Daily Papers

"Code-as-Policy" considers how executable code can complement data-intensive Vision-Language-Action (VLA) methods, yet their effectiveness as autonomous controllers for embodied manipulation remains underexplored. We present CaP-X, an open-access framework for systematically studying Code-as-Policy agents in robot manipulation. At its core is CaP-Gym, an interactive environment in which agents control robots by synthesizing and executing programs that compose perception and control primitives. Building on this foundation, CaP-Bench evaluates frontier language and vision-language models across varying levels of abstraction, interaction, and perceptual grounding. Across 12 models, CaP-Bench reveals a consistent trend: performance improves with human-crafted abstractions but degrades as these priors are removed, exposing a dependence on designer scaffolding. At the same time, we observe that this gap can be mitigated through scaling agentic test-time computation--through multi-turn interaction, structured execution feedback, visual differencing, automatic skill synthesis, and ensembled reasoning--substantially improves robustness even when agents operate over low-level primitives. These findings allow us to derive CaP-Agent0, a training-free framework that recovers human-level reliability on several manipulation tasks in simulation and on real embodiments. We further introduce CaP-RL, showing reinforcement learning with verifiable rewards improves success rates and transfers from sim2real with minimal gap. Together, CaP-X provides a principled, open-access platform for advancing embodied coding agents.

Recent advances in large language models (LLMs) have led to strong reasoning capabilities; however, evaluating such models in low-resource languages remains challenging due to the lack of standardized benchmarks. In particular, Urdu reasoning evaluation has been limited by the sensitivity of machine translation and an emphasis on general language tasks rather than reasoning benchmarks. In this paper, we propose a contextually ensembled translation framework with human-in-the-loop validation that leverages multiple translation systems to develop Urdu reasoning benchmarks while preserving contextual and structural integrity. Using this framework, we translate widely adopted reasoning and question-answering benchmarks, including MGSM, MATH-500, CommonSenseQA, and OpenBookQA, into Urdu, collectively referred to as UrduBench, and conduct a comprehensive evaluation of both reasoning-oriented and instruction-tuned LLMs across multiple prompting strategies. Our analysis reveals performance differences across (1) four datasets, (2) five task difficulty levels, (3) diverse model architectures, (4) multiple model scaling settings, and (5) language consistency tests. We find that multi-step and symbolic reasoning tasks pose significant challenges in Urdu, and that stable language alignment is a critical prerequisite for robust reasoning. Overall, our work establishes a scalable methodology for standardized reasoning evaluation in Urdu and provides empirical insights into multilingual reasoning failures. This experimental setup is also broadly applicable to other low-resource languages. The code and datasets will be publicly released.

Multi-modal large language models have seen rapid advancement alongside large language models. However, while language models can effectively leverage chain-of-thought prompting for zero or few-shot learning, similar prompting strategies are less effective for multi-modal LLMs due to modality gaps and task complexity. To address this challenge, we explore two prompting approaches: a dual-query method that separates multi-modal input analysis and answer generation into two prompting steps, and an ensemble prompting method that combines multiple prompt variations to arrive at the final answer. Although these approaches enhance the model's reasoning capabilities without fine-tuning, they introduce significant inference overhead. Therefore, building on top of these two prompting techniques, we propose a self-distillation framework such that the model can improve itself without any annotated data. Our self-distillation framework learns representation intervention modules from the reasoning traces collected from ensembled dual-query prompts, in the form of hidden representations. The lightweight intervention modules operate in parallel with the frozen original model, which makes it possible to maintain computational efficiency while significantly improving model capability. We evaluate our method on five widely-used VQA benchmarks, demonstrating its effectiveness in performing multi-hop reasoning for complex tasks.

