISampleAccuracy
MMLU-Pro [260]Language Understanding-&12KHuman&AISampleAccuracy
+ +probability of winning outputs and decreases that of losing outputs, whereas APO-down decreases both, but with a stronger decline for losing outputs. + +Another notable challenge related to likelihood collapse is likelihood over-optimization, where the performance of a model on a proxy metric (such as its own likelihood estimates) improves, while its true performance does not. Zhang and Ranganath [236] show that reductions in the likelihood loss of DPO do not necessarily translate into higher win rates. Similarly, Shi et al. [205] further investigates the problem of likelihood over-optimization in DPO, demonstrating that higher completion likelihoods do not necessarily correlate with better model performance and may even degrade it. This study identifies key indicators of over-optimization and highlights the need to balance likelihood optimization with output diversity. e-DPO [187] also shows that DPO can lead to degenerate policies due to overfitting, and proposes a solution using reward model distillation to regularize the implicit reward of the language model. The method trains the language model to match the probability distribution induced by a reward model and introduces a pessimistic extension to handle uncertainty in the reward model, thereby improving the robustness of DPO. + +(b) Alignment Tax. Alignment tax refers to the unintended consequence where improving a model's preference alignment degrades its general capabilities acquired during pretraining [206]. Thakkar et al. [207] demonstrate the sensitivity of DPO to training data composition, showing significantly worse performance degradation than SFT when using mixed-preference datasets. Furthermore, Chen et al. [209] identify that DPO struggles with optimizing ranking tasks. While DPO improves ranking accuracy, it disproportionately harms generative capabilities. Pentyala et al. [118] also observes capability forgetting during sequential training, where DPO objectives conflict with previously learned SFT patterns. To address this, researchers propose model merging strategies that balance alignment and performance. + +PAFT [118] separately trains SFT and DPO objectives on a pretrained model using distinct datasets, then merges the parameters through weighted averaging. Additionally, Lu et al. [208] proposes online merging optimizers, which integrate model merging into each optimization step of DPO to balance human preferences and basic capabilities. By merging gradients with parameter differences between SFT and pretrained models, these optimizers effectively enhance alignment while mitigating alignment tax. + +# 4 BENCHMARKS AND ANALYSIS + +In this section, we provide a comprehensive overview of existing benchmarks and evaluation for DPO methods. We first introduce the key datasets and benchmarks used to train or evaluate DPO models. We then present a comparative analysis of the performance of different DPO methods on these benchmarks, highlighting their strengths and limitations. + +# 4.1 Datasets and Benchmarks + +A diverse range of datasets and benchmarks has been specifically curated to facilitate research in DPO. Table 1 summarizes these datasets and benchmarks, highlighting their task descriptions, dataset sizes, data sources, data structures, and evaluation metrics. These datasets and benchmarks span a broad range of tasks, such as harmlessness and helpfulness evaluation and mathematical reasoning. They also exhibit significant diversity in scale, ranging from smaller, specialized datasets to large-scale collections such as SHP-2, which contains over 3.6 million samples. Additionally, datasets differ in their sources: some rely purely on human annotations, others on AI-generated content, and many adopt a hybrid approach combining human and AI-generated data. The data structures employed across these datasets include single-sample without preference label, point-wise annotations, pair-wise comparisons, and list-wise comparisons. Common evaluation metrics include accuracy + +TABLE 2: Experimental results of different DPO variants on Open LLM Leaderboard. The underline indicates the best performance. + +
ModelMistral-7B-BaseLLaMA-3-8B-Base
IFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGEIFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGE
SFT3.441.19.228.842.027.725.429.046.315.328.641.331.031.9
RRHF [190]10.040.61.726.446.326.125.231.046.813.931.436.830.531.7
SLiC-HF [230]11.044.09.929.242.628.127.541.749.517.530.439.731.735.1
DPO [74]11.143.77.128.543.826.726.834.348.217.231.940.131.533.9
IPO [75]9.442.89.729.739.727.826.535.349.015.932.841.431.934.4
CPO [116]8.042.79.628.942.127.326.432.446.916.830.639.131.832.9
KTO [67]12.943.712.028.946.128.328.640.248.318.031.040.131.134.8
ORPO [117]28.446.413.530.241.429.531.640.049.116.830.738.432.034.5
R-DPO [191]10.043.07.628.739.327.226.036.448.817.231.640.631.534.4
SimPO [166]11.143.18.428.939.527.226.440.848.615.831.040.531.834.7
ModelMistral-7B-InstructLLaMA-3-8B-Instruct
IFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGEIFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGE
SFT48.446.210.929.147.627.134.950.749.326.931.037.935.738.6
RRHF [190]45.245.310.128.544.226.233.351.349.327.229.639.535.338.7
SLiC-HF [230]39.446.211.428.749.026.833.641.650.926.331.339.235.337.4
DPO [74]49.045.611.026.946.126.834.248.950.125.829.438.736.038.2
IPO [75]42.645.311.827.849.327.234.050.449.526.329.637.935.738.2
CPO [116]38.846.010.128.548.426.933.150.649.126.831.338.135.838.6
KTO [67]46.245.710.927.846.027.334.043.150.126.331.238.135.037.3
ORPO [117]37.645.111.228.246.926.532.643.050.626.929.339.135.137.3
R-DPO [191]46.845.99.928.746.227.634.250.950.325.329.839.035.738.5
SimPO [166]45.445.910.428.345.027.133.748.849.225.029.339.235.137.8
+ +(for tasks like mathematical reasoning found in GSM8K and MATH), win rates derived from pairwise comparisons (such as MT-Bench and Anthropic-HH), and attack success rates used for assessing adversarial robustness (AdvBench). + +# 4.2 Results + +To demonstrate the effectiveness of different DPO variants, we conduct experiments on the Open LLM Leaderboard. We compare different DPO variants using Mistral-7B-Base, Mistral-7B-Instruct [261], LLaMA-3-8B-Base, and LLaMA-3-8B-Instruct [235] as starting points. The overall experimental setup follows Meng et al. [166], ensuring a reproducible evaluation of different DPO variants. For Mistral-7B-Base and LLaMA-3-8B-Base, the SFT models are trained based on the UltraChat-200k dataset [262], and subsequently applied different DPO variants on the SFT models using the UltraFeedback dataset [237]. For Mistral-7B-Instruct and LLaMA-3-8B-Instruct, which have already undergone instruction-tuning, the preference dataset is regenerated by collecting responses from the SFT models using prompts from the UltraFeedback dataset [237]. + +The experimental results, as summarized in Table 2, highlight the performance of different DPO variants across various benchmarks. For the Mistral-7B-Base and LLaMA-3-8B-Base models, ORPO consistently achieves the highest average scores, indicating its effectiveness in aligning models with human preferences. Notably, ORPO outperforms other methods on IFEval, BBH, and MATH, demonstrating its superiority in instruction-following and mathematical reasoning tasks. Meanwhile, SLiC-HF and KTO also achieve competitive results, particularly in BBH and GPQA, suggesting that these methods effectively leverage preference data for enhanced performance. For the Mistral-7B-Instruct and LLaMA-3-8B-Instruct models, the improvements across different DPO variants are more nuanced. While DPO and R-DPO show strong performance in IFEval and MMLU-Pro, IPO and CPO demonstrate robustness in handling complex reasoning tasks like MATH and GPQA. Overall, the results indicate that different DPO variants exhibit varying strengths across benchmarks, with some methods excelling in base models while others are more effective for instruct models. + +# 5 APPLICATIONS + +In this section, we discuss the applications of DPO in various domains, including different LLM-based applications, diffusion models, and multi-modal LLMs. We provide an overview of the key challenges and opportunities in each domain and highlight the potential impact of DPO on real-world applications. + +# 5.1 LLM-based Applications + +DPO has emerged as a powerful paradigm for aligning LLMs with human preferences across diverse applications [116, 235, 263, 264]. In code generation, DPO enhances control over code quality by optimizing based on preferences from automated tests [265, 266, 267]. In mathematical reasoning, DPO reduces errors in complex problem-solving by emphasizing step-level preference optimization [100, 101, 129, 268]. Multilingual applications leverage DPO to synchronize cross-lingual preferences, thereby improving translation accuracy and cultural relevance [107, 269]. Recommendation systems utilize DPO to refine personalization by incorporating user preference data to optimize item rankings, thereby enhancing the model ability to distinguish preferred items from less preferred ones [270, 271]. These examples highlight the adaptability of DPO in achieving human-aligned outputs across diverse tasks. + +# 5.2 Diffusion Models + +In the realm of diffusion models, DPO has been adapted to better align generated content with user expectations [272, 273, 274, 275]. By optimizing preferences over image-text pairs, DPO enhances the semantic accuracy of generated images and mitigates the production of undesirable or biased content. Studies have demonstrated that diffusion models fine-tuned with DPO respond more accurately to complex prompts compared to those trained with traditional techniques. Moreover, the efficiency of DPO allows for the fine-tuning of large-scale models using limited preference data, addressing significant computational challenges in training diffusion models [276, 277, 278]. While scaling DPO for high-resolution and dynamic content generation remains + +challenging, its ability to simplify reward modeling makes it a promising method for controlled content creation [279]. + +# 5.3 Multi-Modal LLMs + +For multi-modal LLMs, DPO plays a crucial role in aligning preferences across different data types, thereby improving coherence in tasks such as visual question answering and image captioning [89, 280, 281, 282, 283]. By optimizing alignment between textual responses and visual inputs, DPO reduces hallucinations in multi-modal interactions, ensuring outputs remain faithful to the given context. Although reconciling different types of feedback can be challenging, DPO offers a practical framework for lightweight adaptation, making it well-suited to preference-intensive multi-modal applications [280, 284, 285]. + +# 6 CHALLENGES AND FUTURE DIRECTIONS + +In this section, we discuss the key challenges and future directions in DPO research. We identify several critical issues that need to be addressed to further advance the field. Moreover, we propose several promising research directions that can help overcome these challenges and accelerate the adoption of DPO in the future. + +# 6.1 Efficient Preference Optimization + +Efficient preference optimization remains a pivotal challenge, as current DPO methods hinge on the availability of high-quality preference data, yet the manual collection of human annotations is both time-consuming and labor-intensive while automatically model-generated datasets often suffer from issues such as limited diversity, inherent biases, and insufficient fidelity to human judgment [121, 122, 128, 129]. Moreover, even though DPO circumvents the intricacies of reward model engineering common in RL, it does not fully leverage the exploratory strengths that RL methods offer, as evidenced by recent advances in reasoning approaches where RL-based training has achieved notable successes [18, 19]. This opens up an avenue for future research to not only enhance data efficiency through advanced learning techniques but also to integrate novel exploration mechanisms [138, 141], potentially through hybrid models that amalgamate the direct preference optimization benefits of DPO with the robust exploratory capabilities characteristic of RL. + +# 6.2 Multi-Modal Preference Optimization + +Multi-Modal Preference Optimization presents another frontier, given that existing DPO frameworks have primarily targeted text-based modalities while many real-world applications demand the alignment of diverse human preferences across text, images, audio, and even video [280, 284, 285, 286, 287]. In scenarios where cross-modal cues might conflict, such as the need for concise text paired with richly detailed imagery, the challenge lies in constructing a unified preference representation space that can intelligently and automatically recalibrate the priority of different modalities based on the contextual demands of the task at hand [89, 282, 283]. Future directions in this area could involve the development of innovative multi-modal preference encoding architectures, + +which are capable of disentangling compound preferences into modality-specific and cross-modal components that align conflicting preferences while also adapting dynamically to changing inputs. + +# 6.3 Continuous Preference Optimization + +Continuous preference optimization addresses the dynamic nature of human preferences that evolve over time or vary with different phases of a task, a factor that static DPO models often fail to capture [123, 135, 137, 185]. As social norms and individual preferences shift, there is an increasing need for systems that can continuously recalibrate their alignment strategies in real time while simultaneously mitigating the risk of catastrophic forgetting. Future research in this domain may focus on meta-learning approaches that enable models to learn not only from the current state of preferences but also how to efficiently adapt when these preferences change. By integrating online learning frameworks with mechanisms for detecting temporal shifts and contextual variability in user behavior, researchers can pave the way toward systems that remain consistently relevant and effective in the face of evolving societal and individual expectations. + +# 6.4 Interpretable Preference Optimization + +Interpretable preference optimization is critical for building trust in models that implicitly align human values, as the opaque nature of current DPO complicates the ability to audit and control the alignment process. In practice, human preferences are multi-dimensional [150, 151, 154], encompassing aspects such as factual accuracy, fairness, creativity, and beyond, and there is a pressing need to decompose these complex preferences into interpretable components that can be individually examined and fine-tuned. Future research could leverage advances in explainable techniques to develop models that not only achieve fine-grained alignment across diverse values but also provide transparent insights into how different preference dimensions interact to shape final decisions. This level of interpretability would allow stakeholders to balance competing values more effectively, ensuring that the alignment process remains both accountable and adaptable as societal norms continue to evolve. + +# 7 CONCLUSION + +In recent years, DPO has emerged as a promising paradigm for aligning LLMs with human preferences by directly optimizing model policies using preference data. Despite its potential, the DPO research landscape remains fragmented, with a lack of systematic organization and comparative analysis. In this survey, we present a comprehensive overview of DPO and introduce a novel taxonomy that categorizes existing works into four key dimensions: data strategy, learning framework, constraint mechanism, and model property. We have also discussed the key benchmarks, evaluation results, and applications of DPO, highlighting the challenges and future directions in this field. By providing a systematic analysis of the existing DPO methods, we aim to facilitate further research and development in this area. + +# REFERENCES + +[1] Wayne Xin Zhao et al. A survey of large language models. arXiv, 2023. +[2] Humza Naveed et al. A comprehensive overview of large language models. arXiv, 2023. +[3] Yupeng Chang et al. A survey on evaluation of large language models. TIIS, 2024. +[4] Shervin Minaee et al. 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+ }, + { + "bbox": [ + 63, + 91, + 547, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 91, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 63, + 91, + 547, + 120 + ], + "type": "text", + "content": "Shunyu Liu, Wenkai Fang, Zetian Hu, Junjie Zhang, Yang Zhou, Kongcheng Zhang, Rongcheng Tu, Ting-En Lin, Fei Huang, Mingli Song, Yongbin Li, and Dacheng Tao, Fellow, IEEE" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 137, + 546, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 137, + 546, + 274 + ], + "spans": [ + { + "bbox": [ + 64, + 137, + 546, + 274 + ], + "type": "text", + "content": "Abstract—Large Language Models (LLMs) have demonstrated unprecedented generative capabilities, yet their alignment with human values remains critical for ensuring helpful and harmless deployments. While Reinforcement Learning from Human Feedback (RLHF) has emerged as a powerful paradigm for aligning LLMs with human preferences, its reliance on complex reward modeling introduces inherent trade-offs in computational efficiency and training stability. In this context, Direct Preference Optimization (DPO) has recently gained prominence as a streamlined alternative that directly optimizes LLMs using human preferences, thereby circumventing the need for explicit reward modeling. Owing to its theoretical elegance and computational efficiency, DPO has rapidly attracted substantial research efforts exploring its various implementations and applications. However, this field currently lacks systematic organization and comparative analysis. In this survey, we conduct a comprehensive overview of DPO and introduce a novel taxonomy, categorizing previous works into four key dimensions: data strategy, learning framework, constraint mechanism, and model property. We further present a rigorous empirical analysis of DPO variants across standardized benchmarks. Additionally, we discuss real-world applications, open challenges, and future directions for DPO. This work delivers both a conceptual framework for understanding DPO and practical guidance for practitioners, aiming to advance robust and generalizable alignment paradigms. All collected resources are available and will be continuously updated at https://github.com/liushunyu/awesome-direct-preference-optimization." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 64, + 282, + 537, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 282, + 537, + 293 + ], + "spans": [ + { + "bbox": [ + 64, + 282, + 537, + 293 + ], + "type": "text", + "content": "Index Terms—Alignment, Direct Preference Optimization, Large Language Models, Reinforcement Learning from Human Feedback." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 341, + 140, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 341, + 140, + 353 + ], + "spans": [ + { + "bbox": [ + 45, + 341, + 140, + 353 + ], + "type": "text", + "content": "1 INTRODUCTION" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 44, + 360, + 301, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 360, + 301, + 556 + ], + "spans": [ + { + "bbox": [ + 44, + 360, + 301, + 556 + ], + "type": "text", + "content": "The rapid advancement of Large Language Models (LLMs) has revolutionized artificial intelligence [1, 2, 3, 4, 5, 6, 7, 8], enabling unprecedented generative capabilities across diverse applications, such as dialogue systems [9, 10], code generation [11, 12, 13], and medical diagnosis [14, 15, 16, 17]. Models like OpenAI-o1 [18] and DeepSeekR1 [19] have demonstrated remarkable proficiency in understanding and generating human-like text, outperforming traditional language processing techniques [20]. However, their immense power also introduces significant risks: LLMs may inadvertently produce harmful content (e.g., jailbreak suggestion) [21], exhibit hallucination behaviors (e.g., misinformation) [22], or propagate sociocultural stereotypes (e.g., biased recommendations) [23]. Ensuring that these models align with human values (producing outputs that are helpful, harmless, and honest) has thus become a cornerstone of responsible AI development [24]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 556, + 301, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 556, + 301, + 581 + ], + "spans": [ + { + "bbox": [ + 45, + 556, + 301, + 581 + ], + "type": "text", + "content": "The critical challenge of aligning LLMs with human values stems from the inherent complexity of encoding abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 44, + 591, + 301, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 591, + 301, + 746 + ], + "spans": [ + { + "bbox": [ + 44, + 591, + 301, + 746 + ], + "type": "text", + "content": "This research is supported by the RIE2025 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) (Award I2301E0026), administered by A\\*STAR, as well as supported by Alibaba Group and NTU Singapore through Alibaba-NTU Global e-Sustainability CorpLab (ANGEL). (Corresponding author: Dacheng Tao.) Shunyu Liu, Junjie Zhang, Rongcheng Tu and Dacheng Tao are with Nanyang Technological University, Singapore (e-mail: shunyu.liu@ntu.edu.sg; junjie.zhang@ntu.edu.sg; turongcheng@gmail.com; dacheng.tao@ntu.edu.sg). Wenkai Fang, Yang Zhou, Kongcheng Zhang, and Mingli Song are with the College of Computer Science and Technology, Zhejiang University, China (e-mail: wenkfang@zju.edu.cn; imzhouyang@zju.edu.cn; zhangkc@zju.edu.cn; brooksong@zju.edu.cn). Zetian Hu is with the School of Aerospace Engineering, Tsinghua University, China (e-mail: huzt22@mails.tsinghua.edu.cn). Ting-En Lin, Fei Huang, and Yongbin Li are with the Tongyi Lab, Alibaba Group, China (e-mail: ting-en.lte@alibaba-inc.com; f.huang@alibaba-inc.com; shuide.lyb@alibaba-inc.com)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 342, + 566, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 342, + 566, + 480 + ], + "spans": [ + { + "bbox": [ + 307, + 342, + 566, + 480 + ], + "type": "text", + "content": "ethical principles into concrete model behaviors [25, 26, 27]. Traditional approaches, such as rule-based filtering or supervised learning on curated datasets, often prove inadequate due to their inability to generalize across diverse contexts and adapt to evolving societal norms [28]. The emergence of preference-based alignment paradigms addresses these limitations by framing the problem as optimizing for human feedback rather than inflexible heuristics [29, 30, 31, 32]. This shift recognizes that LLM decision-making often involves nuanced trade-offs between competing values, requiring flexible frameworks capable of incorporating subjective human preferences [33]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 481, + 565, + 734 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 481, + 565, + 734 + ], + "spans": [ + { + "bbox": [ + 308, + 481, + 565, + 734 + ], + "type": "text", + "content": "Building upon these insights, Reinforcement Learning from Human Feedback (RLHF) [34, 35] has emerged as the predominant alignment paradigm, leveraging human preferences to guide model optimization. In the RLHF pipeline, human annotators first rank the outputs generated by the language model, and these comparisons are used to train a reward model that quantifies human preferences. The language model is then fine-tuned using RL guided by this reward model, enabling the language model to align with human values by maximizing the predicted rewards. The success of RLHF in aligning models like ChatGPT [36, 37] and Claude [38, 39] underscores its practical utility. By translating subjective human preferences into an objective reward signal, RLHF facilitates the optimization of model behavior for value alignment. However, this RLHF paradigm suffers from critical limitations of computational complexity and training instability. Training a separate reward model demands substantial computational resources and high-quality human preference data, which scales poorly across different domains. Moreover, the RL phase often struggles with optimization challenges, such as reward hacking [40] and mode collapse [41]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 323, + 734, + 565, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 734, + 565, + 746 + ], + "spans": [ + { + "bbox": [ + 323, + 734, + 565, + 746 + ], + "type": "text", + "content": "These limitations have spurred interest in alternative" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 563, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 563, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 563, + 34 + ], + "type": "text", + "content": "1" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 14, + 206, + 35, + 559 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 14, + 206, + 35, + 559 + ], + "spans": [ + { + "bbox": [ + 14, + 206, + 35, + 559 + ], + "type": "text", + "content": "arXiv:2503.11701v1 [cs.LG] 12 Mar 2025" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 43, + 563, + 473 + ], + "blocks": [ + { + "bbox": [ + 50, + 43, + 563, + 473 + ], + "lines": [ + { + "bbox": [ + 50, + 43, + 563, + 473 + ], + "spans": [ + { + "bbox": [ + 50, + 43, + 563, + 473 + ], + "type": "image", + "image_path": "eec766babe90c18e92b263abf2f3723da32c85a958aae6f3eb98f4722ac37fa7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 44, + 479, + 565, + 499 + ], + "lines": [ + { + "bbox": [ + 44, + 479, + 565, + 499 + ], + "spans": [ + { + "bbox": [ + 44, + 479, + 565, + 499 + ], + "type": "text", + "content": "Fig. 1: A taxonomy of DPO. We categorize existing DPO works into four branches: data strategy, learning framework, constraint mechanism, and model property. Different colored boxes indicate different categories and their corresponding representative references." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 44, + 508, + 303, + 739 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 508, + 303, + 739 + ], + "spans": [ + { + "bbox": [ + 44, + 508, + 303, + 739 + ], + "type": "text", + "content": "alignment methods that bypass reward modeling while preserving the benefits of preference-based learning. Direct Preference Optimization (DPO) [74, 210] represents a groundbreaking shift in this direction. Unlike RLHF, DPO reframes alignment as a supervised learning problem, directly optimizing the LLM policy using preference data without explicit reward modeling. By leveraging a closed-form mapping between reward functions and optimal policies, DPO eliminates the need for iterative RL training, reducing computational overhead and improving stability. Due to its inherent advantages, DPO has rapidly gained increasing attention from research communities. Existing studies vary widely in data strategies (e.g., point-wise v.s. pair-wise feedback) [67, 211], learning frameworks (e.g., offline v.s. online learning) [121, 122, 126], constraint mechanisms (e.g., different divergence constraints) [169, 171], and model properties (e.g., length bias) [191, 195]. Recent advancements in DPO variants have demonstrated remarkable efficacy in enhancing model alignment with human preferences, achieving unprecedented success across diverse domains [32]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 508, + 566, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 508, + 566, + 555 + ], + "spans": [ + { + "bbox": [ + 308, + 508, + 566, + 555 + ], + "type": "text", + "content": "These developments position DPO-based approaches as a compelling alternative to conventional RLHF paradigms for preference alignment tasks. However, despite its promise, the DPO research landscape remains fragmented." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 561, + 565, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 561, + 565, + 746 + ], + "spans": [ + { + "bbox": [ + 308, + 561, + 565, + 746 + ], + "type": "text", + "content": "Several surveys related to DPO have been published in recent years, yet they exhibit notable limitations in their scope and analysis of DPO. (1) Scope limitations. While an early survey of [212] presents a comprehensive overview of preference-based RL methods, it predates the advent of DPO and does not address its applications to modern LLMs. Recent surveys on alignment [24, 26, 213, 214] provide broad overviews of LLM alignment techniques but only offer cursory summaries of DPO-related approaches without in-depth analysis. Similarly, surveys on learning from human feedback [30, 215, 216, 217] also only briefly mention DPO as a potential alternative. (2) Taxonomy deficiencies. Gao et al. [29] and Winata et al. [32] introduce a simplified taxonomy for preference learning, while overlooking technical distinctions within its broad categorization. In contrast, Wang et al. [31] attempt to classify preference learning across dimensions" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "text", + "content": "2" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 44, + 42, + 301, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 42, + 301, + 157 + ], + "spans": [ + { + "bbox": [ + 44, + 42, + 301, + 157 + ], + "type": "text", + "content": "such as reinforcement learning, reward modeling, feedback, and optimization. However, this taxonomy suffers from significant conceptual overlaps (e.g. reinforcement learning inherently involves optimization). A recent work by Xiao et al. [210] categorizes DPO studies through isolated research questions, which, while useful for problem identification, fragments the methodological connections. Our survey addresses these gaps by presenting the first comprehensive analysis specifically focused on DPO. The main contributions of this survey are summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 51, + 160, + 301, + 380 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 51, + 160, + 301, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 160, + 301, + 252 + ], + "spans": [ + { + "bbox": [ + 51, + 160, + 301, + 252 + ], + "type": "text", + "content": "- In this survey, we introduce a novel taxonomy that categorizes existing DPO works into four key dimensions based on different components of the DPO loss: data strategy, learning framework, constraint mechanism, and model property, as shown in Fig. 1. This taxonomy provides a systematic framework for understanding the methodological evolution of DPO and highlights the key distinctions between different variations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 51, + 253, + 301, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 253, + 301, + 311 + ], + "spans": [ + { + "bbox": [ + 51, + 253, + 301, + 311 + ], + "type": "text", + "content": "- We conduct a rigorous empirical analysis of DPO variants across standardized benchmarks, revealing critical insights into their performance in diverse scenarios. This analysis offers a comprehensive evaluation of DPO variants and provides practical guidance for practitioners." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 51, + 311, + 301, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 311, + 301, + 380 + ], + "spans": [ + { + "bbox": [ + 51, + 311, + 301, + 380 + ], + "type": "text", + "content": "- We discuss real-world applications of DPO and highlight its potential to democratize alignment research by enabling efficient and scalable preference learning across diverse domains. We also outline open challenges and future directions for DPO research, emphasizing the need for robust and generalizable alignment paradigms." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 44, + 383, + 301, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 383, + 301, + 487 + ], + "spans": [ + { + "bbox": [ + 44, + 383, + 301, + 487 + ], + "type": "text", + "content": "The remainder of this survey is organized as follows. Section 2 introduces the background and formulation of DPO. Section 3 presents a taxonomy of DPO, categorizing existing works based on key dimensions. Section 4 describes standardized benchmarks for evaluating DPO methods and presents empirical results. Section 5 discusses real-world applications of DPO and highlights its potential. Section 6 outlines open challenges and future directions for DPO research. Finally, Section 7 concludes the survey." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 508, + 235, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 508, + 235, + 519 + ], + "spans": [ + { + "bbox": [ + 45, + 508, + 235, + 519 + ], + "type": "text", + "content": "2 BACKGROUND AND FORMULATION" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "text", + "content": "Preference learning aims to train language model policies to generate responses that better align with human preferences. Specifically, we denote the language model policy as " + }, + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "inline_equation", + "content": "\\pi(y|x)" + }, + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "text", + "content": " represents the input prompt and " + }, + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "text", + "content": " is a candidate response (completion). A language model can be viewed as an autoregressive function that sequentially predicts tokens based on prior context. Mathematically, this is expressed as: " + }, + { + "bbox": [ + 44, + 525, + 302, + 748 + ], + "type": "inline_equation", + "content": "\\pi(y|x) = \\prod_{t=1}^{T} \\pi(y_t | y_{ 0" + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "text", + "content": " is a hyperparameter that controls the strength of the Kullback-Leibler (KL) divergence penalty. Here, the term " + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "inline_equation", + "content": "\\log \\pi_{\\theta}(\\cdot |x) / \\pi_{\\mathrm{ref}}(\\cdot |x)" + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "text", + "content": " represents the KL divergence between the current policy " + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "text", + "content": " and a reference policy " + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{ref}}" + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "text", + "content": ". In practice, the reference policy " + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{ref}}" + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "text", + "content": " is set to the SFT model " + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{sft}}" + }, + { + "bbox": [ + 307, + 619, + 565, + 689 + ], + "type": "text", + "content": ", ensuring that the updated policy remains close to the initial model." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 307, + 689, + 566, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 689, + 566, + 748 + ], + "spans": [ + { + "bbox": [ + 307, + 689, + 566, + 748 + ], + "type": "text", + "content": "To optimize the above objective, Proximal Policy Optimization (PPO) [219] has emerged as a promising RL algorithm for LLMs. PPO stabilizes training by constraining policy updates within a trust region via a clipped objective, which prevents significant deviations from the previous" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "text", + "content": "3" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 44, + 42, + 301, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 42, + 301, + 135 + ], + "spans": [ + { + "bbox": [ + 44, + 42, + 301, + 135 + ], + "type": "text", + "content": "policy. However, PPO requires an additional critic model to estimate value functions for advantage calculation, thereby introducing extra computational and memory overhead. To address this, recent methods, such as RLOO [220], ReMax [221], GRPO [222], and Reinforce++ [223], introduce critic-free advantage estimation to reduce resource demands while maintaining stable optimization, making them more scalable for large-scale LLM training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 147, + 209, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 147, + 209, + 159 + ], + "spans": [ + { + "bbox": [ + 45, + 147, + 209, + 159 + ], + "type": "text", + "content": "2.2 Direct Preference Optimization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 161, + 300, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 161, + 300, + 243 + ], + "spans": [ + { + "bbox": [ + 44, + 161, + 300, + 243 + ], + "type": "text", + "content": "DPO offers an alternative that streamlines the training process by directly optimizing the policy with preference data [74, 224, 225, 226, 227, 228, 229], thereby eliminating the need for explicit reward modeling in RLHF. The key idea of DPO is a closed-form solution of Eq. 3 that connects reward with the optimal policies. Specifically, the optimal policy corresponding to a given " + }, + { + "bbox": [ + 44, + 161, + 300, + 243 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 44, + 161, + 300, + 243 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 82, + 247, + 301, + 273 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 247, + 301, + 273 + ], + "spans": [ + { + "bbox": [ + 82, + 247, + 301, + 273 + ], + "type": "interline_equation", + "content": "\\pi^ {*} (y | x) = \\frac {1}{Z (x)} \\pi_ {\\mathrm {r e f}} (y | x) \\exp \\left(\\frac {1}{\\beta} r (x, y)\\right), \\tag {4}", + "image_path": "9dc889c067202b098696ded0c0e6a5a38cbb79306dce5dcfd06361d0c4acaa7a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 276, + 249, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 276, + 249, + 288 + ], + "spans": [ + { + "bbox": [ + 44, + 276, + 249, + 288 + ], + "type": "text", + "content": "where the partition function " + }, + { + "bbox": [ + 44, + 276, + 249, + 288 + ], + "type": "inline_equation", + "content": "Z(x)" + }, + { + "bbox": [ + 44, + 276, + 249, + 288 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 91, + 292, + 301, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 292, + 301, + 320 + ], + "spans": [ + { + "bbox": [ + 91, + 292, + 301, + 320 + ], + "type": "interline_equation", + "content": "Z (x) = \\sum_ {y} \\pi_ {\\mathrm {r e f}} (y | x) \\exp \\left(\\frac {1}{\\beta} r (x, y)\\right). \\tag {5}", + "image_path": "70b507821c7cbb1add794e8b294a02e6ae3b31264c7247b117d42453c522c637.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 44, + 324, + 301, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 324, + 301, + 348 + ], + "spans": [ + { + "bbox": [ + 44, + 324, + 301, + 348 + ], + "type": "text", + "content": "By rearranging the above equation, the reward " + }, + { + "bbox": [ + 44, + 324, + 301, + 348 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 44, + 324, + 301, + 348 + ], + "type": "text", + "content": " can be recovered from the optimal policy " + }, + { + "bbox": [ + 44, + 324, + 301, + 348 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 44, + 324, + 301, + 348 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 352, + 301, + 377 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 352, + 301, + 377 + ], + "spans": [ + { + "bbox": [ + 91, + 352, + 301, + 377 + ], + "type": "interline_equation", + "content": "r (x, y) = \\beta \\log \\frac {\\pi^ {*} (y | x)}{\\pi_ {\\operatorname {r e f}} (y | x)} + \\beta \\log Z (x). \\tag {6}", + "image_path": "7440338027ac4b3b46a5841636b860b019e625af6aaaf80166eaf81d38767941.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "spans": [ + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "text", + "content": "Notice that the partition function " + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "inline_equation", + "content": "Z(x)" + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "text", + "content": " depends only on the prompt " + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "text", + "content": ". By substituting this expression into the preference model of Eq. 1, the preference probability model that " + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "inline_equation", + "content": "y_{w}" + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "text", + "content": " is preferred over " + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "inline_equation", + "content": "y_{l}" + }, + { + "bbox": [ + 44, + 380, + 301, + 428 + ], + "type": "text", + "content": " becomes:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 52, + 431, + 301, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 431, + 301, + 466 + ], + "spans": [ + { + "bbox": [ + 52, + 431, + 301, + 466 + ], + "type": "interline_equation", + "content": "P \\left(y _ {w} \\succ y _ {l} | x\\right) = \\sigma \\left(\\beta \\log \\frac {\\pi^ {*} \\left(y _ {w} \\mid x\\right)}{\\pi_ {\\text {r e f}} \\left(y _ {w} \\mid x\\right)} - \\beta \\log \\frac {\\pi^ {*} \\left(y _ {l} \\mid x\\right)}{\\pi_ {\\text {r e f}} \\left(y _ {l} \\mid x\\right)}\\right). \\tag {7}", + "image_path": "3fa55e266f94781e62d4d38b6635a107434b9ae21e066958ea4c68c25ad69067.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 44, + 466, + 301, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 466, + 301, + 502 + ], + "spans": [ + { + "bbox": [ + 44, + 466, + 301, + 502 + ], + "type": "text", + "content": "Based on the above preference probability model, DPO directly optimizes the language mode policy " + }, + { + "bbox": [ + 44, + 466, + 301, + 502 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}" + }, + { + "bbox": [ + 44, + 466, + 301, + 502 + ], + "type": "text", + "content": " by minimizing the following negative log-likelihood loss function:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 510, + 301, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 301, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 301, + 564 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {D P O}} (\\theta) = \\\\ - \\mathbb {E} _ {(x, y _ {w}, y _ {l}) \\sim \\mathcal {D}} \\left[ \\log \\sigma \\left(\\beta \\log \\frac {\\pi_ {\\theta} (y _ {w} | x)}{\\pi_ {\\text {r e f}} (y _ {w} | x)} - \\beta \\log \\frac {\\pi_ {\\theta} (y _ {l} | x)}{\\pi_ {\\text {r e f}} (y _ {l} | x)}\\right) \\right], \\tag {8} \\\\ \\end{array}", + "image_path": "6caf22a5ddff5209964e015b2e0c1943e8baf3c949727cf79a171be3e313ed4f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 44, + 568, + 301, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 568, + 301, + 651 + ], + "spans": [ + { + "bbox": [ + 44, + 568, + 301, + 651 + ], + "type": "text", + "content": "where the KL constraint is implicitly integrated through the use of the reference model " + }, + { + "bbox": [ + 44, + 568, + 301, + 651 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{ref}}" + }, + { + "bbox": [ + 44, + 568, + 301, + 651 + ], + "type": "text", + "content": ". By minimizing this DPO loss, we directly train the policy to satisfy human preferences without resorting to a separate reward modeling stage or using reinforcement learning optimization as in RLHF, significantly reducing implementation complexity while improving training stability." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 44, + 662, + 208, + 674 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 662, + 208, + 674 + ], + "spans": [ + { + "bbox": [ + 44, + 662, + 208, + 674 + ], + "type": "text", + "content": "2.3 Other Preference Optimization" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 44, + 677, + 301, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 677, + 301, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 677, + 301, + 748 + ], + "type": "text", + "content": "In addition to DPO, several concurrent preference optimization methods [190, 230, 231] have been proposed that offer alternative approaches to RLHF. These methods explore different strategies for optimizing LLMs to align with human preference without RL. Below, we provide a brief introduction to these approaches." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 309, + 42, + 480, + 53 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 42, + 480, + 53 + ], + "spans": [ + { + "bbox": [ + 309, + 42, + 480, + 53 + ], + "type": "text", + "content": "2.3.1 Sequence Likelihood Calibration" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 308, + 55, + 564, + 101 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 55, + 564, + 101 + ], + "spans": [ + { + "bbox": [ + 308, + 55, + 564, + 101 + ], + "type": "text", + "content": "Zhao et al. [230] propose Sequence Likelihood Calibration with Human Feedback (SLiC-HF) to directly align LLMs with human preferences. Specifically, the loss function of SLiC-HF is defined as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 318, + 109, + 564, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 109, + 564, + 137 + ], + "spans": [ + { + "bbox": [ + 318, + 109, + 564, + 137 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {S L i C - H F}} (\\theta) = \\max (0, \\delta - \\log \\pi_ {\\theta} (y _ {w} | x) + \\log \\pi_ {\\theta} (y _ {l} | x)) \\\\ - \\lambda \\log \\pi_ {\\theta} (y ^ {*} | x), \\tag {9} \\\\ \\end{array}", + "image_path": "1936fc67f1754632849839cda874e2308bca436fc80fd4dd6aed4bbc4627af5b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "spans": [ + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "type": "text", + "content": "where the first term is the rank calibration loss with " + }, + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "type": "text", + "content": " as a margin hyperparameter, and the second term is the cross-entropy regularization loss with " + }, + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "type": "text", + "content": " as a regularization weight. " + }, + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "type": "inline_equation", + "content": "y^{*}" + }, + { + "bbox": [ + 308, + 140, + 565, + 210 + ], + "type": "text", + "content": " is obtained from either high-quality supervised responses in the SFT dataset or the top-ranked candidate response generated by the SFT model." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 309, + 216, + 528, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 216, + 528, + 227 + ], + "spans": [ + { + "bbox": [ + 309, + 216, + 528, + 227 + ], + "type": "text", + "content": "2.3.2 Rank Responses to Align Human Feedback" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "spans": [ + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "type": "text", + "content": "Yuan et al. [190] introduce Rank Responses to align Human Feedback (RRHF) for LLMs. RRHF extends pair-wise ranking by considering the list-wise ranking order of multiple responses, thus better utilizing the preference information. For an input prompt " + }, + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "type": "text", + "content": " candidate responses " + }, + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "type": "inline_equation", + "content": "\\{y_i\\}_{i=1}^N" + }, + { + "bbox": [ + 307, + 228, + 565, + 322 + ], + "type": "text", + "content": ", it optimizes the model to assign higher probabilities to higher-ranked responses via a ranking loss and directly supervises the best response using cross-entropy as follows:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 327, + 564, + 371 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 327, + 564, + 371 + ], + "spans": [ + { + "bbox": [ + 318, + 327, + 564, + 371 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R R H F}} (\\theta) = \\sum_ {r _ {i} < r _ {j}} \\max \\left(0, \\frac {\\log \\pi_ {\\theta} (y _ {i} | x)}{| | y _ {i} | |} - \\frac {\\log \\pi_ {\\theta} (y _ {j} | x)}{| | y _ {j} | |}\\right) \\\\ - \\lambda \\log \\pi_ {\\theta} \\left(y ^ {*} \\mid x\\right), \\tag {10} \\\\ \\end{array}", + "image_path": "b4f2681503f528d1e7c0de33c6ba041c4462b7b9b983ced72c8fcdbec711851a.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "spans": [ + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "inline_equation", + "content": "r_i = r_\\phi(x, y_i)" + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "text", + "content": " represents the reward of the response " + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "inline_equation", + "content": "y^* = \\arg \\max_{y_i} r_i" + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "text", + "content": " is the response with the highest reward. Although RRHF avoids the need for reinforcement learning in RLHF, it still utilizes a reward model " + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "inline_equation", + "content": "r_\\phi" + }, + { + "bbox": [ + 308, + 375, + 564, + 434 + ], + "type": "text", + "content": " to rank candidate responses based on human preferences." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 309, + 439, + 484, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 439, + 484, + 451 + ], + "spans": [ + { + "bbox": [ + 309, + 439, + 484, + 451 + ], + "type": "text", + "content": "2.3.3 Preference Ranking Optimization" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 308, + 453, + 565, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 453, + 565, + 510 + ], + "spans": [ + { + "bbox": [ + 308, + 453, + 565, + 510 + ], + "type": "text", + "content": "Similarly, Song et al. [231] propose Preference Ranking Optimization (PRO) to align LLMs with human preferences by leveraging multiple responses " + }, + { + "bbox": [ + 308, + 453, + 565, + 510 + ], + "type": "inline_equation", + "content": "\\{y_{i}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 308, + 453, + 565, + 510 + ], + "type": "text", + "content": " with the human-annotated order " + }, + { + "bbox": [ + 308, + 453, + 565, + 510 + ], + "type": "inline_equation", + "content": "y_{1} > y_{2} > \\dots >y_{N}" + }, + { + "bbox": [ + 308, + 453, + 565, + 510 + ], + "type": "text", + "content": ". The loss function of PRO is defined as follows:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 316, + 512, + 565, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 512, + 565, + 559 + ], + "spans": [ + { + "bbox": [ + 316, + 512, + 565, + 559 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {P R O}} (\\theta) = - \\sum_ {i = 1} ^ {N - 1} \\log \\frac {\\exp \\left(\\frac {1}{\\| y _ {i} \\|} \\log \\pi_ {\\theta} \\left(y _ {i} | x\\right) / \\mathcal {T} _ {i} ^ {i}\\right)}{\\sum_ {j = i} ^ {N} \\exp \\left(\\frac {1}{\\| y _ {j} \\|} \\log \\pi_ {\\theta} \\left(y _ {j} | x\\right) / \\mathcal {T} _ {i} ^ {j}\\right)}, \\tag {11}", + "image_path": "eae7a85ce86a95c4206bcb6c9511e719f11d3ccff68be6fc564d712b45aa1a2d.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 308, + 559, + 564, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 559, + 564, + 630 + ], + "spans": [ + { + "bbox": [ + 308, + 559, + 564, + 630 + ], + "type": "text", + "content": "where the dynamic penalty temperature is defined as " + }, + { + "bbox": [ + 308, + 559, + 564, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_i^j = 1 / (r_\\phi (x,y^j) - r_\\phi (x,y^i))" + }, + { + "bbox": [ + 308, + 559, + 564, + 630 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 308, + 559, + 564, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_i^i = \\min_{i < j}\\mathcal{T}_i^j" + }, + { + "bbox": [ + 308, + 559, + 564, + 630 + ], + "type": "text", + "content": ". This temperature ensures that the probability gap between higher-ranked and lower-ranked responses is adaptively scaled according to their reward differences, thereby stabilizing the optimization process." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 309, + 638, + 441, + 650 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 638, + 441, + 650 + ], + "spans": [ + { + "bbox": [ + 309, + 638, + 441, + 650 + ], + "type": "text", + "content": "3 A TAXONOMY OF DPO" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 307, + 654, + 565, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 654, + 565, + 746 + ], + "spans": [ + { + "bbox": [ + 307, + 654, + 565, + 746 + ], + "type": "text", + "content": "In this section, we introduce a novel taxonomy that categorizes existing DPO works based on four key dimensions: data strategy, learning framework, constraint mechanism, and model property. As illustrated in Fig. 1, these four dimensions are derived from different components of the DPO loss, providing a systematic framework for understanding the methodological evolution of DPO and highlighting the key distinctions between different variations." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "text", + "content": "4" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 41, + 167, + 54 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 41, + 167, + 54 + ], + "spans": [ + { + "bbox": [ + 45, + 41, + 167, + 54 + ], + "type": "text", + "content": "3.1 Data Strategy of DPO" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 44, + 58, + 301, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 58, + 301, + 118 + ], + "spans": [ + { + "bbox": [ + 44, + 58, + 301, + 118 + ], + "type": "text", + "content": "The data strategy constitutes the foundational pillar of DPO, focusing on how to leverage diverse types of preference data for training LLMs. As shown in Fig. 2, our taxonomy identifies three principal axes of data strategy: quality, feedback, and granularity." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 129, + 132, + 141 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 129, + 132, + 141 + ], + "spans": [ + { + "bbox": [ + 45, + 129, + 132, + 141 + ], + "type": "text", + "content": "3.1.1 Data Quality" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 44, + 144, + 301, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 144, + 301, + 226 + ], + "spans": [ + { + "bbox": [ + 44, + 144, + 301, + 226 + ], + "type": "text", + "content": "The quality of preference data is a critical factor in determining the effectiveness of DPO training. High-quality data ensures that LLMs effectively learn to align with human preferences, while low-quality data may introduce noise and bias, leading to suboptimal model performance. We categorize data quality considerations into three key aspects: heterogeneity, distinguishability, and noise." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 227, + 302, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 227, + 302, + 539 + ], + "spans": [ + { + "bbox": [ + 44, + 227, + 302, + 539 + ], + "type": "text", + "content": "(a) Data Heterogeneity. Conventional DPO methods assume uniform human preferences when annotating data, thereby overlooking the diversity among annotators. This assumption often skews the model toward the preferences of the majority while neglecting minority viewpoints, potentially leading to biases and unfair treatment of underrepresented groups. To address this issue, Chidambaram et al. [42] propose EM-DPO, which learns the distribution of different preference types and their corresponding response strategies. Building on this, they introduce the MinMax-DPO algorithm, which selects a strategy by minimizing the maximum regret across subgroups, ensuring a more balanced representation of preferences among all groups. MallowsPO [43] decomposes the implicit rewards in DPO into prompt dispersion and response scaling rewards. It introduces a novel objective function to capture human preferences for diverse responses to the same prompt. GRPO [44] formulates an objective function that minimizes the loss for the worst-case group, thereby ensuring fairness by prioritizing the disadvantaged groups in the optimization process. GDPO [45] models the language generation process as a combination of belief distribution prediction and belief-based response generation. The corresponding GDPO loss function consists of belief calibration loss and belief-conditioned preference alignment loss. The former encourages the model to capture the diversity of beliefs across groups, while the latter ensures that generated responses align with the given belief." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 44, + 539, + 302, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 539, + 302, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 539, + 302, + 748 + ], + "type": "text", + "content": "(b) Data Distinguishability. A key limitation of DPO is its inability to account for the distinguishability of preference between responses [46, 50, 51, 56, 57]. In some cases, the preferred response is only marginally better than the dispreferred one, while in others, the dispreferred response contains harmful or misleading content, making it significantly worse. Thus, optimization should focus more on cases with substantial preference differences while reducing the effort spent on minor differences. However, most existing methods treat all samples equally, ignoring this data distinguishability. To address this, ODPO [46] introduces a monotonically increasing offset function, requiring the reward of the preferred response to exceed that of the dispreferred one by a certain margin. This ensures stronger updates for larger preference gaps. Similarly, Ada-DPO [54] introduces an instance-specific nonlinear scaling parameter, assigning larger weights to strong preference pairs and smaller weights to ambiguous ones based on the reward differences, thereby capturing" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 313, + 44, + 563, + 296 + ], + "blocks": [ + { + "bbox": [ + 313, + 44, + 563, + 296 + ], + "lines": [ + { + "bbox": [ + 313, + 44, + 563, + 296 + ], + "spans": [ + { + "bbox": [ + 313, + 44, + 563, + 296 + ], + "type": "image", + "image_path": "7d0b0c1f1f41595c2153dd474b54b2117d70052e28f86633cea08504dba7746a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 361, + 304, + 512, + 316 + ], + "lines": [ + { + "bbox": [ + 361, + 304, + 512, + 316 + ], + "spans": [ + { + "bbox": [ + 361, + 304, + 512, + 316 + ], + "type": "text", + "content": "Fig. 2: An overview of DPO data strategy." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "spans": [ + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "text", + "content": "different levels of data distinguishability. DPO-rc [48] also incorporates the preference reward difference as a coefficient in the loss function. " + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "text", + "content": "-DPO [49] introduces an adaptive preference distribution to obtain dynamic reward margins based on the distribution difference between the policy and reference models. " + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "text", + "content": "-DPO [51] analyzes the optimal " + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "text", + "content": " parameter for datasets with different reward margins, which dynamically adjusts " + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "text", + "content": " based on batch-level reward differences. They also introduce " + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 307, + 327, + 566, + 628 + ], + "type": "text", + "content": "-guided data filtering to prioritize valuable training data. Curri-DPO [53] sorts preference pairs by reward differences and trains progressively from large to small differences, enabling curricular learning. Similarly, MPO [47] utilizes a reward model to score responses generated by the SFT model, constructing a preference dataset and partitioning it based on preference differences to learn from simple to complex tasks. sDPO [55] computes reward accuracy for different datasets based on an initial target model and partitions the dataset in descending order of accuracy, allowing the model to first optimize on simpler samples. Ma et al. [58] propose a preference dataset construction method that adjusts update weights based on response accuracy, assigning lower weights when the model demonstrates higher proficiency. Furthermore, fDPO [52] enhances DPO training by filtering out samples where the generated response of the model policy surpasses the preferred dataset response in reward score." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 631, + 565, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 631, + 565, + 746 + ], + "spans": [ + { + "bbox": [ + 308, + 631, + 565, + 746 + ], + "type": "text", + "content": "(c) Data Noise. Human-generated preference annotations often contain inconsistencies, errors, or noise, negatively affecting the performance of DPO. Such noisy data can mislead models, impairing their ability to accurately capture true preferences and generalize effectively to unseen data. Im and Li [64] analyze how noisy feedback influences the generalization performance of preference optimization, showing that increased noise results in higher generalization risks. Specifically, standard DPO loss functions can yield biased estimates under noisy conditions. To address this" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "text", + "content": "5" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 42, + 301, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 42, + 301, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 42, + 301, + 423 + ], + "type": "text", + "content": "issue, rDPO [59] proposes to enhance DPO robustness against noisy annotations and improve overall training performance. Zhang et al. [63] introduce a noise-aware strategy leveraging annotator confidence and stability to identify and downweight noisy samples during training. They also propose an adaptive reward margin, emphasizing clean samples to improve learning effectiveness. Complementary to these approaches, PerpCorrect [60] employs a data-driven method to correct noisy annotations directly in the dataset. It trains a proxy language model on both clean and noisy samples, distinguishing noise through perplexity differences to improve dataset quality. To systematically explore noise effects, Gao et al. [65] artificially inject various noise types (e.g., Gaussian noise) into datasets, controlling noise intensity via hyperparameters. Their analysis highlights how noise impacts model alignment, guiding future research towards mitigating such negative effects. To address the vulnerability of DPO in noisy environments, ROPO [61] introduces a regularization term to enhance noise tolerance. Additionally, ROPO employs a robust-guided rejection sampling technique. This technique supplements the dataset with samples that contribute minimally to the loss, thereby improving the overall data quality. Kim et al. [62] propose the SPA framework, using model-generated responses and associated confidence scores to detect noise in annotations. SPA further incorporates smoothing techniques into the loss function to alleviate the noise problem. Finally, Wu et al. [66] categorize noise into two types: point noise (single annotation errors) and pairwise noise (errors between annotated pairs). While DPO naturally handles point noise well, it struggles with pairwise noise. Their proposed Dr. DPO introduces a novel loss function explicitly designed for robustness against both point and pairwise noise." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 433, + 168, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 168, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 168, + 443 + ], + "type": "text", + "content": "3.1.2 Preference Feedback" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 446, + 300, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 300, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 300, + 538 + ], + "type": "text", + "content": "Preference feedback refers to the label signals provided by annotators regarding their preferences for different responses. It can be categorized into point-wise, pair-wise, and list-wise feedback. Point-wise feedback evaluates each response independently, assigning a score or labeling it as positive or negative. Pair-wise feedback compares two responses to determine which one is preferred, while list-wise feedback ranks multiple responses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 539, + 301, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 301, + 746 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 301, + 746 + ], + "type": "text", + "content": "(a) Point-Wise Feedback. Point-wise feedback is the basic form of feedback. It refers to the type of feedback where individual outputs or samples are evaluated independently, rather than through comparisons with other outputs. This form of feedback is characterized by its simplicity and directness, focusing on the quality or relevance of a single response or item. The predominant methodology in RLHF [35] employs point-wise reward signals generated by reward models to optimize policy models. Similarly, KTO [67] directly maximizes the utility of model generations using loss functions based on prospect theory rather than the log-likelihood of preferences. It requires only a binary signal indicating whether an output is desirable or undesirable for a given input. Furthermore, BCO [68] builds upon the concepts introduced in KTO and explores a new approach to aligning with binary signals. While KTO focuses on optimizing human utility, BCO introduces a binary classifier framework incorporating reward shift and distribution matching that implicitly" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 311, + 42, + 563, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 42, + 563, + 272 + ], + "spans": [ + { + "bbox": [ + 311, + 42, + 563, + 272 + ], + "type": "text", + "content": "minimizes the DPO loss. Chen et al. [72] and GPO [73] adopt explicit rewards using Noise Contrastive Alignment (NCA) and General Preference Model (GRM) respectively, and then directly optimize language model policies from point-wise preference data with rewards. However, some methods leverage implicit reward signals to refine model behaviors. To ensure that the learned implicit rewards are comparable to the ground-truth rewards, Cal-DPO [69] introduces a calibration term to the preference optimization objective, which prevents the likelihood of chosen responses from decreasing during training. ULMA [71] unifies human demonstration and point-wise preference data into a single framework and handles positive and negative samples with a hybrid objective function. Unlike them, DRO [211] adopts a simple mean-squared objective to optimize the model policy and value function jointly for a single trajectory. Additionally, AOT [70] casts the distributional preference constraint as an optimal transport problem with a convex cost function. The key idea is to minimize the violation of stochastic dominance using a smooth, convex cost function." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 311, + 274, + 563, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 274, + 563, + 746 + ], + "spans": [ + { + "bbox": [ + 311, + 274, + 563, + 746 + ], + "type": "text", + "content": "(b) Pair-Wise Feedback. Pair-wise feedback focuses on comparing pairs of data or actions to determine their relative quality or preference. Building upon the theoretical framework of RLHF, DPO implements this paradigm through the utilization of pair-wise preference data, thereby fitting an implicit reward model. Azar et al. [75] introduces a general theoretical framework to unify existing RLHF and DPO methods. The proposed Identity-Preference Optimization (IPO) directly optimizes policies from preferences without relying on reward modeling or the Bradley-Terry assumption, thereby avoiding overfitting issues observed in DPO. Subsequently, DPO-RK and DPO-R [76] integrate the Rao-Kupper and Davidson models into the DPO training objective respectively, thereby extending the capabilities of DPO by explicitly modeling ties in pairwise comparisons. BMC [77] further addresses a key limitation of the weak correlation between winning and losing responses in pairwise data. Specifically, BMC uses \"Bridging\" to enhance the correlation between winning and losing responses by increasing the consistency and informativeness of pairwise preference signals. However, previous attempts for aligning LLMs primarily focus on optimizing the model's output preferences given an instruction, which struggles to effectively perceive the fine-grained constraints within complex instructions. Thus IOPO [78] extends traditional alignment methods by considering both input and output preferences to better understand the constraints within the instructions. As current methods rely heavily on paired preference data (i.e., explicitly labeled preferred vs. dispreferred examples), they can be limiting in scenarios where such paired data is unavailable or insufficient. SAPO [80] addresses this issue based on the concept of self-play, which enhances data exploration and exploitation by automatically generating negative samples and integrating off-policy learning. Furthermore, PMPO [79] extends the EM algorithm to incorporate both preferred and dispreferred outcomes. By introducing the probability distribution of dis-preferred outcomes, PMPO can optimize using both types of samples, even when only negative feedback is available. Similarly, D2O [81] avoids harmful information by maximizing the discrepancy between the generated responses and the negative samples. NPO [82]" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "text", + "content": "6" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 42, + 299, + 99 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 42, + 299, + 99 + ], + "spans": [ + { + "bbox": [ + 47, + 42, + 299, + 99 + ], + "type": "text", + "content": "and SimNPO [83] achieve the goal of forgetting the negative impact by regulating the model's prediction probabilities on negative datasets to be as minimal as possible, where SimNPO further eliminates the reference model bias issue inherent in NPO." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 99, + 300, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 99, + 300, + 620 + ], + "spans": [ + { + "bbox": [ + 47, + 99, + 300, + 620 + ], + "type": "text", + "content": "(c) List-Wise Feedback. List-wise feedback refers to the type of feedback where multiple outputs or responses generated by the model for a given input are evaluated collectively as a list. This approach considers the relative ranking or ordering among the outputs, rather than focusing on individual outputs in isolation. Panacea [84] reframes alignment as a Multi-Dimensional Preference Optimization (MDPO) problem and introduces a method that aims to learn the entire Pareto front to accommodate diverse user preferences. In short, Panacea is designed to adapt a single model to list-wise preferences in a Pareto-optimal manner. LiPO [85] and LIRE [86] also treat LM alignment as a list-wise ranking problem, drawing on the rich literature of Learning-To-Rank (LTR). Specifically, LiPO introduces a specific method LiPO-λ, which leverages a list-wise ranking objective that weights each preference pair based on the difference in ranking metrics; while LIRE optimizes the response probability by calculating the exponential probability distribution and uses the reward model to directly guide the optimization process. To better capture the relative proximity within ordinal multiple responses, OPO [87] utilizes the Normalized Discounted Cumulative Gain (NDCG), a widely used ranking metric, to optimize the model's generation probability to match the permutation of responses based on these labels. Similarly, DRPO [88] leverages NDCG as a key metric to optimize the ranking of model outputs. However, DRPO incorporates novel elements like diffNDCG and Adaptive Rank Policy Score to dynamically adjust the score margins between preferred and non-preferred responses based on their ranking positions. mDPO [232] extends preference optimization to multi-sample comparisons and introduces a framework that evaluates and optimizes the collective properties of sample groups. It not only addresses the limitations of single pair-wise methods but also provides a more robust optimization framework, especially for characteristics like diversity and bias. Furthermore, RPO [90] introduces a contrastive weighting mechanism that constructs a contrast matrix within each mini-batch to compare preferred and less-preferred responses across prompts. The weights of these comparisons are dynamically adjusted based on the semantic similarity between prompts. Additionally, TODO [91] integrates a tie ranking system into list-wise preference modeling, significantly improving the capture of nuances of human preferences, especially in the presence of noisy or inconsistent labels and frequent ties." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 629, + 174, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 174, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 174, + 640 + ], + "type": "text", + "content": "3.1.3 Preference Granularity" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 643, + 299, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 299, + 711 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 299, + 711 + ], + "type": "text", + "content": "Preference granularity refers to the granularity of preference labels, which determines the level at which preferences are assigned to data. It can be categorized into token-level, step-level, sentence-level, and turn-level granularity, ranging from fine-grained focus on individual tokens to broader preferences over entire interaction turns." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 712, + 299, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 712, + 299, + 746 + ], + "spans": [ + { + "bbox": [ + 47, + 712, + 299, + 746 + ], + "type": "text", + "content": "(a) Token-Level Granularity. Token-level alignment operates at the character/subword unit of text generation, providing the finest-grained control over model outputs" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 310, + 42, + 563, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 42, + 563, + 411 + ], + "spans": [ + { + "bbox": [ + 310, + 42, + 563, + 411 + ], + "type": "text", + "content": "Theoretically, Rafailov et al. [92] demonstrate that DPO can represent any dense reward function by reparameterizing it as an optimal advantage function, which allows DPO to optimize policies in the token-level MDP effectively TDPO [93] refines the alignment process from the sentence level to the token level and introduces forward KL divergence constraints. TDPO utilizes the Bradley-Terry model to convert sentence-level preference comparisons into a token-level reward system, which allows the model to dynamically adjust its strategy at each token generation step. Furthermore, TIS-DPO[94] estimates the importance weights of tokens based on the differences in prediction probabilities from contrastive LLMs, performing token-level importance sampling on existing data to approximate optimal distribution by assigning weights to each token based on its reward. Moreover, " + }, + { + "bbox": [ + 310, + 42, + 563, + 411 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{PO}" + }, + { + "bbox": [ + 310, + 42, + 563, + 411 + ], + "type": "text", + "content": " [99] proposes a temporal decay mechanism that dynamically adjusts the contribution of each token-level reward based on its position in the sequences. Unlike these, SparsePO [95] directly learns sparse masks during the training process and controls which tokens are more important for preferences through the sparsity of the masks, thereby achieving dynamic optimization. RTO [96] and SePO [97] first learn a token-level reward function from preference data using DPO, and then RTO optimizes PPO based on this reward signal, while SePO selects key tokens through the estimated reward function. To tackle the need for large-scale annotated data in training, EPO [98] proposes a hierarchical framework that decomposes complex tasks into manageable subgoals using separate LLMs for subgoal prediction and low-level action generation, leveraging environment feedback to automatically generate reward signals and preference data for aligning LLMs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 310, + 412, + 564, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 412, + 564, + 503 + ], + "spans": [ + { + "bbox": [ + 310, + 412, + 564, + 503 + ], + "type": "text", + "content": "To conclude, token-level granularity optimizes models at individual token positions to maximize expected objectives, preserving semantic precision and capturing local syntactic dependencies. However, it increases computational complexity, as processing numerous tokens extends training time, and its sensitivity to noise means errors in a single token can affect the entire sequence. Thus, careful loss function design and regularization are essential for stability." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 310, + 504, + 564, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 504, + 564, + 746 + ], + "spans": [ + { + "bbox": [ + 310, + 504, + 564, + 746 + ], + "type": "text", + "content": "(b) Step-level Granularity. Step-level granularity focuses on the intermediate steps or stages in a process, particularly effective for complex problem-solving tasks requiring multiple intermediate steps. Step-DPO [100] and SCDPO [101] treat individual reasoning steps as the basic units for preference optimization, where preference pairs of correct and incorrect steps are generated using LLMs. Furthermore, CPO [102] and MCTS-DPO [103] first utilize more powerful inference structures to generate multiple candidate thoughts at each reasoning step following the Tree-of-Thought (ToT) and Monte Carlo Tree Search (MCTS) respectively, and construct preference pairs based on the selected and unselected intermediate steps. Then they finetune LLMs to generate reasoning steps preferred by ToT during inference using DPO. TPO [104] proposes a preference learning algorithm specifically designed for preference trees that have multiple branches and multi-step responses, and introduces the adaptive step reward mechanism to address the issue of small reward margins caused by shared subtrajectories. It adjusts the reward values for each step based on semantic similarity, helping the model better distinguish" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "text", + "content": "7" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 44, + 42, + 301, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 42, + 301, + 169 + ], + "spans": [ + { + "bbox": [ + 44, + 42, + 301, + 169 + ], + "type": "text", + "content": "between preference pairs. RDPO [105] extends traditional preference datasets to incorporate a rationale field, which explains why a particular response is preferred. RDPO introduces rationale information into the DPO loss function by maximizing the likelihood of both the preference and the rationale, which allows the model to better understand the logic behind preferences during training. To address the challenges of sparse rewards and training instability, DAPO [106] uses a critic function to generate dense signals for policy optimization and trains the actor and critic independently to avoid instability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 44, + 170, + 301, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 170, + 301, + 331 + ], + "spans": [ + { + "bbox": [ + 44, + 170, + 301, + 331 + ], + "type": "text", + "content": "To conclude, step-level alignment demonstrates unique advantages in multi-step reasoning tasks by decomposing holistic preferences into intermediate decision points. The primary strength of step-level granularity lies in its capacity to decompose complex objectives into verifiable subgoals, enhancing both interpretability and robustness. For instance, in mathematical reasoning, LLMs can receive feedback on equation derivation steps before final answers, reducing error propagation. However, this granularity still have two key challenges: first, the need for precise step segmentation, which may require domain-specific heuristics or auxiliary models to delineate reasoning boundaries; second, the risk of local optima, where over-optimization of individual steps degrades global coherence." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 331, + 301, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 331, + 301, + 550 + ], + "spans": [ + { + "bbox": [ + 44, + 331, + 301, + 550 + ], + "type": "text", + "content": "(c) Sentence-level Granularity. Sentence-level granularity aligns preferences at the complete utterance level, balancing fine-grained control and computational efficiency. This granularity, represented by the original DPO framework, operates on full response sequences as atomic units for preference comparison. MAPO [107] uses a well-trained translation model to calculate alignment scores between answers in nondominant and dominant languages and then employs preference optimization methods to enhance reasoning consistency. EURUS [108] structures each instruction as a preference tree, containing pairs of correct and incorrect actions to facilitate preference learning. Similarly, IRPO [109] focuses on improving the reasoning capabilities of LLMs through an iterative preference optimization on constructed preference pairs such that the winning response has a higher reward than the losing response. FACTALIGN [110] proposes a fine-grained, sentence-level alignment algorithm called fKTO, which extends the KTO method to leverage fine-grained factuality assessments at the sentence level." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 44, + 550, + 301, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 550, + 301, + 643 + ], + "spans": [ + { + "bbox": [ + 44, + 550, + 301, + 643 + ], + "type": "text", + "content": "To conclude, the key strength of sentence-level granularity lies in its capacity to preserve holistic semantics while maintaining tractable optimization complexity. Nevertheless, we must carefully consider task requirements. While suitable for short-form generation and classification tasks, sentence-level methods may insufficiently capture fine-grained stylistic nuances or long-range dependencies critical in generation and reasoning domains." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 643, + 301, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 643, + 301, + 746 + ], + "spans": [ + { + "bbox": [ + 44, + 643, + 301, + 746 + ], + "type": "text", + "content": "(d) Turn-level Granularity. Turn-level granularity focuses on the optimization of model behavior at the level of conversational turns, which is particularly relevant for dialogue systems and interactive agents. This granularity level treats each turn of a conversation as a unit for preference alignment, allowing the LLMs to receive feedback on their responses within the context of a single turn. M-DPO [111] introduces a multi-turn direct preference learning framework to enhance the mathematical reasoning capabilities of LLMs when" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 307, + 42, + 566, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 42, + 566, + 388 + ], + "spans": [ + { + "bbox": [ + 307, + 42, + 566, + 388 + ], + "type": "text", + "content": "integrated with external tools. It leverages feedback from code interpreters and optimizes trajectory-level preferences using signals generated by the Bradley-Terry model to improve model performance in multi-turn reasoning tasks. ETO [112] presents a novel trial-and-error learning method that optimizes LLM agents' policies by contrasting successful and failed trajectories that contain multi-turn interaction. To address the challenges of coarse granularity and training noise in previous methods, SDPO [113] optimizes specific key segments within interactions to improve multi-turn dialogues while minimizing training noise. Specifically, it extracts key segments from the positive sessions that contribute to higher goal and relationship scores and pairs them with corresponding segments from the negative sessions to calculate an adapted DPO loss. Similarly, AgentQ [114] combines MCTS with self-critique mechanisms to provide process-level supervision by ranking actions, and then iterative fine-tuning using DPO. This approach enables LLMs to effectively learn from both successful and unsuccessful trajectories, enhancing their generalization and decision-making capabilities in complex, multi-turn reasoning tasks within interactive environments. DMPO [115] enhances the existing DPO method by replacing the policy constraint with a State-Action Occupancy Measure (SAOM) constraint and incorporating length normalization into the Bradley-Terry model, effectively addressing challenges in multi-turn scenarios. Compared to traditional policy constraints, SAOM constraints better guide the agent to select actions that align with expert trajectories, especially in unexplored states, thereby reducing compounding errors." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 388, + 567, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 388, + 567, + 494 + ], + "spans": [ + { + "bbox": [ + 308, + 388, + 567, + 494 + ], + "type": "text", + "content": "To conclude, turn-level alignment offers critical advantages for interactive systems by optimizing contextually grounded responses while preserving conversational flow. However, in multi-turn dialogue tasks, the turn-level granularity may introduce additional training noise. For example, some correct turns in negative samples may be mistakenly treated as incorrect turns in the loss calculation. Additionally, since each turn needs to be processed independently, this can lead to reduced training efficiency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 309, + 509, + 463, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 509, + 463, + 521 + ], + "spans": [ + { + "bbox": [ + 309, + 509, + 463, + 521 + ], + "type": "text", + "content": "3.2 Learning Framework of DPO" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 524, + 565, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 524, + 565, + 583 + ], + "spans": [ + { + "bbox": [ + 308, + 524, + 565, + 583 + ], + "type": "text", + "content": "The learning framework of DPO focuses on how the language model policy learns from preference data. In this section, we present an overview of the learning framework in DPO, as shown in Fig. 3, which encompasses the learning paradigm and the learning objectives." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 309, + 594, + 424, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 594, + 424, + 605 + ], + "spans": [ + { + "bbox": [ + 309, + 594, + 424, + 605 + ], + "type": "text", + "content": "3.2.1 Learning Paradigm" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 607, + 565, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 607, + 565, + 689 + ], + "spans": [ + { + "bbox": [ + 307, + 607, + 565, + 689 + ], + "type": "text", + "content": "The learning paradigm in DPO determines how preference data is acquired during model training and falls into three distinct categories: offline learning, where the model learns from pre-collected preference datasets; online Learning, where the model updates based on newly generated data; and active Learning, where the model selectively queries annotators obtain preference data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 689, + 566, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 689, + 566, + 748 + ], + "spans": [ + { + "bbox": [ + 308, + 689, + 566, + 748 + ], + "type": "text", + "content": "(a) Offline Learning. The original DPO framework [74] itself is an offline learning paradigm, where the model learns from a static, pre-collected dataset of preference pairs. Recent research has explored different approaches to merging preference optimization and supervised fine-tuning" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "text", + "content": "8" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 44, + 296, + 277 + ], + "blocks": [ + { + "bbox": [ + 50, + 44, + 296, + 277 + ], + "lines": [ + { + "bbox": [ + 50, + 44, + 296, + 277 + ], + "spans": [ + { + "bbox": [ + 50, + 44, + 296, + 277 + ], + "type": "image", + "image_path": "ab1cb06bdd578e7bee29a0deff07d4285154eb2afd39c5194af16ae72fc055ce.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 285, + 261, + 295 + ], + "lines": [ + { + "bbox": [ + 83, + 285, + 261, + 295 + ], + "spans": [ + { + "bbox": [ + 83, + 285, + 261, + 295 + ], + "type": "text", + "content": "Fig. 3: An overview of DPO learning framework." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 44, + 304, + 301, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 304, + 301, + 514 + ], + "spans": [ + { + "bbox": [ + 44, + 304, + 301, + 514 + ], + "type": "text", + "content": "into a single training phase [190]. CPO [116] incorporates a behavior cloning regularizer through KL divergence minimization between the model and preferred data distribution, which effectively combines into adding a negative log-likelihood term on preferred data alongside the contrastive preference loss. Taking a more direct approach, ORPO [117] proposes a monolithic framework that directly augments the standard negative log-likelihood loss with an odds ratio term comparing chosen and rejected responses, eliminating the need for a separate reference policy while preserving SFT's domain adaptation capabilities. ULMA [71] proposes a hybrid method that applies standard SFT loss on positive samples while using a ranking-based DPO loss on negative samples. PAFT [118] introduces a parallel training paradigm where SFT and preference alignment are performed concurrently on the same pre-trained model and then merged using parameter fusion techniques, avoiding the sequential pipeline that can lead to catastrophic forgetting." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 44, + 514, + 301, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 514, + 301, + 631 + ], + "spans": [ + { + "bbox": [ + 44, + 514, + 301, + 631 + ], + "type": "text", + "content": "Several advances explore curriculum learning strategies to enhance DPO performance and training efficiency. CurriDPO [53] introduces curriculum learning by ordering multiple preference pairs from easy to hard based on the rating difference between chosen and rejected responses, where pairs with larger rating gaps are presented first, followed by progressively more challenging pairs with smaller rating differences. sDPO [55] implements curriculum learning by partitioning preference datasets into sequential chunks measured by reward accuracy and applying them incrementally." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 631, + 301, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 631, + 301, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 631, + 301, + 748 + ], + "type": "text", + "content": "To avoid substantial computational and data annotation costs for preference alignment, fine-tuning-free alignment methods have gained popularity. Linear Alignment [119] works by directly estimating the optimal policy through a one-step update to the output distribution during inference without requiring parameter tuning or feedback data. ICDPO [120] reinterprets DPO's reward-policy relationship to create a fine-tuning-free alignment method that harnesses in-context learning, treating models before and after demonstration exposure as amateur and expert policies, respectively," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 42, + 564, + 65 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 42, + 564, + 65 + ], + "spans": [ + { + "bbox": [ + 308, + 42, + 564, + 65 + ], + "type": "text", + "content": "then computing their log probability ratio to score and rank candidate responses." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 65, + 565, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 65, + 565, + 157 + ], + "spans": [ + { + "bbox": [ + 307, + 65, + 565, + 157 + ], + "type": "text", + "content": "(b) Online Learning. DPO faces significant limitations when relying solely on static, pre-collected preference datasets. These datasets, generated by different models, cause a distribution shift that leads to ineffective off-policy learning as the model evolves [145, 152]. By contrast, online DPO employs an iterative framework that continuously updates the policy with real-time feedback, ensuring on-policy learning and reducing misalignment [143, 144, 233]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 157, + 565, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 157, + 565, + 562 + ], + "spans": [ + { + "bbox": [ + 307, + 157, + 565, + 562 + ], + "type": "text", + "content": "As online DPO progresses, researchers have introduced more flexible frameworks to tackle key challenges. For instance, Yuan et al. [123] proposed a self-rewarding language model: the model generates prompts and responses, then serves as its own judge via LLM-as-a-Judge prompting, scoring on a 5-point scale. OAIF [121] uses an LLM as an online annotator for real-time feedback, and OFSDPO [122] addresses catastrophic forgetting by using two Low-Rank Adaptive (LoRA) modules with different optimization speeds. BPO [124] constructs a dynamic trust region around the behavior LLM, adjusting it as preference data is collected, unlike methods that rely on fixed reference models. Furthermore, researchers have refined sampling strategies for online DPO. RSO [126] and RS-DPO [125] employ rejection sampling based on reward gaps. ROPO [61] recovers useful information from discarded queries via robustness-guided rejection sampling. Shi et al. [127] introduced DPO-Mix-R and DPO-Mix-P, demonstrating faster convergence by mixing online samplers with uniform samplers. OPTUNE [128] selectively regenerates responses with low reward scores while reusing high-reward responses. Iterative RPO [109] and DPO-ST [129] enhance CoT reasoning by selecting correct and incorrect answers to form preference pairs at each iteration. Xie et al. [103] used MCTS to collect preference data during training. Researchers have also explored advanced optimization techniques. APO [130] incorporates momentum-based acceleration, using an extrapolation step between the current and previous policies to update the policy. Xiong et al. [131] proposed a two-agent, non-symmetric online DPO framework with a main agent for optimal policy learning and an enhancer agent for exploration. COMAL [132] formulates alignment as a two-player zero-sum game, updating its policy toward a regularized Nash equilibrium in each iteration. PCO [133] iteratively trains the model on preference data with pairwise cringe Loss." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 562, + 565, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 562, + 565, + 748 + ], + "spans": [ + { + "bbox": [ + 307, + 562, + 565, + 748 + ], + "type": "text", + "content": "Recent efforts push for greater autonomy by letting models generate their own feedback [62]. SeRA [134] introduces a self-reviewed preference bootstrapping method, using an implicit reward margin to select informative pairs, and employs an ensemble reward approach across iterations. CREAM [135] mitigates self-improving biases by applying a consistency regularization on the preference rankings of consecutive iterations. D2PO [136] combines human-labeled gold data with concurrently updated, discriminator-labeled data. DLMA [137] uses contrastive prompts to compute self-reward scores via log ratio differences, then integrates these scores directly into the DPO objective. Addressing exploration and uncertainty in online DPO has also been a focus [234]. XPO [138] encourages exploration by adding a bonus for responses outside the initial policy's support, and SELM [139] uses an optimism term in reward fitting to" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 558, + 26, + 564, + 34 + ], + "type": "text", + "content": "9" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 44, + 42, + 301, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 42, + 301, + 133 + ], + "spans": [ + { + "bbox": [ + 44, + 42, + 301, + 133 + ], + "type": "text", + "content": "actively seek high-reward responses. ETO [112] alternates exploration and training phases to collect failure trajectories, while VPO [140] applies optimism by regularizing the reward model to favor higher-value responses. Xiong et al. [111] extended DPO from single-turn to multi-turn tasks, balancing KL-regularized and non-regularized objectives, and COPO [141] incorporates a count-based bonus to encourage novel responses with low visitation counts." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 44, + 134, + 301, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 134, + 301, + 215 + ], + "spans": [ + { + "bbox": [ + 44, + 134, + 301, + 215 + ], + "type": "text", + "content": "Finally, a growing body of work aims to merge online and offline techniques. HyPO [142] uses offline preference data for DPO training while regularizing via online data. MPO [47] combines the strengths of DPO and PPO in a two-stage process: it first trains DPO on an easier dataset, then uses this model as a reference for PPO training on more challenging samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 216, + 301, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 216, + 301, + 307 + ], + "spans": [ + { + "bbox": [ + 44, + 216, + 301, + 307 + ], + "type": "text", + "content": "(c) Active Learning. Active learning in DPO is a strategic approach that aims to reduce the annotation cost and improve sample efficiency by selectively querying annotators for the most informative preference examples. Unlike offline learning that uses a fixed dataset or online learning that generates new data continuously, active learning intelligently selects which data points should be labeled based on model uncertainty or other informativeness criteria." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 308, + 302, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 302, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 302, + 539 + ], + "type": "text", + "content": "Muldrew et al. [146] introduced APL, an iterative data acquisition and fine-tuning loop in which batches of prompt/completion pairs are strategically selected using acquisition functions: a predictive entropy-based approach to measure model uncertainty for prompts and a preference certainty measure based on the implicit Bradley-Terry model for completion pairs in DPO. Unlike two-step selection processes in APL that separately select uncertain input prompts and corresponding completions, divAPO [147] integrates both stages into a single selection phase. divAPO maximizes the preference model certainty by simultaneously evaluating the informativeness of input prompts and completion pairs, while also considering the data distribution of the input prompts. Ji et al. [148] proposed ADPO, which selectively queries human preferences only for responses where the model exhibits high uncertainty while using pseudo-labels for confident cases. Das et al. [149] also employed active learning on RLHF, which actively selects the context-action pairs that maximize exploration and minimize uncertainty in the reward model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 548, + 160, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 548, + 160, + 559 + ], + "spans": [ + { + "bbox": [ + 45, + 548, + 160, + 559 + ], + "type": "text", + "content": "3.2.2 Learning Objective" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 44, + 561, + 301, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 561, + 301, + 631 + ], + "spans": [ + { + "bbox": [ + 44, + 561, + 301, + 631 + ], + "type": "text", + "content": "In what follows, we present the learning objective in DPO, which determines how the model policy is optimized based on preference data. We first discuss multi-objective learning in DPO, which aims to optimize multiple objectives simultaneously. Then, we introduce self-play learning, which leverages self-generated data for preference alignment." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 44, + 632, + 301, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 632, + 301, + 723 + ], + "spans": [ + { + "bbox": [ + 44, + 632, + 301, + 723 + ], + "type": "text", + "content": "(a) Multi-Objective Learning. Multi-objective learning in DPO addresses the challenge of simultaneously optimizing the language model for multiple, potentially competing preference dimensions, such as helpfulness, harmlessness, and truthfulness. This approach aims to find a balanced policy that satisfies multiple human values rather than optimizing for a single objective, which more closely mirrors the complexity of real-world human preferences." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 44, + 723, + 301, + 747 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 723, + 301, + 747 + ], + "spans": [ + { + "bbox": [ + 44, + 723, + 301, + 747 + ], + "type": "text", + "content": "MODPO [150] achieves the sequential optimization of multiple preference objectives by incorporating language" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 42, + 566, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 42, + 566, + 295 + ], + "spans": [ + { + "bbox": [ + 307, + 42, + 566, + 295 + ], + "type": "text", + "content": "modeling directly into reward modeling, using a margin-based loss to maintain performance on previously optimized dimensions. SPO [151] takes a similar iterative constrained optimization approach, optimizing each preference dimension while preventing the degradation of prior alignments through regularization terms. MOSLIM [152] takes a different approach by introducing a multi-head classification reward model that assigns different preference dimensions to separate classification heads, enabling simultaneous optimization of multiple preferences without requiring multiple reward or policy models. HPO [153] incorporates auxiliary objectives through offline RL, where the model uses a weighted maximum likelihood objective that combines a preference alignment term with an advantage-weighted term for maximizing arbitrary auxiliary rewards like readability and safety. CPO [154] introduces explicit preference tokens during training that specify desired scores for different objectives, transforming the multi-objective optimization into a conditional optimization problem. DRDO [155] simultaneously models rewards and preferences through a combination of reward distillation and a contrastive log-unlikelihood term in its loss function." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 296, + 567, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 296, + 567, + 388 + ], + "spans": [ + { + "bbox": [ + 308, + 296, + 567, + 388 + ], + "type": "text", + "content": "(b) Self-Play Learning. Self-play learning in DPO represents an approach where the language model interacts with itself or its previous iterations to generate its own preference data for training, reducing or eliminating the need for human annotations [139, 164]. This method enables continuous self-improvement by leveraging the model's own judgment capabilities to identify and learn from better responses, creating a form of autonomous preference learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 388, + 566, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 388, + 566, + 584 + ], + "spans": [ + { + "bbox": [ + 308, + 388, + 566, + 584 + ], + "type": "text", + "content": "SPIN [156] involves a self-play mechanism where the LLM generates synthetic data from its prior iterations, then fine-tunes itself to distinguish these self-generated responses from those of human-annotated data. The method resembles a two-player game, where the model's current iteration tries to improve its responses to better match the target distribution, while the previous iteration attempts to generate responses as close to human data as possible. SPPO [157] treats LLM alignment as a constant-sum two-player game and iteratively refines itself by competing against its previous iteration. Instead of maintaining two competing policies or a reward model, SPO [158] uses a single policy to sample multiple trajectories and uses the proportion of wins in pairwise comparisons as the reward signal. BoNBoN [159] Alignment likewise relies on sampling responses from a base model, but it selects the best ones among n candidates and fine-tunes itself to approximate that best-of-n distribution." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 585, + 566, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 585, + 566, + 746 + ], + "spans": [ + { + "bbox": [ + 308, + 585, + 566, + 746 + ], + "type": "text", + "content": "Some works approach the alignment problem by leveraging Nash equilibrium [132]. Nash-MD [160] learns a preference model from pairwise human feedback and then computes a Nash equilibrium policy that consistently produces preferred responses. Its self-play approach updates the policy by having it compete against itself (or a slight variant of itself) under the learned preference model, which measures how often one response is preferred to another. DNO [161] extends this concept by implementing a batched on-policy algorithm where the current policy generates multiple outputs that are compared both against each other and against a teacher model's outputs. IPO-MD [162] combines the strengths of IPO and Nash-MD, where the model generates data using a mixture policy between the online and reference" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "spans": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "type": "text", + "content": "10" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + }, + { + "para_blocks": [ + { + "bbox": [ + 44, + 42, + 301, + 112 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 42, + 301, + 112 + ], + "spans": [ + { + "bbox": [ + 44, + 42, + 301, + 112 + ], + "type": "text", + "content": "policies, and uses a preference model to annotate pairs of generations, making the optimization equivalent to finding a Nash equilibrium through self-play. SRPO [163] modifies Nash-MD by introducing a self-improvement policy that refines model outputs through iterative revisions, enabling offline optimization without a learned reward function." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 128, + 209, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 128, + 209, + 139 + ], + "spans": [ + { + "bbox": [ + 45, + 128, + 209, + 139 + ], + "type": "text", + "content": "3.3 Constraint Mechanism of DPO" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 143, + 301, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 143, + 301, + 224 + ], + "spans": [ + { + "bbox": [ + 44, + 143, + 301, + 224 + ], + "type": "text", + "content": "The constraint mechanism of DPO derives from its reformulation of RLHF, which includes a KL divergence constraint between the current policy and a reference policy. As shown in Fig. 4, we re-examine the constraint mechanism of DPO from the perspective of the reference model and different divergence constraints. We also explore various DPO variants with different safety constraints." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 236, + 153, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 236, + 153, + 247 + ], + "spans": [ + { + "bbox": [ + 45, + 236, + 153, + 247 + ], + "type": "text", + "content": "3.3.1 Reference Model" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 249, + 301, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 249, + 301, + 376 + ], + "spans": [ + { + "bbox": [ + 44, + 249, + 301, + 376 + ], + "type": "text", + "content": "The reference model in DPO functions as an anchor to ensure policy updates remain within a controlled range, preventing excessive deviation from initial behaviors. Typically, the reference model is initialized using the SFT model that serves as the starting point for preference optimization. The choice of reference model significantly impacts optimization dynamics. A static reference model ensures stable training but may limit adaptability. In the following subsections, we introduce two advanced approaches: reference-free DPO eliminates reliance on the reference model, while dynamic-reference DPO employs an evolving reference model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 44, + 377, + 301, + 748 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 44, + 377, + 301, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 377, + 301, + 654 + ], + "spans": [ + { + "bbox": [ + 44, + 377, + 301, + 654 + ], + "type": "text", + "content": "(a) Reference-Free DPO. To reduce the computational and memory costs associated with a reference model, many algorithms have explored training modes that do not require loading the reference model. Xu et al. [116] replaces the reference model with a uniform prior distribution, adding an SFT loss term on preferred data to maintain consistency with the desired behavior. ORPO [117] integrates an odds ratio-based penalty with traditional SFT loss, increasing the probability of preferred responses while decreasing undesirable ones, thereby enabling single-stage training without a separate reference model. SimPO [166] directly uses the average log probability as implicit rewards. This removes the requirement for a separate reference model, significantly improving computational and memory efficiency. SimPER [167] also directly optimizes reverse perplexity for preferred versus rejected responses, creating a preference optimization approach that does not require a separate reference model, thus simplifying training. Despite these advancements, [168] argue that a reference model remains crucial. They compared two reference-free variants using posterior probabilities and likelihood functions as rewards, respectively, and found the original DPO consistently outperformed both. Their results indicate that a strong, well-aligned reference policy can significantly enhance DPO performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 44, + 654, + 301, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 654, + 301, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 654, + 301, + 748 + ], + "type": "text", + "content": "(b) Dynamic-Reference DPO. Offline DPO methods often suffer from reward over-optimization, meaning that as the trained model deviates from the reference model, the quality of generated samples tends to degrade. To address this issue, Gorbatovski et al. [165] proposed dynamically updating the reference model using the current model parameters during training, preventing excessive divergence and maintaining high-quality outputs. Curri-DPO [53] and sDPO [55] adopt" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 313, + 42, + 561, + 261 + ], + "blocks": [ + { + "bbox": [ + 313, + 42, + 561, + 261 + ], + "lines": [ + { + "bbox": [ + 313, + 42, + 561, + 261 + ], + "spans": [ + { + "bbox": [ + 313, + 42, + 561, + 261 + ], + "type": "image", + "image_path": "cddebe4de78a02102cffc5e93cf429138280b5deac316fd35c18e11122d7aa8e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 344, + 267, + 529, + 277 + ], + "lines": [ + { + "bbox": [ + 344, + 267, + 529, + 277 + ], + "spans": [ + { + "bbox": [ + 344, + 267, + 529, + 277 + ], + "type": "text", + "content": "Fig. 4: An overview of DPO constraint mechanism." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 283, + 566, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 283, + 566, + 411 + ], + "spans": [ + { + "bbox": [ + 308, + 283, + 566, + 411 + ], + "type": "text", + "content": "curriculum learning by sorting data samples from simpler to more complex based on predefined metrics. At each training iteration, the model from the previous step serves as the updated reference model to provide constraints, facilitating progressive learning. Similarly, MPO [47] partitions datasets according to task difficulty, employing a two-stage training procedure. The model trained in the initial stage serves as the reference for the subsequent stage. Additionally, M-DPO [89] compares the performance of a fixed reference model versus a dynamic reference model, finding that the latter yields superior results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 309, + 421, + 440, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 421, + 440, + 432 + ], + "spans": [ + { + "bbox": [ + 309, + 421, + 440, + 432 + ], + "type": "text", + "content": "3.3.2 Divergence Constraint" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 434, + 566, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 434, + 566, + 503 + ], + "spans": [ + { + "bbox": [ + 308, + 434, + 566, + 503 + ], + "type": "text", + "content": "Divergence constraints in DPO play a crucial role in constraining model optimization, balancing alignment performance and model stability. In the following subsections, we introduce two modifications to the divergence constraint: one for enhancing diversity and the other for improving generalization." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 504, + 567, + 748 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 308, + 504, + 566, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 504, + 566, + 654 + ], + "spans": [ + { + "bbox": [ + 308, + 504, + 566, + 654 + ], + "type": "text", + "content": "(a) Diversity. Standard DPO typically uses reverse KL divergence equivalent to RLHF. However, the mode-seeking nature of reverse KL divergence reduces the diversity of the generated outputs. To overcome this limitation, f-DPO [169] explores various divergences, including forward KL divergence, reverse KL divergence, Jensen-Shannon divergence, and " + }, + { + "bbox": [ + 308, + 504, + 566, + 654 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 308, + 504, + 566, + 654 + ], + "type": "text", + "content": "-divergence, to achieve a better trade-off between alignment performance and diversity. Slocum et al. [170] further proposes splitting the KL divergence term into entropy and cross-entropy terms. This decoupling allows independent control of generation diversity and closeness to the reference model, preserving output diversity without degrading overall model quality." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 308, + 654, + 567, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 654, + 567, + 748 + ], + "spans": [ + { + "bbox": [ + 308, + 654, + 567, + 748 + ], + "type": "text", + "content": "(b) Generalization. Over-optimization in DPO can negatively impact generalization, causing reduced performance on inputs outside the training distribution. To mitigate this, Huang et al. [178] introduce " + }, + { + "bbox": [ + 308, + 654, + 567, + 748 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 308, + 654, + 567, + 748 + ], + "type": "text", + "content": "-divergence as a more aggressive form of regularization compared to KL divergence, alleviating the over-optimization problem. DPO-Kernels [171] employs data-driven methods to select optimal kernel-divergence pairs dynamically, improving task adaptability" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 555, + 26, + 563, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 555, + 26, + 563, + 34 + ], + "spans": [ + { + "bbox": [ + 555, + 26, + 563, + 34 + ], + "type": "text", + "content": "11" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + }, + { + "para_blocks": [ + { + "bbox": [ + 44, + 42, + 301, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 42, + 301, + 343 + ], + "spans": [ + { + "bbox": [ + 44, + 42, + 301, + 343 + ], + "type": "text", + "content": "and robustness. FlipGuard [172] introduces a customized reward characterization to monitor model performance. If performance drops relative to earlier versions, FlipGuard constrains the model's updates to ensure alignment with previous stable behavior. FPO [173] leverages the feature-level constraints using Sparse Autoencoders (SAEs) to improve computational efficiency and training stability. SPO [176] integrates a natural preference loss with a KL divergence-based regularization term computed over the entire model output distribution. By adjusting this divergence term, SPO prevents unwanted shifts beyond the preference dataset, ensuring stable alignment. EXO [175] argues that minimizing the forward KL divergence in DPO introduces bias when approximating the optimal policy. They establish a generalized alignment objective and reveal the equivalence between maximizing KL regularization rewards and minimizing the reverse KL divergence relative to the optimal policy. QDPO [177] utilizes divergence between the quantized model and the full-precision model for preference optimization, effectively addressing the token-flipping issue. Token-flipping refers to the phenomenon where quantization errors skew token distributions, leading to incorrect token selection. GPO [174] constructs a framework that unifies different DPO-related algorithms through theoretical derivations, enabling a deeper understanding of the regularization mechanisms in the DPO family of algorithms." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 354, + 153, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 354, + 153, + 365 + ], + "spans": [ + { + "bbox": [ + 45, + 354, + 153, + 365 + ], + "type": "text", + "content": "3.3.3 Safety Constraint" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 369, + 301, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 369, + 301, + 681 + ], + "spans": [ + { + "bbox": [ + 44, + 369, + 301, + 681 + ], + "type": "text", + "content": "Safety constraints in DPO aim to prevent LLMs from generating harmful, biased, or unethical outputs. However, traditional alignment algorithms often fail to address safety concerns. To enhance the safety alignment, recent studies have introduced several specialized mechanisms based on DPO. SafeDPO [179] introduces a streamlined approach for safety alignment by implicitly optimizing safety objectives within a single stage of policy learning. SACPO [180] addresses safety constraints by explicitly formulating language model alignment as a constrained optimization problem, using DPO to optimize the model under safety constraints. Zhang et al. [184] propose creating a backtracking preference dataset that identifies and reverses unsafe outputs, enhancing the safety and robustness of the model. C-DPO [181] integrates dual gradient descent into DPO to balance safety and utility efficiently. This approach achieves a robust trade-off between helpfulness and harmlessness, offering explicit safety guarantees. ADPO [182] introduces adversarial techniques into DPO. It specifically trains models to reduce the probability of unsafe outputs by deliberately generating harmful responses using controlled toxic tokens. Finally, Lee et al. [183] explore the internal mechanisms through which DPO reduces harmful outputs. Their findings suggest that DPO does not remove harmful behaviors learned during pretraining but instead teaches models to bypass or suppress these behaviors. This insight helps explain certain safety vulnerabilities like jailbreaks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 44, + 696, + 175, + 708 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 696, + 175, + 708 + ], + "spans": [ + { + "bbox": [ + 44, + 696, + 175, + 708 + ], + "type": "text", + "content": "3.4 Model Property of DPO" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 712, + 301, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 712, + 301, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 712, + 301, + 748 + ], + "type": "text", + "content": "DPO has shown great promise in aligning LLMs with human preferences by directly optimizing model outputs based on preference data. During this process, the underlying models" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 315, + 44, + 561, + 259 + ], + "blocks": [ + { + "bbox": [ + 315, + 44, + 561, + 259 + ], + "lines": [ + { + "bbox": [ + 315, + 44, + 561, + 259 + ], + "spans": [ + { + "bbox": [ + 315, + 44, + 561, + 259 + ], + "type": "image", + "image_path": "e5c5a6a0d780ea4b5c9a8a90db2723f6fdb6c09e14347e19016d55dcced76086.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 355, + 266, + 517, + 277 + ], + "lines": [ + { + "bbox": [ + 355, + 266, + 517, + 277 + ], + "spans": [ + { + "bbox": [ + 355, + 266, + 517, + 277 + ], + "type": "text", + "content": "Fig. 5: An overview of DPO model property." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 282, + 565, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 282, + 565, + 354 + ], + "spans": [ + { + "bbox": [ + 308, + 282, + 565, + 354 + ], + "type": "text", + "content": "exhibit certain properties that are crucial for understanding their behavior and effectiveness. These properties can be broadly categorized into two aspects: the generation property and the optimization property, as shown in Fig. 5. In the following sections, we explore these two properties in more detail, analyzing their implications for model alignment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 309, + 363, + 430, + 375 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 363, + 430, + 375 + ], + "spans": [ + { + "bbox": [ + 309, + 363, + 430, + 375 + ], + "type": "text", + "content": "3.4.1 Generation Property" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 376, + 565, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 376, + 565, + 458 + ], + "spans": [ + { + "bbox": [ + 307, + 376, + 565, + 458 + ], + "type": "text", + "content": "The generation property of DPO primarily concerns issues related to distribution shifts and length biases. DPO is sensitive to distribution shifts between the base model outputs and the preference data, which may reduce diversity and generalization. Additionally, DPO has a tendency to favor longer responses, a phenomenon known as morbidity, which can negatively impact performance and user experience." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 458, + 565, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 458, + 565, + 676 + ], + "spans": [ + { + "bbox": [ + 308, + 458, + 565, + 676 + ], + "type": "text", + "content": "(a) Distribution Shift. In RLHF, the reward model is trained on a static set of preference data collected offline. During fine-tuning, the generated responses often differ from this original training data, resulting in a distribution shift. This shift can cause inaccurate reward predictions and lead to over-optimization. The implicit reward model in DPO also suffers from this distribution shift issue. Moreover, Lin et al. [188] have shown that the implicit reward model in DPO performs poorly on Out-Of-Distribution (OOD) data compared to explicit reward models. Experimental results indicate that DPO can transfer probability mass to the highreward response regions covered by the preference data, but it may also cause the distribution of responses generated by the model to deviate significantly from that of the reference policy, resulting in responses that do not meet expectations [189]. To address these problems, many researchers are now exploring online DPO approaches [109, 121, 122, 125], aiming to mitigate OOD by continuously updating preference data during training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 677, + 566, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 677, + 566, + 748 + ], + "spans": [ + { + "bbox": [ + 307, + 677, + 566, + 748 + ], + "type": "text", + "content": "Existing DPO methods also face significant limitations due to their dependence on specific training tasks. Their optimal solutions lack robustness when applied to OOD tasks. Thus, SRPO [163] reframes alignment as a self-improvement process, which optimizes a self-improvement policy and a generative policy using a min-max objective, ensuring" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "type": "text", + "content": "12" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + }, + { + "para_blocks": [ + { + "bbox": [ + 44, + 42, + 301, + 134 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 42, + 301, + 134 + ], + "spans": [ + { + "bbox": [ + 44, + 42, + 301, + 134 + ], + "type": "text", + "content": "robustness by making the solution independent of training tasks. Zhang et al. [139] also identify notable issues in DPO when handling OOD tasks. First, DPO tends to overly favor novel content it has not seen during training. Second, it easily gets stuck in local optima, limiting exploration. To address these problems, they propose Self-Exploring Language Models (SELM), incorporating an optimism term to encourage broader exploration of new responses." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 44, + 134, + 301, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 134, + 301, + 216 + ], + "spans": [ + { + "bbox": [ + 44, + 134, + 301, + 216 + ], + "type": "text", + "content": "Another significant challenge of DPO is preference drift, where human preferences evolve, changing data distributions over time. Traditional DPO algorithms typically overlook such temporal shifts, mistakenly interpreting them as noise. To address this, NS-DPO [185] propose to assign higher weights to recent data, allowing models to better adjust to evolving preferences." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 216, + 301, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 216, + 301, + 320 + ], + "spans": [ + { + "bbox": [ + 44, + 216, + 301, + 320 + ], + "type": "text", + "content": "(b) Length Bias. Length bias in DPO refers to the tendency of model-generated outputs to become excessively long during training. This issue is similar to the length bias observed in RLHF [197] and is particularly pronounced in DPO. Length bias affects response quality and overall model performance. To mitigate this issue, researchers have developed several solutions, which can be categorized into three main approaches: length regularization, length normalization, and length sampling." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 44, + 320, + 301, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 320, + 301, + 504 + ], + "spans": [ + { + "bbox": [ + 44, + 320, + 301, + 504 + ], + "type": "text", + "content": "Length regularization is a common approach to controlling length bias in DPO. By introducing regularization terms into the objective function, the model can constrain response length and reduce morbidity, thereby alleviating the length bias problem. R-DPO [191] introduces a length-based penalty term to the DPO objective function, explicitly discouraging morbidity. " + }, + { + "bbox": [ + 44, + 320, + 301, + 504 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{PO}" + }, + { + "bbox": [ + 44, + 320, + 301, + 504 + ], + "type": "text", + "content": " [99] introduces a dynamic weighting mechanism by incorporating a temporal decay factor. Unlike previous methods that apply uniform reward contributions across sequences, " + }, + { + "bbox": [ + 44, + 320, + 301, + 504 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{PO}" + }, + { + "bbox": [ + 44, + 320, + 301, + 504 + ], + "type": "text", + "content": " adjusts the influence of each reward based on its position in the response. Higher weights are assigned to rewards associated with earlier tokens, as they are more critical for model alignment, while later rewards gradually receive lower weights. This adaptive approach prevents overfitting to less relevant tokens, thereby addressing length bias in DPO." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 504, + 302, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 504, + 302, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 504, + 302, + 748 + ], + "type": "text", + "content": "Length normalization aims to eliminate the loss bias caused by response length differences, allowing the model to evaluate texts of varying lengths more fairly. This approach prevents the model from developing an unreasonable preference for either long or short responses [198]. RRHF [190] and SimPO [166] first propose to apply length normalization to responses, ensuring that the loss remains unaffected by response length. LN-DPO [194] further integrates SimPO-like length normalization into DPO, demonstrating that this approach enhances response quality while mitigating morbidity. LD-DPO [195] achieves length desensitization by reparameterizing the likelihood in DPO. Specifically, it decomposes the likelihood of the longer response in a preference pair into the product of the likelihood of the public-length portion and the likelihood of the excessive portion. It then introduces a hyperparameter to mitigate the morbidity preference. This adjustment smooths the relationship between likelihood and response length, reducing its impact on optimization. For multi-turn dialogue tasks, DMPO [115] introduces length normalization for the number of turns in multi-turn preference optimization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 307, + 42, + 566, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 42, + 566, + 274 + ], + "spans": [ + { + "bbox": [ + 307, + 42, + 566, + 274 + ], + "type": "text", + "content": "An alternative approach to controlling length bias in DPO is through sampling-based methods. SamPO [192] introduces a down-sampling method to compute regularized KL divergences. By balancing token-level probability distributions between preferred and rejected responses, SamPO reduces length bias in DPO training. Yuan et al. [193] propose Length-Instruction Fine-Tuning (LIFT), a method to improve instruction-following models' ability to adhere to length constraints by augmenting existing training data with explicit length instructions and using DPO for training. This enables the model to generalize across prompts requiring different response lengths. For long-context tasks, LongPO [196] enables short-context LLMs to self-evolve for long-context tasks by learning from self-generated short-to-long preference data, which includes paired responses for long-context inputs and their compressed short-context counterparts. LongPO incorporates a short-to-long KL constraint to prevent degradation of short-context performance during long-context alignment, achieving strong performance on both short- and long-context tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 309, + 282, + 437, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 282, + 437, + 295 + ], + "spans": [ + { + "bbox": [ + 309, + 282, + 437, + 295 + ], + "type": "text", + "content": "3.4.2 Optimization Property" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 296, + 566, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 296, + 566, + 376 + ], + "spans": [ + { + "bbox": [ + 307, + 296, + 566, + 376 + ], + "type": "text", + "content": "The optimization property of DPO involves likelihood collapse and alignment tax. While DPO aims to increase the likelihood of preferred responses and decrease dispreferred ones, the actual optimization process does not explicitly enforce this balance. Moreover, alignment improvements often come at the cost of the original capabilities of LLMs, known as alignment tax." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 377, + 566, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 377, + 566, + 608 + ], + "spans": [ + { + "bbox": [ + 308, + 377, + 566, + 608 + ], + "type": "text", + "content": "(a) Likelihood Collapse. Likelihood collapse refers to the unintended reduction in the likelihood of both preferred and dispreferred responses during DPO training [92]. This phenomenon can lead to unintentional unalignment, where the model's outputs deviate from human preferences, potentially producing undesirable or harmful responses. This phenomenon is also referred to as likelihood displacement in prior studies [204]. Additionally, the gradients associated with increasing the likelihood of preferred responses and decreasing that of dispreferred responses can become entangled, hindering effective learning. This entanglement complicates the optimization process, making it challenging to achieve the desired alignment [203]. Theoretical analyses have further elucidated the underlying causes of likelihood collapse. In particular, Feng et al. [202] developed an analytical framework grounded in field theory. Their analysis of the gradient vector field of the DPO loss function revealed that the loss function decreases the probability of generating human-disliked data at a faster rate than it increases the probability of generating human-like data." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 608, + 566, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 608, + 566, + 746 + ], + "spans": [ + { + "bbox": [ + 308, + 608, + 566, + 746 + ], + "type": "text", + "content": "Several strategies have been proposed to address likelihood collapse. Pal et al. [200] introduce DPO-Positive (DPOP), which adds a penalty term to maintain a high log-likelihood for preferred examples. Similarly, LLaMA [235] augments DPO training with a negative log-likelihood term to stabilize training and preserve the log-likelihood of chosen responses [109]. Flex-DPO [201] adaptively adjusts parameters to slow the decline in the likelihood of dispreferred responses and balance gradients for both chosen and rejected outputs. D'Oosterlinck et al. [199] propose Anchored Preference Optimization (APO), which provides fine-grained control over probability updates: APO-zero increases the" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "spans": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "type": "text", + "content": "13" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 49, + 563, + 299 + ], + "blocks": [ + { + "bbox": [ + 149, + 38, + 459, + 49 + ], + "lines": [ + { + "bbox": [ + 149, + 38, + 459, + 49 + ], + "spans": [ + { + "bbox": [ + 149, + 38, + 459, + 49 + ], + "type": "text", + "content": "TABLE 1: An overview of datasets (upper row) and benchmarks (lower row) for DPO." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 49, + 563, + 299 + ], + "lines": [ + { + "bbox": [ + 47, + 49, + 563, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 49, + 563, + 299 + ], + "type": "table", + "html": "
DatasetTask DescriptionData Size (Training & Test)Data SourceData StructureEvaluation Metric
UltraFeedback [237]Instruction-Following, Helpful64K&-AIList-
SafeRLHF [238]Harmless, Helpful73.9K&8.21KHuman&AIPair-
HelpSteer [239]Helpful35.3K&1.8KHumanPoint-
PRM800K [240]Mathematical Reasoning800K&-HumanPoint-
SHP-2 [241]Q&A From Reddit3600K&241KHumanPair-
Nectar [242]Conversations183K&-AIList-
OpenOrca [243]Conversations2940K&-AISample-
Capybara [244]Multi-Turn Conversations16K&-Human&AISample-
Step-DPO [100]Mathematical Reasoning10.8K&-Human&AIPair-
BeaverTails [245]Harmless, Helpful330K&36KHuman&AIPoint-
IMDb [246]Movie Reviews25K&25KHumanSampleAccuracy
Reddit TL;DR [247]Summarization1330K&-HumanSampleWin Rate
Anthropic-HH [248]Harmless, Helpful161K&8.55KAIPairWin Rate
GSM8K [249]Mathematical Reasoning7.47K&1.32KHumanSampleAccuracy
AlpacaEval2 [250]Automatic Evaluation-&0.8KAISampleWin Rate
MT-Bench [251]Multi-Turn Question-&3.3KHumanPairWin Rate
AdvBench [252]Harmful Behaviors-&0.5KHumanSampleAttack Success
Arena-Hard [253]Updating Evaluation-&0.5KAISampleWin Rate
TruthfulQA [254]Truthful-&0.8KHumanPairAccuracy
IFEval [255]Instruction-Following-&0.5KHumanSampleAccuracy
BBH [256]Multistep Reasoning-&23 TasksHumanSampleAccuracy
MATH [257]Mathematical Reasoning7.5K&5KHumanSampleAccuracy
GPQA [258]Biology, Physics, and Chemistry-&0.45KHumanSampleAccuracy
MUSR [259]Multistep Reasoning-&0.76KAISampleAccuracy
MMLU-Pro [260]Language Understanding-&12KHuman&AISampleAccuracy
", + "image_path": "522902a82b6177e867e4aff6c3488ea5e1a2da6b4a249cebc164f52549476e7d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 308, + 301, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 308, + 301, + 344 + ], + "spans": [ + { + "bbox": [ + 44, + 308, + 301, + 344 + ], + "type": "text", + "content": "probability of winning outputs and decreases that of losing outputs, whereas APO-down decreases both, but with a stronger decline for losing outputs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 44, + 348, + 301, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 348, + 301, + 581 + ], + "spans": [ + { + "bbox": [ + 44, + 348, + 301, + 581 + ], + "type": "text", + "content": "Another notable challenge related to likelihood collapse is likelihood over-optimization, where the performance of a model on a proxy metric (such as its own likelihood estimates) improves, while its true performance does not. Zhang and Ranganath [236] show that reductions in the likelihood loss of DPO do not necessarily translate into higher win rates. Similarly, Shi et al. [205] further investigates the problem of likelihood over-optimization in DPO, demonstrating that higher completion likelihoods do not necessarily correlate with better model performance and may even degrade it. This study identifies key indicators of over-optimization and highlights the need to balance likelihood optimization with output diversity. e-DPO [187] also shows that DPO can lead to degenerate policies due to overfitting, and proposes a solution using reward model distillation to regularize the implicit reward of the language model. The method trains the language model to match the probability distribution induced by a reward model and introduces a pessimistic extension to handle uncertainty in the reward model, thereby improving the robustness of DPO." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 584, + 303, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 584, + 303, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 584, + 303, + 748 + ], + "type": "text", + "content": "(b) Alignment Tax. Alignment tax refers to the unintended consequence where improving a model's preference alignment degrades its general capabilities acquired during pretraining [206]. Thakkar et al. [207] demonstrate the sensitivity of DPO to training data composition, showing significantly worse performance degradation than SFT when using mixed-preference datasets. Furthermore, Chen et al. [209] identify that DPO struggles with optimizing ranking tasks. While DPO improves ranking accuracy, it disproportionately harms generative capabilities. Pentyala et al. [118] also observes capability forgetting during sequential training, where DPO objectives conflict with previously learned SFT patterns. To address this, researchers propose model merging strategies that balance alignment and performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 308, + 566, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 308, + 566, + 415 + ], + "spans": [ + { + "bbox": [ + 308, + 308, + 566, + 415 + ], + "type": "text", + "content": "PAFT [118] separately trains SFT and DPO objectives on a pretrained model using distinct datasets, then merges the parameters through weighted averaging. Additionally, Lu et al. [208] proposes online merging optimizers, which integrate model merging into each optimization step of DPO to balance human preferences and basic capabilities. By merging gradients with parameter differences between SFT and pretrained models, these optimizers effectively enhance alignment while mitigating alignment tax." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 309, + 431, + 477, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 431, + 477, + 443 + ], + "spans": [ + { + "bbox": [ + 309, + 431, + 477, + 443 + ], + "type": "text", + "content": "4 BENCHMARKS AND ANALYSIS" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 449, + 566, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 449, + 566, + 519 + ], + "spans": [ + { + "bbox": [ + 308, + 449, + 566, + 519 + ], + "type": "text", + "content": "In this section, we provide a comprehensive overview of existing benchmarks and evaluation for DPO methods. We first introduce the key datasets and benchmarks used to train or evaluate DPO models. We then present a comparative analysis of the performance of different DPO methods on these benchmarks, highlighting their strengths and limitations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 309, + 534, + 454, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 534, + 454, + 546 + ], + "spans": [ + { + "bbox": [ + 309, + 534, + 454, + 546 + ], + "type": "text", + "content": "4.1 Datasets and Benchmarks" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 550, + 566, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 550, + 566, + 748 + ], + "spans": [ + { + "bbox": [ + 307, + 550, + 566, + 748 + ], + "type": "text", + "content": "A diverse range of datasets and benchmarks has been specifically curated to facilitate research in DPO. Table 1 summarizes these datasets and benchmarks, highlighting their task descriptions, dataset sizes, data sources, data structures, and evaluation metrics. These datasets and benchmarks span a broad range of tasks, such as harmlessness and helpfulness evaluation and mathematical reasoning. They also exhibit significant diversity in scale, ranging from smaller, specialized datasets to large-scale collections such as SHP-2, which contains over 3.6 million samples. Additionally, datasets differ in their sources: some rely purely on human annotations, others on AI-generated content, and many adopt a hybrid approach combining human and AI-generated data. The data structures employed across these datasets include single-sample without preference label, point-wise annotations, pair-wise comparisons, and list-wise comparisons. Common evaluation metrics include accuracy" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "type": "text", + "content": "14" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 13 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 49, + 563, + 257 + ], + "blocks": [ + { + "bbox": [ + 69, + 38, + 541, + 49 + ], + "lines": [ + { + "bbox": [ + 69, + 38, + 541, + 49 + ], + "spans": [ + { + "bbox": [ + 69, + 38, + 541, + 49 + ], + "type": "text", + "content": "TABLE 2: Experimental results of different DPO variants on Open LLM Leaderboard. The underline indicates the best performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 49, + 563, + 257 + ], + "lines": [ + { + "bbox": [ + 47, + 49, + 563, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 49, + 563, + 257 + ], + "type": "table", + "html": "
ModelMistral-7B-BaseLLaMA-3-8B-Base
IFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGEIFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGE
SFT3.441.19.228.842.027.725.429.046.315.328.641.331.031.9
RRHF [190]10.040.61.726.446.326.125.231.046.813.931.436.830.531.7
SLiC-HF [230]11.044.09.929.242.628.127.541.749.517.530.439.731.735.1
DPO [74]11.143.77.128.543.826.726.834.348.217.231.940.131.533.9
IPO [75]9.442.89.729.739.727.826.535.349.015.932.841.431.934.4
CPO [116]8.042.79.628.942.127.326.432.446.916.830.639.131.832.9
KTO [67]12.943.712.028.946.128.328.640.248.318.031.040.131.134.8
ORPO [117]28.446.413.530.241.429.531.640.049.116.830.738.432.034.5
R-DPO [191]10.043.07.628.739.327.226.036.448.817.231.640.631.534.4
SimPO [166]11.143.18.428.939.527.226.440.848.615.831.040.531.834.7
ModelMistral-7B-InstructLLaMA-3-8B-Instruct
IFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGEIFEvalBBHMATHGPQAMUSRMMLU-ProAVERAGE
SFT48.446.210.929.147.627.134.950.749.326.931.037.935.738.6
RRHF [190]45.245.310.128.544.226.233.351.349.327.229.639.535.338.7
SLiC-HF [230]39.446.211.428.749.026.833.641.650.926.331.339.235.337.4
DPO [74]49.045.611.026.946.126.834.248.950.125.829.438.736.038.2
IPO [75]42.645.311.827.849.327.234.050.449.526.329.637.935.738.2
CPO [116]38.846.010.128.548.426.933.150.649.126.831.338.135.838.6
KTO [67]46.245.710.927.846.027.334.043.150.126.331.238.135.037.3
ORPO [117]37.645.111.228.246.926.532.643.050.626.929.339.135.137.3
R-DPO [191]46.845.99.928.746.227.634.250.950.325.329.839.035.738.5
SimPO [166]45.445.910.428.345.027.133.748.849.225.029.339.235.137.8
", + "image_path": "6f8f061ab915d05683da8b9488cffb80716ed95531ead04552cb45454c8c4d61.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 267, + 301, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 267, + 301, + 316 + ], + "spans": [ + { + "bbox": [ + 44, + 267, + 301, + 316 + ], + "type": "text", + "content": "(for tasks like mathematical reasoning found in GSM8K and MATH), win rates derived from pairwise comparisons (such as MT-Bench and Anthropic-HH), and attack success rates used for assessing adversarial robustness (AdvBench)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 327, + 105, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 327, + 105, + 338 + ], + "spans": [ + { + "bbox": [ + 45, + 327, + 105, + 338 + ], + "type": "text", + "content": "4.2 Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 342, + 301, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 342, + 301, + 514 + ], + "spans": [ + { + "bbox": [ + 44, + 342, + 301, + 514 + ], + "type": "text", + "content": "To demonstrate the effectiveness of different DPO variants, we conduct experiments on the Open LLM Leaderboard. We compare different DPO variants using Mistral-7B-Base, Mistral-7B-Instruct [261], LLaMA-3-8B-Base, and LLaMA-3-8B-Instruct [235] as starting points. The overall experimental setup follows Meng et al. [166], ensuring a reproducible evaluation of different DPO variants. For Mistral-7B-Base and LLaMA-3-8B-Base, the SFT models are trained based on the UltraChat-200k dataset [262], and subsequently applied different DPO variants on the SFT models using the UltraFeedback dataset [237]. For Mistral-7B-Instruct and LLaMA-3-8B-Instruct, which have already undergone instruction-tuning, the preference dataset is regenerated by collecting responses from the SFT models using prompts from the UltraFeedback dataset [237]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 44, + 515, + 302, + 746 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 515, + 302, + 746 + ], + "spans": [ + { + "bbox": [ + 44, + 515, + 302, + 746 + ], + "type": "text", + "content": "The experimental results, as summarized in Table 2, highlight the performance of different DPO variants across various benchmarks. For the Mistral-7B-Base and LLaMA-3-8B-Base models, ORPO consistently achieves the highest average scores, indicating its effectiveness in aligning models with human preferences. Notably, ORPO outperforms other methods on IFEval, BBH, and MATH, demonstrating its superiority in instruction-following and mathematical reasoning tasks. Meanwhile, SLiC-HF and KTO also achieve competitive results, particularly in BBH and GPQA, suggesting that these methods effectively leverage preference data for enhanced performance. For the Mistral-7B-Instruct and LLaMA-3-8B-Instruct models, the improvements across different DPO variants are more nuanced. While DPO and R-DPO show strong performance in IFEval and MMLU-Pro, IPO and CPO demonstrate robustness in handling complex reasoning tasks like MATH and GPQA. Overall, the results indicate that different DPO variants exhibit varying strengths across benchmarks, with some methods excelling in base models while others are more effective for instruct models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 309, + 266, + 403, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 266, + 403, + 278 + ], + "spans": [ + { + "bbox": [ + 309, + 266, + 403, + 278 + ], + "type": "text", + "content": "5 APPLICATIONS" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 281, + 567, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 281, + 567, + 353 + ], + "spans": [ + { + "bbox": [ + 308, + 281, + 567, + 353 + ], + "type": "text", + "content": "In this section, we discuss the applications of DPO in various domains, including different LLM-based applications, diffusion models, and multi-modal LLMs. We provide an overview of the key challenges and opportunities in each domain and highlight the potential impact of DPO on real-world applications." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 309, + 366, + 446, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 366, + 446, + 379 + ], + "spans": [ + { + "bbox": [ + 309, + 366, + 446, + 379 + ], + "type": "text", + "content": "5.1 LLM-based Applications" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 380, + 566, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 380, + 566, + 567 + ], + "spans": [ + { + "bbox": [ + 307, + 380, + 566, + 567 + ], + "type": "text", + "content": "DPO has emerged as a powerful paradigm for aligning LLMs with human preferences across diverse applications [116, 235, 263, 264]. In code generation, DPO enhances control over code quality by optimizing based on preferences from automated tests [265, 266, 267]. In mathematical reasoning, DPO reduces errors in complex problem-solving by emphasizing step-level preference optimization [100, 101, 129, 268]. Multilingual applications leverage DPO to synchronize cross-lingual preferences, thereby improving translation accuracy and cultural relevance [107, 269]. Recommendation systems utilize DPO to refine personalization by incorporating user preference data to optimize item rankings, thereby enhancing the model ability to distinguish preferred items from less preferred ones [270, 271]. These examples highlight the adaptability of DPO in achieving human-aligned outputs across diverse tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 309, + 581, + 411, + 592 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 581, + 411, + 592 + ], + "spans": [ + { + "bbox": [ + 309, + 581, + 411, + 592 + ], + "type": "text", + "content": "5.2 Diffusion Models" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 595, + 566, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 595, + 566, + 748 + ], + "spans": [ + { + "bbox": [ + 307, + 595, + 566, + 748 + ], + "type": "text", + "content": "In the realm of diffusion models, DPO has been adapted to better align generated content with user expectations [272, 273, 274, 275]. By optimizing preferences over image-text pairs, DPO enhances the semantic accuracy of generated images and mitigates the production of undesirable or biased content. Studies have demonstrated that diffusion models fine-tuned with DPO respond more accurately to complex prompts compared to those trained with traditional techniques. Moreover, the efficiency of DPO allows for the fine-tuning of large-scale models using limited preference data, addressing significant computational challenges in training diffusion models [276, 277, 278]. While scaling DPO for high-resolution and dynamic content generation remains" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "spans": [ + { + "bbox": [ + 555, + 26, + 564, + 34 + ], + "type": "text", + "content": "15" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 14 + }, + { + "para_blocks": [ + { + "bbox": [ + 44, + 42, + 301, + 67 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 42, + 301, + 67 + ], + "spans": [ + { + "bbox": [ + 44, + 42, + 301, + 67 + ], + "type": "text", + "content": "challenging, its ability to simplify reward modeling makes it a promising method for controlled content creation [279]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 81, + 151, + 92 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 81, + 151, + 92 + ], + "spans": [ + { + "bbox": [ + 45, + 81, + 151, + 92 + ], + "type": "text", + "content": "5.3 Multi-Modal LLMs" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 44, + 96, + 301, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 96, + 301, + 224 + ], + "spans": [ + { + "bbox": [ + 44, + 96, + 301, + 224 + ], + "type": "text", + "content": "For multi-modal LLMs, DPO plays a crucial role in aligning preferences across different data types, thereby improving coherence in tasks such as visual question answering and image captioning [89, 280, 281, 282, 283]. By optimizing alignment between textual responses and visual inputs, DPO reduces hallucinations in multi-modal interactions, ensuring outputs remain faithful to the given context. Although reconciling different types of feedback can be challenging, DPO offers a practical framework for lightweight adaptation, making it well-suited to preference-intensive multi-modal applications [280, 284, 285]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 241, + 265, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 241, + 265, + 253 + ], + "spans": [ + { + "bbox": [ + 45, + 241, + 265, + 253 + ], + "type": "text", + "content": "6 CHALLENGES AND FUTURE DIRECTIONS" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 257, + 301, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 257, + 301, + 327 + ], + "spans": [ + { + "bbox": [ + 44, + 257, + 301, + 327 + ], + "type": "text", + "content": "In this section, we discuss the key challenges and future directions in DPO research. We identify several critical issues that need to be addressed to further advance the field. Moreover, we propose several promising research directions that can help overcome these challenges and accelerate the adoption of DPO in the future." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 342, + 221, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 342, + 221, + 354 + ], + "spans": [ + { + "bbox": [ + 45, + 342, + 221, + 354 + ], + "type": "text", + "content": "6.1 Efficient Preference Optimization" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 44, + 357, + 302, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 357, + 302, + 567 + ], + "spans": [ + { + "bbox": [ + 44, + 357, + 302, + 567 + ], + "type": "text", + "content": "Efficient preference optimization remains a pivotal challenge, as current DPO methods hinge on the availability of high-quality preference data, yet the manual collection of human annotations is both time-consuming and labor-intensive while automatically model-generated datasets often suffer from issues such as limited diversity, inherent biases, and insufficient fidelity to human judgment [121, 122, 128, 129]. Moreover, even though DPO circumvents the intricacies of reward model engineering common in RL, it does not fully leverage the exploratory strengths that RL methods offer, as evidenced by recent advances in reasoning approaches where RL-based training has achieved notable successes [18, 19]. This opens up an avenue for future research to not only enhance data efficiency through advanced learning techniques but also to integrate novel exploration mechanisms [138, 141], potentially through hybrid models that amalgamate the direct preference optimization benefits of DPO with the robust exploratory capabilities characteristic of RL." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 581, + 236, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 581, + 236, + 593 + ], + "spans": [ + { + "bbox": [ + 45, + 581, + 236, + 593 + ], + "type": "text", + "content": "6.2 Multi-Modal Preference Optimization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 44, + 596, + 303, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 596, + 303, + 748 + ], + "spans": [ + { + "bbox": [ + 44, + 596, + 303, + 748 + ], + "type": "text", + "content": "Multi-Modal Preference Optimization presents another frontier, given that existing DPO frameworks have primarily targeted text-based modalities while many real-world applications demand the alignment of diverse human preferences across text, images, audio, and even video [280, 284, 285, 286, 287]. In scenarios where cross-modal cues might conflict, such as the need for concise text paired with richly detailed imagery, the challenge lies in constructing a unified preference representation space that can intelligently and automatically recalibrate the priority of different modalities based on the contextual demands of the task at hand [89, 282, 283]. Future directions in this area could involve the development of innovative multi-modal preference encoding architectures," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 42, + 566, + 90 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 42, + 566, + 90 + ], + "spans": [ + { + "bbox": [ + 308, + 42, + 566, + 90 + ], + "type": "text", + "content": "which are capable of disentangling compound preferences into modality-specific and cross-modal components that align conflicting preferences while also adapting dynamically to changing inputs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 309, + 108, + 500, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 108, + 500, + 120 + ], + "spans": [ + { + "bbox": [ + 309, + 108, + 500, + 120 + ], + "type": "text", + "content": "6.3 Continuous Preference Optimization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 125, + 566, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 125, + 566, + 311 + ], + "spans": [ + { + "bbox": [ + 308, + 125, + 566, + 311 + ], + "type": "text", + "content": "Continuous preference optimization addresses the dynamic nature of human preferences that evolve over time or vary with different phases of a task, a factor that static DPO models often fail to capture [123, 135, 137, 185]. As social norms and individual preferences shift, there is an increasing need for systems that can continuously recalibrate their alignment strategies in real time while simultaneously mitigating the risk of catastrophic forgetting. Future research in this domain may focus on meta-learning approaches that enable models to learn not only from the current state of preferences but also how to efficiently adapt when these preferences change. By integrating online learning frameworks with mechanisms for detecting temporal shifts and contextual variability in user behavior, researchers can pave the way toward systems that remain consistently relevant and effective in the face of evolving societal and individual expectations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 309, + 330, + 504, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 330, + 504, + 342 + ], + "spans": [ + { + "bbox": [ + 309, + 330, + 504, + 342 + ], + "type": "text", + "content": "6.4 Interpretable Preference Optimization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 346, + 567, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 346, + 567, + 544 + ], + "spans": [ + { + "bbox": [ + 308, + 346, + 567, + 544 + ], + "type": "text", + "content": "Interpretable preference optimization is critical for building trust in models that implicitly align human values, as the opaque nature of current DPO complicates the ability to audit and control the alignment process. In practice, human preferences are multi-dimensional [150, 151, 154], encompassing aspects such as factual accuracy, fairness, creativity, and beyond, and there is a pressing need to decompose these complex preferences into interpretable components that can be individually examined and fine-tuned. Future research could leverage advances in explainable techniques to develop models that not only achieve fine-grained alignment across diverse values but also provide transparent insights into how different preference dimensions interact to shape final decisions. This level of interpretability would allow stakeholders to balance competing values more effectively, ensuring that the alignment process remains both accountable and adaptable as societal norms continue to evolve." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 309, + 565, + 397, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 565, + 397, + 577 + ], + "spans": [ + { + "bbox": [ + 309, + 565, + 397, + 577 + ], + "type": "text", + "content": "7 CONCLUSION" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 308, + 584, + 566, + 748 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 584, + 566, + 748 + ], + "spans": [ + { + "bbox": [ + 308, + 584, + 566, + 748 + ], + "type": "text", + "content": "In recent years, DPO has emerged as a promising paradigm for aligning LLMs with human preferences by directly optimizing model policies using preference data. Despite its potential, the DPO research landscape remains fragmented, with a lack of systematic organization and comparative analysis. In this survey, we present a comprehensive overview of DPO and introduce a novel taxonomy that categorizes existing works into four key dimensions: data strategy, learning framework, constraint mechanism, and model property. We have also discussed the key benchmarks, evaluation results, and applications of DPO, highlighting the challenges and future directions in this field. By providing a systematic analysis of the existing DPO methods, we aim to facilitate further research and development in this area." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "spans": [ + { + "bbox": [ + 555, + 26, + 565, + 34 + ], + "type": "text", + "content": "16" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 15 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 41, + 115, + 53 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 41, + 115, + 53 + ], + "spans": [ + { + "bbox": [ + 46, + 41, + 115, + 53 + ], + "type": "text", + "content": "REFERENCES" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 60, + 301, + 746 + ], + "type": "list", + "angle": 0, + "index": 38, + "blocks": [ + { + "bbox": [ + 47, + 60, + 301, + 78 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 60, + 301, + 78 + ], + "spans": [ + { + "bbox": [ + 47, + 60, + 301, + 78 + ], + "type": "text", + "content": "[1] Wayne Xin Zhao et al. 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Traditional deep learning approaches have significantly advanced this field, particularly in the stage of ST data mining. However, these models remain task-specific and often require extensive labeled data. Inspired by the success of Foundation Models (FM), especially large language models, researchers have begun exploring the concept of Spatio-Temporal Foundation Models (STFMs) to enhance adaptability and generalization across diverse ST tasks. Unlike prior architectures, STFMs empower the entire workflow of ST data science, ranging from data sensing, management, to mining, thereby offering a more holistic and scalable approach. Despite rapid progress, a systematic study of STFMs for ST data science remains lacking. This survey aims to provide a comprehensive review of STFMs, categorizing existing methodologies and identifying key research directions to advance ST general intelligence.", + "bbox": [ + 81, + 301, + 483, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction", + "text_level": 1, + "bbox": [ + 83, + 555, + 218, + 569 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Humans live in a world shaped by the dynamic interplay of countless elements across space and time. Spatio-Temporal (ST) Data, which refer to data that encapsulate ST phenomena, track the evolution of objects or events across locations and time [5], such as meteorological records, traffic patterns, and human traces. These data are frequently sourced from a wide array of platforms, ranging from IoT devices, GPS sensors, social media, to remote sensing.", + "bbox": [ + 81, + 573, + 482, + 670 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Within this context, Spatio-Temporal Data Science focuses on sensing, managing, and mining these datasets to uncover patterns, understand complex systems, and predict future dynamics. Motivated by its transformative potential, this field addresses critical challenges across urban environments and even the entire planet, enabling decision-making and fostering innovations that contribute to building smarter, more sustainable, and resilient systems [178].", + "bbox": [ + 81, + 670, + 482, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org.", + "bbox": [ + 81, + 779, + 482, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 83, + 853, + 303, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "© 2025 Copyright held by the owner/author(s). Publication rights licensed to ACM.", + "bbox": [ + 83, + 864, + 472, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ACM ISBN 978-x-xxxxx-xxxxx-x/YY/MM", + "bbox": [ + 84, + 875, + 269, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://doi.org/10.1145/nnnnnnn.nnnnnnn", + "bbox": [ + 84, + 883, + 284, + 895 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/585a84a4e1c2d564b53b7198e4a5ac28aaf09f4523682713f3c283074ed415a4.jpg", + "image_caption": [ + "Figure 1: ST Foundation Models (STFM), which include LLM and PFM, are pretrained with or applied to diverse ST data, with the abilities of perception, optimization, and reasoning. STFMs can, in turn, enhance each stage of ST data science." + ], + "image_footnote": [], + "bbox": [ + 519, + 282, + 906, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the era of deep learning, the community has primarily concentrated on spatio-temporal representation learning, as a fundamental step of ST data mining [129]. Key advancements include the development of Spatio-Temporal Graph Neural Networks (STGNN) [51] and transformer-based architectures, which have shown remarkable success in tasks such as traffic forecasting [80, 146], air quality prediction [82], and human mobility analytics [132]. STGNNs integrate Graph Neural Networks (GNN) with temporal learning modules (e.g., GRU [6, 70], TCN [140, 141]) to model ST correlations, while transformer models leverage self-attention mechanisms [37, 78, 177] to process complex dependencies across space and time. Additionally, there has been significant research on self-supervised learning [46, 74, 92], where models are trained to extract powerful representations with minimal reliance on large annotated datasets.", + "bbox": [ + 511, + 493, + 915, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Driven by the success of Foundation Models (FM), especially Large Language Models (LLM), researchers have recently begun exploring the concept of Spatio-Temporal Foundation Models (STFM) [32, 81, 169]. By harnessing LLMs, it becomes possible to develop more generalized, adaptable solutions that can be fine-tuned for specific tasks with minimal data. Another prominent approach involves pretraining FMs (denoted as PFM) on cross-domain ST data and adapting them for particular domains. In contrast to previous architectures (e.g., STGNNs), STFMs integrates the capabilities of perception, reasoning and optimization, which not only promises to revolutionize ST data mining, but also empowers other stages of ST data science, such as ST data sensing and management (See Figure 1). This shift has the potential to enhance the scalability and efficiency of ST applications, offering a more holistic approach to addressing challenges in urban computing, climate science, etc.", + "bbox": [ + 511, + 688, + 915, + 896 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "arXiv:2503.13502v1 [cs.DB] 12 Mar 2025", + "bbox": [ + 22, + 260, + 57, + 705 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/08bcc66a52134813071d6c4eb50489b0a630570ee89c53dc5e3c14381549b4d2.jpg", + "table_caption": [ + "Table 1: Our survey vs. related surveys on FMs for learning ST data, such as locations (L), trajectories (T), events (E), ST rasters (R), and ST graphs (G). The applications (App.) include numerical (N) and inferential (I) problems." + ], + "table_footnote": [], + "table_body": "
SurveyYearVenueSensingManage.MiningApp.Data
Jin et al. [54]2023-✓NR,G
Jiang et al. [48]2024IJCAI✓NR,G
Liang et al. [81]2024KDD✓NT,E,R,G
Zhang et al. [169]2024KDD✓N,IL,T,E,R,G
Goodge et al. [32]2025-✓NT,E,R,G
Ours2025-✓✓✓N,IL,T,E,R,G