Despite recent advances in large language models, open-source models often struggle to consistently perform well on complex reasoning tasks. Existing ensemble methods, whether applied at the token or output levels, fail to address these challenges. In response, we present Language model Ensemble with Monte Carlo Tree Search (LE-MCTS), a novel framework for process-level ensembling of language models. LE-MCTS formulates step-by-step reasoning with an ensemble of language models as a Markov decision process. In this framework, states represent intermediate reasoning paths, while actions consist of generating the next reasoning step using one of the language models selected from a predefined pool. Guided by a process-based reward model, LE-MCTS performs a tree search over the reasoning steps generated by different language models, identifying the most accurate reasoning chain. Experimental results on five mathematical reasoning benchmarks demonstrate that our approach outperforms both single language model decoding algorithms and language model ensemble methods. Notably, LE-MCTS improves performance by 3.6% and 4.3% on the MATH and MQA datasets, respectively, highlighting its effectiveness in solving complex reasoning problems.

Selecting an appropriate reasoning method for a given query remains a key challenge in language model generation. Existing approaches typically generate multiple candidate responses and use an aggregation strategy to select the output answer, often assuming that more candidate answers yield higher accuracy. We revisit this assumption through a rigorous theoretical analysis, deriving accuracy bounds for standard aggregation methods under fixed generation distributions and candidate sizes. Building on these insights, we introduce EPIC, an Ensemble Planning with Contrastive learning framework to learn a shared representation space that captures both model reasoning abilities and query-method compatibility. EPIC incorporates our probability bounds as a regularizer in a utility-driven optimization that balances accuracy and computational cost. Experiments on diverse mathematical reasoning tasks show that EPIC consistently selects optimal reasoning methods, improving accuracy while reducing computational overhead. Our code can be found at https://github.com/nguyenngocbaocmt02/EPIC.

Large language models (LLMs) are documented to struggle in settings that require complex reasoning. Nevertheless, instructing the model to break down the problem into smaller reasoning steps (Wei et al., 2022), or ensembling various generations through modifying decoding steps (Wang et al., 2023) boosts performance. Current methods assume that the input prompt is fixed and expect the decoding strategies to introduce the diversity needed for ensembling. In this work, we relax this assumption and discuss how one can create and leverage variations of the input prompt as a means to diversity of thought to improve model performance. We propose a method that automatically improves prompt diversity by soliciting feedback from the LLM to ideate approaches that fit for the problem. We then ensemble the diverse prompts in our method DIV-SE (DIVerse reasoning path Self-Ensemble) across multiple inference calls. We also propose a cost-effective alternative where diverse prompts are used within a single inference call; we call this IDIV-SE (In-call DIVerse reasoning path Self-Ensemble). Under a fixed generation budget, DIV-SE and IDIV-SE outperform the previously discussed baselines using both GPT-3.5 and GPT-4 on several reasoning benchmarks, without modifying the decoding process. Additionally, DIV-SE advances state-of-the-art performance on recent planning benchmarks (Valmeekam et al., 2023), exceeding the highest previously reported accuracy by at least 29.6 percentage points on the most challenging 4/5 Blocksworld task. Our results shed light on how to enforce prompt diversity toward LLM reasoning and thereby improve the pareto frontier of the accuracy-cost trade-off.

Although chain-of-thought (CoT) prompting combined with language models has achieved encouraging results on complex reasoning tasks, the naive greedy decoding used in CoT prompting usually causes the repetitiveness and local optimality. To address this shortcoming, ensemble-optimization tries to obtain multiple reasoning paths to get the final answer assembly. However, current ensemble-optimization methods either simply employ rule-based post-processing such as self-consistency, or train an additional model based on several task-related human annotations to select the best one among multiple reasoning paths, yet fail to generalize to realistic settings where the type of input questions is unknown or the answer format of reasoning paths is unknown. To avoid their limitations, we propose self-agreement, a generalizable ensemble-optimization method applying in almost all scenarios where the type of input questions and the answer format of reasoning paths may be known or unknown. Self-agreement firstly samples from language model's decoder to generate a diverse set of reasoning paths, and subsequently prompts the language model one more time to determine the optimal answer by selecting the most agreed answer among the sampled reasoning paths. Self-agreement simultaneously achieves remarkable performance on six public reasoning benchmarks and superior generalization capabilities.

Recent advancements in Chain-of-Thought prompting have facilitated significant breakthroughs for Large Language Models (LLMs) in complex reasoning tasks. Current research enhances the reasoning performance of LLMs by sampling multiple reasoning chains and ensembling based on the answer frequency. However, this approach fails in scenarios where the correct answers are in the minority. We identify this as a primary factor constraining the reasoning capabilities of LLMs, a limitation that cannot be resolved solely based on the predicted answers. To address this shortcoming, we introduce a hierarchical reasoning aggregation framework AoR (Aggregation of Reasoning), which selects answers based on the evaluation of reasoning chains. Additionally, AoR incorporates dynamic sampling, adjusting the number of reasoning chains in accordance with the complexity of the task. Experimental results on a series of complex reasoning tasks show that AoR outperforms prominent ensemble methods. Further analysis reveals that AoR not only adapts various LLMs but also achieves a superior performance ceiling when compared to current methods.

Recent research has shown that rationales, or step-by-step chains of thought, can be used to improve performance in multi-step reasoning tasks. We reconsider rationale-augmented prompting for few-shot in-context learning, where (input -> output) prompts are expanded to (input, rationale -> output) prompts. For rationale-augmented prompting we demonstrate how existing approaches, which rely on manual prompt engineering, are subject to sub-optimal rationales that may harm performance. To mitigate this brittleness, we propose a unified framework of rationale-augmented ensembles, where we identify rationale sampling in the output space as the key component to robustly improve performance. This framework is general and can easily be extended to common natural language processing tasks, even those that do not traditionally leverage intermediate steps, such as question answering, word sense disambiguation, and sentiment analysis. We demonstrate that rationale-augmented ensembles achieve more accurate and interpretable results than existing prompting approaches--including standard prompting without rationales and rationale-based chain-of-thought prompting--while simultaneously improving interpretability of model predictions through the associated rationales.

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical reasoning skills. Existing approaches to address this challenge often rely on ensemble methods and suffer from the problem of data scarcity in target domains. In this work, we present a novel method to enhance LLMs' capabilities in mathematical reasoning tasks. Motivated by the need to bridge this gap, our approach incorporates a question paraphrase strategy, which aims at diversifying the linguistic forms of mathematical questions to improve generalization. Additionally, specialized training objectives are employed to guide the model's learning process, focusing on enhancing its understanding of mathematical concepts and reasoning processes. We conduct experiments on four datasets using different LLMs, and demonstrate the effectiveness of our approach in improving LLMs' performance on mathematical reasoning tasks. Our findings underscore the significance of our methodology in the advancement of large language models and its potential implications for real-world applications that require mathematical reasoning abilities.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

Existing methods usually leverage a fixed strategy, such as natural language reasoning, code-augmented reasoning, tool-integrated reasoning, or ensemble-based reasoning, to guide Large Language Models (LLMs) to perform mathematical reasoning. Our analysis reveals that the single strategy cannot adapt to problem-specific requirements and thus overlooks the trade-off between effectiveness and efficiency. To address these issues, we propose Planning and Routing through Instance-Specific Modeling (PRISM), a novel framework that decouples mathematical reasoning into two stages: strategy planning and targeted execution. Specifically, we first curate a multi-strategy preference dataset, which we call MathStrat, capturing correctness, process quality, and computational efficiency for each problem--strategy pair. Then, we train a lightweight Strategy Adapter based on the dataset to obtain confidence distributions over the mentioned four reasoning strategies. At inference time, an adaptive routing policy dynamically tailors the reasoning approach based on predictor confidence. It directs the model to use single-strategy execution for high-confidence predictions, dual-strategy verification for competitive scenarios, or comprehensive multi-strategy exploration for uncertain cases. Extensive experiments across five mathematical reasoning benchmarks demonstrate that PRISM consistently outperforms individual strategies and ensemble baselines, achieving improvements ranging from 0.9% to 7.6% across different base models. The adaptive routing approach shows particularly strong benefits for mathematical reasoning tasks across diverse model architectures. Our code is released at https://github.com/reml-group/PRISM.