", + "bbox": [ + 86, + 162, + 478, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite their rapid advancements, a systematic analysis of STFMs across the entire workflow of ST data science remains lacking. First, prior surveys have primarily focused on utilizing LLMs as the key tool for ST data mining [32, 54, 81, 169], leaving a significant gap in understanding how these models can be integrated throughout the entire process, i.e., with less focus placed on their role in the earlier stages of sensing and management. Second, they predominantly examine the applications of STFMs to numerical problems (e.g., forecasting, imputation) while overlooking their role in inferential problem-solving such as decision-making systems.", + "bbox": [ + 81, + 241, + 482, + 380 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To bridge these gaps, this paper aims to provide a more comprehensive survey of STFMs across all stages of ST data science, spanning data sensing, management, and mining (see Figure 1). For example, LLMs can enhance ST data sensing by actively processing citizen reports, optimizing participatory sensing strategies, and generating synthetic data at scale. In terms of data management, they can automate data cleaning tasks, construct meaningful knowledge graphs for data integration, and facilitate more efficient retrieval of cross-modal datasets. Beyond these stages, our survey also explores how STFMs support a broader range of downstream applications, including numerical and inferential problems. Through this endeavor, we seek to illuminate an overall vision of STFMs, thereby enhancing comprehension regarding their potential to optimize ST data science, fostering more integrated and adaptable solutions.", + "bbox": [ + 81, + 380, + 482, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Meanwhile, we systematically investigate the key methodologies of STFMs for modeling a variety of ST data. We begin by categorizing existing STFMs into two main classes: LLMs and Pretrained Foundation Models (PFMs). For LLMs, which are pretrained on linguistic data, we focus on their usage as a zero-shot [33] or few-shot learner [53, 73], where various prompting and fine-tuning strategies have been explored, respectively. For PFMs, which are trained from scratch based on cross-domain ST data [40, 158, 189], we examine their neural architectures, pretraining methods, and their adaptability to different types of ST data, including location data, trajectory data, events, ST raster data, and ST graph data.", + "bbox": [ + 81, + 573, + 482, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our major contributions lie in three aspects:", + "bbox": [ + 98, + 726, + 444, + 739 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Comprehensive and up-to-date survey: We provide the first comprehensive and modern survey of FMs across the entire workflow of ST data science, covering data sensing, management, and mining. We also explore a broader range of downstream tasks and data types compared to most existing surveys (See Table 1).", + "- Vision and Methodologies: We propose a vision for STFMs, identifying key capabilities essential for their success, and discuss current methodologies for implementing these abilities in detail.", + "- Future directions: We highlight promising directions for advancing ST data science with foundation models, encouraging further research and exploration in this emerging field." + ], + "bbox": [ + 83, + 739, + 482, + 891 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Paper Organization. The remainder of this paper is organized as follows: Sec. 2 provides essential background on FMs and ST data. Sec. 3 and 4 present a taxonomy of STFMs regarding the workflow and methodologies, respectively. Sec. 5 offers concluding remarks, and Appendix A highlights promising avenues for future research.", + "bbox": [ + 511, + 106, + 915, + 176 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Background", + "text_level": 1, + "bbox": [ + 514, + 181, + 645, + 198 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Foundation models. FMs are deep neural networks trained on vast datasets, enabling them to acquire broad, cross-domain knowledge and exceptional adaptability [45]. Unlike earlier task-specific models, FMs can be efficiently fine-tuned with relatively small amounts of task-specific data, offering remarkable flexibility, effectiveness, and cost efficiency. Pioneering attempts like BERT [58] and GPT-3 [11] have reshaped natural language processing. More recent models, e.g., GPT-4o [45] and DeepSeek-R1 [36], further push the frontiers of generative capabilities, enabling more nuanced reasoning, robust domain adaptation, and improved context-awareness in diverse tasks. In ST domains, recent FMs like Time-MoE [119], Chronos [4], and UniST [158] have made remarkable strides in time series analysis and universal ST forecasting, while UniTraj [189] serves as a versatile foundation for various trajectory-related tasks. Inspired by these successes, this survey delves into the utilization of FMs in the entire workflow of ST data science, covering data sensing, management, and mining.", + "bbox": [ + 511, + 200, + 915, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Formulation of Spatio-Temporal Data. ST data refer to datasets that integrate spatial (location-based) and temporal (time-based) information, capturing dynamic patterns and relationships over space and time. Figure 2 depicts the basic ST data structures discussed in this survey, including locations, trajectories, events, ST rasters, and ST graphs. Their definitions are delineated as follows.", + "bbox": [ + 511, + 439, + 915, + 521 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Definition 1 (Location). A location refers to a fixed spatial point or object in a geographical space, represented by the geospatial coordinates $l \\in \\mathbb{R}^2$ , i.e., latitude and longitude. It is often profiled by the corresponding satellite image, street-view image, and descriptions.", + "bbox": [ + 511, + 521, + 913, + 578 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Definition 2 (Trajectory). A trajectory is a sequence of time-ordered locations that describe the movements of an object in the geographical space. It can be formulated as $\\mathcal{T} = p_1\\rightarrow p_2\\rightarrow \\dots \\rightarrow p_T$ where $p_i = (l_i,t_i)$ , and $l_{i}$ denotes the object's location at time $t_i$ .", + "bbox": [ + 511, + 578, + 915, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Definition 3 (Event). An event sequence is a series of timestamped events, denoted as $\\mathcal{E} = v_{1}\\rightarrow v_{2}\\rightarrow \\dots \\rightarrow v_{T}$ , describing the progress of actions or occurrences, where $v_{i} = (e_{i},t_{i})$ and $e_i\\in \\mathbb{R}^d$ is an event and $t_i$ denotes the time when $e_i$ occurs.", + "bbox": [ + 511, + 633, + 913, + 689 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/037cc7fecab764f3c9489d19c64e195a2e4237fe21b75687cf6cec155fb66656.jpg", + "image_caption": [ + "Figure 2: Illustration of various types of ST data." + ], + "image_footnote": [], + "bbox": [ + 531, + 691, + 890, + 875 + ], + "page_idx": 1 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 83, + 75, + 313, + 87 + ], + "page_idx": 1 + }, + { + "type": "header", + "text": "Yuxuan Liang et al.", + "bbox": [ + 818, + 75, + 911, + 87 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Definition 4 (Spatio-Temporal Raster). An ST raster can be denoted as $\\mathcal{X} = < \\mathbf{X}_1,\\mathbf{X}_2,\\dots ,\\mathbf{X}_T > \\in \\mathbb{R}^{H\\times W\\times T\\times D}$ , where $\\mathbf{X}_t\\in \\mathbb{R}^{H\\times W\\times D}$ denotes the signals collected from $N = HW$ evenly distributed locations at time $t$ , each characterized by $D$ feature attributes.", + "bbox": [ + 81, + 106, + 480, + 161 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 5 (Spatio-Temporal Graph). An ST graph extends the ST raster to be $X = < \\mathbf{X}_1, \\mathbf{X}_2, \\ldots, \\mathbf{X}_T > \\in \\mathbb{R}^{N \\times T \\times D}$ by explicitly incorporating spatial correlations with a graph $G_t = (V, E_t, \\mathbf{A}_t)$ when $N$ locations are not uniformly distributed. Here $V$ is the set of nodes, $E_t$ is the set of edges, and $\\mathbf{A}_t \\in \\mathbb{R}^{N \\times N}$ is the adjacency matrix at time $t$ . The size of $V$ is usually static.", + "bbox": [ + 81, + 162, + 480, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 The Workflow Perspective", + "text_level": 1, + "bbox": [ + 83, + 258, + 330, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 3, we examine STFMs from a holistic, bottom-up perspective, emphasizing their composition across four key aspects:", + "bbox": [ + 81, + 276, + 482, + 305 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- ST Data Sensing refers to the acquisition of data that varies over both space and time from diverse resources (e.g., sensors, satellites, social media), to capture dynamic environmental, geographic, or social phenomena. We also consider synthetic data generation for enhancing data diversity and quantity.", + "- ST Data Management focuses on storing, indexing, and organizing these large-scale, heterogeneous ST datasets, incorporating strategies like distributed architectures for efficient retrieval and integration. FMs can enhance this process by facilitating data cleaning, query & retrieval, and data integration.", + "- ST Data Mining involves learning and analyzing ST data that varies across both space and time to uncover patterns, trends, and relationships, using data mining (DM), deep learning (DL) techniques, or the newly-proposed STFMs with strong capabilities in perception, optimization, and reasoning.", + "- Downstream Applications: This stage harnesses the above insights from ST data to drive real-world applications, ranging from numerical problems to inferential problems, where informed actions and policies are formulated." + ], + "bbox": [ + 83, + 306, + 482, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By examining these four aspects, we can better understand how STFMs advance from raw data acquisition to high-level service providing, ultimately enabling more intelligent, adaptable, and impactful solutions. We will detail each stage in the following sections.", + "bbox": [ + 81, + 573, + 482, + 628 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7550fb89f980864400839d7d1a4cff676d111c15a655bac2fa282342c99fd317.jpg", + "image_caption": [ + "Figure 3: The framework of STFMs for ST data science." + ], + "image_footnote": [], + "bbox": [ + 86, + 637, + 478, + 875 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 Spatio-Temporal Data Sensing", + "text_level": 1, + "bbox": [ + 514, + 104, + 803, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "FMs revolutionize ST data sensing from two complementary aspects: real-world data sensing, which involves collecting data from physical sources, and synthetic data generation, which creates synthetic ST data through foundation models.", + "bbox": [ + 511, + 125, + 915, + 179 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Real-World Data Sensing. Advances in sensing and data acquisition technologies have led to the generation of vast amounts of ST data. FMs are increasingly applied in human-centric active sensing, particularly in the context of citizen reporting for urban and environmental monitoring [41]. These models act as powerful agents for collecting and processing real-time data from citizens, enabling the efficient handling of ST data [19, 27, 101]. For example, citizens might constantly report incidents, environmental changes, or social events through text or voice [178]. By understanding these reports, LLMs can categorize, prioritize, and trigger appropriate responses for various urban issues, from traffic congestion to environmental hazards. This enhances the decision-making process by continuously updating their models with new data streams. Thus, LLMs are not just passive analytical tools but active participants that help make urban environments more responsive and adaptive to citizen inputs, transforming traditional citizen feedback into actionable knowledge, enabling more sustainable and resilient cities.", + "bbox": [ + 511, + 183, + 913, + 419 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "FMs can also function as intelligent schedulers or simulate multiagent systems to optimize the recruitment and coordination of participants for crowdsensing, particularly under budget constraints [41, 139, 191]. By analyzing ST data and understanding context, LLMs can identify regions and times where crowdsensing efforts will yield the most valuable information. They dynamically recruit participants based on proximity, availability, and past contributions, reducing redundant data collection. Additionally, LLMs simulate multiple agents interacting in real time, ensuring the efficient distribution of sensing tasks across a network of citizens or devices [190]. This strategic scheduling and agent-based coordination maximize coverage while minimizing costs, ensuring that crowdsensing delivers valuable, real-time insights under budgetary constraints.", + "bbox": [ + 511, + 419, + 913, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.2 Synthetic Data Generation. FMs can also facilitate data generation, which enhances ST data by increasing its diversity, improving model robustness, and compensating for missing or sparse information [95]. This is crucial for ST tasks like mobility analytics, where collecting real-world data is often costly or raises privacy concerns. For instance, Trajectory-LLM [154] generates vehicle trajectories from brief textual descriptions of vehicle interactions, whereas Traj-LLM [56] generates human trajectories by leveraging personas, memory modules, and routine profiles. LLMob [126] advances mobility data generation, offering flexibility in modeling diverse urban activities and personal mobility patterns, thus improving transportation system modeling and analysis. LLMs have also been employed to construct synthetic environments that replicate real-world conditions across diverse domains, including intelligent transportation [1] and disaster management [31].", + "bbox": [ + 511, + 602, + 913, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2 Spatio-Temporal Data Management", + "text_level": 1, + "bbox": [ + 513, + 821, + 846, + 837 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Upon the acquisition of ST data, the challenge of effective management emerges, particularly in addressing data quality issues (e.g., missing values/views) and facilitating data retrieval and integration. Within this context, FMs can be harnessed in the following ways.", + "bbox": [ + 511, + 840, + 913, + 896 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey", + "bbox": [ + 83, + 75, + 447, + 87 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 684, + 75, + 913, + 87 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Data Cleaning. Data cleaning is the process of improving data quality by addressing issues such as missing values, low sampling rates, and noise. For example, ST data often exhibit missing values due to various factors like sensor malfunctions and transmission disruptions [178]. Filling in these missing values[113] is crucial for ensuring the integrity of predictive models, optimizing strategies, and facilitating informed decision-making. Recent literature reveals that LLMs can serve as powerful zero-shot [164] or few-shot [17, 172] learners to data imputation by leveraging their ability to identify and learn complex ST patterns. PLMTrajRec [135], utilizing a pretrained language model to recover sparse trajectory data by unifying intervals and inferring road conditions, showing effective generalization across varied sampling intervals in tests. Moreover, scholars have investigated the potential of leveraging LLMs to augment missing views or information, such as urban region profiling [40, 150, 163] and traffic video captioning [25].", + "bbox": [ + 86, + 107, + 480, + 328 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Query & Retrieval. Meanwhile, LLM can be applied to querying and retrieval to enhance information retrieval accuracy under the ST context. By leveraging their advanced natural language understanding capabilities, LLMs can process user queries in a more contextual and semantically rich manner, enabling precise retrieval of relevant information from structured and unstructured data sources. For instance, UrbanLLM [47] finetunes LLMs for urban activity planning and management, which serves as a problem solver that decodes urban-related queries into several sub-tasks, with each one solved by suitable spatio-temporal AI models. Alamsyah et al. [2] propose an automated smart city planning system that utilizes a personalized LLM with Retrieval Augmented Generation (RAG) [30] to generate tailored urban planning recommendations while ensuring data privacy, where RAG is used to retrieve relevant urban planning documents for context-aware responses. Another line of work [67, 75, 170, 179] utilizes Multimodal LLM for cross-modal information retrieval to enhance urban computing tasks.", + "bbox": [ + 86, + 334, + 480, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.3 Data Integration. Data integration seeks to combine information from disparate sources, often necessitating the understanding and mapping of relationships between entities in heterogeneous datasets. LLMs are increasingly being employed in this domain, particularly for knowledge graph construction [24], where they automate and enhance the extraction, integration, and reasoning of related data. In the context of ST data, LLMs facilitate data integration by leveraging heterogeneous urban data sources, performing relational triplet extraction, and completing knowledge graphs through geospatial reasoning [94, 106]. A pioneering study UrbanKGent [105] proposes an LLM-based Agent framework to automate the process of urban knowledge graph construction.", + "bbox": [ + 86, + 571, + 480, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3 Spatio-Temporal Data Mining", + "text_level": 1, + "bbox": [ + 86, + 752, + 367, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unlike traditional data mining, which primarily focuses on structured datasets, ST data mining captures intricate spatial and temporal dependencies within ST data using machine learning or deep learning techniques [51, 129, 167]. With the emergence of FMs and LLMs, Spatio-Temporal Foundation Models (STFMs) offer new possibilities by integrating perception, optimization, and reasoning capabilities to enhance ST data mining. In this section, we explore these key capabilities, while their specific applications across different domains are detailed in Sec. 3.4.", + "bbox": [ + 86, + 771, + 480, + 893 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Perception. In STFMs, perception encompasses the ability to effectively model, interpret, and generalize complex spatial and temporal patterns, enabling a deeper understanding of dynamic environments. This capability can be categorized into two key perspectives. The first view pertains to an agent's ability to perceive and understand its surrounding environment, capturing visual or contextual interactions within real-world scenarios such as smart cities [151], indoor activities [152, 153], and mobile Apps [127].", + "bbox": [ + 517, + 107, + 911, + 217 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The second aspect involves interpreting and extracting ST patterns from sensor data, ensuring accurate predictions across diverse domains. Domain-agnostic approaches, such as STEP [117] and GPT-ST [74], have employed pretraining strategies that leverage historical observations to enhance forecasting performance. In urban computing, models like TFM [130] and OpenCity [72] utilize graph-based FMs to analyze behaviors and interactions within transportation systems, yielding promising results in traffic prediction. In climate science, Pangu [9], trained on 39 years of global climate data, delivers superior deterministic forecasting outcomes across all evaluated variables when compared to leading numerical weather prediction systems. Additional notable examples in this area include the works [60, 76, 104, 108]. Despite these advances, achieving robust generalization remains a critical challenge, as most existing research has been confined to in-domain applications. While models like UniST [158] are designed as one-for-all solutions for diverse ST scenarios, their training datasets and evaluation testbeds are predominantly limited to transportation. Nevertheless, their underlying technique stacks show promise for broader cross-domain and cross-modality generalization. Other significant contributions in this realm include UniFlow [159] and UrbanDiT [160].", + "bbox": [ + 517, + 218, + 911, + 507 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 Optimization. Building upon the perceptual foundations, the optimization ability focuses on refining and adapting models to achieve specific, task-oriented objectives. In other words, models are not only expected to capture rich ST patterns but also to drive actionable decision-making in dynamic, real-world scenarios. This involves integrating advanced optimization strategies that tailor model behavior to the unique demands of applications.", + "bbox": [ + 517, + 508, + 911, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A prominent approach involves agent-based frameworks. For example, in traffic signal control, traditional methods (e.g., RL) are now augmented by frameworks that use LLMs as decision-making agents [61]. These systems leverage real-time traffic data and expert prompts to enable human-like planning, resulting in more adaptive and interpretable control strategies. Similarly, CityGPT [35] decomposes ST analysis into specialized sub-tasks, handled by temporal, spatial, and fusion agents, to efficiently process IoT data and generate insightful visualizations. AgentMove [28] addresses human mobility prediction by breaking down the task into modules for individual pattern mining, urban structure analysis, and collective behavior extraction. In geo-science, systems like Geode [38] integrate explicit optimization modules with ST data retrieval and machine learning inference to tackle zero-shot geospatial QA with enhanced precision. In urban planning, an innovative work [185] simulates planners and residents by LLM agents and enables their interactions to optimize inclusive land-use plans efficiently. Despite these promising developments, significant challenges remain. Seamlessly integrating perceptual capabilities with targeted optimization strategies is crucial for next-generation ST models that are both versatile and effective across diverse operational contexts.", + "bbox": [ + 517, + 604, + 911, + 893 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 84, + 75, + 313, + 87 + ], + "page_idx": 3 + }, + { + "type": "header", + "text": "Yuxuan Liang et al.", + "bbox": [ + 818, + 75, + 911, + 85 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/7bf729db0134e8592812df53324e7a0bdf9e7208c0a94f185406b5acb97be084.jpg", + "table_caption": [ + "Table 2: Summary of representative FMs tailored for ST data science." + ], + "table_footnote": [], + "table_body": "
StageTask & CapabilityExampleMethodCategoryVenueYear
SensingReal-World Data SensingIdentifying Citizen-Related Issues from Social Mediados Santos et al. [27]LLMCAiSE2024
Real-World Data SensingIntelligent Crowdsensing CoordinationAutoWebCrowds [190]LLMICWE2024
Synthetic Data GenerationTrajectories GenerationTrajectory-LLM [154]LLMICLR2025
Synthetic Data GenerationHuman Activity Data GenerationLLMob [126]LLMNeurIPS2024
ManagementData CleaningFew-Shot Learner for Filling Missing ValuesNuwaTS [17]PFMPreprint2024
Data CleaningTrajectory RecoveryPLMTrajRec [135]LLMPreprint2024
Data CleaningAugment Additional Views of DataUrbanCLIP [150]LLMWWW2024
Query & RetrievalAutonomous Query Processor for Urban ManagementUrbanLLM [47]LLMEMNLP2024
Data IntegrationUrban Knowledge Graph ConstructionUrbanKGent [105]LLMNeurIPS2024
MiningPerceptionUnderstand the EnvironmentMagma [152]PFMCVPR2025
PerceptionInterpret and Extract ST PatternsSTEP [117]PFMKDD2022
OptimizationDrive Actionable Decision-Making in Dynamic ScenariosAgentMove [28]LLMPreprint2024
OptimizationOptimize Land-Use Plans by LLM AgentsZhou et al. [185]LLMPreprint2024
ReasoningCommon-sense ReasoningCausal-VidQA [66]PFMCVPR2022
ReasoningNumerical ReasoningUrbanGPT [73]LLMKDD2024
ReasoningCausal ReasoningNuwaDynamics [128]PFMICLR2024
ApplicationForecastingGlobal Weather ForecastingPangu [9]PFMNature2023
ImputationGenerative Adversarial Network for Traffic Data ImputationSTGAN [162]PFMIEEE TBD2022
Anomaly DetectionTransformer-based Anomaly DetectorXu et al. [145]PFMICLR2022
Event AnalysisDetecting and Interpreting EventsLAMP [120]LLMNeurIPS2023
Physical GroundingGeo-localizationGeoGPT [174]LLMJAG2023
Decision MakingTransportation Analytics and ControlTrafficGPT [168]LLMTransport Policy2024
Scenario SimulationSimulation of Human BehaviorPark et al. [107]LLMUIST2023
", + "bbox": [ + 84, + 119, + 911, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Reasoning. While current ST models have demonstrated notable success in recognition and agent-based tasks, their reasoning and cognitive capabilities remain underdeveloped compared to advanced systems like DeepSeek-R1 [36]. To progress toward ST general intelligence, we identify three key aspects of reasoning:", + "bbox": [ + 81, + 378, + 480, + 449 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Common-sense Reasoning harnesses everyday knowledge and contextual cues to draw implicit inferences from complex data. For instance, Causal-VidQA [66] enables models to infer explanations, predict future states, and generate counterfactual scenarios in video question-answering, while SituatedGen [173] integrates geographical and temporal contexts to generate coherent and contextually plausible statements.", + "- Numerical Reasoning involves interpreting and manipulating quantitative information to perform arithmetic operations, assess uncertainties, and discern relationships within ST data; for instance, STBench [69] evaluates these abilities in LLMs, while UrbanGPT [73] enhances ST forecasting with instruction tuning.", + "- Causal Reasoning seeks to uncover cause-effect relations within ST data, crucial for robust and interpretable predictions. For example, NuwaDynamics [128] identifies causal regions and applies interventions to improve generalization, and GCIM [176] learns latent causal structures to disentangle spurious correlations." + ], + "bbox": [ + 83, + 450, + 482, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Collectively, these dimensions offer a promising yet underexplored pathway toward achieving ST general intelligence, bridging the gap between pattern recognition and true cognitive understanding.", + "bbox": [ + 81, + 688, + 482, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4 Downstream Applications", + "text_level": 1, + "bbox": [ + 83, + 739, + 339, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.1 STFMs for Numerical Problems. ST data is predominately numeric in many real-world scenarios. Addressing these numeric challenges is critical for tasks like forecasting, imputation, and anomaly detection [52], which demand an accurate understanding of the physical world. STFMs excel in these areas by uncovering intricate patterns and dependencies, ultimately enabling more reliable data-driven decision-making.", + "bbox": [ + 81, + 757, + 482, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- Forecasting. Early forecasting approaches often relied on task-specific neural networks like STGNNs [51, 52, 110, 116], whereas recent developments have shifted toward universal forecasting [91,", + "bbox": [ + 81, + 854, + 482, + 896 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "137, 167]. For instance, GPT-ST [74] leverages pretraining on historical observations to boost predictive performance, while UniST [158] unifies multiple traffic prediction tasks within a single model by coupling sequence modeling with attention-based mechanisms. Building on this progress, ST-LLM [86] and STG-LLM [90] enhance traffic predictions by combining ST inputs with partially frozen large language models, and UrbanGPT [73] extends this paradigm further by employing ST instruction tuning to better align textual and ST data. Similar approaches have also been widely used in other domains, such as ClimaX [104], Geo-Bench [60], and Orca [76].", + "bbox": [ + 511, + 378, + 913, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- Imputation. This has likewise benefited from techniques that capture ST dependencies to accurately restore missing or corrupted data. For instance, NuwaTS [17] repurposes pretrained language models with contrastive learning and specialized patch embeddings (capturing missing patterns/statistics) to enable cross-domain time series imputation through a unified framework. STD-LLM [44] employs LLMs with spatial-temporal tokenizers and hypergraph learning modules to handle missing values in spatio-temporal data while capturing non-pairwise correlations through topology-aware node embeddings. DrIM [83] combines LLM-derived text representations (from masked tabular data conversions) with contrastive learning to measure similarities for nearest-neighbor imputation in heterogeneous datasets.", + "bbox": [ + 511, + 517, + 913, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- Anomaly Detection. Anomaly detection in ST data has advanced by leveraging models that learn the normal dynamics of ST systems to identify deviations indicative of abnormal events. Whereas prior methods relied on statistical thresholding and clustering to flag outliers, recent FMs learn robust ST representations to detect even subtle anomalies. For example, early attempts [26, 89, 186] investigate the feasibility of using LLMs for anomaly detection in time series data. SigLLM [3] employs GPT-series with signal-to-text conversion techniques, offering dual pipelines (anomaly prompting and deviation detection) for time series analysis through textual or visual representations of numerical data. AD-LLM [156] introduces a benchmark framework combining GPT-4's zero-shot reasoning with contrastive learning for anomaly context enrichment and automated model selection through chain-of-thought prompting.", + "bbox": [ + 511, + 698, + 913, + 892 + ], + "page_idx": 4 + }, + { + "type": "header", + "text": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey", + "bbox": [ + 83, + 75, + 446, + 87 + ], + "page_idx": 4 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 684, + 75, + 913, + 87 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- Others. Furthermore, FMs have demonstrated great potential in other numerical problems such as time series classification [18], geospatial prediction [39, 100], traffic speed inference [7], and socioeconomic indicator prediction [40, 142, 150].", + "bbox": [ + 81, + 106, + 483, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4.2 STFMs for Inferential Problems. Inferential problems in ST data require the integration of both reasoning and understanding of environments. These problems involve high-level cognitive tasks where accurate representation of locations, movements, and environmental context is essential. Addressing such problems goes beyond numerical predictions — it necessitates answering critical inferential questions: What happened? Where is it? What to do? What if? FMs have shown their potential to enhance solutions for these challenges by leveraging their capacity to handle ST knowledge and interpret complex, unstructured data.", + "bbox": [ + 81, + 174, + 482, + 313 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "\"What happened?\" - Event Analysis. Detecting events aims to recognize and explain significant events in time and space. Traditional models struggle with scalability, interpretability, and incorporating external knowledge. To this end, LAMP [120] integrates LLMs with event models, using abductive reasoning to suggest plausible causes for predicted events, retrieve supporting evidence, and rank predictions for improved accuracy. Meanwhile, LEAP [165] replaces GNNs and RNNs with LLMs by framing event detection as a question-answering task, predicting missing event components and forecasting future relations through self-attention mechanisms.", + "bbox": [ + 81, + 320, + 482, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "\"Where is it?\"- Physical Grounding. Grounding ST models in real-world geographical contexts is essential for various applications such as geo-localization, map reconstruction, intelligent routing and navigation. Geo-localization aims to determine an object's location based on multimodal inputs, including images, text, and sensor data. By processing these cues in conjunction with map data, LLMs such as GPT-4o, DeepSeek [36], and GeoGPT [174] can infer geographic coordinates or identify specific locations described in natural language. Map reconstruction, on the other hand, involves creating or updating digital maps by synthesizing information from satellite imagery, sensor readings, and textual reports. LLMs contribute by interpreting and generating map content, correcting inaccuracies, and filling in missing details. For instance, MapGPT [14] employs language-guided updates, incorporating textual descriptions of environmental changes into existing map structures. In personalized routing, ItiNera [123] combines LLMs with spatial optimization to generate personalized \"Citywalk\" itineraries, providing user-specific and spatially coherent urban exploration; ChinaTravel [115] provides a benchmark for real-world Chinese travel planning, enabling scalable evaluation of constraint satisfaction and preference optimization while highlighting the strengths of neuro-symbolic agents. Navigation systems further benefit from LLMs' ability to understand contextual instructions, interpret user queries, and reason about dynamic environments. For example, NavGPT [182] and NavGPT-v2 [181] integrate natural language with real-time traffic and indoor video data to generate personalized and optimized routing solutions. By incorporating STFMs across these domains, physical grounding models facilitate more precise localization, efficient navigation, and adaptive urban mobility solutions, ultimately bridging the gap between digital intelligence and real-world spatial reasoning.", + "bbox": [ + 81, + 465, + 482, + 896 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0dd90631ab1ad6054f2db1a2e36db5801f8436c980eebbece0578f2d29976011.jpg", + "image_caption": [ + "Figure 4: STFMs for addressing inferential problems." + ], + "image_footnote": [], + "bbox": [ + 524, + 106, + 906, + 256 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "\"What to do?\" - Decision Making. Optimizing policies and real-time decision-making in dynamic environments based on inferential insights plays a crucial role in a wide range of applications, including traffic control, autonomous vehicles, and disaster response. In traffic control and management, LLMs improve adaptability and interpretability compared to traditional reinforcement learning approaches [61]. Additionally, they facilitate sim-to-real transfer by modeling real-world traffic dynamics, improving the reliability of traffic signal optimization [22]. Beyond signal control, models like TrafficGPT [168] integrate multimodal traffic data with structured reasoning to analyze, predict, and optimize traffic efficiency and safety in real time. In autonomous vehicles, STFMs contribute to decision-making through both direct and indirect mechanisms. Directly, models such as DDM-Lag [88] employ diffusion-based frameworks with Lagrangian safety enhancements and hybrid policy updates to refine policy articulation and ensure safety. Indirectly, STFMs enhance autonomous driving by predicting realistic driving behaviors [55, 114] and leveraging multi-modal perception to integrate sensor data, bird's eye view maps, and traffic contexts [20, 184], improving situational awareness and vehicle control. Beyond transportation, STFMs play a critical role in disaster management and emergency response by integrating diverse spatio-temporal data sources, such as weather forecasts, remote sensing, and social media signals, to predict disaster impacts and optimize evacuation strategies [16, 31, 65].", + "bbox": [ + 511, + 284, + 915, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "\"What if?\"- Scenario Simulation. STFMs, with their advanced perception and reasoning capabilities, enable the development of STFM-based agents that integrate into Multi-Agent Systems (MAS) to model complex interactions across diverse domains [29]. In urban planning and social simulation, MAS facilitates participatory urban design by simulating interactions between planners and residents. For example, LLM-driven MAS has been used to collaboratively refine land-use plans, leading to improved accessibility and ecological outcomes that surpass human expert solutions [185]. Beyond urban planning, MAS contributes to social science research by modeling human-like behaviors in AI-driven networks. Studies such as [23, 107, 109] demonstrate that LLM-based agents can naturally develop social structures, providing valuable insights into emergent social dynamics. Beyond urban applications, MAS significantly advances game AI and strategic decision-making. Recent studies [112, 133, 187] highlight how MAS-powered reinforcement learning enables strategic gameplay, real-time opponent modeling, and interactive storytelling, fostering the development of more adaptive, intelligent, and realistic virtual agents.", + "bbox": [ + 511, + 632, + 915, + 896 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 84, + 75, + 313, + 85 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "Yuxuan Liang et al.", + "bbox": [ + 818, + 75, + 911, + 87 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 The Methodology Perspective", + "text_level": 1, + "bbox": [ + 81, + 104, + 354, + 121 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Figure 5, we delve into STFMs from a methodology perspective, focusing on $i)$ LLM-based models, which are widely applied across the entire workflow of $ST$ data science by zero-shot utilization or fine-tuning and $ii)$ PFM-based models, i.e., pretraining FMs from scratch, which is mainly utilized for $ST$ data mining. The comparison between them can be found in Appendix C.", + "bbox": [ + 81, + 125, + 480, + 207 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/60d69dbcc8c85b62a9fac9cb5b695647836692fdc243ddfde0484cf9e89d35d3.jpg", + "image_caption": [ + "Figure 5: A method-centric taxonomy. Full version: Fig. 7." + ], + "image_footnote": [], + "bbox": [ + 84, + 215, + 475, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1 Large Language Models (LLM)", + "text_level": 1, + "bbox": [ + 81, + 515, + 372, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1.1 Zero-shot Learner. LLMs exhibit strong reasoning and contextual understanding capabilities, making them highly effective across various ST tasks, including data sensing, management, and mining. As shown in Appendix B, they can function as augmenters, predictors, or agents. To ease the presentation, we adopt a broad definition of LLMs, encompassing standard LLMs, Vision-Language Models (VLM), and Multimodal LLMs (MLLM). The zero-shot utilization of LLMs can be categorized into two primary classes.", + "bbox": [ + 81, + 534, + 482, + 645 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Prompt Engineering. When taking LLMs as zero-shot predictors [33, 53, 125] or data augmenters [150] for various tasks, prompt engineering plays an essential role in shaping model outputs. Below, we summarize key aspects for prompt engineering in current research: a) Prompt Construction: A well-designed prompt typically contains key elements like Task Instruction, Tokenization, and Few-shot Examples. Task instruction [53, 147, 149] aims to explicitly guide LLMs to execute specific operations, incorporating domain knowledge [157] if applicable. Tokenization [33, 53] is crucial to aligning ST data formats with LLM input structures. Additionally, presenting a small number of annotated examples [175] facilitates in-context learning, enabling LLMs to better generalize to complex tasks while ensuring output consistency and adherence to the expected format. b) Prompt Learning: [73, 148] Also known as instruction-tuning, this method learns prompts dynamically rather than relying on manually crafted ones. By optimizing prompt structures during training, it provides a flexible and efficient way to adapt LLMs to new tasks without altering their underlying model weights.", + "bbox": [ + 81, + 646, + 482, + 896 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "c) Chain-of-Thought (CoT) Prompting: CoT [87, 175] enhances LLMs' reasoning capabilities by guiding them through step-by-step logical progression. This method improves their ability to tackle complex spatio-temporal tasks, ensuring more interpretable, structured, and accurate outputs in decision-making processes.", + "bbox": [ + 511, + 106, + 913, + 176 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Agentic Engineering. The emergence of LLM-based agents [49, 144, 168, 174, 185] with reasoning, memory and tool-calling capabilities is transforming ST data science, enabling more adaptive and autonomous decision-making. When designing agent-based solutions, existing works primarily consider the following key aspects: a) Role Assignment. [50, 144, 174] clearly specify the responsibilities and functional boundaries of each agent within the system. b) Memorization [64, 174] refers to the agent's capability to store, recall, and leverage past information and context during task execution. A basic approach involves embedding past interactions into prompts, while more advanced techniques like Retrieval-Augmented Generation (RAG) [143, 155] dynamically retrieve relevant information from external knowledge bases, incorporating only the most pertinent content into the prompt. c) Tool Definition [168, 174], which identify and integrate various tools and functionalities that an agent can call upon to solve complex tasks. In ST data science, various expert models like STGNNs [51] can be wrapped as a tool and added into the agent in a plug-and-play manner. d) Multi-Agent System. Deploying multiple specialized agents to work collaboratively (each with distinct roles) enhances the efficiency and robustness of solutions for intricate ST challenges [49, 63, 185].", + "bbox": [ + 511, + 178, + 913, + 469 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1.2 Supervised Fine-Tuning for LLMs. Fine-tuning adapts LLMs to ST tasks by adjusting their parameters based on domain-specific datasets, sometimes incorporating additional modalities such as texts [79, 150] and vision [180]. We categorize fine-tuning methods into three approaches based on the extent of parameter updates:", + "bbox": [ + 511, + 477, + 913, + 546 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Full Parameter Fine-Tuning [68, 98, 100, 104, 108] updates all model parameters based on downstream ST datasets, achieving maximal adaptation to specific tasks. However, it requires substantial labeled data and high computational resources, making it impractical for many real-world applications.", + "- Partial Parameter Fine-tuning. To reduce computational overhead, this method [13, 183] freezes most parameters, such as attention weights, while fine-tuning only a small subset (e.g., position encodings and layer normalization). However, modifying a subset of parameters can disrupt the LLM's learned representations, leading to catastrophic forgetting of general knowledge.", + "- Add-on Parameter Fine-Tuning. To mitigate forgetting while maintaining efficiency, this technique [61] introduces trainable low-rank matrices (e.g., LoRA [42]), while keeping the original LLM weights frozen. This strategy preserves pretrained knowledge while enabling efficient adaptation to ST tasks. Besides fine-tuning LLMs' weights, another way is training additional layers for input tokenization or task adaption. For instance, TimeLLM [53] trains a self-attention layer that aligns patched time series representations with pretrained text prototype embeddings. Similarly, Time-VLM [180] trains a memory-enhanced attention to capture both short- and long-term dependencies. For task adaption, existing methods typically train an additional prediction head (e.g., linear layers) to project the LLM's output embeddings into a domain-specific space [53, 180]." + ], + "bbox": [ + 514, + 549, + 913, + 895 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey", + "bbox": [ + 83, + 75, + 446, + 87 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 684, + 75, + 913, + 87 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2 Pretrained Foundation Models (PFM)", + "text_level": 1, + "bbox": [ + 81, + 104, + 426, + 119 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Unlike LLMs, which build STFMs by directly using or fine-tuning LLMs, PFMs are developed from scratch, independent of existing LLMs. This approach enables domain-specific optimization, allowing models to better capture ST dependencies from cross-domain ST data without constraints imposed by linguistic priors. Following this, we examine PFMs through three key dimensions:", + "bbox": [ + 81, + 123, + 482, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2.1 Neural Architecture. The architecture of PFMs is a fundamental design choice that directly influences their capabilities, efficiency, and adaptability in ST tasks, which can be categorized into:", + "bbox": [ + 81, + 210, + 482, + 253 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Transformer-based PFMs. Transformers have been the predominant architecture choice for building PFMs thanks to its powerful sequential modeling ability introduced by the self-attention mechanism [7, 72, 77, 85, 158].", + "- Diffusion-based PFMs. Diffusion-based models have recently emerged as a powerful approach for ST representation learning [12, 21, 136, 160, 161, 188], particularly in generative and predictive modeling. These models iteratively learn to reverse a stochastic noise process, enabling them to generate high-fidelity spatio-temporal sequences with strong generalization properties.", + "- Graph-based PFMs. Unlike sequential models, GNNs excel at representing spatially structured data such as road networks. [62, 130] build FMs based on graph neural networks to learn the complex correlation between different entities in ST applications.", + "- Others. Another emerging class of PFMs is State Space Model (SSM)-based models [8, 43, 97], which construct PFMs using structured state-space representations. Meanwhile, several studies utilize CNNs [118] as backbones for developing PFMs." + ], + "bbox": [ + 83, + 257, + 482, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2.2 Pretraining Scheme. To enhance generalization ability, PFMs are usually pretrained based on cross-domain datasets [91, 137, 158], enabling them to learn diverse ST patterns across multiple domains. Existing pretraining schemes of PFMs can be classified into three types based on the training objectives: a) Generative Pretraining [85, 98, 130, 138, 189] focuses on reconstructing input data by learning its underlying distribution, enabling the model to generate realistic time series or ST data, while b) Contrastive Pretraining [7, 84, 171] emphasize distinguishing between similar and dissimilar data pairs to learn robust representations by maximizing agreement between augmented views of the same sample. It is particularly effective in multimodal ST learning, aligning heterogeneous data sources such as satellite imagery and its text description. c) Hybrid Pretraining [77] integrates both generative and contrastive objectives, leveraging their complementary strengths.", + "bbox": [ + 81, + 513, + 482, + 722 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2.3 Data Modality. ST data manifests in various modalities, each characterized by unique properties (see Section 2), necessitating the development of modality-specific STFMs:", + "bbox": [ + 81, + 726, + 482, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "- Location. PFMs for location data [7, 40, 71, 124, 138, 150, 171] aim to learn general embedding for geographical entities. For instance, GeoVectors [124] and SpaBERT [71] learn location embeddings based on open-source data such OpenStreetMap, while G2PTL [138] learns from massive logistics delivery data. Notably, there is a noticeable trend that leverages multi-modalities (such as satellite image and text) for comprehensive location embeddings. For example, both UrbanCLIP [150], UrbanVLP [40], and ReFound [142] utilize satellite images for urban region profiling.", + "bbox": [ + 83, + 770, + 482, + 896 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04153b45ab02f3e79c0ab49c30b7605ee00c77f9060519cff8dcabcf84cc5fc2.jpg", + "image_caption": [ + "Figure 6: Representative PFMs for different types of ST data." + ], + "image_footnote": [], + "bbox": [ + 517, + 102, + 903, + 273 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Trajectory & Event. PFMs for trajectory/event data [21, 84, 85, 103, 121, 189] are designed to learn general sequential patterns from inputs. A pioneering effort in this direction is TrajFM [85], which introduces a trajectory FM capable of supporting both regional and task transferability. Pretrained on vehicle trajectories from multiple cities, TrajFM employs a trajectory-masking and autoregressive recovery mechanism to enhance its learning capabilities. To tackle the limited resources of cross-domain trajectories, UniTraj [189] curates a billion-scale mobility dataset spanning diverse geographic regions to facilitate the advancement of trajectory-based FMs. For event data, MOTOR [121] proposes a time-to-event FM for structured medical records.", + "- ST Raster. PFMs for ST raster data [10, 15, 98, 104, 108, 117, 160] organize spatial information in a grid-like format, with a typical applied domain being weather/climate forecasting. For instance, W-MAE [98] trains a mask autoencoder for ST grid forecasting. CimaX [104] develops a general-purpose climate foundation model, pretrained on diverse datasets spanning various variables, ST scales, and physical contexts. Pangu [10] is trained on 39 years of global climate data, which achieves superior forecasting performance compared to leading numerical weather prediction systems. UniST [158] first pretrains the model in various ST raster data via masked pretraining, and then proposes a learnable ST prompt to enhance the model's generalization ability.", + "- ST Graph. PFMs for ST graph data [62, 72, 93, 111, 117, 134] learn the ST dependencies from ST graphs that generalize effectively in unseen spatial and temporal contexts. Unlike ST Raster PFMs, there are limited works in this area, which is more challenging due to the complex graph correlation. One representative is OpenCity [72] for ST graph forecasting, which integrates Transformer and GNN to model the ST dependencies in traffic data." + ], + "bbox": [ + 514, + 294, + 915, + 723 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5 Conclusion and Future Directions", + "text_level": 1, + "bbox": [ + 514, + 727, + 818, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The rapid advancement of FMs has transformed ST data science, impacting sensing, management, and mining. This survey provides a comprehensive review of FMs for ST data science, identifying key capabilities such as perception, reasoning, and optimization while exploring diverse downstream tasks and datasets. We also establish a systematic taxonomy of methodologies, enhancing understanding of how STFMs model ST data. Despite progress, challenges remain in generalization, interpretability, and efficiency. By consolidating recent advances and outlining future directions (see Appendix A), this survey aims to inspire further innovations, driving the development of scalable and adaptive STFMs for real practice.", + "bbox": [ + 511, + 743, + 915, + 896 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 83, + 75, + 313, + 87 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "Yuxuan Liang et al.", + "bbox": [ + 818, + 75, + 911, + 87 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 84, + 104, + 176, + 119 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Oluwanifemi Adebayo Moses Adekanye. 2024. LIm-powered synthetic environments for self-driving scenarios. 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We have identified a significant challenge in developing FMs for addressing numerical problems in ST data science. Directly leveraging LLMs for numerical tasks such as forecasting proves to be non-trivial [34]. Meanwhile, fine-tuning LLMs or training STFMs from scratch using large-scale, cross-domain ST data often comes at the cost of interactive capabilities, thereby hindering interpretability in the prediction outcomes. These limitations motivate us to explore a novel paradigm that not only retains strong numerical reasoning abilities but also enhances interpretability, bridging the gap between predictive accuracy and explanatory insight.", + "- Large foundation models are all we need? While the extensive parameterization of FMs enables impressive generalization capabilities, particularly in zero/few-shot settings, their superiority over smaller expert models remains context-dependent. In ST domains such as time series analysis [122] and urban planning [57], smaller expert models often outperform FMs when provided with sufficient domain-specific training data. This raises fundamental questions about the trade-offs between model scalability, efficiency, and task-specific optimization. Future research should delve into hybrid approaches that combine the adaptability of large models with the precision of expert models.", + "- One-fit-all FMs across the full workflow. While current FMs are typically designed to support only specific stages of ST data science, we envision a more unified FM capable of seamlessly" + ], + "bbox": [ + 83, + 547, + 482, + 893 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "spanning the entire workflow, from initial data sensing and management to mining and supporting downstream applications. Achieving this goal will likely require the development of advanced LLM agents that can function as full-stack engineers (i.e., strongly benefiting all stages) for ST data science.", + "bbox": [ + 526, + 106, + 915, + 176 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "- Integrating STFMs with multimodal understanding. While current STFMs excel in processing structured ST data, their ability to integrate and reason over multimodal information, including text, images, video, and sensor data, remains underdeveloped. Many tasks require models to jointly interpret geospatial context, temporal dynamics, and text descriptions. Future research can focus on designing multimodal STFMs that effectively align, fuse, and reason over heterogeneous data sources, enabling more context-aware and human-interpretable decision-making.", + "bbox": [ + 514, + 176, + 915, + 301 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "B Zero-shot Utilization of LLMs", + "text_level": 1, + "bbox": [ + 514, + 311, + 790, + 325 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "There are three ways of directly using LLMs for various ST tasks:", + "bbox": [ + 514, + 330, + 911, + 344 + ], + "page_idx": 12 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- LLM-as-Augmenter. Pretrained LLMs can enhance both data understanding and model performance. On the one hand, it can serve as the input augmenter, which enhances data interoperability or provides external information [40, 79] (e.g., textual or visual). On the other hand, LLMs can serve as a parameter-frozen model component [102, 150, 166], thus augmenting domain models by injecting the pretrained external knowledge in LLMs.", + "- LLM-as-Predictor. LLMs can be directly employed as predictors [33, 53, 73, 125] for various tasks. Due to the modality gap between text and ST data, preprocessing is required to fit the input spaces of LLMs. Such step typically contains prompt engineering [73, 125, 147-149] or patch & tokenization [53].", + "- LLM-as-Agent. LLM-based agents are typically equipped with the ability to memorize and call various tools. When applied to ST data science, various domain-expert models can be wrapped as a tool and added into the agent in a plug-and-play manner [144, 168, 174]. As such, LLM serves as a router to access different models with both flexibility and performance guarantees. Furthermore, multi-agent systems [185] can be built to solve more complex tasks in the ST domain." + ], + "bbox": [ + 514, + 347, + 913, + 623 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "C Comparison between LLMs and PFMs", + "text_level": 1, + "bbox": [ + 514, + 635, + 854, + 651 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Table 3 demonstrates the comparison between LLMs and PFMs on their capabilities, including perception, optimization, and reasoning. For example, PFMs excel in exceptional numerical reasoning abilities, yet they often struggle with common-sense understanding. There is still no free lunch, and the user can choose either LLMs or PFMs according to the downstream applications.", + "bbox": [ + 511, + 654, + 913, + 737 + ], + "page_idx": 12 + }, + { + "type": "table", + "img_path": "images/146f81da04a218bcff0caa24a2b9f78a939ebf9ec6c05eb8643c1f4789377d85.jpg", + "table_caption": [ + "Table 3: A capability comparison between LLMs and PFMs for ST data science." + ], + "table_footnote": [], + "table_body": "