Ensemble learning of LLMs has emerged as a promising alternative to enhance performance, but existing approaches typically treat models as black boxes, combining the inputs or final outputs while overlooking the rich internal representations and interactions across models.In this work, we introduce LLMBoost, a novel ensemble fine-tuning framework that breaks this barrier by explicitly leveraging intermediate states of LLMs. Inspired by the boosting paradigm, LLMBoost incorporates three key innovations. First, a cross-model attention mechanism enables successor models to access and fuse hidden states from predecessors, facilitating hierarchical error correction and knowledge transfer. Second, a chain training paradigm progressively fine-tunes connected models with an error-suppression objective, ensuring that each model rectifies the mispredictions of its predecessor with minimal additional computation. Third, a near-parallel inference paradigm design pipelines hidden states across models layer by layer, achieving inference efficiency approaching single-model decoding. We further establish the theoretical foundations of LLMBoost, proving that sequential integration guarantees monotonic improvements under bounded correction assumptions. Extensive experiments on commonsense reasoning and arithmetic reasoning tasks demonstrate that LLMBoost consistently boosts accuracy while reducing inference latency.

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including poor generalizability due to task-specific prompts, inefficiencies caused by the lack of separation between knowledge and queries, and restricted inferential capabilities. These shortcomings hinder their scalability and applicability across diverse domains. In this paper, we introduce VERUS-LM, a novel framework designed to address these challenges. VERUS-LM employs a generic prompting mechanism, clearly separates domain knowledge from queries, and supports a wide range of different logical reasoning tasks. This framework enhances adaptability, reduces computational cost, and allows for richer forms of reasoning, such as optimization and constraint satisfaction. We show that our approach succeeds in diverse reasoning on a novel dataset, markedly outperforming LLMs. Additionally, our system achieves competitive results on common reasoning benchmarks when compared to other state-of-the-art approaches, and significantly surpasses them on the difficult AR-LSAT dataset. By pushing the boundaries of hybrid reasoning, VERUS-LM represents a significant step towards more versatile neurosymbolic AI systems

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

We present Hermes 4, a family of hybrid reasoning models that combine structured, multi-turn reasoning with broad instruction-following ability. We describe the challenges encountered during data curation, synthesis, training, and evaluation, and outline the solutions employed to address these challenges at scale. We comprehensively evaluate across mathematical reasoning, coding, knowledge, comprehension, and alignment benchmarks, and we report both quantitative performance and qualitative behavioral analysis. To support open research, all model weights are published publicly at https://huggingface.co/collections/NousResearch/hermes-4-collection-68a731bfd452e20816725728

LLM Ensemble -- which involves the comprehensive use of multiple large language models (LLMs), each aimed at handling user queries during downstream inference, to benefit from their individual strengths -- has gained substantial attention recently. The widespread availability of LLMs, coupled with their varying strengths and out-of-the-box usability, has profoundly advanced the field of LLM Ensemble. This paper presents the first systematic review of recent developments in LLM Ensemble. First, we introduce our taxonomy of LLM Ensemble and discuss several related research problems. Then, we provide a more in-depth classification of the methods under the broad categories of "ensemble-before-inference, ensemble-during-inference, ensemble-after-inference'', and review all relevant methods. Finally, we introduce related benchmarks and applications, summarize existing studies, and suggest several future research directions. A curated list of papers on LLM Ensemble is available at https://github.com/junchenzhi/Awesome-LLM-Ensemble.

Knowledge graph (KG) embedding is a fundamental task in natural language processing, and various methods have been proposed to explore semantic patterns in distinctive ways. In this paper, we propose to learn an ensemble by leveraging existing methods in a relation-aware manner. However, exploring these semantics using relation-aware ensemble leads to a much larger search space than general ensemble methods. To address this issue, we propose a divide-search-combine algorithm RelEns-DSC that searches the relation-wise ensemble weights independently. This algorithm has the same computation cost as general ensemble methods but with much better performance. Experimental results on benchmark datasets demonstrate the effectiveness of the proposed method in efficiently searching relation-aware ensemble weights and achieving state-of-the-art embedding performance. The code is public at https://github.com/LARS-research/RelEns.

Sequential Recommendation (SeqRec) aims to predict the next item by capturing sequential patterns from users' historical interactions, playing a crucial role in many real-world recommender systems. However, existing approaches predominantly adopt a direct forward computation paradigm, where the final hidden state of the sequence encoder serves as the user representation. We argue that this inference paradigm, due to its limited computational depth, struggles to model the complex evolving nature of user preferences and lacks a nuanced understanding of long-tail items, leading to suboptimal performance. To address this issue, we propose ReaRec, the first inference-time computing framework for recommender systems, which enhances user representations through implicit multi-step reasoning. Specifically, ReaRec autoregressively feeds the sequence's last hidden state into the sequential recommender while incorporating special reasoning position embeddings to decouple the original item encoding space from the multi-step reasoning space. Moreover, we introduce two lightweight reasoning-based learning methods, Ensemble Reasoning Learning (ERL) and Progressive Reasoning Learning (PRL), to further effectively exploit ReaRec's reasoning potential. Extensive experiments on five public real-world datasets and different SeqRec architectures demonstrate the generality and effectiveness of our proposed ReaRec. Remarkably, post-hoc analyses reveal that ReaRec significantly elevates the performance ceiling of multiple sequential recommendation backbones by approximately 30\%-50\%. Thus, we believe this work can open a new and promising avenue for future research in inference-time computing for sequential recommendation.

Reasoning presents a significant and challenging issue for Large Language Models (LLMs). The predominant focus of research has revolved around developing diverse prompting strategies to guide and structure the reasoning processes of LLMs. However, these approaches based on decoder-only causal language models often operate the input question in a single forward pass, potentially missing the rich, back-and-forth interactions inherent in human reasoning. Scant attention has been paid to a critical dimension, i.e., the input question itself embedded within the prompts. In response, we introduce a deceptively simple yet highly effective prompting strategy, termed question "re-reading". Drawing inspiration from human learning and problem-solving, re-reading entails revisiting the question information embedded within input prompts. This approach aligns seamlessly with the cognitive principle of reinforcement, enabling LLMs to extract deeper insights, identify intricate patterns, establish more nuanced connections, and ultimately enhance their reasoning capabilities across various tasks. Experiments conducted on a series of reasoning benchmarks serve to underscore the effectiveness and generality of our method. Moreover, our findings demonstrate that our approach seamlessly integrates with various language models, though-eliciting prompting methods, and ensemble techniques, further underscoring its versatility and compatibility in the realm of LLMs.

Large language models (LLMs) have shown remarkable capabilities in various natural language understanding tasks. With only a few demonstration examples, these LLMs can quickly adapt to target tasks without expensive gradient updates. Common strategies to boost such 'in-context' learning ability are to ensemble multiple model decoded results and require the model to generate an explanation along with the prediction. However, these models often treat different class predictions equally and neglect the potential discrepancy between the explanations and predictions. To fully unleash the power of explanations, we propose EASE, an Explanation-Aware Soft Ensemble framework to empower in-context learning with LLMs. We design two techniques, explanation-guided ensemble, and soft probability aggregation, to mitigate the effect of unreliable explanations and improve the consistency between explanations and final predictions. Experiments on seven natural language understanding tasks and four varying-size LLMs demonstrate the effectiveness of our proposed framework.

Large language models often require costly optimization, such as reinforcement learning, to master complex reasoning tasks. This work demonstrates that reasoning ability, once learned, can be extracted and transferred between models as a compact task vector. We source two publicly available, identically initialized Qwen2.5 models, one fine-tuned with supervised fine-tuning (SFT) and the other with group relative policy optimization (GRPO) on the same dataset. From these, we extract a reasoning vector: v_{reason} = theta_{GRPO} - theta_{SFT}. We hypothesize that this vector captures the reasoning capability instilled by reinforcement learning while factoring out shared knowledge from the SFT process. When added to compatible instruction-tuned models through simple arithmetic, this vector consistently improves performance across diverse reasoning benchmarks: GSM8K (+4.9%), HumanEval (+4.3%), SciQ (+1.7%), and BigBenchHard (+12.3% for the 1.5B model). The performance improvements persist under adversarial conditions. Conversely, subtracting the vector causes significant performance degradation (-11.8% on GSM8K), demonstrating the vector's strong contribution to the model's reasoning abilities. This work shows how reasoning capabilities, typically developed through expensive training, can be extracted from existing open-source models and reused through simple tensor arithmetic, offering a practical way to enhance models by recycling prior computational investments.