CapabilitiesLarge Language Models (LLMs)Pretrained Foundation Models (PFMs)
Perception▲ Limited native ST perception; can be enhanced via fine-tuning✓ Strong ST perception, integrating sensor data and domain-specific learning
Optimization✓ Agent-based reasoning for decision-making; relies on prompting and heuristics▲ Limited; lacks decision-making ability for control and planning
Common-sense Reasoning✓ Strong via pretraining on vast textual data; can be enhanced with fine-tuning▲ Limited; relies on structured ST data rather than broad world knowledge
Numerical Reasoning▲ Handles arithmetic but struggles with structured ST computations✓ Designed for numerical problems, e.g., forecasting, anomaly detection
Causal Reasoning▲ Can infer causal relations from text but lacks structured ST modeling✓ Built-in graph-based and ST causal modeling
", + "bbox": [ + 517, + 792, + 906, + 890 + ], + "page_idx": 12 + }, + { + "type": "header", + "text": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey", + "bbox": [ + 83, + 75, + 446, + 87 + ], + "page_idx": 12 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 684, + 75, + 913, + 87 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/0e2c71ca92a3b1948076a1507053343e497304cd0c184fa18d2ff53d67b1e756.jpg", + "image_caption": [ + "Figure 7: Taxonomy from the methodology perspective." + ], + "image_footnote": [], + "bbox": [ + 84, + 103, + 911, + 478 + ], + "page_idx": 13 + }, + { + "type": "header", + "text": "Conference'17, July 2017, Washington, DC, USA", + "bbox": [ + 84, + 75, + 313, + 87 + ], + "page_idx": 13 + }, + { + "type": "header", + "text": "Yuxuan Liang et al.", + "bbox": [ + 818, + 75, + 911, + 87 + ], + "page_idx": 13 + } +] \ No newline at end of file diff --git a/data/2025/2503_13xxx/2503.13502/db12ade8-3943-4647-bb0d-ce8160710750_model.json b/data/2025/2503_13xxx/2503.13502/db12ade8-3943-4647-bb0d-ce8160710750_model.json new file mode 100644 index 0000000000000000000000000000000000000000..45d9aeee5904ae1665c548daac6e8894fbb18ea3 --- /dev/null +++ b/data/2025/2503_13xxx/2503.13502/db12ade8-3943-4647-bb0d-ce8160710750_model.json @@ -0,0 +1,4111 @@ +[ + [ + { + "type": "aside_text", + "bbox": [ + 0.023, + 0.261, + 0.058, + 0.707 + ], + "angle": 270, + "content": "arXiv:2503.13502v1 [cs.DB] 12 Mar 2025" + }, + { + "type": "title", + "bbox": [ + 0.156, + 0.102, + 0.848, + 0.152 + ], + "angle": 0, + "content": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.163, + 0.77, + 0.199 + ], + "angle": 0, + "content": "Yuxuan Liang\\(^{1}\\), Haomin Wen\\(^{2,1}\\), Yutong Xia\\(^{3}\\), Ming Jin\\(^{4}\\), Bin Yang\\(^{5}\\), Flora Salim\\(^{6}\\), Qingsong Wen\\(^{7}\\), Shirui Pan\\(^{4}\\), Gao Cong\\(^{8}\\)" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.199, + 0.831, + 0.277 + ], + "angle": 0, + "content": "1The Hong Kong University of Science and Technology (Guangzhou) 2Carnegie Mellon University 3National University of Singapore 4Griffith University 5East China Normal University 6University of New South Wales 7Squirrel AI Learning, USA 8Nanyang Technology University {yuxiang,yutong.x}@outlook.com,{wenhaomin.whm,mingjinedu,qingsongedu}@gmail.com flora.salim@unsw.edu.au,byang@dase.ecnu.edu.cn,s.pan@griffith.edu.au,gaocong@ntu.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.284, + 0.158, + 0.298 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.303, + 0.484, + 0.552 + ], + "angle": 0, + "content": "Spatio-Temporal (ST) data science, which includes sensing, managing, and mining large-scale data across space and time, is fundamental to understanding complex systems in domains such as urban computing, climate science, and intelligent transportation. Traditional deep learning approaches have significantly advanced this field, particularly in the stage of ST data mining. However, these models remain task-specific and often require extensive labeled data. Inspired by the success of Foundation Models (FM), especially large language models, researchers have begun exploring the concept of Spatio-Temporal Foundation Models (STFMs) to enhance adaptability and generalization across diverse ST tasks. Unlike prior architectures, STFMs empower the entire workflow of ST data science, ranging from data sensing, management, to mining, thereby offering a more holistic and scalable approach. Despite rapid progress, a systematic study of STFMs for ST data science remains lacking. This survey aims to provide a comprehensive review of STFMs, categorizing existing methodologies and identifying key research directions to advance ST general intelligence." + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.556, + 0.22, + 0.57 + ], + "angle": 0, + "content": "1 Introduction" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.574, + 0.483, + 0.671 + ], + "angle": 0, + "content": "Humans live in a world shaped by the dynamic interplay of countless elements across space and time. Spatio-Temporal (ST) Data, which refer to data that encapsulate ST phenomena, track the evolution of objects or events across locations and time [5], such as meteorological records, traffic patterns, and human traces. These data are frequently sourced from a wide array of platforms, ranging from IoT devices, GPS sensors, social media, to remote sensing." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.671, + 0.483, + 0.769 + ], + "angle": 0, + "content": "Within this context, Spatio-Temporal Data Science focuses on sensing, managing, and mining these datasets to uncover patterns, understand complex systems, and predict future dynamics. Motivated by its transformative potential, this field addresses critical challenges across urban environments and even the entire planet, enabling decision-making and fostering innovations that contribute to building smarter, more sustainable, and resilient systems [178]." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.78, + 0.483, + 0.853 + ], + "angle": 0, + "content": "Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.854, + 0.305, + 0.864 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.865, + 0.473, + 0.875 + ], + "angle": 0, + "content": "© 2025 Copyright held by the owner/author(s). Publication rights licensed to ACM." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.875, + 0.27, + 0.884 + ], + "angle": 0, + "content": "ACM ISBN 978-x-xxxxx-xxxxx-x/YY/MM" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.885, + 0.285, + 0.896 + ], + "angle": 0, + "content": "https://doi.org/10.1145/nnnnnnn.nnnnnnn" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.283, + 0.907, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.433, + 0.916, + 0.49 + ], + "angle": 0, + "content": "Figure 1: ST Foundation Models (STFM), which include LLM and PFM, are pretrained with or applied to diverse ST data, with the abilities of perception, optimization, and reasoning. STFMs can, in turn, enhance each stage of ST data science." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.494, + 0.916, + 0.688 + ], + "angle": 0, + "content": "In the era of deep learning, the community has primarily concentrated on spatio-temporal representation learning, as a fundamental step of ST data mining [129]. Key advancements include the development of Spatio-Temporal Graph Neural Networks (STGNN) [51] and transformer-based architectures, which have shown remarkable success in tasks such as traffic forecasting [80, 146], air quality prediction [82], and human mobility analytics [132]. STGNNs integrate Graph Neural Networks (GNN) with temporal learning modules (e.g., GRU [6, 70], TCN [140, 141]) to model ST correlations, while transformer models leverage self-attention mechanisms [37, 78, 177] to process complex dependencies across space and time. Additionally, there has been significant research on self-supervised learning [46, 74, 92], where models are trained to extract powerful representations with minimal reliance on large annotated datasets." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.689, + 0.916, + 0.897 + ], + "angle": 0, + "content": "Driven by the success of Foundation Models (FM), especially Large Language Models (LLM), researchers have recently begun exploring the concept of Spatio-Temporal Foundation Models (STFM) [32, 81, 169]. By harnessing LLMs, it becomes possible to develop more generalized, adaptable solutions that can be fine-tuned for specific tasks with minimal data. Another prominent approach involves pretraining FMs (denoted as PFM) on cross-domain ST data and adapting them for particular domains. In contrast to previous architectures (e.g., STGNNs), STFMs integrates the capabilities of perception, reasoning and optimization, which not only promises to revolutionize ST data mining, but also empowers other stages of ST data science, such as ST data sensing and management (See Figure 1). This shift has the potential to enhance the scalability and efficiency of ST applications, offering a more holistic approach to addressing challenges in urban computing, climate science, etc." + } + ], + [ + { + "type": "header", + "bbox": [ + 0.084, + 0.076, + 0.314, + 0.088 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "header", + "bbox": [ + 0.819, + 0.076, + 0.913, + 0.088 + ], + "angle": 0, + "content": "Yuxuan Liang et al." + }, + { + "type": "table_caption", + "bbox": [ + 0.082, + 0.105, + 0.483, + 0.161 + ], + "angle": 0, + "content": "Table 1: Our survey vs. related surveys on FMs for learning ST data, such as locations (L), trajectories (T), events (E), ST rasters (R), and ST graphs (G). The applications (App.) include numerical (N) and inferential (I) problems." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.163, + 0.48, + 0.24 + ], + "angle": 0, + "content": "
SurveyYearVenueSensingManage.MiningApp.Data
Jin et al. [54]2023-✓NR,G
Jiang et al. [48]2024IJCAI✓NR,G
Liang et al. [81]2024KDD✓NT,E,R,G
Zhang et al. [169]2024KDD✓N,IL,T,E,R,G
Goodge et al. [32]2025-✓NT,E,R,G
Ours2025-✓✓✓N,IL,T,E,R,G
" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.242, + 0.483, + 0.381 + ], + "angle": 0, + "content": "Despite their rapid advancements, a systematic analysis of STFMs across the entire workflow of ST data science remains lacking. First, prior surveys have primarily focused on utilizing LLMs as the key tool for ST data mining [32, 54, 81, 169], leaving a significant gap in understanding how these models can be integrated throughout the entire process, i.e., with less focus placed on their role in the earlier stages of sensing and management. Second, they predominantly examine the applications of STFMs to numerical problems (e.g., forecasting, imputation) while overlooking their role in inferential problem-solving such as decision-making systems." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.381, + 0.483, + 0.573 + ], + "angle": 0, + "content": "To bridge these gaps, this paper aims to provide a more comprehensive survey of STFMs across all stages of ST data science, spanning data sensing, management, and mining (see Figure 1). For example, LLMs can enhance ST data sensing by actively processing citizen reports, optimizing participatory sensing strategies, and generating synthetic data at scale. In terms of data management, they can automate data cleaning tasks, construct meaningful knowledge graphs for data integration, and facilitate more efficient retrieval of cross-modal datasets. Beyond these stages, our survey also explores how STFMs support a broader range of downstream applications, including numerical and inferential problems. Through this endeavor, we seek to illuminate an overall vision of STFMs, thereby enhancing comprehension regarding their potential to optimize ST data science, fostering more integrated and adaptable solutions." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.574, + 0.483, + 0.727 + ], + "angle": 0, + "content": "Meanwhile, we systematically investigate the key methodologies of STFMs for modeling a variety of ST data. We begin by categorizing existing STFMs into two main classes: LLMs and Pretrained Foundation Models (PFMs). For LLMs, which are pretrained on linguistic data, we focus on their usage as a zero-shot [33] or few-shot learner [53, 73], where various prompting and fine-tuning strategies have been explored, respectively. For PFMs, which are trained from scratch based on cross-domain ST data [40, 158, 189], we examine their neural architectures, pretraining methods, and their adaptability to different types of ST data, including location data, trajectory data, events, ST raster data, and ST graph data." + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.727, + 0.446, + 0.74 + ], + "angle": 0, + "content": "In summary, our major contributions lie in three aspects:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.74, + 0.483, + 0.809 + ], + "angle": 0, + "content": "- Comprehensive and up-to-date survey: We provide the first comprehensive and modern survey of FMs across the entire workflow of ST data science, covering data sensing, management, and mining. We also explore a broader range of downstream tasks and data types compared to most existing surveys (See Table 1)." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.81, + 0.483, + 0.851 + ], + "angle": 0, + "content": "- Vision and Methodologies: We propose a vision for STFMs, identifying key capabilities essential for their success, and discuss current methodologies for implementing these abilities in detail." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.851, + 0.483, + 0.892 + ], + "angle": 0, + "content": "- Future directions: We highlight promising directions for advancing ST data science with foundation models, encouraging further research and exploration in this emerging field." + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.74, + 0.483, + 0.892 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.107, + 0.916, + 0.178 + ], + "angle": 0, + "content": "Paper Organization. The remainder of this paper is organized as follows: Sec. 2 provides essential background on FMs and ST data. Sec. 3 and 4 present a taxonomy of STFMs regarding the workflow and methodologies, respectively. Sec. 5 offers concluding remarks, and Appendix A highlights promising avenues for future research." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.183, + 0.646, + 0.199 + ], + "angle": 0, + "content": "2 Background" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.201, + 0.916, + 0.437 + ], + "angle": 0, + "content": "Foundation models. FMs are deep neural networks trained on vast datasets, enabling them to acquire broad, cross-domain knowledge and exceptional adaptability [45]. Unlike earlier task-specific models, FMs can be efficiently fine-tuned with relatively small amounts of task-specific data, offering remarkable flexibility, effectiveness, and cost efficiency. Pioneering attempts like BERT [58] and GPT-3 [11] have reshaped natural language processing. More recent models, e.g., GPT-4o [45] and DeepSeek-R1 [36], further push the frontiers of generative capabilities, enabling more nuanced reasoning, robust domain adaptation, and improved context-awareness in diverse tasks. In ST domains, recent FMs like Time-MoE [119], Chronos [4], and UniST [158] have made remarkable strides in time series analysis and universal ST forecasting, while UniTraj [189] serves as a versatile foundation for various trajectory-related tasks. Inspired by these successes, this survey delves into the utilization of FMs in the entire workflow of ST data science, covering data sensing, management, and mining." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.44, + 0.916, + 0.522 + ], + "angle": 0, + "content": "Formulation of Spatio-Temporal Data. ST data refer to datasets that integrate spatial (location-based) and temporal (time-based) information, capturing dynamic patterns and relationships over space and time. Figure 2 depicts the basic ST data structures discussed in this survey, including locations, trajectories, events, ST rasters, and ST graphs. Their definitions are delineated as follows." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.522, + 0.915, + 0.579 + ], + "angle": 0, + "content": "Definition 1 (Location). A location refers to a fixed spatial point or object in a geographical space, represented by the geospatial coordinates \\( l \\in \\mathbb{R}^2 \\), i.e., latitude and longitude. It is often profiled by the corresponding satellite image, street-view image, and descriptions." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.579, + 0.916, + 0.634 + ], + "angle": 0, + "content": "Definition 2 (Trajectory). A trajectory is a sequence of time-ordered locations that describe the movements of an object in the geographical space. It can be formulated as \\(\\mathcal{T} = p_1\\rightarrow p_2\\rightarrow \\dots \\rightarrow p_T\\) where \\(p_i = (l_i,t_i)\\), and \\(l_{i}\\) denotes the object's location at time \\(t_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.634, + 0.915, + 0.69 + ], + "angle": 0, + "content": "Definition 3 (Event). An event sequence is a series of timestamped events, denoted as \\(\\mathcal{E} = v_{1}\\rightarrow v_{2}\\rightarrow \\dots \\rightarrow v_{T}\\), describing the progress of actions or occurrences, where \\(v_{i} = (e_{i},t_{i})\\) and \\(e_i\\in \\mathbb{R}^d\\) is an event and \\(t_i\\) denotes the time when \\(e_i\\) occurs." + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.692, + 0.892, + 0.876 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.878, + 0.878, + 0.894 + ], + "angle": 0, + "content": "Figure 2: Illustration of various types of ST data." + } + ], + [ + { + "type": "header", + "bbox": [ + 0.084, + 0.076, + 0.448, + 0.088 + ], + "angle": 0, + "content": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey" + }, + { + "type": "header", + "bbox": [ + 0.685, + 0.076, + 0.914, + 0.088 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.107, + 0.482, + 0.162 + ], + "angle": 0, + "content": "Definition 4 (Spatio-Temporal Raster). An ST raster can be denoted as \\(\\mathcal{X} = < \\mathbf{X}_1,\\mathbf{X}_2,\\dots ,\\mathbf{X}_T > \\in \\mathbb{R}^{H\\times W\\times T\\times D}\\), where \\(\\mathbf{X}_t\\in \\mathbb{R}^{H\\times W\\times D}\\) denotes the signals collected from \\(N = HW\\) evenly distributed locations at time \\(t\\), each characterized by \\(D\\) feature attributes." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.163, + 0.482, + 0.248 + ], + "angle": 0, + "content": "Definition 5 (Spatio-Temporal Graph). An ST graph extends the ST raster to be \\( X = < \\mathbf{X}_1, \\mathbf{X}_2, \\ldots, \\mathbf{X}_T > \\in \\mathbb{R}^{N \\times T \\times D} \\) by explicitly incorporating spatial correlations with a graph \\( G_t = (V, E_t, \\mathbf{A}_t) \\) when \\( N \\) locations are not uniformly distributed. Here \\( V \\) is the set of nodes, \\( E_t \\) is the set of edges, and \\( \\mathbf{A}_t \\in \\mathbb{R}^{N \\times N} \\) is the adjacency matrix at time \\( t \\). The size of \\( V \\) is usually static." + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.259, + 0.331, + 0.274 + ], + "angle": 0, + "content": "3 The Workflow Perspective" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.277, + 0.483, + 0.306 + ], + "angle": 0, + "content": "As shown in Figure 3, we examine STFMs from a holistic, bottom-up perspective, emphasizing their composition across four key aspects:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.308, + 0.483, + 0.377 + ], + "angle": 0, + "content": "- ST Data Sensing refers to the acquisition of data that varies over both space and time from diverse resources (e.g., sensors, satellites, social media), to capture dynamic environmental, geographic, or social phenomena. We also consider synthetic data generation for enhancing data diversity and quantity." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.378, + 0.483, + 0.446 + ], + "angle": 0, + "content": "- ST Data Management focuses on storing, indexing, and organizing these large-scale, heterogeneous ST datasets, incorporating strategies like distributed architectures for efficient retrieval and integration. FMs can enhance this process by facilitating data cleaning, query & retrieval, and data integration." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.447, + 0.483, + 0.516 + ], + "angle": 0, + "content": "- ST Data Mining involves learning and analyzing ST data that varies across both space and time to uncover patterns, trends, and relationships, using data mining (DM), deep learning (DL) techniques, or the newly-proposed STFMs with strong capabilities in perception, optimization, and reasoning." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.516, + 0.483, + 0.571 + ], + "angle": 0, + "content": "- Downstream Applications: This stage harnesses the above insights from ST data to drive real-world applications, ranging from numerical problems to inferential problems, where informed actions and policies are formulated." + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.308, + 0.483, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.574, + 0.483, + 0.63 + ], + "angle": 0, + "content": "By examining these four aspects, we can better understand how STFMs advance from raw data acquisition to high-level service providing, ultimately enabling more intelligent, adaptable, and impactful solutions. We will detail each stage in the following sections." + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.638, + 0.479, + 0.876 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.879, + 0.466, + 0.892 + ], + "angle": 0, + "content": "Figure 3: The framework of STFMs for ST data science." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.106, + 0.805, + 0.122 + ], + "angle": 0, + "content": "3.1 Spatio-Temporal Data Sensing" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.125, + 0.916, + 0.18 + ], + "angle": 0, + "content": "FMs revolutionize ST data sensing from two complementary aspects: real-world data sensing, which involves collecting data from physical sources, and synthetic data generation, which creates synthetic ST data through foundation models." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.184, + 0.915, + 0.42 + ], + "angle": 0, + "content": "3.1.1 Real-World Data Sensing. Advances in sensing and data acquisition technologies have led to the generation of vast amounts of ST data. FMs are increasingly applied in human-centric active sensing, particularly in the context of citizen reporting for urban and environmental monitoring [41]. These models act as powerful agents for collecting and processing real-time data from citizens, enabling the efficient handling of ST data [19, 27, 101]. For example, citizens might constantly report incidents, environmental changes, or social events through text or voice [178]. By understanding these reports, LLMs can categorize, prioritize, and trigger appropriate responses for various urban issues, from traffic congestion to environmental hazards. This enhances the decision-making process by continuously updating their models with new data streams. Thus, LLMs are not just passive analytical tools but active participants that help make urban environments more responsive and adaptive to citizen inputs, transforming traditional citizen feedback into actionable knowledge, enabling more sustainable and resilient cities." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.42, + 0.915, + 0.6 + ], + "angle": 0, + "content": "FMs can also function as intelligent schedulers or simulate multiagent systems to optimize the recruitment and coordination of participants for crowdsensing, particularly under budget constraints [41, 139, 191]. By analyzing ST data and understanding context, LLMs can identify regions and times where crowdsensing efforts will yield the most valuable information. They dynamically recruit participants based on proximity, availability, and past contributions, reducing redundant data collection. Additionally, LLMs simulate multiple agents interacting in real time, ensuring the efficient distribution of sensing tasks across a network of citizens or devices [190]. This strategic scheduling and agent-based coordination maximize coverage while minimizing costs, ensuring that crowdsensing delivers valuable, real-time insights under budgetary constraints." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.603, + 0.915, + 0.812 + ], + "angle": 0, + "content": "3.1.2 Synthetic Data Generation. FMs can also facilitate data generation, which enhances ST data by increasing its diversity, improving model robustness, and compensating for missing or sparse information [95]. This is crucial for ST tasks like mobility analytics, where collecting real-world data is often costly or raises privacy concerns. For instance, Trajectory-LLM [154] generates vehicle trajectories from brief textual descriptions of vehicle interactions, whereas Traj-LLM [56] generates human trajectories by leveraging personas, memory modules, and routine profiles. LLMob [126] advances mobility data generation, offering flexibility in modeling diverse urban activities and personal mobility patterns, thus improving transportation system modeling and analysis. LLMs have also been employed to construct synthetic environments that replicate real-world conditions across diverse domains, including intelligent transportation [1] and disaster management [31]." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.822, + 0.848, + 0.838 + ], + "angle": 0, + "content": "3.2 Spatio-Temporal Data Management" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.841, + 0.915, + 0.897 + ], + "angle": 0, + "content": "Upon the acquisition of ST data, the challenge of effective management emerges, particularly in addressing data quality issues (e.g., missing values/views) and facilitating data retrieval and integration. Within this context, FMs can be harnessed in the following ways." + } + ], + [ + { + "type": "header", + "bbox": [ + 0.085, + 0.076, + 0.314, + 0.088 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "header", + "bbox": [ + 0.82, + 0.076, + 0.912, + 0.087 + ], + "angle": 0, + "content": "Yuxuan Liang et al." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.108, + 0.482, + 0.329 + ], + "angle": 0, + "content": "3.2.1 Data Cleaning. Data cleaning is the process of improving data quality by addressing issues such as missing values, low sampling rates, and noise. For example, ST data often exhibit missing values due to various factors like sensor malfunctions and transmission disruptions [178]. Filling in these missing values[113] is crucial for ensuring the integrity of predictive models, optimizing strategies, and facilitating informed decision-making. Recent literature reveals that LLMs can serve as powerful zero-shot [164] or few-shot [17, 172] learners to data imputation by leveraging their ability to identify and learn complex ST patterns. PLMTrajRec [135], utilizing a pretrained language model to recover sparse trajectory data by unifying intervals and inferring road conditions, showing effective generalization across varied sampling intervals in tests. Moreover, scholars have investigated the potential of leveraging LLMs to augment missing views or information, such as urban region profiling [40, 150, 163] and traffic video captioning [25]." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.335, + 0.482, + 0.57 + ], + "angle": 0, + "content": "3.2.2 Query & Retrieval. Meanwhile, LLM can be applied to querying and retrieval to enhance information retrieval accuracy under the ST context. By leveraging their advanced natural language understanding capabilities, LLMs can process user queries in a more contextual and semantically rich manner, enabling precise retrieval of relevant information from structured and unstructured data sources. For instance, UrbanLLM [47] finetunes LLMs for urban activity planning and management, which serves as a problem solver that decodes urban-related queries into several sub-tasks, with each one solved by suitable spatio-temporal AI models. Alamsyah et al. [2] propose an automated smart city planning system that utilizes a personalized LLM with Retrieval Augmented Generation (RAG) [30] to generate tailored urban planning recommendations while ensuring data privacy, where RAG is used to retrieve relevant urban planning documents for context-aware responses. Another line of work [67, 75, 170, 179] utilizes Multimodal LLM for cross-modal information retrieval to enhance urban computing tasks." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.573, + 0.482, + 0.739 + ], + "angle": 0, + "content": "3.2.3 Data Integration. Data integration seeks to combine information from disparate sources, often necessitating the understanding and mapping of relationships between entities in heterogeneous datasets. LLMs are increasingly being employed in this domain, particularly for knowledge graph construction [24], where they automate and enhance the extraction, integration, and reasoning of related data. In the context of ST data, LLMs facilitate data integration by leveraging heterogeneous urban data sources, performing relational triplet extraction, and completing knowledge graphs through geospatial reasoning [94, 106]. A pioneering study UrbanKGent [105] proposes an LLM-based Agent framework to automate the process of urban knowledge graph construction." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.753, + 0.368, + 0.769 + ], + "angle": 0, + "content": "3.3 Spatio-Temporal Data Mining" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.772, + 0.482, + 0.895 + ], + "angle": 0, + "content": "Unlike traditional data mining, which primarily focuses on structured datasets, ST data mining captures intricate spatial and temporal dependencies within ST data using machine learning or deep learning techniques [51, 129, 167]. With the emergence of FMs and LLMs, Spatio-Temporal Foundation Models (STFMs) offer new possibilities by integrating perception, optimization, and reasoning capabilities to enhance ST data mining. In this section, we explore these key capabilities, while their specific applications across different domains are detailed in Sec. 3.4." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.108, + 0.913, + 0.218 + ], + "angle": 0, + "content": "3.3.1 Perception. In STFMs, perception encompasses the ability to effectively model, interpret, and generalize complex spatial and temporal patterns, enabling a deeper understanding of dynamic environments. This capability can be categorized into two key perspectives. The first view pertains to an agent's ability to perceive and understand its surrounding environment, capturing visual or contextual interactions within real-world scenarios such as smart cities [151], indoor activities [152, 153], and mobile Apps [127]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.219, + 0.913, + 0.508 + ], + "angle": 0, + "content": "The second aspect involves interpreting and extracting ST patterns from sensor data, ensuring accurate predictions across diverse domains. Domain-agnostic approaches, such as STEP [117] and GPT-ST [74], have employed pretraining strategies that leverage historical observations to enhance forecasting performance. In urban computing, models like TFM [130] and OpenCity [72] utilize graph-based FMs to analyze behaviors and interactions within transportation systems, yielding promising results in traffic prediction. In climate science, Pangu [9], trained on 39 years of global climate data, delivers superior deterministic forecasting outcomes across all evaluated variables when compared to leading numerical weather prediction systems. Additional notable examples in this area include the works [60, 76, 104, 108]. Despite these advances, achieving robust generalization remains a critical challenge, as most existing research has been confined to in-domain applications. While models like UniST [158] are designed as one-for-all solutions for diverse ST scenarios, their training datasets and evaluation testbeds are predominantly limited to transportation. Nevertheless, their underlying technique stacks show promise for broader cross-domain and cross-modality generalization. Other significant contributions in this realm include UniFlow [159] and UrbanDiT [160]." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.509, + 0.913, + 0.605 + ], + "angle": 0, + "content": "3.3.2 Optimization. Building upon the perceptual foundations, the optimization ability focuses on refining and adapting models to achieve specific, task-oriented objectives. In other words, models are not only expected to capture rich ST patterns but also to drive actionable decision-making in dynamic, real-world scenarios. This involves integrating advanced optimization strategies that tailor model behavior to the unique demands of applications." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.606, + 0.913, + 0.895 + ], + "angle": 0, + "content": "A prominent approach involves agent-based frameworks. For example, in traffic signal control, traditional methods (e.g., RL) are now augmented by frameworks that use LLMs as decision-making agents [61]. These systems leverage real-time traffic data and expert prompts to enable human-like planning, resulting in more adaptive and interpretable control strategies. Similarly, CityGPT [35] decomposes ST analysis into specialized sub-tasks, handled by temporal, spatial, and fusion agents, to efficiently process IoT data and generate insightful visualizations. AgentMove [28] addresses human mobility prediction by breaking down the task into modules for individual pattern mining, urban structure analysis, and collective behavior extraction. In geo-science, systems like Geode [38] integrate explicit optimization modules with ST data retrieval and machine learning inference to tackle zero-shot geospatial QA with enhanced precision. In urban planning, an innovative work [185] simulates planners and residents by LLM agents and enables their interactions to optimize inclusive land-use plans efficiently. Despite these promising developments, significant challenges remain. Seamlessly integrating perceptual capabilities with targeted optimization strategies is crucial for next-generation ST models that are both versatile and effective across diverse operational contexts." + } + ], + [ + { + "type": "header", + "bbox": [ + 0.084, + 0.076, + 0.447, + 0.088 + ], + "angle": 0, + "content": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey" + }, + { + "type": "header", + "bbox": [ + 0.685, + 0.076, + 0.914, + 0.088 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "table_caption", + "bbox": [ + 0.269, + 0.105, + 0.726, + 0.118 + ], + "angle": 0, + "content": "Table 2: Summary of representative FMs tailored for ST data science." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.121, + 0.913, + 0.372 + ], + "angle": 0, + "content": "
StageTask & CapabilityExampleMethodCategoryVenueYear
SensingReal-World Data SensingIdentifying Citizen-Related Issues from Social Mediados Santos et al. [27]LLMCAiSE2024
Real-World Data SensingIntelligent Crowdsensing CoordinationAutoWebCrowds [190]LLMICWE2024
Synthetic Data GenerationTrajectories GenerationTrajectory-LLM [154]LLMICLR2025
Synthetic Data GenerationHuman Activity Data GenerationLLMob [126]LLMNeurIPS2024
ManagementData CleaningFew-Shot Learner for Filling Missing ValuesNuwaTS [17]PFMPreprint2024
Data CleaningTrajectory RecoveryPLMTrajRec [135]LLMPreprint2024
Data CleaningAugment Additional Views of DataUrbanCLIP [150]LLMWWW2024
Query & RetrievalAutonomous Query Processor for Urban ManagementUrbanLLM [47]LLMEMNLP2024
Data IntegrationUrban Knowledge Graph ConstructionUrbanKGent [105]LLMNeurIPS2024
MiningPerceptionUnderstand the EnvironmentMagma [152]PFMCVPR2025
PerceptionInterpret and Extract ST PatternsSTEP [117]PFMKDD2022
OptimizationDrive Actionable Decision-Making in Dynamic ScenariosAgentMove [28]LLMPreprint2024
OptimizationOptimize Land-Use Plans by LLM AgentsZhou et al. [185]LLMPreprint2024
ReasoningCommon-sense ReasoningCausal-VidQA [66]PFMCVPR2022
ReasoningNumerical ReasoningUrbanGPT [73]LLMKDD2024
ReasoningCausal ReasoningNuwaDynamics [128]PFMICLR2024
ApplicationForecastingGlobal Weather ForecastingPangu [9]PFMNature2023
ImputationGenerative Adversarial Network for Traffic Data ImputationSTGAN [162]PFMIEEE TBD2022
Anomaly DetectionTransformer-based Anomaly DetectorXu et al. [145]PFMICLR2022
Event AnalysisDetecting and Interpreting EventsLAMP [120]LLMNeurIPS2023
Physical GroundingGeo-localizationGeoGPT [174]LLMJAG2023
Decision MakingTransportation Analytics and ControlTrafficGPT [168]LLMTransport Policy2024
Scenario SimulationSimulation of Human BehaviorPark et al. [107]LLMUIST2023
" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.38, + 0.482, + 0.45 + ], + "angle": 0, + "content": "3.3.3 Reasoning. While current ST models have demonstrated notable success in recognition and agent-based tasks, their reasoning and cognitive capabilities remain underdeveloped compared to advanced systems like DeepSeek-R1 [36]. To progress toward ST general intelligence, we identify three key aspects of reasoning:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.452, + 0.483, + 0.547 + ], + "angle": 0, + "content": "- Common-sense Reasoning harnesses everyday knowledge and contextual cues to draw implicit inferences from complex data. For instance, Causal-VidQA [66] enables models to infer explanations, predict future states, and generate counterfactual scenarios in video question-answering, while SituatedGen [173] integrates geographical and temporal contexts to generate coherent and contextually plausible statements." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.548, + 0.483, + 0.618 + ], + "angle": 0, + "content": "- Numerical Reasoning involves interpreting and manipulating quantitative information to perform arithmetic operations, assess uncertainties, and discern relationships within ST data; for instance, STBench [69] evaluates these abilities in LLMs, while UrbanGPT [73] enhances ST forecasting with instruction tuning." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.618, + 0.483, + 0.687 + ], + "angle": 0, + "content": "- Causal Reasoning seeks to uncover cause-effect relations within ST data, crucial for robust and interpretable predictions. For example, NuwaDynamics [128] identifies causal regions and applies interventions to improve generalization, and GCIM [176] learns latent causal structures to disentangle spurious correlations." + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.452, + 0.483, + 0.687 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.689, + 0.483, + 0.732 + ], + "angle": 0, + "content": "Collectively, these dimensions offer a promising yet underexplored pathway toward achieving ST general intelligence, bridging the gap between pattern recognition and true cognitive understanding." + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.74, + 0.34, + 0.755 + ], + "angle": 0, + "content": "3.4 Downstream Applications" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.758, + 0.483, + 0.854 + ], + "angle": 0, + "content": "3.4.1 STFMs for Numerical Problems. ST data is predominately numeric in many real-world scenarios. Addressing these numeric challenges is critical for tasks like forecasting, imputation, and anomaly detection [52], which demand an accurate understanding of the physical world. STFMs excel in these areas by uncovering intricate patterns and dependencies, ultimately enabling more reliable data-driven decision-making." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.855, + 0.483, + 0.897 + ], + "angle": 0, + "content": "- Forecasting. Early forecasting approaches often relied on task-specific neural networks like STGNNs [51, 52, 110, 116], whereas recent developments have shifted toward universal forecasting [91," + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.38, + 0.915, + 0.518 + ], + "angle": 0, + "content": "137, 167]. For instance, GPT-ST [74] leverages pretraining on historical observations to boost predictive performance, while UniST [158] unifies multiple traffic prediction tasks within a single model by coupling sequence modeling with attention-based mechanisms. Building on this progress, ST-LLM [86] and STG-LLM [90] enhance traffic predictions by combining ST inputs with partially frozen large language models, and UrbanGPT [73] extends this paradigm further by employing ST instruction tuning to better align textual and ST data. Similar approaches have also been widely used in other domains, such as ClimaX [104], Geo-Bench [60], and Orca [76]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.518, + 0.915, + 0.698 + ], + "angle": 0, + "content": "- Imputation. This has likewise benefited from techniques that capture ST dependencies to accurately restore missing or corrupted data. For instance, NuwaTS [17] repurposes pretrained language models with contrastive learning and specialized patch embeddings (capturing missing patterns/statistics) to enable cross-domain time series imputation through a unified framework. STD-LLM [44] employs LLMs with spatial-temporal tokenizers and hypergraph learning modules to handle missing values in spatio-temporal data while capturing non-pairwise correlations through topology-aware node embeddings. DrIM [83] combines LLM-derived text representations (from masked tabular data conversions) with contrastive learning to measure similarities for nearest-neighbor imputation in heterogeneous datasets." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.699, + 0.915, + 0.893 + ], + "angle": 0, + "content": "- Anomaly Detection. Anomaly detection in ST data has advanced by leveraging models that learn the normal dynamics of ST systems to identify deviations indicative of abnormal events. Whereas prior methods relied on statistical thresholding and clustering to flag outliers, recent FMs learn robust ST representations to detect even subtle anomalies. For example, early attempts [26, 89, 186] investigate the feasibility of using LLMs for anomaly detection in time series data. SigLLM [3] employs GPT-series with signal-to-text conversion techniques, offering dual pipelines (anomaly prompting and deviation detection) for time series analysis through textual or visual representations of numerical data. AD-LLM [156] introduces a benchmark framework combining GPT-4's zero-shot reasoning with contrastive learning for anomaly context enrichment and automated model selection through chain-of-thought prompting." + } + ], + [ + { + "type": "header", + "bbox": [ + 0.085, + 0.076, + 0.314, + 0.087 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "header", + "bbox": [ + 0.82, + 0.076, + 0.913, + 0.088 + ], + "angle": 0, + "content": "Yuxuan Liang et al." + }, + { + "type": "text", + "bbox": [ + 0.083, + 0.107, + 0.485, + 0.164 + ], + "angle": 0, + "content": "- Others. Furthermore, FMs have demonstrated great potential in other numerical problems such as time series classification [18], geospatial prediction [39, 100], traffic speed inference [7], and socioeconomic indicator prediction [40, 142, 150]." + }, + { + "type": "text", + "bbox": [ + 0.083, + 0.175, + 0.483, + 0.314 + ], + "angle": 0, + "content": "3.4.2 STFMs for Inferential Problems. Inferential problems in ST data require the integration of both reasoning and understanding of environments. These problems involve high-level cognitive tasks where accurate representation of locations, movements, and environmental context is essential. Addressing such problems goes beyond numerical predictions — it necessitates answering critical inferential questions: What happened? Where is it? What to do? What if? FMs have shown their potential to enhance solutions for these challenges by leveraging their capacity to handle ST knowledge and interpret complex, unstructured data." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.321, + 0.483, + 0.461 + ], + "angle": 0, + "content": "\"What happened?\" - Event Analysis. Detecting events aims to recognize and explain significant events in time and space. Traditional models struggle with scalability, interpretability, and incorporating external knowledge. To this end, LAMP [120] integrates LLMs with event models, using abductive reasoning to suggest plausible causes for predicted events, retrieve supporting evidence, and rank predictions for improved accuracy. Meanwhile, LEAP [165] replaces GNNs and RNNs with LLMs by framing event detection as a question-answering task, predicting missing event components and forecasting future relations through self-attention mechanisms." + }, + { + "type": "text", + "bbox": [ + 0.083, + 0.467, + 0.483, + 0.897 + ], + "angle": 0, + "content": "\"Where is it?\"- Physical Grounding. Grounding ST models in real-world geographical contexts is essential for various applications such as geo-localization, map reconstruction, intelligent routing and navigation. Geo-localization aims to determine an object's location based on multimodal inputs, including images, text, and sensor data. By processing these cues in conjunction with map data, LLMs such as GPT-4o, DeepSeek [36], and GeoGPT [174] can infer geographic coordinates or identify specific locations described in natural language. Map reconstruction, on the other hand, involves creating or updating digital maps by synthesizing information from satellite imagery, sensor readings, and textual reports. LLMs contribute by interpreting and generating map content, correcting inaccuracies, and filling in missing details. For instance, MapGPT [14] employs language-guided updates, incorporating textual descriptions of environmental changes into existing map structures. In personalized routing, ItiNera [123] combines LLMs with spatial optimization to generate personalized \"Citywalk\" itineraries, providing user-specific and spatially coherent urban exploration; ChinaTravel [115] provides a benchmark for real-world Chinese travel planning, enabling scalable evaluation of constraint satisfaction and preference optimization while highlighting the strengths of neuro-symbolic agents. Navigation systems further benefit from LLMs' ability to understand contextual instructions, interpret user queries, and reason about dynamic environments. For example, NavGPT [182] and NavGPT-v2 [181] integrate natural language with real-time traffic and indoor video data to generate personalized and optimized routing solutions. By incorporating STFMs across these domains, physical grounding models facilitate more precise localization, efficient navigation, and adaptive urban mobility solutions, ultimately bridging the gap between digital intelligence and real-world spatial reasoning." + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.107, + 0.907, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.537, + 0.265, + 0.89, + 0.279 + ], + "angle": 0, + "content": "Figure 4: STFMs for addressing inferential problems." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.285, + 0.916, + 0.632 + ], + "angle": 0, + "content": "\"What to do?\" - Decision Making. Optimizing policies and real-time decision-making in dynamic environments based on inferential insights plays a crucial role in a wide range of applications, including traffic control, autonomous vehicles, and disaster response. In traffic control and management, LLMs improve adaptability and interpretability compared to traditional reinforcement learning approaches [61]. Additionally, they facilitate sim-to-real transfer by modeling real-world traffic dynamics, improving the reliability of traffic signal optimization [22]. Beyond signal control, models like TrafficGPT [168] integrate multimodal traffic data with structured reasoning to analyze, predict, and optimize traffic efficiency and safety in real time. In autonomous vehicles, STFMs contribute to decision-making through both direct and indirect mechanisms. Directly, models such as DDM-Lag [88] employ diffusion-based frameworks with Lagrangian safety enhancements and hybrid policy updates to refine policy articulation and ensure safety. Indirectly, STFMs enhance autonomous driving by predicting realistic driving behaviors [55, 114] and leveraging multi-modal perception to integrate sensor data, bird's eye view maps, and traffic contexts [20, 184], improving situational awareness and vehicle control. Beyond transportation, STFMs play a critical role in disaster management and emergency response by integrating diverse spatio-temporal data sources, such as weather forecasts, remote sensing, and social media signals, to predict disaster impacts and optimize evacuation strategies [16, 31, 65]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.633, + 0.916, + 0.897 + ], + "angle": 0, + "content": "\"What if?\"- Scenario Simulation. STFMs, with their advanced perception and reasoning capabilities, enable the development of STFM-based agents that integrate into Multi-Agent Systems (MAS) to model complex interactions across diverse domains [29]. In urban planning and social simulation, MAS facilitates participatory urban design by simulating interactions between planners and residents. For example, LLM-driven MAS has been used to collaboratively refine land-use plans, leading to improved accessibility and ecological outcomes that surpass human expert solutions [185]. Beyond urban planning, MAS contributes to social science research by modeling human-like behaviors in AI-driven networks. Studies such as [23, 107, 109] demonstrate that LLM-based agents can naturally develop social structures, providing valuable insights into emergent social dynamics. Beyond urban applications, MAS significantly advances game AI and strategic decision-making. Recent studies [112, 133, 187] highlight how MAS-powered reinforcement learning enables strategic gameplay, real-time opponent modeling, and interactive storytelling, fostering the development of more adaptive, intelligent, and realistic virtual agents." + } + ], + [ + { + "type": "header", + "bbox": [ + 0.084, + 0.076, + 0.447, + 0.088 + ], + "angle": 0, + "content": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey" + }, + { + "type": "header", + "bbox": [ + 0.685, + 0.076, + 0.914, + 0.088 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "title", + "bbox": [ + 0.083, + 0.106, + 0.356, + 0.122 + ], + "angle": 0, + "content": "4 The Methodology Perspective" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.125, + 0.482, + 0.208 + ], + "angle": 0, + "content": "As shown in Figure 5, we delve into STFMs from a methodology perspective, focusing on \\( i) \\) LLM-based models, which are widely applied across the entire workflow of \\( ST \\) data science by zero-shot utilization or fine-tuning and \\( ii) \\) PFM-based models, i.e., pretraining FMs from scratch, which is mainly utilized for \\( ST \\) data mining. The comparison between them can be found in Appendix C." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.216, + 0.476, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.489, + 0.476, + 0.503 + ], + "angle": 0, + "content": "Figure 5: A method-centric taxonomy. Full version: Fig. 7." + }, + { + "type": "title", + "bbox": [ + 0.083, + 0.516, + 0.373, + 0.532 + ], + "angle": 0, + "content": "4.1 Large Language Models (LLM)" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.535, + 0.483, + 0.646 + ], + "angle": 0, + "content": "4.1.1 Zero-shot Learner. LLMs exhibit strong reasoning and contextual understanding capabilities, making them highly effective across various ST tasks, including data sensing, management, and mining. As shown in Appendix B, they can function as augmenters, predictors, or agents. To ease the presentation, we adopt a broad definition of LLMs, encompassing standard LLMs, Vision-Language Models (VLM), and Multimodal LLMs (MLLM). The zero-shot utilization of LLMs can be categorized into two primary classes." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.647, + 0.483, + 0.897 + ], + "angle": 0, + "content": "- Prompt Engineering. When taking LLMs as zero-shot predictors [33, 53, 125] or data augmenters [150] for various tasks, prompt engineering plays an essential role in shaping model outputs. Below, we summarize key aspects for prompt engineering in current research: a) Prompt Construction: A well-designed prompt typically contains key elements like Task Instruction, Tokenization, and Few-shot Examples. Task instruction [53, 147, 149] aims to explicitly guide LLMs to execute specific operations, incorporating domain knowledge [157] if applicable. Tokenization [33, 53] is crucial to aligning ST data formats with LLM input structures. Additionally, presenting a small number of annotated examples [175] facilitates in-context learning, enabling LLMs to better generalize to complex tasks while ensuring output consistency and adherence to the expected format. b) Prompt Learning: [73, 148] Also known as instruction-tuning, this method learns prompts dynamically rather than relying on manually crafted ones. By optimizing prompt structures during training, it provides a flexible and efficient way to adapt LLMs to new tasks without altering their underlying model weights." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.107, + 0.915, + 0.177 + ], + "angle": 0, + "content": "c) Chain-of-Thought (CoT) Prompting: CoT [87, 175] enhances LLMs' reasoning capabilities by guiding them through step-by-step logical progression. This method improves their ability to tackle complex spatio-temporal tasks, ensuring more interpretable, structured, and accurate outputs in decision-making processes." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.179, + 0.915, + 0.47 + ], + "angle": 0, + "content": "- Agentic Engineering. The emergence of LLM-based agents [49, 144, 168, 174, 185] with reasoning, memory and tool-calling capabilities is transforming ST data science, enabling more adaptive and autonomous decision-making. When designing agent-based solutions, existing works primarily consider the following key aspects: a) Role Assignment. [50, 144, 174] clearly specify the responsibilities and functional boundaries of each agent within the system. b) Memorization [64, 174] refers to the agent's capability to store, recall, and leverage past information and context during task execution. A basic approach involves embedding past interactions into prompts, while more advanced techniques like Retrieval-Augmented Generation (RAG) [143, 155] dynamically retrieve relevant information from external knowledge bases, incorporating only the most pertinent content into the prompt. c) Tool Definition [168, 174], which identify and integrate various tools and functionalities that an agent can call upon to solve complex tasks. In ST data science, various expert models like STGNNs [51] can be wrapped as a tool and added into the agent in a plug-and-play manner. d) Multi-Agent System. Deploying multiple specialized agents to work collaboratively (each with distinct roles) enhances the efficiency and robustness of solutions for intricate ST challenges [49, 63, 185]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.478, + 0.915, + 0.547 + ], + "angle": 0, + "content": "4.1.2 Supervised Fine-Tuning for LLMs. Fine-tuning adapts LLMs to ST tasks by adjusting their parameters based on domain-specific datasets, sometimes incorporating additional modalities such as texts [79, 150] and vision [180]. We categorize fine-tuning methods into three approaches based on the extent of parameter updates:" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.55, + 0.913, + 0.618 + ], + "angle": 0, + "content": "- Full Parameter Fine-Tuning [68, 98, 100, 104, 108] updates all model parameters based on downstream ST datasets, achieving maximal adaptation to specific tasks. However, it requires substantial labeled data and high computational resources, making it impractical for many real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.62, + 0.913, + 0.701 + ], + "angle": 0, + "content": "- Partial Parameter Fine-tuning. To reduce computational overhead, this method [13, 183] freezes most parameters, such as attention weights, while fine-tuning only a small subset (e.g., position encodings and layer normalization). However, modifying a subset of parameters can disrupt the LLM's learned representations, leading to catastrophic forgetting of general knowledge." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.703, + 0.914, + 0.896 + ], + "angle": 0, + "content": "- Add-on Parameter Fine-Tuning. To mitigate forgetting while maintaining efficiency, this technique [61] introduces trainable low-rank matrices (e.g., LoRA [42]), while keeping the original LLM weights frozen. This strategy preserves pretrained knowledge while enabling efficient adaptation to ST tasks. Besides fine-tuning LLMs' weights, another way is training additional layers for input tokenization or task adaption. For instance, TimeLLM [53] trains a self-attention layer that aligns patched time series representations with pretrained text prototype embeddings. Similarly, Time-VLM [180] trains a memory-enhanced attention to capture both short- and long-term dependencies. For task adaption, existing methods typically train an additional prediction head (e.g., linear layers) to project the LLM's output embeddings into a domain-specific space [53, 180]." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.55, + 0.914, + 0.896 + ], + "angle": 0, + "content": null + } + ], + [ + { + "type": "header", + "bbox": [ + 0.084, + 0.076, + 0.314, + 0.088 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "header", + "bbox": [ + 0.82, + 0.076, + 0.913, + 0.088 + ], + "angle": 0, + "content": "Yuxuan Liang et al." + }, + { + "type": "title", + "bbox": [ + 0.083, + 0.106, + 0.428, + 0.121 + ], + "angle": 0, + "content": "4.2 Pretrained Foundation Models (PFM)" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.124, + 0.483, + 0.207 + ], + "angle": 0, + "content": "Unlike LLMs, which build STFMs by directly using or fine-tuning LLMs, PFMs are developed from scratch, independent of existing LLMs. This approach enables domain-specific optimization, allowing models to better capture ST dependencies from cross-domain ST data without constraints imposed by linguistic priors. Following this, we examine PFMs through three key dimensions:" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.212, + 0.483, + 0.255 + ], + "angle": 0, + "content": "4.2.1 Neural Architecture. The architecture of PFMs is a fundamental design choice that directly influences their capabilities, efficiency, and adaptability in ST tasks, which can be categorized into:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.258, + 0.483, + 0.313 + ], + "angle": 0, + "content": "- Transformer-based PFMs. Transformers have been the predominant architecture choice for building PFMs thanks to its powerful sequential modeling ability introduced by the self-attention mechanism [7, 72, 77, 85, 158]." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.314, + 0.483, + 0.397 + ], + "angle": 0, + "content": "- Diffusion-based PFMs. Diffusion-based models have recently emerged as a powerful approach for ST representation learning [12, 21, 136, 160, 161, 188], particularly in generative and predictive modeling. These models iteratively learn to reverse a stochastic noise process, enabling them to generate high-fidelity spatio-temporal sequences with strong generalization properties." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.397, + 0.483, + 0.452 + ], + "angle": 0, + "content": "- Graph-based PFMs. Unlike sequential models, GNNs excel at representing spatially structured data such as road networks. [62, 130] build FMs based on graph neural networks to learn the complex correlation between different entities in ST applications." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.452, + 0.483, + 0.507 + ], + "angle": 0, + "content": "- Others. Another emerging class of PFMs is State Space Model (SSM)-based models [8, 43, 97], which construct PFMs using structured state-space representations. Meanwhile, several studies utilize CNNs [118] as backbones for developing PFMs." + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.258, + 0.483, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.515, + 0.483, + 0.723 + ], + "angle": 0, + "content": "4.2.2 Pretraining Scheme. To enhance generalization ability, PFMs are usually pretrained based on cross-domain datasets [91, 137, 158], enabling them to learn diverse ST patterns across multiple domains. Existing pretraining schemes of PFMs can be classified into three types based on the training objectives: a) Generative Pretraining [85, 98, 130, 138, 189] focuses on reconstructing input data by learning its underlying distribution, enabling the model to generate realistic time series or ST data, while b) Contrastive Pretraining [7, 84, 171] emphasize distinguishing between similar and dissimilar data pairs to learn robust representations by maximizing agreement between augmented views of the same sample. It is particularly effective in multimodal ST learning, aligning heterogeneous data sources such as satellite imagery and its text description. c) Hybrid Pretraining [77] integrates both generative and contrastive objectives, leveraging their complementary strengths." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.727, + 0.483, + 0.769 + ], + "angle": 0, + "content": "4.2.3 Data Modality. ST data manifests in various modalities, each characterized by unique properties (see Section 2), necessitating the development of modality-specific STFMs:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.771, + 0.483, + 0.897 + ], + "angle": 0, + "content": "- Location. PFMs for location data [7, 40, 71, 124, 138, 150, 171] aim to learn general embedding for geographical entities. For instance, GeoVectors [124] and SpaBERT [71] learn location embeddings based on open-source data such OpenStreetMap, while G2PTL [138] learns from massive logistics delivery data. Notably, there is a noticeable trend that leverages multi-modalities (such as satellite image and text) for comprehensive location embeddings. For example, both UrbanCLIP [150], UrbanVLP [40], and ReFound [142] utilize satellite images for urban region profiling." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.103, + 0.905, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.276, + 0.913, + 0.291 + ], + "angle": 0, + "content": "Figure 6: Representative PFMs for different types of ST data." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.295, + 0.916, + 0.461 + ], + "angle": 0, + "content": "- Trajectory & Event. PFMs for trajectory/event data [21, 84, 85, 103, 121, 189] are designed to learn general sequential patterns from inputs. A pioneering effort in this direction is TrajFM [85], which introduces a trajectory FM capable of supporting both regional and task transferability. Pretrained on vehicle trajectories from multiple cities, TrajFM employs a trajectory-masking and autoregressive recovery mechanism to enhance its learning capabilities. To tackle the limited resources of cross-domain trajectories, UniTraj [189] curates a billion-scale mobility dataset spanning diverse geographic regions to facilitate the advancement of trajectory-based FMs. For event data, MOTOR [121] proposes a time-to-event FM for structured medical records." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.461, + 0.915, + 0.627 + ], + "angle": 0, + "content": "- ST Raster. PFMs for ST raster data [10, 15, 98, 104, 108, 117, 160] organize spatial information in a grid-like format, with a typical applied domain being weather/climate forecasting. For instance, W-MAE [98] trains a mask autoencoder for ST grid forecasting. CimaX [104] develops a general-purpose climate foundation model, pretrained on diverse datasets spanning various variables, ST scales, and physical contexts. Pangu [10] is trained on 39 years of global climate data, which achieves superior forecasting performance compared to leading numerical weather prediction systems. UniST [158] first pretrains the model in various ST raster data via masked pretraining, and then proposes a learnable ST prompt to enhance the model's generalization ability." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.628, + 0.915, + 0.724 + ], + "angle": 0, + "content": "- ST Graph. PFMs for ST graph data [62, 72, 93, 111, 117, 134] learn the ST dependencies from ST graphs that generalize effectively in unseen spatial and temporal contexts. Unlike ST Raster PFMs, there are limited works in this area, which is more challenging due to the complex graph correlation. One representative is OpenCity [72] for ST graph forecasting, which integrates Transformer and GNN to model the ST dependencies in traffic data." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.295, + 0.916, + 0.724 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.728, + 0.82, + 0.741 + ], + "angle": 0, + "content": "5 Conclusion and Future Directions" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.744, + 0.916, + 0.897 + ], + "angle": 0, + "content": "The rapid advancement of FMs has transformed ST data science, impacting sensing, management, and mining. This survey provides a comprehensive review of FMs for ST data science, identifying key capabilities such as perception, reasoning, and optimization while exploring diverse downstream tasks and datasets. We also establish a systematic taxonomy of methodologies, enhancing understanding of how STFMs model ST data. Despite progress, challenges remain in generalization, interpretability, and efficiency. By consolidating recent advances and outlining future directions (see Appendix A), this survey aims to inspire further innovations, driving the development of scalable and adaptive STFMs for real practice." + } + ], + [ + { + "type": "header", + "bbox": [ + 0.085, + 0.076, + 0.447, + 0.088 + ], + "angle": 0, + "content": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey" + }, + { + "type": "header", + "bbox": [ + 0.685, + 0.076, + 0.914, + 0.088 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "title", + "bbox": [ + 0.085, + 0.106, + 0.178, + 0.12 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.124, + 0.483, + 0.154 + ], + "angle": 0, + "content": "[1] Oluwanifemi Adebayo Moses Adekanye. 2024. LIm-powered synthetic environments for self-driving scenarios. 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Conversational Crowdsensing: A Parallel Intelligence Powered Novel Sensing Approach. arXiv preprint arXiv:2402.06654 (2024)." + }, + { + "type": "list", + "bbox": [ + 0.085, + 0.109, + 0.484, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.485, + 0.424, + 0.502 + ], + "angle": 0, + "content": "A Limitations and Future Opportunities" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.504, + 0.482, + 0.546 + ], + "angle": 0, + "content": "We further discuss the potential limitations of current research and identify several key future directions aimed at advancing the development of more powerful, transparent, and reliable STFMs:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.548, + 0.483, + 0.7 + ], + "angle": 0, + "content": "- The curse of accuracy against interpretability. We have identified a significant challenge in developing FMs for addressing numerical problems in ST data science. Directly leveraging LLMs for numerical tasks such as forecasting proves to be non-trivial [34]. Meanwhile, fine-tuning LLMs or training STFMs from scratch using large-scale, cross-domain ST data often comes at the cost of interactive capabilities, thereby hindering interpretability in the prediction outcomes. These limitations motivate us to explore a novel paradigm that not only retains strong numerical reasoning abilities but also enhances interpretability, bridging the gap between predictive accuracy and explanatory insight." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.7, + 0.483, + 0.852 + ], + "angle": 0, + "content": "- Large foundation models are all we need? While the extensive parameterization of FMs enables impressive generalization capabilities, particularly in zero/few-shot settings, their superiority over smaller expert models remains context-dependent. In ST domains such as time series analysis [122] and urban planning [57], smaller expert models often outperform FMs when provided with sufficient domain-specific training data. This raises fundamental questions about the trade-offs between model scalability, efficiency, and task-specific optimization. Future research should delve into hybrid approaches that combine the adaptability of large models with the precision of expert models." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.852, + 0.482, + 0.894 + ], + "angle": 0, + "content": "- One-fit-all FMs across the full workflow. While current FMs are typically designed to support only specific stages of ST data science, we envision a more unified FM capable of seamlessly" + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.548, + 0.483, + 0.894 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.107, + 0.916, + 0.177 + ], + "angle": 0, + "content": "spanning the entire workflow, from initial data sensing and management to mining and supporting downstream applications. Achieving this goal will likely require the development of advanced LLM agents that can function as full-stack engineers (i.e., strongly benefiting all stages) for ST data science." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.177, + 0.916, + 0.302 + ], + "angle": 0, + "content": "- Integrating STFMs with multimodal understanding. While current STFMs excel in processing structured ST data, their ability to integrate and reason over multimodal information, including text, images, video, and sensor data, remains underdeveloped. Many tasks require models to jointly interpret geospatial context, temporal dynamics, and text descriptions. Future research can focus on designing multimodal STFMs that effectively align, fuse, and reason over heterogeneous data sources, enabling more context-aware and human-interpretable decision-making." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.313, + 0.791, + 0.327 + ], + "angle": 0, + "content": "B Zero-shot Utilization of LLMs" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.331, + 0.912, + 0.345 + ], + "angle": 0, + "content": "There are three ways of directly using LLMs for various ST tasks:" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.348, + 0.915, + 0.445 + ], + "angle": 0, + "content": "- LLM-as-Augmenter. Pretrained LLMs can enhance both data understanding and model performance. On the one hand, it can serve as the input augmenter, which enhances data interoperability or provides external information [40, 79] (e.g., textual or visual). On the other hand, LLMs can serve as a parameter-frozen model component [102, 150, 166], thus augmenting domain models by injecting the pretrained external knowledge in LLMs." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.445, + 0.915, + 0.514 + ], + "angle": 0, + "content": "- LLM-as-Predictor. LLMs can be directly employed as predictors [33, 53, 73, 125] for various tasks. Due to the modality gap between text and ST data, preprocessing is required to fit the input spaces of LLMs. Such step typically contains prompt engineering [73, 125, 147-149] or patch & tokenization [53]." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.514, + 0.915, + 0.624 + ], + "angle": 0, + "content": "- LLM-as-Agent. LLM-based agents are typically equipped with the ability to memorize and call various tools. When applied to ST data science, various domain-expert models can be wrapped as a tool and added into the agent in a plug-and-play manner [144, 168, 174]. As such, LLM serves as a router to access different models with both flexibility and performance guarantees. Furthermore, multi-agent systems [185] can be built to solve more complex tasks in the ST domain." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.348, + 0.915, + 0.624 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.636, + 0.855, + 0.652 + ], + "angle": 0, + "content": "C Comparison between LLMs and PFMs" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.655, + 0.915, + 0.738 + ], + "angle": 0, + "content": "Table 3 demonstrates the comparison between LLMs and PFMs on their capabilities, including perception, optimization, and reasoning. For example, PFMs excel in exceptional numerical reasoning abilities, yet they often struggle with common-sense understanding. There is still no free lunch, and the user can choose either LLMs or PFMs according to the downstream applications." + }, + { + "type": "table_caption", + "bbox": [ + 0.515, + 0.751, + 0.915, + 0.779 + ], + "angle": 0, + "content": "Table 3: A capability comparison between LLMs and PFMs for ST data science." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.793, + 0.908, + 0.891 + ], + "angle": 0, + "content": "
CapabilitiesLarge Language Models (LLMs)Pretrained Foundation Models (PFMs)
Perception▲ Limited native ST perception; can be enhanced via fine-tuning✓ Strong ST perception, integrating sensor data and domain-specific learning
Optimization✓ Agent-based reasoning for decision-making; relies on prompting and heuristics▲ Limited; lacks decision-making ability for control and planning
Common-sense Reasoning✓ Strong via pretraining on vast textual data; can be enhanced with fine-tuning▲ Limited; relies on structured ST data rather than broad world knowledge
Numerical Reasoning▲ Handles arithmetic but struggles with structured ST computations✓ Designed for numerical problems, e.g., forecasting, anomaly detection
Causal Reasoning▲ Can infer causal relations from text but lacks structured ST modeling✓ Built-in graph-based and ST causal modeling
" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.085, + 0.076, + 0.314, + 0.088 + ], + "angle": 0, + "content": "Conference'17, July 2017, Washington, DC, USA" + }, + { + "type": "header", + "bbox": [ + 0.82, + 0.076, + 0.913, + 0.088 + ], + "angle": 0, + "content": "Yuxuan Liang et al." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.104, + 0.913, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.311, + 0.493, + 0.687, + 0.508 + ], + "angle": 0, + "content": "Figure 7: Taxonomy from the methodology perspective." + } + ] +] \ No newline at end of file diff --git a/data/2025/2503_13xxx/2503.13502/db12ade8-3943-4647-bb0d-ce8160710750_origin.pdf b/data/2025/2503_13xxx/2503.13502/db12ade8-3943-4647-bb0d-ce8160710750_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8a9279f518b89ea7231843d80dba89fe9abd3f55 --- /dev/null +++ b/data/2025/2503_13xxx/2503.13502/db12ade8-3943-4647-bb0d-ce8160710750_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:921bec8beb6829b7708e9c18780360a634a628e54bf7c721c7c3d8e09a19da6d +size 3508704 diff --git a/data/2025/2503_13xxx/2503.13502/full.md b/data/2025/2503_13xxx/2503.13502/full.md new file mode 100644 index 0000000000000000000000000000000000000000..11e9de6545465a37851496e82bbcaeb79d20df51 --- /dev/null +++ b/data/2025/2503_13xxx/2503.13502/full.md @@ -0,0 +1,442 @@ +# Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey + +Yuxuan Liang $^{1}$ , Haomin Wen $^{2,1}$ , Yutong Xia $^{3}$ , Ming Jin $^{4}$ , Bin Yang $^{5}$ , Flora Salim $^{6}$ , Qingsong Wen $^{7}$ , Shirui Pan $^{4}$ , Gao Cong $^{8}$ + +1The Hong Kong University of Science and Technology (Guangzhou) 2Carnegie Mellon University 3National University of Singapore 4Griffith University 5East China Normal University 6University of New South Wales 7Squirrel AI Learning, USA 8Nanyang Technology University {yuxiang,yutong.x}@outlook.com,{wenhaomin.whm,mingjinedu,qingsongedu}@gmail.com flora.salim@unsw.edu.au,byang@dase.ecnu.edu.cn,s.pan@griffith.edu.au,gaocong@ntu.edu.sg + +# Abstract + +Spatio-Temporal (ST) data science, which includes sensing, managing, and mining large-scale data across space and time, is fundamental to understanding complex systems in domains such as urban computing, climate science, and intelligent transportation. Traditional deep learning approaches have significantly advanced this field, particularly in the stage of ST data mining. However, these models remain task-specific and often require extensive labeled data. Inspired by the success of Foundation Models (FM), especially large language models, researchers have begun exploring the concept of Spatio-Temporal Foundation Models (STFMs) to enhance adaptability and generalization across diverse ST tasks. Unlike prior architectures, STFMs empower the entire workflow of ST data science, ranging from data sensing, management, to mining, thereby offering a more holistic and scalable approach. Despite rapid progress, a systematic study of STFMs for ST data science remains lacking. This survey aims to provide a comprehensive review of STFMs, categorizing existing methodologies and identifying key research directions to advance ST general intelligence. + +# 1 Introduction + +Humans live in a world shaped by the dynamic interplay of countless elements across space and time. Spatio-Temporal (ST) Data, which refer to data that encapsulate ST phenomena, track the evolution of objects or events across locations and time [5], such as meteorological records, traffic patterns, and human traces. These data are frequently sourced from a wide array of platforms, ranging from IoT devices, GPS sensors, social media, to remote sensing. + +Within this context, Spatio-Temporal Data Science focuses on sensing, managing, and mining these datasets to uncover patterns, understand complex systems, and predict future dynamics. Motivated by its transformative potential, this field addresses critical challenges across urban environments and even the entire planet, enabling decision-making and fostering innovations that contribute to building smarter, more sustainable, and resilient systems [178]. + +Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. + +Conference'17, July 2017, Washington, DC, USA + +© 2025 Copyright held by the owner/author(s). Publication rights licensed to ACM. + +ACM ISBN 978-x-xxxxx-xxxxx-x/YY/MM + +https://doi.org/10.1145/nnnnnnn.nnnnnnn + +![](images/585a84a4e1c2d564b53b7198e4a5ac28aaf09f4523682713f3c283074ed415a4.jpg) +Figure 1: ST Foundation Models (STFM), which include LLM and PFM, are pretrained with or applied to diverse ST data, with the abilities of perception, optimization, and reasoning. STFMs can, in turn, enhance each stage of ST data science. + +In the era of deep learning, the community has primarily concentrated on spatio-temporal representation learning, as a fundamental step of ST data mining [129]. Key advancements include the development of Spatio-Temporal Graph Neural Networks (STGNN) [51] and transformer-based architectures, which have shown remarkable success in tasks such as traffic forecasting [80, 146], air quality prediction [82], and human mobility analytics [132]. STGNNs integrate Graph Neural Networks (GNN) with temporal learning modules (e.g., GRU [6, 70], TCN [140, 141]) to model ST correlations, while transformer models leverage self-attention mechanisms [37, 78, 177] to process complex dependencies across space and time. Additionally, there has been significant research on self-supervised learning [46, 74, 92], where models are trained to extract powerful representations with minimal reliance on large annotated datasets. + +Driven by the success of Foundation Models (FM), especially Large Language Models (LLM), researchers have recently begun exploring the concept of Spatio-Temporal Foundation Models (STFM) [32, 81, 169]. By harnessing LLMs, it becomes possible to develop more generalized, adaptable solutions that can be fine-tuned for specific tasks with minimal data. Another prominent approach involves pretraining FMs (denoted as PFM) on cross-domain ST data and adapting them for particular domains. In contrast to previous architectures (e.g., STGNNs), STFMs integrates the capabilities of perception, reasoning and optimization, which not only promises to revolutionize ST data mining, but also empowers other stages of ST data science, such as ST data sensing and management (See Figure 1). This shift has the potential to enhance the scalability and efficiency of ST applications, offering a more holistic approach to addressing challenges in urban computing, climate science, etc. + +Table 1: Our survey vs. related surveys on FMs for learning ST data, such as locations (L), trajectories (T), events (E), ST rasters (R), and ST graphs (G). The applications (App.) include numerical (N) and inferential (I) problems. + +
SurveyYearVenueSensingManage.MiningApp.Data
Jin et al. [54]2023-✓NR,G
Jiang et al. [48]2024IJCAI✓NR,G
Liang et al. [81]2024KDD✓NT,E,R,G
Zhang et al. [169]2024KDD✓N,IL,T,E,R,G
Goodge et al. [32]2025-✓NT,E,R,G
Ours2025-✓✓✓N,IL,T,E,R,G
+ +Despite their rapid advancements, a systematic analysis of STFMs across the entire workflow of ST data science remains lacking. First, prior surveys have primarily focused on utilizing LLMs as the key tool for ST data mining [32, 54, 81, 169], leaving a significant gap in understanding how these models can be integrated throughout the entire process, i.e., with less focus placed on their role in the earlier stages of sensing and management. Second, they predominantly examine the applications of STFMs to numerical problems (e.g., forecasting, imputation) while overlooking their role in inferential problem-solving such as decision-making systems. + +To bridge these gaps, this paper aims to provide a more comprehensive survey of STFMs across all stages of ST data science, spanning data sensing, management, and mining (see Figure 1). For example, LLMs can enhance ST data sensing by actively processing citizen reports, optimizing participatory sensing strategies, and generating synthetic data at scale. In terms of data management, they can automate data cleaning tasks, construct meaningful knowledge graphs for data integration, and facilitate more efficient retrieval of cross-modal datasets. Beyond these stages, our survey also explores how STFMs support a broader range of downstream applications, including numerical and inferential problems. Through this endeavor, we seek to illuminate an overall vision of STFMs, thereby enhancing comprehension regarding their potential to optimize ST data science, fostering more integrated and adaptable solutions. + +Meanwhile, we systematically investigate the key methodologies of STFMs for modeling a variety of ST data. We begin by categorizing existing STFMs into two main classes: LLMs and Pretrained Foundation Models (PFMs). For LLMs, which are pretrained on linguistic data, we focus on their usage as a zero-shot [33] or few-shot learner [53, 73], where various prompting and fine-tuning strategies have been explored, respectively. For PFMs, which are trained from scratch based on cross-domain ST data [40, 158, 189], we examine their neural architectures, pretraining methods, and their adaptability to different types of ST data, including location data, trajectory data, events, ST raster data, and ST graph data. + +In summary, our major contributions lie in three aspects: + +- Comprehensive and up-to-date survey: We provide the first comprehensive and modern survey of FMs across the entire workflow of ST data science, covering data sensing, management, and mining. We also explore a broader range of downstream tasks and data types compared to most existing surveys (See Table 1). +- Vision and Methodologies: We propose a vision for STFMs, identifying key capabilities essential for their success, and discuss current methodologies for implementing these abilities in detail. +- Future directions: We highlight promising directions for advancing ST data science with foundation models, encouraging further research and exploration in this emerging field. + +Paper Organization. The remainder of this paper is organized as follows: Sec. 2 provides essential background on FMs and ST data. Sec. 3 and 4 present a taxonomy of STFMs regarding the workflow and methodologies, respectively. Sec. 5 offers concluding remarks, and Appendix A highlights promising avenues for future research. + +# 2 Background + +Foundation models. FMs are deep neural networks trained on vast datasets, enabling them to acquire broad, cross-domain knowledge and exceptional adaptability [45]. Unlike earlier task-specific models, FMs can be efficiently fine-tuned with relatively small amounts of task-specific data, offering remarkable flexibility, effectiveness, and cost efficiency. Pioneering attempts like BERT [58] and GPT-3 [11] have reshaped natural language processing. More recent models, e.g., GPT-4o [45] and DeepSeek-R1 [36], further push the frontiers of generative capabilities, enabling more nuanced reasoning, robust domain adaptation, and improved context-awareness in diverse tasks. In ST domains, recent FMs like Time-MoE [119], Chronos [4], and UniST [158] have made remarkable strides in time series analysis and universal ST forecasting, while UniTraj [189] serves as a versatile foundation for various trajectory-related tasks. Inspired by these successes, this survey delves into the utilization of FMs in the entire workflow of ST data science, covering data sensing, management, and mining. + +Formulation of Spatio-Temporal Data. ST data refer to datasets that integrate spatial (location-based) and temporal (time-based) information, capturing dynamic patterns and relationships over space and time. Figure 2 depicts the basic ST data structures discussed in this survey, including locations, trajectories, events, ST rasters, and ST graphs. Their definitions are delineated as follows. + +Definition 1 (Location). A location refers to a fixed spatial point or object in a geographical space, represented by the geospatial coordinates $l \in \mathbb{R}^2$ , i.e., latitude and longitude. It is often profiled by the corresponding satellite image, street-view image, and descriptions. + +Definition 2 (Trajectory). A trajectory is a sequence of time-ordered locations that describe the movements of an object in the geographical space. It can be formulated as $\mathcal{T} = p_1\rightarrow p_2\rightarrow \dots \rightarrow p_T$ where $p_i = (l_i,t_i)$ , and $l_{i}$ denotes the object's location at time $t_i$ . + +Definition 3 (Event). An event sequence is a series of timestamped events, denoted as $\mathcal{E} = v_{1}\rightarrow v_{2}\rightarrow \dots \rightarrow v_{T}$ , describing the progress of actions or occurrences, where $v_{i} = (e_{i},t_{i})$ and $e_i\in \mathbb{R}^d$ is an event and $t_i$ denotes the time when $e_i$ occurs. + +![](images/037cc7fecab764f3c9489d19c64e195a2e4237fe21b75687cf6cec155fb66656.jpg) +Figure 2: Illustration of various types of ST data. + +Definition 4 (Spatio-Temporal Raster). An ST raster can be denoted as $\mathcal{X} = < \mathbf{X}_1,\mathbf{X}_2,\dots ,\mathbf{X}_T > \in \mathbb{R}^{H\times W\times T\times D}$ , where $\mathbf{X}_t\in \mathbb{R}^{H\times W\times D}$ denotes the signals collected from $N = HW$ evenly distributed locations at time $t$ , each characterized by $D$ feature attributes. + +Definition 5 (Spatio-Temporal Graph). An ST graph extends the ST raster to be $X = < \mathbf{X}_1, \mathbf{X}_2, \ldots, \mathbf{X}_T > \in \mathbb{R}^{N \times T \times D}$ by explicitly incorporating spatial correlations with a graph $G_t = (V, E_t, \mathbf{A}_t)$ when $N$ locations are not uniformly distributed. Here $V$ is the set of nodes, $E_t$ is the set of edges, and $\mathbf{A}_t \in \mathbb{R}^{N \times N}$ is the adjacency matrix at time $t$ . The size of $V$ is usually static. + +# 3 The Workflow Perspective + +As shown in Figure 3, we examine STFMs from a holistic, bottom-up perspective, emphasizing their composition across four key aspects: + +- ST Data Sensing refers to the acquisition of data that varies over both space and time from diverse resources (e.g., sensors, satellites, social media), to capture dynamic environmental, geographic, or social phenomena. We also consider synthetic data generation for enhancing data diversity and quantity. +- ST Data Management focuses on storing, indexing, and organizing these large-scale, heterogeneous ST datasets, incorporating strategies like distributed architectures for efficient retrieval and integration. FMs can enhance this process by facilitating data cleaning, query & retrieval, and data integration. +- ST Data Mining involves learning and analyzing ST data that varies across both space and time to uncover patterns, trends, and relationships, using data mining (DM), deep learning (DL) techniques, or the newly-proposed STFMs with strong capabilities in perception, optimization, and reasoning. +- Downstream Applications: This stage harnesses the above insights from ST data to drive real-world applications, ranging from numerical problems to inferential problems, where informed actions and policies are formulated. + +By examining these four aspects, we can better understand how STFMs advance from raw data acquisition to high-level service providing, ultimately enabling more intelligent, adaptable, and impactful solutions. We will detail each stage in the following sections. + +![](images/7550fb89f980864400839d7d1a4cff676d111c15a655bac2fa282342c99fd317.jpg) +Figure 3: The framework of STFMs for ST data science. + +# 3.1 Spatio-Temporal Data Sensing + +FMs revolutionize ST data sensing from two complementary aspects: real-world data sensing, which involves collecting data from physical sources, and synthetic data generation, which creates synthetic ST data through foundation models. + +3.1.1 Real-World Data Sensing. Advances in sensing and data acquisition technologies have led to the generation of vast amounts of ST data. FMs are increasingly applied in human-centric active sensing, particularly in the context of citizen reporting for urban and environmental monitoring [41]. These models act as powerful agents for collecting and processing real-time data from citizens, enabling the efficient handling of ST data [19, 27, 101]. For example, citizens might constantly report incidents, environmental changes, or social events through text or voice [178]. By understanding these reports, LLMs can categorize, prioritize, and trigger appropriate responses for various urban issues, from traffic congestion to environmental hazards. This enhances the decision-making process by continuously updating their models with new data streams. Thus, LLMs are not just passive analytical tools but active participants that help make urban environments more responsive and adaptive to citizen inputs, transforming traditional citizen feedback into actionable knowledge, enabling more sustainable and resilient cities. + +FMs can also function as intelligent schedulers or simulate multiagent systems to optimize the recruitment and coordination of participants for crowdsensing, particularly under budget constraints [41, 139, 191]. By analyzing ST data and understanding context, LLMs can identify regions and times where crowdsensing efforts will yield the most valuable information. They dynamically recruit participants based on proximity, availability, and past contributions, reducing redundant data collection. Additionally, LLMs simulate multiple agents interacting in real time, ensuring the efficient distribution of sensing tasks across a network of citizens or devices [190]. This strategic scheduling and agent-based coordination maximize coverage while minimizing costs, ensuring that crowdsensing delivers valuable, real-time insights under budgetary constraints. + +3.1.2 Synthetic Data Generation. FMs can also facilitate data generation, which enhances ST data by increasing its diversity, improving model robustness, and compensating for missing or sparse information [95]. This is crucial for ST tasks like mobility analytics, where collecting real-world data is often costly or raises privacy concerns. For instance, Trajectory-LLM [154] generates vehicle trajectories from brief textual descriptions of vehicle interactions, whereas Traj-LLM [56] generates human trajectories by leveraging personas, memory modules, and routine profiles. LLMob [126] advances mobility data generation, offering flexibility in modeling diverse urban activities and personal mobility patterns, thus improving transportation system modeling and analysis. LLMs have also been employed to construct synthetic environments that replicate real-world conditions across diverse domains, including intelligent transportation [1] and disaster management [31]. + +# 3.2 Spatio-Temporal Data Management + +Upon the acquisition of ST data, the challenge of effective management emerges, particularly in addressing data quality issues (e.g., missing values/views) and facilitating data retrieval and integration. Within this context, FMs can be harnessed in the following ways. + +3.2.1 Data Cleaning. Data cleaning is the process of improving data quality by addressing issues such as missing values, low sampling rates, and noise. For example, ST data often exhibit missing values due to various factors like sensor malfunctions and transmission disruptions [178]. Filling in these missing values[113] is crucial for ensuring the integrity of predictive models, optimizing strategies, and facilitating informed decision-making. Recent literature reveals that LLMs can serve as powerful zero-shot [164] or few-shot [17, 172] learners to data imputation by leveraging their ability to identify and learn complex ST patterns. PLMTrajRec [135], utilizing a pretrained language model to recover sparse trajectory data by unifying intervals and inferring road conditions, showing effective generalization across varied sampling intervals in tests. Moreover, scholars have investigated the potential of leveraging LLMs to augment missing views or information, such as urban region profiling [40, 150, 163] and traffic video captioning [25]. + +3.2.2 Query & Retrieval. Meanwhile, LLM can be applied to querying and retrieval to enhance information retrieval accuracy under the ST context. By leveraging their advanced natural language understanding capabilities, LLMs can process user queries in a more contextual and semantically rich manner, enabling precise retrieval of relevant information from structured and unstructured data sources. For instance, UrbanLLM [47] finetunes LLMs for urban activity planning and management, which serves as a problem solver that decodes urban-related queries into several sub-tasks, with each one solved by suitable spatio-temporal AI models. Alamsyah et al. [2] propose an automated smart city planning system that utilizes a personalized LLM with Retrieval Augmented Generation (RAG) [30] to generate tailored urban planning recommendations while ensuring data privacy, where RAG is used to retrieve relevant urban planning documents for context-aware responses. Another line of work [67, 75, 170, 179] utilizes Multimodal LLM for cross-modal information retrieval to enhance urban computing tasks. + +3.2.3 Data Integration. Data integration seeks to combine information from disparate sources, often necessitating the understanding and mapping of relationships between entities in heterogeneous datasets. LLMs are increasingly being employed in this domain, particularly for knowledge graph construction [24], where they automate and enhance the extraction, integration, and reasoning of related data. In the context of ST data, LLMs facilitate data integration by leveraging heterogeneous urban data sources, performing relational triplet extraction, and completing knowledge graphs through geospatial reasoning [94, 106]. A pioneering study UrbanKGent [105] proposes an LLM-based Agent framework to automate the process of urban knowledge graph construction. + +# 3.3 Spatio-Temporal Data Mining + +Unlike traditional data mining, which primarily focuses on structured datasets, ST data mining captures intricate spatial and temporal dependencies within ST data using machine learning or deep learning techniques [51, 129, 167]. With the emergence of FMs and LLMs, Spatio-Temporal Foundation Models (STFMs) offer new possibilities by integrating perception, optimization, and reasoning capabilities to enhance ST data mining. In this section, we explore these key capabilities, while their specific applications across different domains are detailed in Sec. 3.4. + +3.3.1 Perception. In STFMs, perception encompasses the ability to effectively model, interpret, and generalize complex spatial and temporal patterns, enabling a deeper understanding of dynamic environments. This capability can be categorized into two key perspectives. The first view pertains to an agent's ability to perceive and understand its surrounding environment, capturing visual or contextual interactions within real-world scenarios such as smart cities [151], indoor activities [152, 153], and mobile Apps [127]. + +The second aspect involves interpreting and extracting ST patterns from sensor data, ensuring accurate predictions across diverse domains. Domain-agnostic approaches, such as STEP [117] and GPT-ST [74], have employed pretraining strategies that leverage historical observations to enhance forecasting performance. In urban computing, models like TFM [130] and OpenCity [72] utilize graph-based FMs to analyze behaviors and interactions within transportation systems, yielding promising results in traffic prediction. In climate science, Pangu [9], trained on 39 years of global climate data, delivers superior deterministic forecasting outcomes across all evaluated variables when compared to leading numerical weather prediction systems. Additional notable examples in this area include the works [60, 76, 104, 108]. Despite these advances, achieving robust generalization remains a critical challenge, as most existing research has been confined to in-domain applications. While models like UniST [158] are designed as one-for-all solutions for diverse ST scenarios, their training datasets and evaluation testbeds are predominantly limited to transportation. Nevertheless, their underlying technique stacks show promise for broader cross-domain and cross-modality generalization. Other significant contributions in this realm include UniFlow [159] and UrbanDiT [160]. + +3.3.2 Optimization. Building upon the perceptual foundations, the optimization ability focuses on refining and adapting models to achieve specific, task-oriented objectives. In other words, models are not only expected to capture rich ST patterns but also to drive actionable decision-making in dynamic, real-world scenarios. This involves integrating advanced optimization strategies that tailor model behavior to the unique demands of applications. + +A prominent approach involves agent-based frameworks. For example, in traffic signal control, traditional methods (e.g., RL) are now augmented by frameworks that use LLMs as decision-making agents [61]. These systems leverage real-time traffic data and expert prompts to enable human-like planning, resulting in more adaptive and interpretable control strategies. Similarly, CityGPT [35] decomposes ST analysis into specialized sub-tasks, handled by temporal, spatial, and fusion agents, to efficiently process IoT data and generate insightful visualizations. AgentMove [28] addresses human mobility prediction by breaking down the task into modules for individual pattern mining, urban structure analysis, and collective behavior extraction. In geo-science, systems like Geode [38] integrate explicit optimization modules with ST data retrieval and machine learning inference to tackle zero-shot geospatial QA with enhanced precision. In urban planning, an innovative work [185] simulates planners and residents by LLM agents and enables their interactions to optimize inclusive land-use plans efficiently. Despite these promising developments, significant challenges remain. Seamlessly integrating perceptual capabilities with targeted optimization strategies is crucial for next-generation ST models that are both versatile and effective across diverse operational contexts. + +Table 2: Summary of representative FMs tailored for ST data science. + +
StageTask & CapabilityExampleMethodCategoryVenueYear
SensingReal-World Data SensingIdentifying Citizen-Related Issues from Social Mediados Santos et al. [27]LLMCAiSE2024
Real-World Data SensingIntelligent Crowdsensing CoordinationAutoWebCrowds [190]LLMICWE2024
Synthetic Data GenerationTrajectories GenerationTrajectory-LLM [154]LLMICLR2025
Synthetic Data GenerationHuman Activity Data GenerationLLMob [126]LLMNeurIPS2024
ManagementData CleaningFew-Shot Learner for Filling Missing ValuesNuwaTS [17]PFMPreprint2024
Data CleaningTrajectory RecoveryPLMTrajRec [135]LLMPreprint2024
Data CleaningAugment Additional Views of DataUrbanCLIP [150]LLMWWW2024
Query & RetrievalAutonomous Query Processor for Urban ManagementUrbanLLM [47]LLMEMNLP2024
Data IntegrationUrban Knowledge Graph ConstructionUrbanKGent [105]LLMNeurIPS2024
MiningPerceptionUnderstand the EnvironmentMagma [152]PFMCVPR2025
PerceptionInterpret and Extract ST PatternsSTEP [117]PFMKDD2022
OptimizationDrive Actionable Decision-Making in Dynamic ScenariosAgentMove [28]LLMPreprint2024
OptimizationOptimize Land-Use Plans by LLM AgentsZhou et al. [185]LLMPreprint2024
ReasoningCommon-sense ReasoningCausal-VidQA [66]PFMCVPR2022
ReasoningNumerical ReasoningUrbanGPT [73]LLMKDD2024
ReasoningCausal ReasoningNuwaDynamics [128]PFMICLR2024
ApplicationForecastingGlobal Weather ForecastingPangu [9]PFMNature2023
ImputationGenerative Adversarial Network for Traffic Data ImputationSTGAN [162]PFMIEEE TBD2022
Anomaly DetectionTransformer-based Anomaly DetectorXu et al. [145]PFMICLR2022
Event AnalysisDetecting and Interpreting EventsLAMP [120]LLMNeurIPS2023
Physical GroundingGeo-localizationGeoGPT [174]LLMJAG2023
Decision MakingTransportation Analytics and ControlTrafficGPT [168]LLMTransport Policy2024
Scenario SimulationSimulation of Human BehaviorPark et al. [107]LLMUIST2023
+ +3.3.3 Reasoning. While current ST models have demonstrated notable success in recognition and agent-based tasks, their reasoning and cognitive capabilities remain underdeveloped compared to advanced systems like DeepSeek-R1 [36]. To progress toward ST general intelligence, we identify three key aspects of reasoning: + +- Common-sense Reasoning harnesses everyday knowledge and contextual cues to draw implicit inferences from complex data. For instance, Causal-VidQA [66] enables models to infer explanations, predict future states, and generate counterfactual scenarios in video question-answering, while SituatedGen [173] integrates geographical and temporal contexts to generate coherent and contextually plausible statements. +- Numerical Reasoning involves interpreting and manipulating quantitative information to perform arithmetic operations, assess uncertainties, and discern relationships within ST data; for instance, STBench [69] evaluates these abilities in LLMs, while UrbanGPT [73] enhances ST forecasting with instruction tuning. +- Causal Reasoning seeks to uncover cause-effect relations within ST data, crucial for robust and interpretable predictions. For example, NuwaDynamics [128] identifies causal regions and applies interventions to improve generalization, and GCIM [176] learns latent causal structures to disentangle spurious correlations. + +Collectively, these dimensions offer a promising yet underexplored pathway toward achieving ST general intelligence, bridging the gap between pattern recognition and true cognitive understanding. + +# 3.4 Downstream Applications + +3.4.1 STFMs for Numerical Problems. ST data is predominately numeric in many real-world scenarios. Addressing these numeric challenges is critical for tasks like forecasting, imputation, and anomaly detection [52], which demand an accurate understanding of the physical world. STFMs excel in these areas by uncovering intricate patterns and dependencies, ultimately enabling more reliable data-driven decision-making. + +- Forecasting. Early forecasting approaches often relied on task-specific neural networks like STGNNs [51, 52, 110, 116], whereas recent developments have shifted toward universal forecasting [91, + +137, 167]. For instance, GPT-ST [74] leverages pretraining on historical observations to boost predictive performance, while UniST [158] unifies multiple traffic prediction tasks within a single model by coupling sequence modeling with attention-based mechanisms. Building on this progress, ST-LLM [86] and STG-LLM [90] enhance traffic predictions by combining ST inputs with partially frozen large language models, and UrbanGPT [73] extends this paradigm further by employing ST instruction tuning to better align textual and ST data. Similar approaches have also been widely used in other domains, such as ClimaX [104], Geo-Bench [60], and Orca [76]. + +- Imputation. This has likewise benefited from techniques that capture ST dependencies to accurately restore missing or corrupted data. For instance, NuwaTS [17] repurposes pretrained language models with contrastive learning and specialized patch embeddings (capturing missing patterns/statistics) to enable cross-domain time series imputation through a unified framework. STD-LLM [44] employs LLMs with spatial-temporal tokenizers and hypergraph learning modules to handle missing values in spatio-temporal data while capturing non-pairwise correlations through topology-aware node embeddings. DrIM [83] combines LLM-derived text representations (from masked tabular data conversions) with contrastive learning to measure similarities for nearest-neighbor imputation in heterogeneous datasets. + +- Anomaly Detection. Anomaly detection in ST data has advanced by leveraging models that learn the normal dynamics of ST systems to identify deviations indicative of abnormal events. Whereas prior methods relied on statistical thresholding and clustering to flag outliers, recent FMs learn robust ST representations to detect even subtle anomalies. For example, early attempts [26, 89, 186] investigate the feasibility of using LLMs for anomaly detection in time series data. SigLLM [3] employs GPT-series with signal-to-text conversion techniques, offering dual pipelines (anomaly prompting and deviation detection) for time series analysis through textual or visual representations of numerical data. AD-LLM [156] introduces a benchmark framework combining GPT-4's zero-shot reasoning with contrastive learning for anomaly context enrichment and automated model selection through chain-of-thought prompting. + +- Others. Furthermore, FMs have demonstrated great potential in other numerical problems such as time series classification [18], geospatial prediction [39, 100], traffic speed inference [7], and socioeconomic indicator prediction [40, 142, 150]. + +3.4.2 STFMs for Inferential Problems. Inferential problems in ST data require the integration of both reasoning and understanding of environments. These problems involve high-level cognitive tasks where accurate representation of locations, movements, and environmental context is essential. Addressing such problems goes beyond numerical predictions — it necessitates answering critical inferential questions: What happened? Where is it? What to do? What if? FMs have shown their potential to enhance solutions for these challenges by leveraging their capacity to handle ST knowledge and interpret complex, unstructured data. + +"What happened?" - Event Analysis. Detecting events aims to recognize and explain significant events in time and space. Traditional models struggle with scalability, interpretability, and incorporating external knowledge. To this end, LAMP [120] integrates LLMs with event models, using abductive reasoning to suggest plausible causes for predicted events, retrieve supporting evidence, and rank predictions for improved accuracy. Meanwhile, LEAP [165] replaces GNNs and RNNs with LLMs by framing event detection as a question-answering task, predicting missing event components and forecasting future relations through self-attention mechanisms. + +"Where is it?"- Physical Grounding. Grounding ST models in real-world geographical contexts is essential for various applications such as geo-localization, map reconstruction, intelligent routing and navigation. Geo-localization aims to determine an object's location based on multimodal inputs, including images, text, and sensor data. By processing these cues in conjunction with map data, LLMs such as GPT-4o, DeepSeek [36], and GeoGPT [174] can infer geographic coordinates or identify specific locations described in natural language. Map reconstruction, on the other hand, involves creating or updating digital maps by synthesizing information from satellite imagery, sensor readings, and textual reports. LLMs contribute by interpreting and generating map content, correcting inaccuracies, and filling in missing details. For instance, MapGPT [14] employs language-guided updates, incorporating textual descriptions of environmental changes into existing map structures. In personalized routing, ItiNera [123] combines LLMs with spatial optimization to generate personalized "Citywalk" itineraries, providing user-specific and spatially coherent urban exploration; ChinaTravel [115] provides a benchmark for real-world Chinese travel planning, enabling scalable evaluation of constraint satisfaction and preference optimization while highlighting the strengths of neuro-symbolic agents. Navigation systems further benefit from LLMs' ability to understand contextual instructions, interpret user queries, and reason about dynamic environments. For example, NavGPT [182] and NavGPT-v2 [181] integrate natural language with real-time traffic and indoor video data to generate personalized and optimized routing solutions. By incorporating STFMs across these domains, physical grounding models facilitate more precise localization, efficient navigation, and adaptive urban mobility solutions, ultimately bridging the gap between digital intelligence and real-world spatial reasoning. + +![](images/0dd90631ab1ad6054f2db1a2e36db5801f8436c980eebbece0578f2d29976011.jpg) +Figure 4: STFMs for addressing inferential problems. + +"What to do?" - Decision Making. Optimizing policies and real-time decision-making in dynamic environments based on inferential insights plays a crucial role in a wide range of applications, including traffic control, autonomous vehicles, and disaster response. In traffic control and management, LLMs improve adaptability and interpretability compared to traditional reinforcement learning approaches [61]. Additionally, they facilitate sim-to-real transfer by modeling real-world traffic dynamics, improving the reliability of traffic signal optimization [22]. Beyond signal control, models like TrafficGPT [168] integrate multimodal traffic data with structured reasoning to analyze, predict, and optimize traffic efficiency and safety in real time. In autonomous vehicles, STFMs contribute to decision-making through both direct and indirect mechanisms. Directly, models such as DDM-Lag [88] employ diffusion-based frameworks with Lagrangian safety enhancements and hybrid policy updates to refine policy articulation and ensure safety. Indirectly, STFMs enhance autonomous driving by predicting realistic driving behaviors [55, 114] and leveraging multi-modal perception to integrate sensor data, bird's eye view maps, and traffic contexts [20, 184], improving situational awareness and vehicle control. Beyond transportation, STFMs play a critical role in disaster management and emergency response by integrating diverse spatio-temporal data sources, such as weather forecasts, remote sensing, and social media signals, to predict disaster impacts and optimize evacuation strategies [16, 31, 65]. + +"What if?"