A growing body of research in continual learning focuses on the catastrophic forgetting problem. While many attempts have been made to alleviate this problem, the majority of the methods assume a single model in the continual learning setup. In this work, we question this assumption and show that employing ensemble models can be a simple yet effective method to improve continual performance. However, ensembles' training and inference costs can increase significantly as the number of models grows. Motivated by this limitation, we study different ensemble models to understand their benefits and drawbacks in continual learning scenarios. Finally, to overcome the high compute cost of ensembles, we leverage recent advances in neural network subspace to propose a computationally cheap algorithm with similar runtime to a single model yet enjoying the performance benefits of ensembles.

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in high-stakes contexts, such as medical diagnosis and finance. We show that this inconsistent behavior extends beyond predictions to feature attributions, which may likewise have negative implications for the intelligibility of a model, and one's ability to find recourse for subjects. We then introduce selective ensembles to mitigate such inconsistencies by applying hypothesis testing to the predictions of a set of models trained using randomly-selected starting conditions; importantly, selective ensembles can abstain in cases where a consistent outcome cannot be achieved up to a specified confidence level. We prove that that prediction disagreement between selective ensembles is bounded, and empirically demonstrate that selective ensembles achieve consistent predictions and feature attributions while maintaining low abstention rates. On several benchmark datasets, selective ensembles reach zero inconsistently predicted points, with abstention rates as low 1.5%.

We propose a deep-learning system -- for the SQuAD2.0 task -- that finds, or indicates the lack of, a correct answer to a question in a context paragraph. Our goal is to learn an ensemble of heterogeneous SQuAD2.0 models that, when blended properly, outperforms the best model in the ensemble per se. We created a stacking ensemble that combines top-N predictions from two models, based on ALBERT and RoBERTa, into a multiclass classification task to pick the best answer out of their predictions. We explored various ensemble configurations, input representations, and model architectures. For evaluation, we examined test-set EM and F1 scores; our best-performing ensemble incorporated a CNN-based meta-model and scored 87.117 and 90.306, respectively -- a relative improvement of 0.55% for EM and 0.61% for F1 scores, compared to the baseline performance of the best model in the ensemble, an ALBERT-based model, at 86.644 for EM and 89.760 for F1.

Large reasoning models (LRMs) exhibit diverse high-level reasoning patterns (e.g., direct solution, reflection-and-verification, and exploring multiple solutions), yet prevailing training recipes implicitly bias models toward a limited set of dominant patterns. Through a systematic analysis, we identify substantial accuracy variance across these patterns on mathematics and science benchmarks, revealing that a model's default reasoning pattern is often sub-optimal for a given problem. To address this, we introduce Group Pattern Selection Optimization (GPSO), a reinforcement learning framework that extends GRPO by incorporating multi-pattern rollouts, verifier-guided optimal pattern selection per problem, and attention masking during optimization to prevent the leakage of explicit pattern suffixes into the learned policy. By exploring a portfolio of diverse reasoning strategies and optimizing the policy on the most effective ones, GPSO enables the model to internalize the mapping from problem characteristics to optimal reasoning patterns. Extensive experiments demonstrate that GPSO delivers consistent and substantial performance gains across various model backbones and benchmarks, effectively mitigating pattern sub-optimality and fostering more robust, adaptable reasoning. All data and codes are available at https://github.com/wanghanbinpanda/GPSO.