- Scenario Simulation. STFMs, with their advanced perception and reasoning capabilities, enable the development of STFM-based agents that integrate into Multi-Agent Systems (MAS) to model complex interactions across diverse domains [29]. In urban planning and social simulation, MAS facilitates participatory urban design by simulating interactions between planners and residents. For example, LLM-driven MAS has been used to collaboratively refine land-use plans, leading to improved accessibility and ecological outcomes that surpass human expert solutions [185]. Beyond urban planning, MAS contributes to social science research by modeling human-like behaviors in AI-driven networks. Studies such as [23, 107, 109] demonstrate that LLM-based agents can naturally develop social structures, providing valuable insights into emergent social dynamics. Beyond urban applications, MAS significantly advances game AI and strategic decision-making. Recent studies [112, 133, 187] highlight how MAS-powered reinforcement learning enables strategic gameplay, real-time opponent modeling, and interactive storytelling, fostering the development of more adaptive, intelligent, and realistic virtual agents. + +# 4 The Methodology Perspective + +As shown in Figure 5, we delve into STFMs from a methodology perspective, focusing on $i)$ LLM-based models, which are widely applied across the entire workflow of $ST$ data science by zero-shot utilization or fine-tuning and $ii)$ PFM-based models, i.e., pretraining FMs from scratch, which is mainly utilized for $ST$ data mining. The comparison between them can be found in Appendix C. + +![](images/60d69dbcc8c85b62a9fac9cb5b695647836692fdc243ddfde0484cf9e89d35d3.jpg) +Figure 5: A method-centric taxonomy. Full version: Fig. 7. + +# 4.1 Large Language Models (LLM) + +4.1.1 Zero-shot Learner. LLMs exhibit strong reasoning and contextual understanding capabilities, making them highly effective across various ST tasks, including data sensing, management, and mining. As shown in Appendix B, they can function as augmenters, predictors, or agents. To ease the presentation, we adopt a broad definition of LLMs, encompassing standard LLMs, Vision-Language Models (VLM), and Multimodal LLMs (MLLM). The zero-shot utilization of LLMs can be categorized into two primary classes. + +- Prompt Engineering. When taking LLMs as zero-shot predictors [33, 53, 125] or data augmenters [150] for various tasks, prompt engineering plays an essential role in shaping model outputs. Below, we summarize key aspects for prompt engineering in current research: a) Prompt Construction: A well-designed prompt typically contains key elements like Task Instruction, Tokenization, and Few-shot Examples. Task instruction [53, 147, 149] aims to explicitly guide LLMs to execute specific operations, incorporating domain knowledge [157] if applicable. Tokenization [33, 53] is crucial to aligning ST data formats with LLM input structures. Additionally, presenting a small number of annotated examples [175] facilitates in-context learning, enabling LLMs to better generalize to complex tasks while ensuring output consistency and adherence to the expected format. b) Prompt Learning: [73, 148] Also known as instruction-tuning, this method learns prompts dynamically rather than relying on manually crafted ones. By optimizing prompt structures during training, it provides a flexible and efficient way to adapt LLMs to new tasks without altering their underlying model weights. + +c) Chain-of-Thought (CoT) Prompting: CoT [87, 175] enhances LLMs' reasoning capabilities by guiding them through step-by-step logical progression. This method improves their ability to tackle complex spatio-temporal tasks, ensuring more interpretable, structured, and accurate outputs in decision-making processes. + +- Agentic Engineering. The emergence of LLM-based agents [49, 144, 168, 174, 185] with reasoning, memory and tool-calling capabilities is transforming ST data science, enabling more adaptive and autonomous decision-making. When designing agent-based solutions, existing works primarily consider the following key aspects: a) Role Assignment. [50, 144, 174] clearly specify the responsibilities and functional boundaries of each agent within the system. b) Memorization [64, 174] refers to the agent's capability to store, recall, and leverage past information and context during task execution. A basic approach involves embedding past interactions into prompts, while more advanced techniques like Retrieval-Augmented Generation (RAG) [143, 155] dynamically retrieve relevant information from external knowledge bases, incorporating only the most pertinent content into the prompt. c) Tool Definition [168, 174], which identify and integrate various tools and functionalities that an agent can call upon to solve complex tasks. In ST data science, various expert models like STGNNs [51] can be wrapped as a tool and added into the agent in a plug-and-play manner. d) Multi-Agent System. Deploying multiple specialized agents to work collaboratively (each with distinct roles) enhances the efficiency and robustness of solutions for intricate ST challenges [49, 63, 185]. + +4.1.2 Supervised Fine-Tuning for LLMs. Fine-tuning adapts LLMs to ST tasks by adjusting their parameters based on domain-specific datasets, sometimes incorporating additional modalities such as texts [79, 150] and vision [180]. We categorize fine-tuning methods into three approaches based on the extent of parameter updates: + +- Full Parameter Fine-Tuning [68, 98, 100, 104, 108] updates all model parameters based on downstream ST datasets, achieving maximal adaptation to specific tasks. However, it requires substantial labeled data and high computational resources, making it impractical for many real-world applications. +- Partial Parameter Fine-tuning. To reduce computational overhead, this method [13, 183] freezes most parameters, such as attention weights, while fine-tuning only a small subset (e.g., position encodings and layer normalization). However, modifying a subset of parameters can disrupt the LLM's learned representations, leading to catastrophic forgetting of general knowledge. +- Add-on Parameter Fine-Tuning. To mitigate forgetting while maintaining efficiency, this technique [61] introduces trainable low-rank matrices (e.g., LoRA [42]), while keeping the original LLM weights frozen. This strategy preserves pretrained knowledge while enabling efficient adaptation to ST tasks. Besides fine-tuning LLMs' weights, another way is training additional layers for input tokenization or task adaption. For instance, TimeLLM [53] trains a self-attention layer that aligns patched time series representations with pretrained text prototype embeddings. Similarly, Time-VLM [180] trains a memory-enhanced attention to capture both short- and long-term dependencies. For task adaption, existing methods typically train an additional prediction head (e.g., linear layers) to project the LLM's output embeddings into a domain-specific space [53, 180]. + +# 4.2 Pretrained Foundation Models (PFM) + +Unlike LLMs, which build STFMs by directly using or fine-tuning LLMs, PFMs are developed from scratch, independent of existing LLMs. This approach enables domain-specific optimization, allowing models to better capture ST dependencies from cross-domain ST data without constraints imposed by linguistic priors. Following this, we examine PFMs through three key dimensions: + +4.2.1 Neural Architecture. The architecture of PFMs is a fundamental design choice that directly influences their capabilities, efficiency, and adaptability in ST tasks, which can be categorized into: + +- Transformer-based PFMs. Transformers have been the predominant architecture choice for building PFMs thanks to its powerful sequential modeling ability introduced by the self-attention mechanism [7, 72, 77, 85, 158]. +- Diffusion-based PFMs. Diffusion-based models have recently emerged as a powerful approach for ST representation learning [12, 21, 136, 160, 161, 188], particularly in generative and predictive modeling. These models iteratively learn to reverse a stochastic noise process, enabling them to generate high-fidelity spatio-temporal sequences with strong generalization properties. +- Graph-based PFMs. Unlike sequential models, GNNs excel at representing spatially structured data such as road networks. [62, 130] build FMs based on graph neural networks to learn the complex correlation between different entities in ST applications. +- Others. Another emerging class of PFMs is State Space Model (SSM)-based models [8, 43, 97], which construct PFMs using structured state-space representations. Meanwhile, several studies utilize CNNs [118] as backbones for developing PFMs. + +4.2.2 Pretraining Scheme. To enhance generalization ability, PFMs are usually pretrained based on cross-domain datasets [91, 137, 158], enabling them to learn diverse ST patterns across multiple domains. Existing pretraining schemes of PFMs can be classified into three types based on the training objectives: a) Generative Pretraining [85, 98, 130, 138, 189] focuses on reconstructing input data by learning its underlying distribution, enabling the model to generate realistic time series or ST data, while b) Contrastive Pretraining [7, 84, 171] emphasize distinguishing between similar and dissimilar data pairs to learn robust representations by maximizing agreement between augmented views of the same sample. It is particularly effective in multimodal ST learning, aligning heterogeneous data sources such as satellite imagery and its text description. c) Hybrid Pretraining [77] integrates both generative and contrastive objectives, leveraging their complementary strengths. + +4.2.3 Data Modality. ST data manifests in various modalities, each characterized by unique properties (see Section 2), necessitating the development of modality-specific STFMs: + +- Location. PFMs for location data [7, 40, 71, 124, 138, 150, 171] aim to learn general embedding for geographical entities. For instance, GeoVectors [124] and SpaBERT [71] learn location embeddings based on open-source data such OpenStreetMap, while G2PTL [138] learns from massive logistics delivery data. Notably, there is a noticeable trend that leverages multi-modalities (such as satellite image and text) for comprehensive location embeddings. For example, both UrbanCLIP [150], UrbanVLP [40], and ReFound [142] utilize satellite images for urban region profiling. + +![](images/04153b45ab02f3e79c0ab49c30b7605ee00c77f9060519cff8dcabcf84cc5fc2.jpg) +Figure 6: Representative PFMs for different types of ST data. + +- Trajectory & Event. PFMs for trajectory/event data [21, 84, 85, 103, 121, 189] are designed to learn general sequential patterns from inputs. A pioneering effort in this direction is TrajFM [85], which introduces a trajectory FM capable of supporting both regional and task transferability. Pretrained on vehicle trajectories from multiple cities, TrajFM employs a trajectory-masking and autoregressive recovery mechanism to enhance its learning capabilities. To tackle the limited resources of cross-domain trajectories, UniTraj [189] curates a billion-scale mobility dataset spanning diverse geographic regions to facilitate the advancement of trajectory-based FMs. For event data, MOTOR [121] proposes a time-to-event FM for structured medical records. +- ST Raster. PFMs for ST raster data [10, 15, 98, 104, 108, 117, 160] organize spatial information in a grid-like format, with a typical applied domain being weather/climate forecasting. For instance, W-MAE [98] trains a mask autoencoder for ST grid forecasting. CimaX [104] develops a general-purpose climate foundation model, pretrained on diverse datasets spanning various variables, ST scales, and physical contexts. Pangu [10] is trained on 39 years of global climate data, which achieves superior forecasting performance compared to leading numerical weather prediction systems. UniST [158] first pretrains the model in various ST raster data via masked pretraining, and then proposes a learnable ST prompt to enhance the model's generalization ability. +- ST Graph. PFMs for ST graph data [62, 72, 93, 111, 117, 134] learn the ST dependencies from ST graphs that generalize effectively in unseen spatial and temporal contexts. Unlike ST Raster PFMs, there are limited works in this area, which is more challenging due to the complex graph correlation. One representative is OpenCity [72] for ST graph forecasting, which integrates Transformer and GNN to model the ST dependencies in traffic data. + +# 5 Conclusion and Future Directions + +The rapid advancement of FMs has transformed ST data science, impacting sensing, management, and mining. This survey provides a comprehensive review of FMs for ST data science, identifying key capabilities such as perception, reasoning, and optimization while exploring diverse downstream tasks and datasets. We also establish a systematic taxonomy of methodologies, enhancing understanding of how STFMs model ST data. Despite progress, challenges remain in generalization, interpretability, and efficiency. By consolidating recent advances and outlining future directions (see Appendix A), this survey aims to inspire further innovations, driving the development of scalable and adaptive STFMs for real practice. + +# References + +[1] Oluwanifemi Adebayo Moses Adekanye. 2024. 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We have identified a significant challenge in developing FMs for addressing numerical problems in ST data science. Directly leveraging LLMs for numerical tasks such as forecasting proves to be non-trivial [34]. Meanwhile, fine-tuning LLMs or training STFMs from scratch using large-scale, cross-domain ST data often comes at the cost of interactive capabilities, thereby hindering interpretability in the prediction outcomes. These limitations motivate us to explore a novel paradigm that not only retains strong numerical reasoning abilities but also enhances interpretability, bridging the gap between predictive accuracy and explanatory insight. +- Large foundation models are all we need? While the extensive parameterization of FMs enables impressive generalization capabilities, particularly in zero/few-shot settings, their superiority over smaller expert models remains context-dependent. In ST domains such as time series analysis [122] and urban planning [57], smaller expert models often outperform FMs when provided with sufficient domain-specific training data. This raises fundamental questions about the trade-offs between model scalability, efficiency, and task-specific optimization. Future research should delve into hybrid approaches that combine the adaptability of large models with the precision of expert models. +- One-fit-all FMs across the full workflow. While current FMs are typically designed to support only specific stages of ST data science, we envision a more unified FM capable of seamlessly + +spanning the entire workflow, from initial data sensing and management to mining and supporting downstream applications. Achieving this goal will likely require the development of advanced LLM agents that can function as full-stack engineers (i.e., strongly benefiting all stages) for ST data science. + +- Integrating STFMs with multimodal understanding. While current STFMs excel in processing structured ST data, their ability to integrate and reason over multimodal information, including text, images, video, and sensor data, remains underdeveloped. Many tasks require models to jointly interpret geospatial context, temporal dynamics, and text descriptions. Future research can focus on designing multimodal STFMs that effectively align, fuse, and reason over heterogeneous data sources, enabling more context-aware and human-interpretable decision-making. + +# B Zero-shot Utilization of LLMs + +There are three ways of directly using LLMs for various ST tasks: + +- LLM-as-Augmenter. Pretrained LLMs can enhance both data understanding and model performance. On the one hand, it can serve as the input augmenter, which enhances data interoperability or provides external information [40, 79] (e.g., textual or visual). On the other hand, LLMs can serve as a parameter-frozen model component [102, 150, 166], thus augmenting domain models by injecting the pretrained external knowledge in LLMs. +- LLM-as-Predictor. LLMs can be directly employed as predictors [33, 53, 73, 125] for various tasks. Due to the modality gap between text and ST data, preprocessing is required to fit the input spaces of LLMs. Such step typically contains prompt engineering [73, 125, 147-149] or patch & tokenization [53]. +- LLM-as-Agent. LLM-based agents are typically equipped with the ability to memorize and call various tools. When applied to ST data science, various domain-expert models can be wrapped as a tool and added into the agent in a plug-and-play manner [144, 168, 174]. As such, LLM serves as a router to access different models with both flexibility and performance guarantees. Furthermore, multi-agent systems [185] can be built to solve more complex tasks in the ST domain. + +# C Comparison between LLMs and PFMs + +Table 3 demonstrates the comparison between LLMs and PFMs on their capabilities, including perception, optimization, and reasoning. For example, PFMs excel in exceptional numerical reasoning abilities, yet they often struggle with common-sense understanding. There is still no free lunch, and the user can choose either LLMs or PFMs according to the downstream applications. + +Table 3: A capability comparison between LLMs and PFMs for ST data science. + +
CapabilitiesLarge Language Models (LLMs)Pretrained Foundation Models (PFMs)
Perception▲ Limited native ST perception; can be enhanced via fine-tuning✓ Strong ST perception, integrating sensor data and domain-specific learning
Optimization✓ Agent-based reasoning for decision-making; relies on prompting and heuristics▲ Limited; lacks decision-making ability for control and planning
Common-sense Reasoning✓ Strong via pretraining on vast textual data; can be enhanced with fine-tuning▲ Limited; relies on structured ST data rather than broad world knowledge
Numerical Reasoning▲ Handles arithmetic but struggles with structured ST computations✓ Designed for numerical problems, e.g., forecasting, anomaly detection
Causal Reasoning▲ Can infer causal relations from text but lacks structured ST modeling✓ Built-in graph-based and ST causal modeling
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"type": "text", + "content": ", Gao Cong" + }, + { + "bbox": [ + 140, + 129, + 471, + 157 + ], + "type": "inline_equation", + "content": "^{8}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 102, + 157, + 508, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 157, + 508, + 219 + ], + "spans": [ + { + "bbox": [ + 102, + 157, + 508, + 219 + ], + "type": "text", + "content": "1The Hong Kong University of Science and Technology (Guangzhou) 2Carnegie Mellon University 3National University of Singapore 4Griffith University 5East China Normal University 6University of New South Wales 7Squirrel AI Learning, USA 8Nanyang Technology University {yuxiang,yutong.x}@outlook.com,{wenhaomin.whm,mingjinedu,qingsongedu}@gmail.com flora.salim@unsw.edu.au,byang@dase.ecnu.edu.cn,s.pan@griffith.edu.au,gaocong@ntu.edu.sg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 51, + 224, + 96, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 224, + 96, + 236 + ], + "spans": [ + { + "bbox": [ + 51, + 224, + 96, + 236 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 50, + 239, + 296, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 239, + 296, + 437 + ], + "spans": [ + { + "bbox": [ + 50, + 239, + 296, + 437 + ], + "type": "text", + "content": "Spatio-Temporal (ST) data science, which includes sensing, managing, and mining large-scale data across space and time, is fundamental to understanding complex systems in domains such as urban computing, climate science, and intelligent transportation. Traditional deep learning approaches have significantly advanced this field, particularly in the stage of ST data mining. However, these models remain task-specific and often require extensive labeled data. Inspired by the success of Foundation Models (FM), especially large language models, researchers have begun exploring the concept of Spatio-Temporal Foundation Models (STFMs) to enhance adaptability and generalization across diverse ST tasks. Unlike prior architectures, STFMs empower the entire workflow of ST data science, ranging from data sensing, management, to mining, thereby offering a more holistic and scalable approach. Despite rapid progress, a systematic study of STFMs for ST data science remains lacking. This survey aims to provide a comprehensive review of STFMs, categorizing existing methodologies and identifying key research directions to advance ST general intelligence." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 440, + 134, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 440, + 134, + 451 + ], + "spans": [ + { + "bbox": [ + 51, + 440, + 134, + 451 + ], + "type": "text", + "content": "1 Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 50, + 454, + 295, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 454, + 295, + 531 + ], + "spans": [ + { + "bbox": [ + 50, + 454, + 295, + 531 + ], + "type": "text", + "content": "Humans live in a world shaped by the dynamic interplay of countless elements across space and time. Spatio-Temporal (ST) Data, which refer to data that encapsulate ST phenomena, track the evolution of objects or events across locations and time [5], such as meteorological records, traffic patterns, and human traces. These data are frequently sourced from a wide array of platforms, ranging from IoT devices, GPS sensors, social media, to remote sensing." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 50, + 531, + 295, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 531, + 295, + 609 + ], + "spans": [ + { + "bbox": [ + 50, + 531, + 295, + 609 + ], + "type": "text", + "content": "Within this context, Spatio-Temporal Data Science focuses on sensing, managing, and mining these datasets to uncover patterns, understand complex systems, and predict future dynamics. Motivated by its transformative potential, this field addresses critical challenges across urban environments and even the entire planet, enabling decision-making and fostering innovations that contribute to building smarter, more sustainable, and resilient systems [178]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 50, + 617, + 295, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 617, + 295, + 675 + ], + "spans": [ + { + "bbox": [ + 50, + 617, + 295, + 675 + ], + "type": "text", + "content": "Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 51, + 676, + 186, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 676, + 186, + 684 + ], + "spans": [ + { + "bbox": [ + 51, + 676, + 186, + 684 + ], + "type": "text", + "content": "Conference'17, July 2017, Washington, DC, USA" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 51, + 685, + 289, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 685, + 289, + 693 + ], + "spans": [ + { + "bbox": [ + 51, + 685, + 289, + 693 + ], + "type": "text", + "content": "© 2025 Copyright held by the owner/author(s). Publication rights licensed to ACM." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 52, + 693, + 165, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 693, + 165, + 700 + ], + "spans": [ + { + "bbox": [ + 52, + 693, + 165, + 700 + ], + "type": "text", + "content": "ACM ISBN 978-x-xxxxx-xxxxx-x/YY/MM" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 52, + 700, + 174, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 700, + 174, + 709 + ], + "spans": [ + { + "bbox": [ + 52, + 700, + 174, + 709 + ], + "type": "text", + "content": "https://doi.org/10.1145/nnnnnnn.nnnnnnn" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 318, + 224, + 555, + 337 + ], + "blocks": [ + { + "bbox": [ + 318, + 224, + 555, + 337 + ], + "lines": [ + { + "bbox": [ + 318, + 224, + 555, + 337 + ], + "spans": [ + { + "bbox": [ + 318, + 224, + 555, + 337 + ], + "type": "image", + "image_path": "585a84a4e1c2d564b53b7198e4a5ac28aaf09f4523682713f3c283074ed415a4.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 314, + 342, + 560, + 388 + ], + "lines": [ + { + "bbox": [ + 314, + 342, + 560, + 388 + ], + "spans": [ + { + "bbox": [ + 314, + 342, + 560, + 388 + ], + "type": "text", + "content": "Figure 1: ST Foundation Models (STFM), which include LLM and PFM, are pretrained with or applied to diverse ST data, with the abilities of perception, optimization, and reasoning. STFMs can, in turn, enhance each stage of ST data science." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 391, + 560, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 391, + 560, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 391, + 560, + 544 + ], + "type": "text", + "content": "In the era of deep learning, the community has primarily concentrated on spatio-temporal representation learning, as a fundamental step of ST data mining [129]. Key advancements include the development of Spatio-Temporal Graph Neural Networks (STGNN) [51] and transformer-based architectures, which have shown remarkable success in tasks such as traffic forecasting [80, 146], air quality prediction [82], and human mobility analytics [132]. STGNNs integrate Graph Neural Networks (GNN) with temporal learning modules (e.g., GRU [6, 70], TCN [140, 141]) to model ST correlations, while transformer models leverage self-attention mechanisms [37, 78, 177] to process complex dependencies across space and time. Additionally, there has been significant research on self-supervised learning [46, 74, 92], where models are trained to extract powerful representations with minimal reliance on large annotated datasets." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 545, + 560, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 545, + 560, + 710 + ], + "spans": [ + { + "bbox": [ + 313, + 545, + 560, + 710 + ], + "type": "text", + "content": "Driven by the success of Foundation Models (FM), especially Large Language Models (LLM), researchers have recently begun exploring the concept of Spatio-Temporal Foundation Models (STFM) [32, 81, 169]. By harnessing LLMs, it becomes possible to develop more generalized, adaptable solutions that can be fine-tuned for specific tasks with minimal data. Another prominent approach involves pretraining FMs (denoted as PFM) on cross-domain ST data and adapting them for particular domains. In contrast to previous architectures (e.g., STGNNs), STFMs integrates the capabilities of perception, reasoning and optimization, which not only promises to revolutionize ST data mining, but also empowers other stages of ST data science, such as ST data sensing and management (See Figure 1). This shift has the potential to enhance the scalability and efficiency of ST applications, offering a more holistic approach to addressing challenges in urban computing, climate science, etc." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 14, + 206, + 35, + 559 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 14, + 206, + 35, + 559 + ], + "spans": [ + { + "bbox": [ + 14, + 206, + 35, + 559 + ], + "type": "text", + "content": "arXiv:2503.13502v1 [cs.DB] 12 Mar 2025" + } + ] + } + ], + "index": 0 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 129, + 293, + 190 + ], + "blocks": [ + { + "bbox": [ + 50, + 83, + 295, + 127 + ], + "lines": [ + { + "bbox": [ + 50, + 83, + 295, + 127 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 295, + 127 + ], + "type": "text", + "content": "Table 1: Our survey vs. related surveys on FMs for learning ST data, such as locations (L), trajectories (T), events (E), ST rasters (R), and ST graphs (G). The applications (App.) include numerical (N) and inferential (I) problems." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 129, + 293, + 190 + ], + "lines": [ + { + "bbox": [ + 53, + 129, + 293, + 190 + ], + "spans": [ + { + "bbox": [ + 53, + 129, + 293, + 190 + ], + "type": "table", + "html": "
SurveyYearVenueSensingManage.MiningApp.Data
Jin et al. [54]2023-✓NR,G
Jiang et al. [48]2024IJCAI✓NR,G
Liang et al. [81]2024KDD✓NT,E,R,G
Zhang et al. [169]2024KDD✓N,IL,T,E,R,G
Goodge et al. [32]2025-✓NT,E,R,G
Ours2025-✓✓✓N,IL,T,E,R,G
", + "image_path": "08bcc66a52134813071d6c4eb50489b0a630570ee89c53dc5e3c14381549b4d2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 50, + 191, + 295, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 191, + 295, + 301 + ], + "spans": [ + { + "bbox": [ + 50, + 191, + 295, + 301 + ], + "type": "text", + "content": "Despite their rapid advancements, a systematic analysis of STFMs across the entire workflow of ST data science remains lacking. First, prior surveys have primarily focused on utilizing LLMs as the key tool for ST data mining [32, 54, 81, 169], leaving a significant gap in understanding how these models can be integrated throughout the entire process, i.e., with less focus placed on their role in the earlier stages of sensing and management. Second, they predominantly examine the applications of STFMs to numerical problems (e.g., forecasting, imputation) while overlooking their role in inferential problem-solving such as decision-making systems." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 50, + 301, + 295, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 301, + 295, + 453 + ], + "spans": [ + { + "bbox": [ + 50, + 301, + 295, + 453 + ], + "type": "text", + "content": "To bridge these gaps, this paper aims to provide a more comprehensive survey of STFMs across all stages of ST data science, spanning data sensing, management, and mining (see Figure 1). For example, LLMs can enhance ST data sensing by actively processing citizen reports, optimizing participatory sensing strategies, and generating synthetic data at scale. In terms of data management, they can automate data cleaning tasks, construct meaningful knowledge graphs for data integration, and facilitate more efficient retrieval of cross-modal datasets. Beyond these stages, our survey also explores how STFMs support a broader range of downstream applications, including numerical and inferential problems. Through this endeavor, we seek to illuminate an overall vision of STFMs, thereby enhancing comprehension regarding their potential to optimize ST data science, fostering more integrated and adaptable solutions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 50, + 454, + 295, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 454, + 295, + 575 + ], + "spans": [ + { + "bbox": [ + 50, + 454, + 295, + 575 + ], + "type": "text", + "content": "Meanwhile, we systematically investigate the key methodologies of STFMs for modeling a variety of ST data. We begin by categorizing existing STFMs into two main classes: LLMs and Pretrained Foundation Models (PFMs). For LLMs, which are pretrained on linguistic data, we focus on their usage as a zero-shot [33] or few-shot learner [53, 73], where various prompting and fine-tuning strategies have been explored, respectively. For PFMs, which are trained from scratch based on cross-domain ST data [40, 158, 189], we examine their neural architectures, pretraining methods, and their adaptability to different types of ST data, including location data, trajectory data, events, ST raster data, and ST graph data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 60, + 575, + 272, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 575, + 272, + 586 + ], + "spans": [ + { + "bbox": [ + 60, + 575, + 272, + 586 + ], + "type": "text", + "content": "In summary, our major contributions lie in three aspects:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 51, + 586, + 295, + 706 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 51, + 586, + 295, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 586, + 295, + 640 + ], + "spans": [ + { + "bbox": [ + 51, + 586, + 295, + 640 + ], + "type": "text", + "content": "- Comprehensive and up-to-date survey: We provide the first comprehensive and modern survey of FMs across the entire workflow of ST data science, covering data sensing, management, and mining. We also explore a broader range of downstream tasks and data types compared to most existing surveys (See Table 1)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 51, + 641, + 295, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 641, + 295, + 673 + ], + "spans": [ + { + "bbox": [ + 51, + 641, + 295, + 673 + ], + "type": "text", + "content": "- Vision and Methodologies: We propose a vision for STFMs, identifying key capabilities essential for their success, and discuss current methodologies for implementing these abilities in detail." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 51, + 673, + 295, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 673, + 295, + 706 + ], + "spans": [ + { + "bbox": [ + 51, + 673, + 295, + 706 + ], + "type": "text", + "content": "- Future directions: We highlight promising directions for advancing ST data science with foundation models, encouraging further research and exploration in this emerging field." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 84, + 560, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 84, + 560, + 140 + ], + "spans": [ + { + "bbox": [ + 313, + 84, + 560, + 140 + ], + "type": "text", + "content": "Paper Organization. The remainder of this paper is organized as follows: Sec. 2 provides essential background on FMs and ST data. Sec. 3 and 4 present a taxonomy of STFMs regarding the workflow and methodologies, respectively. Sec. 5 offers concluding remarks, and Appendix A highlights promising avenues for future research." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 144, + 395, + 157 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 144, + 395, + 157 + ], + "spans": [ + { + "bbox": [ + 315, + 144, + 395, + 157 + ], + "type": "text", + "content": "2 Background" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 159, + 560, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 159, + 560, + 346 + ], + "spans": [ + { + "bbox": [ + 313, + 159, + 560, + 346 + ], + "type": "text", + "content": "Foundation models. FMs are deep neural networks trained on vast datasets, enabling them to acquire broad, cross-domain knowledge and exceptional adaptability [45]. Unlike earlier task-specific models, FMs can be efficiently fine-tuned with relatively small amounts of task-specific data, offering remarkable flexibility, effectiveness, and cost efficiency. Pioneering attempts like BERT [58] and GPT-3 [11] have reshaped natural language processing. More recent models, e.g., GPT-4o [45] and DeepSeek-R1 [36], further push the frontiers of generative capabilities, enabling more nuanced reasoning, robust domain adaptation, and improved context-awareness in diverse tasks. In ST domains, recent FMs like Time-MoE [119], Chronos [4], and UniST [158] have made remarkable strides in time series analysis and universal ST forecasting, while UniTraj [189] serves as a versatile foundation for various trajectory-related tasks. Inspired by these successes, this survey delves into the utilization of FMs in the entire workflow of ST data science, covering data sensing, management, and mining." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 348, + 560, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 348, + 560, + 413 + ], + "spans": [ + { + "bbox": [ + 313, + 348, + 560, + 413 + ], + "type": "text", + "content": "Formulation of Spatio-Temporal Data. ST data refer to datasets that integrate spatial (location-based) and temporal (time-based) information, capturing dynamic patterns and relationships over space and time. Figure 2 depicts the basic ST data structures discussed in this survey, including locations, trajectories, events, ST rasters, and ST graphs. Their definitions are delineated as follows." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 413, + 559, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 413, + 559, + 458 + ], + "spans": [ + { + "bbox": [ + 313, + 413, + 559, + 458 + ], + "type": "text", + "content": "Definition 1 (Location). A location refers to a fixed spatial point or object in a geographical space, represented by the geospatial coordinates " + }, + { + "bbox": [ + 313, + 413, + 559, + 458 + ], + "type": "inline_equation", + "content": "l \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 313, + 413, + 559, + 458 + ], + "type": "text", + "content": ", i.e., latitude and longitude. It is often profiled by the corresponding satellite image, street-view image, and descriptions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "spans": [ + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "text", + "content": "Definition 2 (Trajectory). A trajectory is a sequence of time-ordered locations that describe the movements of an object in the geographical space. It can be formulated as " + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = p_1\\rightarrow p_2\\rightarrow \\dots \\rightarrow p_T" + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "inline_equation", + "content": "p_i = (l_i,t_i)" + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "text", + "content": " denotes the object's location at time " + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 313, + 458, + 560, + 502 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "spans": [ + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "text", + "content": "Definition 3 (Event). An event sequence is a series of timestamped events, denoted as " + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "inline_equation", + "content": "\\mathcal{E} = v_{1}\\rightarrow v_{2}\\rightarrow \\dots \\rightarrow v_{T}" + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "text", + "content": ", describing the progress of actions or occurrences, where " + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "inline_equation", + "content": "v_{i} = (e_{i},t_{i})" + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "inline_equation", + "content": "e_i\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "text", + "content": " is an event and " + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "text", + "content": " denotes the time when " + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 313, + 502, + 559, + 546 + ], + "type": "text", + "content": " occurs." + } + ] + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 325, + 548, + 545, + 693 + ], + "blocks": [ + { + "bbox": [ + 325, + 548, + 545, + 693 + ], + "lines": [ + { + "bbox": [ + 325, + 548, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 325, + 548, + 545, + 693 + ], + "type": "image", + "image_path": "037cc7fecab764f3c9489d19c64e195a2e4237fe21b75687cf6cec155fb66656.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 695, + 537, + 708 + ], + "lines": [ + { + "bbox": [ + 337, + 695, + 537, + 708 + ], + "spans": [ + { + "bbox": [ + 337, + 695, + 537, + 708 + ], + "type": "text", + "content": "Figure 2: Illustration of various types of ST data." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 51, + 60, + 192, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 60, + 192, + 69 + ], + "spans": [ + { + "bbox": [ + 51, + 60, + 192, + 69 + ], + "type": "text", + "content": "Conference'17, July 2017, Washington, DC, USA" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "spans": [ + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "type": "text", + "content": "Yuxuan Liang et al." + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "spans": [ + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "text", + "content": "Definition 4 (Spatio-Temporal Raster). An ST raster can be denoted as " + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = < \\mathbf{X}_1,\\mathbf{X}_2,\\dots ,\\mathbf{X}_T > \\in \\mathbb{R}^{H\\times W\\times T\\times D}" + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_t\\in \\mathbb{R}^{H\\times W\\times D}" + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "text", + "content": " denotes the signals collected from " + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "inline_equation", + "content": "N = HW" + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "text", + "content": " evenly distributed locations at time " + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "text", + "content": ", each characterized by " + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 50, + 84, + 294, + 128 + ], + "type": "text", + "content": " feature attributes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "spans": [ + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": "Definition 5 (Spatio-Temporal Graph). An ST graph extends the ST raster to be " + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "inline_equation", + "content": "X = < \\mathbf{X}_1, \\mathbf{X}_2, \\ldots, \\mathbf{X}_T > \\in \\mathbb{R}^{N \\times T \\times D}" + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": " by explicitly incorporating spatial correlations with a graph " + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "inline_equation", + "content": "G_t = (V, E_t, \\mathbf{A}_t)" + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": " locations are not uniformly distributed. Here " + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": " is the set of nodes, " + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "inline_equation", + "content": "E_t" + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": " is the set of edges, and " + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": " is the adjacency matrix at time " + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": ". The size of " + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 50, + 129, + 294, + 196 + ], + "type": "text", + "content": " is usually static." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 51, + 205, + 202, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 205, + 202, + 217 + ], + "spans": [ + { + "bbox": [ + 51, + 205, + 202, + 217 + ], + "type": "text", + "content": "3 The Workflow Perspective" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 50, + 219, + 295, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 219, + 295, + 242 + ], + "spans": [ + { + "bbox": [ + 50, + 219, + 295, + 242 + ], + "type": "text", + "content": "As shown in Figure 3, we examine STFMs from a holistic, bottom-up perspective, emphasizing their composition across four key aspects:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 243, + 295, + 452 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 51, + 243, + 295, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 243, + 295, + 298 + ], + "spans": [ + { + "bbox": [ + 51, + 243, + 295, + 298 + ], + "type": "text", + "content": "- ST Data Sensing refers to the acquisition of data that varies over both space and time from diverse resources (e.g., sensors, satellites, social media), to capture dynamic environmental, geographic, or social phenomena. We also consider synthetic data generation for enhancing data diversity and quantity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 299, + 295, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 299, + 295, + 353 + ], + "spans": [ + { + "bbox": [ + 51, + 299, + 295, + 353 + ], + "type": "text", + "content": "- ST Data Management focuses on storing, indexing, and organizing these large-scale, heterogeneous ST datasets, incorporating strategies like distributed architectures for efficient retrieval and integration. FMs can enhance this process by facilitating data cleaning, query & retrieval, and data integration." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 51, + 354, + 295, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 354, + 295, + 408 + ], + "spans": [ + { + "bbox": [ + 51, + 354, + 295, + 408 + ], + "type": "text", + "content": "- ST Data Mining involves learning and analyzing ST data that varies across both space and time to uncover patterns, trends, and relationships, using data mining (DM), deep learning (DL) techniques, or the newly-proposed STFMs with strong capabilities in perception, optimization, and reasoning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 51, + 408, + 295, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 408, + 295, + 452 + ], + "spans": [ + { + "bbox": [ + 51, + 408, + 295, + 452 + ], + "type": "text", + "content": "- Downstream Applications: This stage harnesses the above insights from ST data to drive real-world applications, ranging from numerical problems to inferential problems, where informed actions and policies are formulated." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 50, + 454, + 295, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 454, + 295, + 498 + ], + "spans": [ + { + "bbox": [ + 50, + 454, + 295, + 498 + ], + "type": "text", + "content": "By examining these four aspects, we can better understand how STFMs advance from raw data acquisition to high-level service providing, ultimately enabling more intelligent, adaptable, and impactful solutions. We will detail each stage in the following sections." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 53, + 505, + 293, + 693 + ], + "blocks": [ + { + "bbox": [ + 53, + 505, + 293, + 693 + ], + "lines": [ + { + "bbox": [ + 53, + 505, + 293, + 693 + ], + "spans": [ + { + "bbox": [ + 53, + 505, + 293, + 693 + ], + "type": "image", + "image_path": "7550fb89f980864400839d7d1a4cff676d111c15a655bac2fa282342c99fd317.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 60, + 696, + 285, + 706 + ], + "lines": [ + { + "bbox": [ + 60, + 696, + 285, + 706 + ], + "spans": [ + { + "bbox": [ + 60, + 696, + 285, + 706 + ], + "type": "text", + "content": "Figure 3: The framework of STFMs for ST data science." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 83, + 492, + 96 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 83, + 492, + 96 + ], + "spans": [ + { + "bbox": [ + 315, + 83, + 492, + 96 + ], + "type": "text", + "content": "3.1 Spatio-Temporal Data Sensing" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 99, + 560, + 142 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 99, + 560, + 142 + ], + "spans": [ + { + "bbox": [ + 313, + 99, + 560, + 142 + ], + "type": "text", + "content": "FMs revolutionize ST data sensing from two complementary aspects: real-world data sensing, which involves collecting data from physical sources, and synthetic data generation, which creates synthetic ST data through foundation models." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 145, + 559, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 145, + 559, + 332 + ], + "spans": [ + { + "bbox": [ + 313, + 145, + 559, + 332 + ], + "type": "text", + "content": "3.1.1 Real-World Data Sensing. Advances in sensing and data acquisition technologies have led to the generation of vast amounts of ST data. FMs are increasingly applied in human-centric active sensing, particularly in the context of citizen reporting for urban and environmental monitoring [41]. These models act as powerful agents for collecting and processing real-time data from citizens, enabling the efficient handling of ST data [19, 27, 101]. For example, citizens might constantly report incidents, environmental changes, or social events through text or voice [178]. By understanding these reports, LLMs can categorize, prioritize, and trigger appropriate responses for various urban issues, from traffic congestion to environmental hazards. This enhances the decision-making process by continuously updating their models with new data streams. Thus, LLMs are not just passive analytical tools but active participants that help make urban environments more responsive and adaptive to citizen inputs, transforming traditional citizen feedback into actionable knowledge, enabling more sustainable and resilient cities." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 332, + 559, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 332, + 559, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 332, + 559, + 475 + ], + "type": "text", + "content": "FMs can also function as intelligent schedulers or simulate multiagent systems to optimize the recruitment and coordination of participants for crowdsensing, particularly under budget constraints [41, 139, 191]. By analyzing ST data and understanding context, LLMs can identify regions and times where crowdsensing efforts will yield the most valuable information. They dynamically recruit participants based on proximity, availability, and past contributions, reducing redundant data collection. Additionally, LLMs simulate multiple agents interacting in real time, ensuring the efficient distribution of sensing tasks across a network of citizens or devices [190]. This strategic scheduling and agent-based coordination maximize coverage while minimizing costs, ensuring that crowdsensing delivers valuable, real-time insights under budgetary constraints." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 477, + 559, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 477, + 559, + 643 + ], + "spans": [ + { + "bbox": [ + 313, + 477, + 559, + 643 + ], + "type": "text", + "content": "3.1.2 Synthetic Data Generation. FMs can also facilitate data generation, which enhances ST data by increasing its diversity, improving model robustness, and compensating for missing or sparse information [95]. This is crucial for ST tasks like mobility analytics, where collecting real-world data is often costly or raises privacy concerns. For instance, Trajectory-LLM [154] generates vehicle trajectories from brief textual descriptions of vehicle interactions, whereas Traj-LLM [56] generates human trajectories by leveraging personas, memory modules, and routine profiles. LLMob [126] advances mobility data generation, offering flexibility in modeling diverse urban activities and personal mobility patterns, thus improving transportation system modeling and analysis. LLMs have also been employed to construct synthetic environments that replicate real-world conditions across diverse domains, including intelligent transportation [1] and disaster management [31]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 314, + 651, + 518, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 651, + 518, + 663 + ], + "spans": [ + { + "bbox": [ + 314, + 651, + 518, + 663 + ], + "type": "text", + "content": "3.2 Spatio-Temporal Data Management" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 666, + 559, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 666, + 559, + 710 + ], + "spans": [ + { + "bbox": [ + 313, + 666, + 559, + 710 + ], + "type": "text", + "content": "Upon the acquisition of ST data, the challenge of effective management emerges, particularly in addressing data quality issues (e.g., missing values/views) and facilitating data retrieval and integration. Within this context, FMs can be harnessed in the following ways." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 51, + 60, + 274, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 60, + 274, + 69 + ], + "spans": [ + { + "bbox": [ + 51, + 60, + 274, + 69 + ], + "type": "text", + "content": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "spans": [ + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "type": "text", + "content": "Conference'17, July 2017, Washington, DC, USA" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 53, + 85, + 294, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 85, + 294, + 260 + ], + "spans": [ + { + "bbox": [ + 53, + 85, + 294, + 260 + ], + "type": "text", + "content": "3.2.1 Data Cleaning. Data cleaning is the process of improving data quality by addressing issues such as missing values, low sampling rates, and noise. For example, ST data often exhibit missing values due to various factors like sensor malfunctions and transmission disruptions [178]. Filling in these missing values[113] is crucial for ensuring the integrity of predictive models, optimizing strategies, and facilitating informed decision-making. Recent literature reveals that LLMs can serve as powerful zero-shot [164] or few-shot [17, 172] learners to data imputation by leveraging their ability to identify and learn complex ST patterns. PLMTrajRec [135], utilizing a pretrained language model to recover sparse trajectory data by unifying intervals and inferring road conditions, showing effective generalization across varied sampling intervals in tests. Moreover, scholars have investigated the potential of leveraging LLMs to augment missing views or information, such as urban region profiling [40, 150, 163] and traffic video captioning [25]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 265, + 294, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 265, + 294, + 451 + ], + "spans": [ + { + "bbox": [ + 53, + 265, + 294, + 451 + ], + "type": "text", + "content": "3.2.2 Query & Retrieval. Meanwhile, LLM can be applied to querying and retrieval to enhance information retrieval accuracy under the ST context. By leveraging their advanced natural language understanding capabilities, LLMs can process user queries in a more contextual and semantically rich manner, enabling precise retrieval of relevant information from structured and unstructured data sources. For instance, UrbanLLM [47] finetunes LLMs for urban activity planning and management, which serves as a problem solver that decodes urban-related queries into several sub-tasks, with each one solved by suitable spatio-temporal AI models. Alamsyah et al. [2] propose an automated smart city planning system that utilizes a personalized LLM with Retrieval Augmented Generation (RAG) [30] to generate tailored urban planning recommendations while ensuring data privacy, where RAG is used to retrieve relevant urban planning documents for context-aware responses. Another line of work [67, 75, 170, 179] utilizes Multimodal LLM for cross-modal information retrieval to enhance urban computing tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 453, + 294, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 453, + 294, + 585 + ], + "spans": [ + { + "bbox": [ + 53, + 453, + 294, + 585 + ], + "type": "text", + "content": "3.2.3 Data Integration. Data integration seeks to combine information from disparate sources, often necessitating the understanding and mapping of relationships between entities in heterogeneous datasets. LLMs are increasingly being employed in this domain, particularly for knowledge graph construction [24], where they automate and enhance the extraction, integration, and reasoning of related data. In the context of ST data, LLMs facilitate data integration by leveraging heterogeneous urban data sources, performing relational triplet extraction, and completing knowledge graphs through geospatial reasoning [94, 106]. A pioneering study UrbanKGent [105] proposes an LLM-based Agent framework to automate the process of urban knowledge graph construction." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 596, + 225, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 596, + 225, + 609 + ], + "spans": [ + { + "bbox": [ + 53, + 596, + 225, + 609 + ], + "type": "text", + "content": "3.3 Spatio-Temporal Data Mining" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 611, + 294, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 611, + 294, + 708 + ], + "spans": [ + { + "bbox": [ + 53, + 611, + 294, + 708 + ], + "type": "text", + "content": "Unlike traditional data mining, which primarily focuses on structured datasets, ST data mining captures intricate spatial and temporal dependencies within ST data using machine learning or deep learning techniques [51, 129, 167]. With the emergence of FMs and LLMs, Spatio-Temporal Foundation Models (STFMs) offer new possibilities by integrating perception, optimization, and reasoning capabilities to enhance ST data mining. In this section, we explore these key capabilities, while their specific applications across different domains are detailed in Sec. 3.4." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 85, + 558, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 85, + 558, + 172 + ], + "spans": [ + { + "bbox": [ + 317, + 85, + 558, + 172 + ], + "type": "text", + "content": "3.3.1 Perception. In STFMs, perception encompasses the ability to effectively model, interpret, and generalize complex spatial and temporal patterns, enabling a deeper understanding of dynamic environments. This capability can be categorized into two key perspectives. The first view pertains to an agent's ability to perceive and understand its surrounding environment, capturing visual or contextual interactions within real-world scenarios such as smart cities [151], indoor activities [152, 153], and mobile Apps [127]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 173, + 558, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 173, + 558, + 402 + ], + "spans": [ + { + "bbox": [ + 317, + 173, + 558, + 402 + ], + "type": "text", + "content": "The second aspect involves interpreting and extracting ST patterns from sensor data, ensuring accurate predictions across diverse domains. Domain-agnostic approaches, such as STEP [117] and GPT-ST [74], have employed pretraining strategies that leverage historical observations to enhance forecasting performance. In urban computing, models like TFM [130] and OpenCity [72] utilize graph-based FMs to analyze behaviors and interactions within transportation systems, yielding promising results in traffic prediction. In climate science, Pangu [9], trained on 39 years of global climate data, delivers superior deterministic forecasting outcomes across all evaluated variables when compared to leading numerical weather prediction systems. Additional notable examples in this area include the works [60, 76, 104, 108]. Despite these advances, achieving robust generalization remains a critical challenge, as most existing research has been confined to in-domain applications. While models like UniST [158] are designed as one-for-all solutions for diverse ST scenarios, their training datasets and evaluation testbeds are predominantly limited to transportation. Nevertheless, their underlying technique stacks show promise for broader cross-domain and cross-modality generalization. Other significant contributions in this realm include UniFlow [159] and UrbanDiT [160]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 403, + 558, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 403, + 558, + 479 + ], + "spans": [ + { + "bbox": [ + 317, + 403, + 558, + 479 + ], + "type": "text", + "content": "3.3.2 Optimization. Building upon the perceptual foundations, the optimization ability focuses on refining and adapting models to achieve specific, task-oriented objectives. In other words, models are not only expected to capture rich ST patterns but also to drive actionable decision-making in dynamic, real-world scenarios. This involves integrating advanced optimization strategies that tailor model behavior to the unique demands of applications." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 479, + 558, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 479, + 558, + 708 + ], + "spans": [ + { + "bbox": [ + 317, + 479, + 558, + 708 + ], + "type": "text", + "content": "A prominent approach involves agent-based frameworks. For example, in traffic signal control, traditional methods (e.g., RL) are now augmented by frameworks that use LLMs as decision-making agents [61]. These systems leverage real-time traffic data and expert prompts to enable human-like planning, resulting in more adaptive and interpretable control strategies. Similarly, CityGPT [35] decomposes ST analysis into specialized sub-tasks, handled by temporal, spatial, and fusion agents, to efficiently process IoT data and generate insightful visualizations. AgentMove [28] addresses human mobility prediction by breaking down the task into modules for individual pattern mining, urban structure analysis, and collective behavior extraction. In geo-science, systems like Geode [38] integrate explicit optimization modules with ST data retrieval and machine learning inference to tackle zero-shot geospatial QA with enhanced precision. In urban planning, an innovative work [185] simulates planners and residents by LLM agents and enables their interactions to optimize inclusive land-use plans efficiently. Despite these promising developments, significant challenges remain. Seamlessly integrating perceptual capabilities with targeted optimization strategies is crucial for next-generation ST models that are both versatile and effective across diverse operational contexts." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 52, + 60, + 192, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 60, + 192, + 69 + ], + "spans": [ + { + "bbox": [ + 52, + 60, + 192, + 69 + ], + "type": "text", + "content": "Conference'17, July 2017, Washington, DC, USA" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 501, + 60, + 558, + 68 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 501, + 60, + 558, + 68 + ], + "spans": [ + { + "bbox": [ + 501, + 60, + 558, + 68 + ], + "type": "text", + "content": "Yuxuan Liang et al." + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 95, + 558, + 294 + ], + "blocks": [ + { + "bbox": [ + 164, + 83, + 444, + 93 + ], + "lines": [ + { + "bbox": [ + 164, + 83, + 444, + 93 + ], + "spans": [ + { + "bbox": [ + 164, + 83, + 444, + 93 + ], + "type": "text", + "content": "Table 2: Summary of representative FMs tailored for ST data science." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 95, + 558, + 294 + ], + "lines": [ + { + "bbox": [ + 52, + 95, + 558, + 294 + ], + "spans": [ + { + "bbox": [ + 52, + 95, + 558, + 294 + ], + "type": "table", + "html": "
StageTask & CapabilityExampleMethodCategoryVenueYear
SensingReal-World Data SensingIdentifying Citizen-Related Issues from Social Mediados Santos et al. [27]LLMCAiSE2024
Real-World Data SensingIntelligent Crowdsensing CoordinationAutoWebCrowds [190]LLMICWE2024
Synthetic Data GenerationTrajectories GenerationTrajectory-LLM [154]LLMICLR2025
Synthetic Data GenerationHuman Activity Data GenerationLLMob [126]LLMNeurIPS2024
ManagementData CleaningFew-Shot Learner for Filling Missing ValuesNuwaTS [17]PFMPreprint2024
Data CleaningTrajectory RecoveryPLMTrajRec [135]LLMPreprint2024
Data CleaningAugment Additional Views of DataUrbanCLIP [150]LLMWWW2024
Query & RetrievalAutonomous Query Processor for Urban ManagementUrbanLLM [47]LLMEMNLP2024
Data IntegrationUrban Knowledge Graph ConstructionUrbanKGent [105]LLMNeurIPS2024
MiningPerceptionUnderstand the EnvironmentMagma [152]PFMCVPR2025
PerceptionInterpret and Extract ST PatternsSTEP [117]PFMKDD2022
OptimizationDrive Actionable Decision-Making in Dynamic ScenariosAgentMove [28]LLMPreprint2024
OptimizationOptimize Land-Use Plans by LLM AgentsZhou et al. [185]LLMPreprint2024
ReasoningCommon-sense ReasoningCausal-VidQA [66]PFMCVPR2022
ReasoningNumerical ReasoningUrbanGPT [73]LLMKDD2024
ReasoningCausal ReasoningNuwaDynamics [128]PFMICLR2024
ApplicationForecastingGlobal Weather ForecastingPangu [9]PFMNature2023
ImputationGenerative Adversarial Network for Traffic Data ImputationSTGAN [162]PFMIEEE TBD2022
Anomaly DetectionTransformer-based Anomaly DetectorXu et al. [145]PFMICLR2022
Event AnalysisDetecting and Interpreting EventsLAMP [120]LLMNeurIPS2023
Physical GroundingGeo-localizationGeoGPT [174]LLMJAG2023
Decision MakingTransportation Analytics and ControlTrafficGPT [168]LLMTransport Policy2024
Scenario SimulationSimulation of Human BehaviorPark et al. [107]LLMUIST2023
", + "image_path": "7bf729db0134e8592812df53324e7a0bdf9e7208c0a94f185406b5acb97be084.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 50, + 300, + 294, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 300, + 294, + 356 + ], + "spans": [ + { + "bbox": [ + 50, + 300, + 294, + 356 + ], + "type": "text", + "content": "3.3.3 Reasoning. While current ST models have demonstrated notable success in recognition and agent-based tasks, their reasoning and cognitive capabilities remain underdeveloped compared to advanced systems like DeepSeek-R1 [36]. To progress toward ST general intelligence, we identify three key aspects of reasoning:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 357, + 295, + 544 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 51, + 357, + 295, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 357, + 295, + 433 + ], + "spans": [ + { + "bbox": [ + 51, + 357, + 295, + 433 + ], + "type": "text", + "content": "- Common-sense Reasoning harnesses everyday knowledge and contextual cues to draw implicit inferences from complex data. For instance, Causal-VidQA [66] enables models to infer explanations, predict future states, and generate counterfactual scenarios in video question-answering, while SituatedGen [173] integrates geographical and temporal contexts to generate coherent and contextually plausible statements." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 434, + 295, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 434, + 295, + 489 + ], + "spans": [ + { + "bbox": [ + 51, + 434, + 295, + 489 + ], + "type": "text", + "content": "- Numerical Reasoning involves interpreting and manipulating quantitative information to perform arithmetic operations, assess uncertainties, and discern relationships within ST data; for instance, STBench [69] evaluates these abilities in LLMs, while UrbanGPT [73] enhances ST forecasting with instruction tuning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 489, + 295, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 489, + 295, + 544 + ], + "spans": [ + { + "bbox": [ + 51, + 489, + 295, + 544 + ], + "type": "text", + "content": "- Causal Reasoning seeks to uncover cause-effect relations within ST data, crucial for robust and interpretable predictions. For example, NuwaDynamics [128] identifies causal regions and applies interventions to improve generalization, and GCIM [176] learns latent causal structures to disentangle spurious correlations." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 50, + 545, + 295, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 545, + 295, + 579 + ], + "spans": [ + { + "bbox": [ + 50, + 545, + 295, + 579 + ], + "type": "text", + "content": "Collectively, these dimensions offer a promising yet underexplored pathway toward achieving ST general intelligence, bridging the gap between pattern recognition and true cognitive understanding." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 51, + 586, + 208, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 586, + 208, + 597 + ], + "spans": [ + { + "bbox": [ + 51, + 586, + 208, + 597 + ], + "type": "text", + "content": "3.4 Downstream Applications" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 50, + 600, + 295, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 600, + 295, + 676 + ], + "spans": [ + { + "bbox": [ + 50, + 600, + 295, + 676 + ], + "type": "text", + "content": "3.4.1 STFMs for Numerical Problems. ST data is predominately numeric in many real-world scenarios. Addressing these numeric challenges is critical for tasks like forecasting, imputation, and anomaly detection [52], which demand an accurate understanding of the physical world. STFMs excel in these areas by uncovering intricate patterns and dependencies, ultimately enabling more reliable data-driven decision-making." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 50, + 677, + 295, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 677, + 295, + 710 + ], + "spans": [ + { + "bbox": [ + 50, + 677, + 295, + 710 + ], + "type": "text", + "content": "- Forecasting. Early forecasting approaches often relied on task-specific neural networks like STGNNs [51, 52, 110, 116], whereas recent developments have shifted toward universal forecasting [91," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 300, + 559, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 559, + 410 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 559, + 410 + ], + "type": "text", + "content": "137, 167]. For instance, GPT-ST [74] leverages pretraining on historical observations to boost predictive performance, while UniST [158] unifies multiple traffic prediction tasks within a single model by coupling sequence modeling with attention-based mechanisms. Building on this progress, ST-LLM [86] and STG-LLM [90] enhance traffic predictions by combining ST inputs with partially frozen large language models, and UrbanGPT [73] extends this paradigm further by employing ST instruction tuning to better align textual and ST data. Similar approaches have also been widely used in other domains, such as ClimaX [104], Geo-Bench [60], and Orca [76]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 410, + 559, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 410, + 559, + 552 + ], + "spans": [ + { + "bbox": [ + 313, + 410, + 559, + 552 + ], + "type": "text", + "content": "- Imputation. This has likewise benefited from techniques that capture ST dependencies to accurately restore missing or corrupted data. For instance, NuwaTS [17] repurposes pretrained language models with contrastive learning and specialized patch embeddings (capturing missing patterns/statistics) to enable cross-domain time series imputation through a unified framework. STD-LLM [44] employs LLMs with spatial-temporal tokenizers and hypergraph learning modules to handle missing values in spatio-temporal data while capturing non-pairwise correlations through topology-aware node embeddings. DrIM [83] combines LLM-derived text representations (from masked tabular data conversions) with contrastive learning to measure similarities for nearest-neighbor imputation in heterogeneous datasets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 553, + 559, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 553, + 559, + 707 + ], + "spans": [ + { + "bbox": [ + 313, + 553, + 559, + 707 + ], + "type": "text", + "content": "- Anomaly Detection. Anomaly detection in ST data has advanced by leveraging models that learn the normal dynamics of ST systems to identify deviations indicative of abnormal events. Whereas prior methods relied on statistical thresholding and clustering to flag outliers, recent FMs learn robust ST representations to detect even subtle anomalies. For example, early attempts [26, 89, 186] investigate the feasibility of using LLMs for anomaly detection in time series data. SigLLM [3] employs GPT-series with signal-to-text conversion techniques, offering dual pipelines (anomaly prompting and deviation detection) for time series analysis through textual or visual representations of numerical data. AD-LLM [156] introduces a benchmark framework combining GPT-4's zero-shot reasoning with contrastive learning for anomaly context enrichment and automated model selection through chain-of-thought prompting." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 51, + 60, + 273, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 60, + 273, + 69 + ], + "spans": [ + { + "bbox": [ + 51, + 60, + 273, + 69 + ], + "type": "text", + "content": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "spans": [ + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "type": "text", + "content": "Conference'17, July 2017, Washington, DC, USA" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 50, + 84, + 296, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 84, + 296, + 129 + ], + "spans": [ + { + "bbox": [ + 50, + 84, + 296, + 129 + ], + "type": "text", + "content": "- Others. Furthermore, FMs have demonstrated great potential in other numerical problems such as time series classification [18], geospatial prediction [39, 100], traffic speed inference [7], and socioeconomic indicator prediction [40, 142, 150]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 50, + 138, + 295, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 138, + 295, + 248 + ], + "spans": [ + { + "bbox": [ + 50, + 138, + 295, + 248 + ], + "type": "text", + "content": "3.4.2 STFMs for Inferential Problems. Inferential problems in ST data require the integration of both reasoning and understanding of environments. These problems involve high-level cognitive tasks where accurate representation of locations, movements, and environmental context is essential. Addressing such problems goes beyond numerical predictions — it necessitates answering critical inferential questions: What happened? Where is it? What to do? What if? FMs have shown their potential to enhance solutions for these challenges by leveraging their capacity to handle ST knowledge and interpret complex, unstructured data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 50, + 254, + 295, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 254, + 295, + 365 + ], + "spans": [ + { + "bbox": [ + 50, + 254, + 295, + 365 + ], + "type": "text", + "content": "\"What happened?\" - Event Analysis. Detecting events aims to recognize and explain significant events in time and space. Traditional models struggle with scalability, interpretability, and incorporating external knowledge. To this end, LAMP [120] integrates LLMs with event models, using abductive reasoning to suggest plausible causes for predicted events, retrieve supporting evidence, and rank predictions for improved accuracy. Meanwhile, LEAP [165] replaces GNNs and RNNs with LLMs by framing event detection as a question-answering task, predicting missing event components and forecasting future relations through self-attention mechanisms." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 50, + 369, + 295, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 369, + 295, + 710 + ], + "spans": [ + { + "bbox": [ + 50, + 369, + 295, + 710 + ], + "type": "text", + "content": "\"Where is it?\"- Physical Grounding. Grounding ST models in real-world geographical contexts is essential for various applications such as geo-localization, map reconstruction, intelligent routing and navigation. Geo-localization aims to determine an object's location based on multimodal inputs, including images, text, and sensor data. By processing these cues in conjunction with map data, LLMs such as GPT-4o, DeepSeek [36], and GeoGPT [174] can infer geographic coordinates or identify specific locations described in natural language. Map reconstruction, on the other hand, involves creating or updating digital maps by synthesizing information from satellite imagery, sensor readings, and textual reports. LLMs contribute by interpreting and generating map content, correcting inaccuracies, and filling in missing details. For instance, MapGPT [14] employs language-guided updates, incorporating textual descriptions of environmental changes into existing map structures. In personalized routing, ItiNera [123] combines LLMs with spatial optimization to generate personalized \"Citywalk\" itineraries, providing user-specific and spatially coherent urban exploration; ChinaTravel [115] provides a benchmark for real-world Chinese travel planning, enabling scalable evaluation of constraint satisfaction and preference optimization while highlighting the strengths of neuro-symbolic agents. Navigation systems further benefit from LLMs' ability to understand contextual instructions, interpret user queries, and reason about dynamic environments. For example, NavGPT [182] and NavGPT-v2 [181] integrate natural language with real-time traffic and indoor video data to generate personalized and optimized routing solutions. By incorporating STFMs across these domains, physical grounding models facilitate more precise localization, efficient navigation, and adaptive urban mobility solutions, ultimately bridging the gap between digital intelligence and real-world spatial reasoning." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 321, + 84, + 555, + 203 + ], + "blocks": [ + { + "bbox": [ + 321, + 84, + 555, + 203 + ], + "lines": [ + { + "bbox": [ + 321, + 84, + 555, + 203 + ], + "spans": [ + { + "bbox": [ + 321, + 84, + 555, + 203 + ], + "type": "image", + "image_path": "0dd90631ab1ad6054f2db1a2e36db5801f8436c980eebbece0578f2d29976011.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 209, + 544, + 220 + ], + "lines": [ + { + "bbox": [ + 328, + 209, + 544, + 220 + ], + "spans": [ + { + "bbox": [ + 328, + 209, + 544, + 220 + ], + "type": "text", + "content": "Figure 4: STFMs for addressing inferential problems." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 225, + 560, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 225, + 560, + 500 + ], + "spans": [ + { + "bbox": [ + 313, + 225, + 560, + 500 + ], + "type": "text", + "content": "\"What to do?\" - Decision Making. Optimizing policies and real-time decision-making in dynamic environments based on inferential insights plays a crucial role in a wide range of applications, including traffic control, autonomous vehicles, and disaster response. In traffic control and management, LLMs improve adaptability and interpretability compared to traditional reinforcement learning approaches [61]. Additionally, they facilitate sim-to-real transfer by modeling real-world traffic dynamics, improving the reliability of traffic signal optimization [22]. Beyond signal control, models like TrafficGPT [168] integrate multimodal traffic data with structured reasoning to analyze, predict, and optimize traffic efficiency and safety in real time. In autonomous vehicles, STFMs contribute to decision-making through both direct and indirect mechanisms. Directly, models such as DDM-Lag [88] employ diffusion-based frameworks with Lagrangian safety enhancements and hybrid policy updates to refine policy articulation and ensure safety. Indirectly, STFMs enhance autonomous driving by predicting realistic driving behaviors [55, 114] and leveraging multi-modal perception to integrate sensor data, bird's eye view maps, and traffic contexts [20, 184], improving situational awareness and vehicle control. Beyond transportation, STFMs play a critical role in disaster management and emergency response by integrating diverse spatio-temporal data sources, such as weather forecasts, remote sensing, and social media signals, to predict disaster impacts and optimize evacuation strategies [16, 31, 65]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 501, + 560, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 501, + 560, + 710 + ], + "spans": [ + { + "bbox": [ + 313, + 501, + 560, + 710 + ], + "type": "text", + "content": "\"What if?\"- Scenario Simulation. STFMs, with their advanced perception and reasoning capabilities, enable the development of STFM-based agents that integrate into Multi-Agent Systems (MAS) to model complex interactions across diverse domains [29]. In urban planning and social simulation, MAS facilitates participatory urban design by simulating interactions between planners and residents. For example, LLM-driven MAS has been used to collaboratively refine land-use plans, leading to improved accessibility and ecological outcomes that surpass human expert solutions [185]. Beyond urban planning, MAS contributes to social science research by modeling human-like behaviors in AI-driven networks. Studies such as [23, 107, 109] demonstrate that LLM-based agents can naturally develop social structures, providing valuable insights into emergent social dynamics. Beyond urban applications, MAS significantly advances game AI and strategic decision-making. Recent studies [112, 133, 187] highlight how MAS-powered reinforcement learning enables strategic gameplay, real-time opponent modeling, and interactive storytelling, fostering the development of more adaptive, intelligent, and realistic virtual agents." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 52, + 60, + 192, + 68 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 60, + 192, + 68 + ], + "spans": [ + { + "bbox": [ + 52, + 60, + 192, + 68 + ], + "type": "text", + "content": "Conference'17, July 2017, Washington, DC, USA" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "spans": [ + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "type": "text", + "content": "Yuxuan Liang et al." + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 50, + 83, + 217, + 96 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 83, + 217, + 96 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 217, + 96 + ], + "type": "text", + "content": "4 The Methodology Perspective" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "spans": [ + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "text", + "content": "As shown in Figure 5, we delve into STFMs from a methodology perspective, focusing on " + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "inline_equation", + "content": "i)" + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "text", + "content": " LLM-based models, which are widely applied across the entire workflow of " + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "inline_equation", + "content": "ST" + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "text", + "content": " data science by zero-shot utilization or fine-tuning and " + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "inline_equation", + "content": "ii)" + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "text", + "content": " PFM-based models, i.e., pretraining FMs from scratch, which is mainly utilized for " + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "inline_equation", + "content": "ST" + }, + { + "bbox": [ + 50, + 99, + 294, + 164 + ], + "type": "text", + "content": " data mining. The comparison between them can be found in Appendix C." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 52, + 171, + 291, + 384 + ], + "blocks": [ + { + "bbox": [ + 52, + 171, + 291, + 384 + ], + "lines": [ + { + "bbox": [ + 52, + 171, + 291, + 384 + ], + "spans": [ + { + "bbox": [ + 52, + 171, + 291, + 384 + ], + "type": "image", + "image_path": "60d69dbcc8c85b62a9fac9cb5b695647836692fdc243ddfde0484cf9e89d35d3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 387, + 291, + 398 + ], + "lines": [ + { + "bbox": [ + 54, + 387, + 291, + 398 + ], + "spans": [ + { + "bbox": [ + 54, + 387, + 291, + 398 + ], + "type": "text", + "content": "Figure 5: A method-centric taxonomy. Full version: Fig. 7." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 50, + 408, + 228, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 408, + 228, + 421 + ], + "spans": [ + { + "bbox": [ + 50, + 408, + 228, + 421 + ], + "type": "text", + "content": "4.1 Large Language Models (LLM)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 50, + 423, + 295, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 423, + 295, + 511 + ], + "spans": [ + { + "bbox": [ + 50, + 423, + 295, + 511 + ], + "type": "text", + "content": "4.1.1 Zero-shot Learner. LLMs exhibit strong reasoning and contextual understanding capabilities, making them highly effective across various ST tasks, including data sensing, management, and mining. As shown in Appendix B, they can function as augmenters, predictors, or agents. To ease the presentation, we adopt a broad definition of LLMs, encompassing standard LLMs, Vision-Language Models (VLM), and Multimodal LLMs (MLLM). The zero-shot utilization of LLMs can be categorized into two primary classes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 50, + 512, + 295, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 512, + 295, + 710 + ], + "spans": [ + { + "bbox": [ + 50, + 512, + 295, + 710 + ], + "type": "text", + "content": "- Prompt Engineering. When taking LLMs as zero-shot predictors [33, 53, 125] or data augmenters [150] for various tasks, prompt engineering plays an essential role in shaping model outputs. Below, we summarize key aspects for prompt engineering in current research: a) Prompt Construction: A well-designed prompt typically contains key elements like Task Instruction, Tokenization, and Few-shot Examples. Task instruction [53, 147, 149] aims to explicitly guide LLMs to execute specific operations, incorporating domain knowledge [157] if applicable. Tokenization [33, 53] is crucial to aligning ST data formats with LLM input structures. Additionally, presenting a small number of annotated examples [175] facilitates in-context learning, enabling LLMs to better generalize to complex tasks while ensuring output consistency and adherence to the expected format. b) Prompt Learning: [73, 148] Also known as instruction-tuning, this method learns prompts dynamically rather than relying on manually crafted ones. By optimizing prompt structures during training, it provides a flexible and efficient way to adapt LLMs to new tasks without altering their underlying model weights." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 84, + 559, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 84, + 559, + 140 + ], + "spans": [ + { + "bbox": [ + 313, + 84, + 559, + 140 + ], + "type": "text", + "content": "c) Chain-of-Thought (CoT) Prompting: CoT [87, 175] enhances LLMs' reasoning capabilities by guiding them through step-by-step logical progression. This method improves their ability to tackle complex spatio-temporal tasks, ensuring more interpretable, structured, and accurate outputs in decision-making processes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 141, + 559, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 141, + 559, + 372 + ], + "spans": [ + { + "bbox": [ + 313, + 141, + 559, + 372 + ], + "type": "text", + "content": "- Agentic Engineering. The emergence of LLM-based agents [49, 144, 168, 174, 185] with reasoning, memory and tool-calling capabilities is transforming ST data science, enabling more adaptive and autonomous decision-making. When designing agent-based solutions, existing works primarily consider the following key aspects: a) Role Assignment. [50, 144, 174] clearly specify the responsibilities and functional boundaries of each agent within the system. b) Memorization [64, 174] refers to the agent's capability to store, recall, and leverage past information and context during task execution. A basic approach involves embedding past interactions into prompts, while more advanced techniques like Retrieval-Augmented Generation (RAG) [143, 155] dynamically retrieve relevant information from external knowledge bases, incorporating only the most pertinent content into the prompt. c) Tool Definition [168, 174], which identify and integrate various tools and functionalities that an agent can call upon to solve complex tasks. In ST data science, various expert models like STGNNs [51] can be wrapped as a tool and added into the agent in a plug-and-play manner. d) Multi-Agent System. Deploying multiple specialized agents to work collaboratively (each with distinct roles) enhances the efficiency and robustness of solutions for intricate ST challenges [49, 63, 185]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 378, + 559, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 378, + 559, + 433 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 559, + 433 + ], + "type": "text", + "content": "4.1.2 Supervised Fine-Tuning for LLMs. Fine-tuning adapts LLMs to ST tasks by adjusting their parameters based on domain-specific datasets, sometimes incorporating additional modalities such as texts [79, 150] and vision [180]. We categorize fine-tuning methods into three approaches based on the extent of parameter updates:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 435, + 559, + 709 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 315, + 435, + 558, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 435, + 558, + 489 + ], + "spans": [ + { + "bbox": [ + 315, + 435, + 558, + 489 + ], + "type": "text", + "content": "- Full Parameter Fine-Tuning [68, 98, 100, 104, 108] updates all model parameters based on downstream ST datasets, achieving maximal adaptation to specific tasks. However, it requires substantial labeled data and high computational resources, making it impractical for many real-world applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 491, + 558, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 491, + 558, + 555 + ], + "spans": [ + { + "bbox": [ + 315, + 491, + 558, + 555 + ], + "type": "text", + "content": "- Partial Parameter Fine-tuning. To reduce computational overhead, this method [13, 183] freezes most parameters, such as attention weights, while fine-tuning only a small subset (e.g., position encodings and layer normalization). However, modifying a subset of parameters can disrupt the LLM's learned representations, leading to catastrophic forgetting of general knowledge." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 556, + 559, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 556, + 559, + 709 + ], + "spans": [ + { + "bbox": [ + 315, + 556, + 559, + 709 + ], + "type": "text", + "content": "- Add-on Parameter Fine-Tuning. To mitigate forgetting while maintaining efficiency, this technique [61] introduces trainable low-rank matrices (e.g., LoRA [42]), while keeping the original LLM weights frozen. This strategy preserves pretrained knowledge while enabling efficient adaptation to ST tasks. Besides fine-tuning LLMs' weights, another way is training additional layers for input tokenization or task adaption. For instance, TimeLLM [53] trains a self-attention layer that aligns patched time series representations with pretrained text prototype embeddings. Similarly, Time-VLM [180] trains a memory-enhanced attention to capture both short- and long-term dependencies. For task adaption, existing methods typically train an additional prediction head (e.g., linear layers) to project the LLM's output embeddings into a domain-specific space [53, 180]." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 51, + 60, + 273, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 60, + 273, + 69 + ], + "spans": [ + { + "bbox": [ + 51, + 60, + 273, + 69 + ], + "type": "text", + "content": "Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "spans": [ + { + "bbox": [ + 419, + 60, + 559, + 69 + ], + "type": "text", + "content": "Conference'17, July 2017, Washington, DC, USA" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 50, + 83, + 261, + 95 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 83, + 261, + 95 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 261, + 95 + ], + "type": "text", + "content": "4.2 Pretrained Foundation Models (PFM)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 50, + 98, + 295, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 98, + 295, + 163 + ], + "spans": [ + { + "bbox": [ + 50, + 98, + 295, + 163 + ], + "type": "text", + "content": "Unlike LLMs, which build STFMs by directly using or fine-tuning LLMs, PFMs are developed from scratch, independent of existing LLMs. This approach enables domain-specific optimization, allowing models to better capture ST dependencies from cross-domain ST data without constraints imposed by linguistic priors. Following this, we examine PFMs through three key dimensions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 50, + 167, + 295, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 167, + 295, + 201 + ], + "spans": [ + { + "bbox": [ + 50, + 167, + 295, + 201 + ], + "type": "text", + "content": "4.2.1 Neural Architecture. The architecture of PFMs is a fundamental design choice that directly influences their capabilities, efficiency, and adaptability in ST tasks, which can be categorized into:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 204, + 295, + 401 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 51, + 204, + 295, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 204, + 295, + 247 + ], + "spans": [ + { + "bbox": [ + 51, + 204, + 295, + 247 + ], + "type": "text", + "content": "- Transformer-based PFMs. Transformers have been the predominant architecture choice for building PFMs thanks to its powerful sequential modeling ability introduced by the self-attention mechanism [7, 72, 77, 85, 158]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 248, + 295, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 248, + 295, + 314 + ], + "spans": [ + { + "bbox": [ + 51, + 248, + 295, + 314 + ], + "type": "text", + "content": "- Diffusion-based PFMs. Diffusion-based models have recently emerged as a powerful approach for ST representation learning [12, 21, 136, 160, 161, 188], particularly in generative and predictive modeling. These models iteratively learn to reverse a stochastic noise process, enabling them to generate high-fidelity spatio-temporal sequences with strong generalization properties." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 314, + 295, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 314, + 295, + 357 + ], + "spans": [ + { + "bbox": [ + 51, + 314, + 295, + 357 + ], + "type": "text", + "content": "- Graph-based PFMs. Unlike sequential models, GNNs excel at representing spatially structured data such as road networks. [62, 130] build FMs based on graph neural networks to learn the complex correlation between different entities in ST applications." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 51, + 357, + 295, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 357, + 295, + 401 + ], + "spans": [ + { + "bbox": [ + 51, + 357, + 295, + 401 + ], + "type": "text", + "content": "- Others. Another emerging class of PFMs is State Space Model (SSM)-based models [8, 43, 97], which construct PFMs using structured state-space representations. Meanwhile, several studies utilize CNNs [118] as backbones for developing PFMs." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 50, + 407, + 295, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 407, + 295, + 572 + ], + "spans": [ + { + "bbox": [ + 50, + 407, + 295, + 572 + ], + "type": "text", + "content": "4.2.2 Pretraining Scheme. To enhance generalization ability, PFMs are usually pretrained based on cross-domain datasets [91, 137, 158], enabling them to learn diverse ST patterns across multiple domains. Existing pretraining schemes of PFMs can be classified into three types based on the training objectives: a) Generative Pretraining [85, 98, 130, 138, 189] focuses on reconstructing input data by learning its underlying distribution, enabling the model to generate realistic time series or ST data, while b) Contrastive Pretraining [7, 84, 171] emphasize distinguishing between similar and dissimilar data pairs to learn robust representations by maximizing agreement between augmented views of the same sample. It is particularly effective in multimodal ST learning, aligning heterogeneous data sources such as satellite imagery and its text description. c) Hybrid Pretraining [77] integrates both generative and contrastive objectives, leveraging their complementary strengths." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 50, + 575, + 295, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 575, + 295, + 609 + ], + "spans": [ + { + "bbox": [ + 50, + 575, + 295, + 609 + ], + "type": "text", + "content": "4.2.3 Data Modality. ST data manifests in various modalities, each characterized by unique properties (see Section 2), necessitating the development of modality-specific STFMs:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 51, + 610, + 295, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 610, + 295, + 710 + ], + "spans": [ + { + "bbox": [ + 51, + 610, + 295, + 710 + ], + "type": "text", + "content": "- Location. PFMs for location data [7, 40, 71, 124, 138, 150, 171] aim to learn general embedding for geographical entities. For instance, GeoVectors [124] and SpaBERT [71] learn location embeddings based on open-source data such OpenStreetMap, while G2PTL [138] learns from massive logistics delivery data. Notably, there is a noticeable trend that leverages multi-modalities (such as satellite image and text) for comprehensive location embeddings. For example, both UrbanCLIP [150], UrbanVLP [40], and ReFound [142] utilize satellite images for urban region profiling." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 317, + 81, + 553, + 217 + ], + "blocks": [ + { + "bbox": [ + 317, + 81, + 553, + 217 + ], + "lines": [ + { + "bbox": [ + 317, + 81, + 553, + 217 + ], + "spans": [ + { + "bbox": [ + 317, + 81, + 553, + 217 + ], + "type": "image", + "image_path": "04153b45ab02f3e79c0ab49c30b7605ee00c77f9060519cff8dcabcf84cc5fc2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 218, + 558, + 230 + ], + "lines": [ + { + "bbox": [ + 315, + 218, + 558, + 230 + ], + "spans": [ + { + "bbox": [ + 315, + 218, + 558, + 230 + ], + "type": "text", + "content": "Figure 6: Representative PFMs for different types of ST data." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 233, + 560, + 573 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 315, + 233, + 560, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 233, + 560, + 365 + ], + "spans": [ + { + "bbox": [ + 315, + 233, + 560, + 365 + ], + "type": "text", + "content": "- Trajectory & Event. PFMs for trajectory/event data [21, 84, 85, 103, 121, 189] are designed to learn general sequential patterns from inputs. A pioneering effort in this direction is TrajFM [85], which introduces a trajectory FM capable of supporting both regional and task transferability. Pretrained on vehicle trajectories from multiple cities, TrajFM employs a trajectory-masking and autoregressive recovery mechanism to enhance its learning capabilities. To tackle the limited resources of cross-domain trajectories, UniTraj [189] curates a billion-scale mobility dataset spanning diverse geographic regions to facilitate the advancement of trajectory-based FMs. For event data, MOTOR [121] proposes a time-to-event FM for structured medical records." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 365, + 559, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 365, + 559, + 496 + ], + "spans": [ + { + "bbox": [ + 315, + 365, + 559, + 496 + ], + "type": "text", + "content": "- ST Raster. PFMs for ST raster data [10, 15, 98, 104, 108, 117, 160] organize spatial information in a grid-like format, with a typical applied domain being weather/climate forecasting. For instance, W-MAE [98] trains a mask autoencoder for ST grid forecasting. CimaX [104] develops a general-purpose climate foundation model, pretrained on diverse datasets spanning various variables, ST scales, and physical contexts. Pangu [10] is trained on 39 years of global climate data, which achieves superior forecasting performance compared to leading numerical weather prediction systems. UniST [158] first pretrains the model in various ST raster data via masked pretraining, and then proposes a learnable ST prompt to enhance the model's generalization ability." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 497, + 559, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 497, + 559, + 573 + ], + "spans": [ + { + "bbox": [ + 315, + 497, + 559, + 573 + ], + "type": "text", + "content": "- ST Graph. PFMs for ST graph data [62, 72, 93, 111, 117, 134] learn the ST dependencies from ST graphs that generalize effectively in unseen spatial and temporal contexts. Unlike ST Raster PFMs, there are limited works in this area, which is more challenging due to the complex graph correlation. One representative is OpenCity [72] for ST graph forecasting, which integrates Transformer and GNN to model the ST dependencies in traffic data." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 576, + 501, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 576, + 501, + 586 + ], + "spans": [ + { + "bbox": [ + 315, + 576, + 501, + 586 + ], + "type": "text", + "content": "5 Conclusion and Future Directions" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 589, + 560, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 589, + 560, + 710 + ], + "spans": [ + { + "bbox": [ + 313, + 589, + 560, + 710 + ], + "type": "text", + "content": "The rapid advancement of FMs has transformed ST data science, impacting sensing, management, and mining. This survey provides a comprehensive review of FMs for ST data science, identifying key capabilities such as perception, reasoning, and optimization while exploring diverse downstream tasks and datasets. We also establish a systematic taxonomy of methodologies, enhancing understanding of how STFMs model ST data. Despite progress, challenges remain in generalization, interpretability, and efficiency. By consolidating recent advances and outlining future directions (see Appendix A), this survey aims to inspire further innovations, driving the development of scalable and adaptive STFMs for real practice." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 51, + 60, + 192, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 60, + 192, + 69 + ], + "spans": [ + { + "bbox": [ + 51, + 60, + 192, + 69 + ], + "type": "text", + "content": "Conference'17, July 2017, Washington, DC, USA" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "spans": [ + { + "bbox": [ + 501, + 60, + 558, + 69 + ], + "type": "text", + "content": "Yuxuan Liang et al." + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 52, + 83, + 108, + 95 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 83, + 108, + 95 + ], + "spans": [ + { + "bbox": [ + 52, + 83, + 108, + 95 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 98, + 295, + 703 + ], + "type": "list", + "angle": 0, + "index": 25, + "blocks": [ + { + "bbox": [ + 58, + 98, + 295, + 121 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 98, + 295, + 121 + ], + "spans": [ + { + "bbox": [ + 58, + 98, + 295, + 121 + ], + "type": "text", + "content": "[1] Oluwanifemi Adebayo Moses Adekanye. 2024. 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A Prototype Design of LLM-Based Autonomous Web Crowdsensing. In International Conference on Web Engineering. Springer, 406-409." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 53, + 342, + 294, + 373 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 342, + 294, + 373 + ], + "spans": [ + { + "bbox": [ + 53, + 342, + 294, + 373 + ], + "type": "text", + "content": "[191] Zhengqiu Zhu, Yong Zhao, Bin Chen, Sihang Qiu, Kai Xu, Quanjun Yin, Jincai Huang, Zhong Liu, and Fei-Yue Wang. 2024. Conversational Crowdsensing: A Parallel Intelligence Powered Novel Sensing Approach. arXiv preprint arXiv:2402.06654 (2024)." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 51, + 384, + 259, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 384, + 259, + 397 + ], + "spans": [ + { + "bbox": [ + 51, + 384, + 259, + 397 + ], + "type": "text", + "content": "A Limitations and Future Opportunities" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 50, + 399, + 294, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 399, + 294, + 432 + ], + "spans": [ + { + "bbox": [ + 50, + 399, + 294, + 432 + ], + "type": "text", + "content": "We further discuss the potential limitations of current research and identify several key future directions aimed at advancing the development of more powerful, transparent, and reliable STFMs:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 51, + 434, + 295, + 708 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 51, + 434, + 295, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 434, + 295, + 554 + ], + "spans": [ + { + "bbox": [ + 51, + 434, + 295, + 554 + ], + "type": "text", + "content": "- The curse of accuracy against interpretability. We have identified a significant challenge in developing FMs for addressing numerical problems in ST data science. Directly leveraging LLMs for numerical tasks such as forecasting proves to be non-trivial [34]. Meanwhile, fine-tuning LLMs or training STFMs from scratch using large-scale, cross-domain ST data often comes at the cost of interactive capabilities, thereby hindering interpretability in the prediction outcomes. These limitations motivate us to explore a novel paradigm that not only retains strong numerical reasoning abilities but also enhances interpretability, bridging the gap between predictive accuracy and explanatory insight." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 51, + 554, + 295, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 554, + 295, + 674 + ], + "spans": [ + { + "bbox": [ + 51, + 554, + 295, + 674 + ], + "type": "text", + "content": "- Large foundation models are all we need? While the extensive parameterization of FMs enables impressive generalization capabilities, particularly in zero/few-shot settings, their superiority over smaller expert models remains context-dependent. In ST domains such as time series analysis [122] and urban planning [57], smaller expert models often outperform FMs when provided with sufficient domain-specific training data. This raises fundamental questions about the trade-offs between model scalability, efficiency, and task-specific optimization. Future research should delve into hybrid approaches that combine the adaptability of large models with the precision of expert models." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 51, + 674, + 294, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 674, + 294, + 708 + ], + "spans": [ + { + "bbox": [ + 51, + 674, + 294, + 708 + ], + "type": "text", + "content": "- One-fit-all FMs across the full workflow. While current FMs are typically designed to support only specific stages of ST data science, we envision a more unified FM capable of seamlessly" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 322, + 84, + 560, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 84, + 560, + 140 + ], + "spans": [ + { + "bbox": [ + 322, + 84, + 560, + 140 + ], + "type": "text", + "content": "spanning the entire workflow, from initial data sensing and management to mining and supporting downstream applications. Achieving this goal will likely require the development of advanced LLM agents that can function as full-stack engineers (i.e., strongly benefiting all stages) for ST data science." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 315, + 140, + 560, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 140, + 560, + 239 + ], + "spans": [ + { + "bbox": [ + 315, + 140, + 560, + 239 + ], + "type": "text", + "content": "- Integrating STFMs with multimodal understanding. While current STFMs excel in processing structured ST data, their ability to integrate and reason over multimodal information, including text, images, video, and sensor data, remains underdeveloped. Many tasks require models to jointly interpret geospatial context, temporal dynamics, and text descriptions. Future research can focus on designing multimodal STFMs that effectively align, fuse, and reason over heterogeneous data sources, enabling more context-aware and human-interpretable decision-making." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 315, + 247, + 484, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 247, + 484, + 258 + ], + "spans": [ + { + "bbox": [ + 315, + 247, + 484, + 258 + ], + "type": "text", + "content": "B Zero-shot Utilization of LLMs" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 315, + 262, + 558, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 262, + 558, + 273 + ], + "spans": [ + { + "bbox": [ + 315, + 262, + 558, + 273 + ], + "type": "text", + "content": "There are three ways of directly using LLMs for various ST tasks:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 315, + 275, + 559, + 494 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 315, + 275, + 559, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 275, + 559, + 352 + ], + "spans": [ + { + "bbox": [ + 315, + 275, + 559, + 352 + ], + "type": "text", + "content": "- LLM-as-Augmenter. Pretrained LLMs can enhance both data understanding and model performance. On the one hand, it can serve as the input augmenter, which enhances data interoperability or provides external information [40, 79] (e.g., textual or visual). On the other hand, LLMs can serve as a parameter-frozen model component [102, 150, 166], thus augmenting domain models by injecting the pretrained external knowledge in LLMs." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 315, + 352, + 559, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 352, + 559, + 407 + ], + "spans": [ + { + "bbox": [ + 315, + 352, + 559, + 407 + ], + "type": "text", + "content": "- LLM-as-Predictor. LLMs can be directly employed as predictors [33, 53, 73, 125] for various tasks. Due to the modality gap between text and ST data, preprocessing is required to fit the input spaces of LLMs. Such step typically contains prompt engineering [73, 125, 147-149] or patch & tokenization [53]." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 315, + 407, + 559, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 407, + 559, + 494 + ], + "spans": [ + { + "bbox": [ + 315, + 407, + 559, + 494 + ], + "type": "text", + "content": "- LLM-as-Agent. LLM-based agents are typically equipped with the ability to memorize and call various tools. When applied to ST data science, various domain-expert models can be wrapped as a tool and added into the agent in a plug-and-play manner [144, 168, 174]. As such, LLM serves as a router to access different models with both flexibility and performance guarantees. Furthermore, multi-agent systems [185] can be built to solve more complex tasks in the ST domain." + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 503, + 523, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 503, + 523, + 516 + ], + "spans": [ + { + "bbox": [ + 315, + 503, + 523, + 516 + ], + "type": "text", + "content": "C Comparison between LLMs and PFMs" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 518, + 559, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 518, + 559, + 584 + ], + "spans": [ + { + "bbox": [ + 313, + 518, + 559, + 584 + ], + "type": "text", + "content": "Table 3 demonstrates the comparison between LLMs and PFMs on their capabilities, including perception, optimization, and reasoning. For example, PFMs excel in exceptional numerical reasoning abilities, yet they often struggle with common-sense understanding. There is still no free lunch, and the user can choose either LLMs or PFMs according to the downstream applications." + } + ] + } + ], + "index": 29 + }, + { + "type": "table", + "bbox": [ + 317, + 628, + 555, + 705 + ], + "blocks": [ + { + "bbox": [ + 315, + 594, + 559, + 616 + ], + "lines": [ + { + "bbox": [ + 315, + 594, + 559, + 616 + ], + "spans": [ + { + "bbox": [ + 315, + 594, + 559, + 616 + ], + "type": "text", + "content": "Table 3: A capability comparison between LLMs and PFMs for ST data science." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 628, + 555, + 705 + ], + "lines": [ + { + "bbox": [ + 317, + 628, + 555, + 705 + ], + "spans": [ + { + "bbox": [ + 317, + 628, + 555, + 705 + ], + "type": "table", + "html": "
CapabilitiesLarge Language Models (LLMs)Pretrained Foundation Models (PFMs)
Perception▲ Limited native ST perception; can be enhanced via fine-tuning✓ Strong ST perception, integrating sensor data and domain-specific learning
Optimization✓ Agent-based reasoning for decision-making; relies on prompting and heuristics▲ Limited; lacks decision-making ability for control and planning
Common-sense Reasoning✓ Strong via pretraining on vast textual data; can be enhanced with fine-tuning▲ Limited; relies on structured ST data rather than broad world knowledge
Numerical Reasoning▲ Handles arithmetic but struggles with structured ST computations✓ Designed for numerical problems, e.g., forecasting, anomaly detection
Causal Reasoning▲ Can infer causal relations from text but lacks structured ST modeling✓ Built-in graph-based and ST causal modeling
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