The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to characterize and filter model errors, improving precision often comes at the cost of reduced recall. This paper addresses the hypothesis that leveraging multiple pre-trained models can mitigate this recall reduction. We formulate the challenge of identifying and managing conflicting predictions from various models as a consistency-based abduction problem. The input predictions and the learned error detection rules derived from each model are encoded in a logic program. We then seek an abductive explanation--a subset of model predictions--that maximizes prediction coverage while ensuring the rate of logical inconsistencies (derived from domain constraints) remains below a specified threshold. We propose two algorithms for this knowledge representation task: an exact method based on Integer Programming (IP) and an efficient Heuristic Search (HS). Through extensive experiments on a simulated aerial imagery dataset featuring controlled, complex distributional shifts, we demonstrate that our abduction-based framework outperforms individual models and standard ensemble baselines, achieving, for instance, average relative improvements of approximately 13.6% in F1-score and 16.6% in accuracy across 15 diverse test datasets when compared to the best individual model. Our results validate the use of consistency-based abduction as an effective mechanism to robustly integrate knowledge from multiple imperfect reasoners in challenging, novel scenarios.

Neural networks are known to produce poor uncertainty estimations, and a variety of approaches have been proposed to remedy this issue. This includes deep ensemble, a simple and effective method that achieves state-of-the-art results for uncertainty-aware learning tasks. In this work, we explore a combinatorial generalization of deep ensemble called deep combinatorial aggregation (DCA). DCA creates multiple instances of network components and aggregates their combinations to produce diversified model proposals and predictions. DCA components can be defined at different levels of granularity. And we discovered that coarse-grain DCAs can outperform deep ensemble for uncertainty-aware learning both in terms of predictive performance and uncertainty estimation. For fine-grain DCAs, we discover that an average parameterization approach named deep combinatorial weight averaging (DCWA) can improve the baseline training. It is on par with stochastic weight averaging (SWA) but does not require any custom training schedule or adaptation of BatchNorm layers. Furthermore, we propose a consistency enforcing loss that helps the training of DCWA and modelwise DCA. We experiment on in-domain, distributional shift, and out-of-distribution image classification tasks, and empirically confirm the effectiveness of DCWA and DCA approaches.

Model selection is a strategy aimed at creating accurate and robust models. A key challenge in designing these algorithms is identifying the optimal model for classifying any particular input sample. This paper addresses this challenge and proposes a novel framework for differentiable model selection integrating machine learning and combinatorial optimization. The framework is tailored for ensemble learning, a strategy that combines the outputs of individually pre-trained models, and learns to select appropriate ensemble members for a particular input sample by transforming the ensemble learning task into a differentiable selection program trained end-to-end within the ensemble learning model. Tested on various tasks, the proposed framework demonstrates its versatility and effectiveness, outperforming conventional and advanced consensus rules across a variety of settings and learning tasks.

Reasoning has become a central paradigm for large language models (LLMs), consistently boosting accuracy across diverse benchmarks. Yet its suitability for precision-sensitive tasks remains unclear. We present the first systematic study of reasoning for classification tasks under strict low false positive rate (FPR) regimes. Our analysis covers two tasks--safety detection and hallucination detection--evaluated in both fine-tuned and zero-shot settings, using standard LLMs and Large Reasoning Models (LRMs). Our results reveal a clear trade-off: Think On (reasoning-augmented) generation improves overall accuracy, but underperforms at the low-FPR thresholds essential for practical use. In contrast, Think Off (no reasoning during inference) dominates in these precision-sensitive regimes, with Think On surpassing only when higher FPRs are acceptable. In addition, we find token-based scoring substantially outperforms self-verbalized confidence for precision-sensitive deployments. Finally, a simple ensemble of the two modes recovers the strengths of each. Taken together, our findings position reasoning as a double-edged tool: beneficial for average accuracy, but often ill-suited for applications requiring strict precision.

Automating machine learning has achieved remarkable technological developments in recent years, and building an automated machine learning pipeline is now an essential task. The model ensemble is the technique of combining multiple models to get a better and more robust model. However, existing automated machine learning tends to be simplistic in handling the model ensemble, where the ensemble strategy is fixed, such as stacked generalization. There have been many techniques on different ensemble methods, especially ensemble selection, and the fixed ensemble strategy limits the upper limit of the model's performance. In this article, we present a novel framework for automated machine learning. Our framework incorporates advances in dynamic ensemble selection, and to our best knowledge, our approach is the first in the field of AutoML to search and optimize ensemble strategies. In the comparison experiments, our method outperforms the state-of-the-art automated machine learning frameworks with the same CPU time in 42 classification datasets from the OpenML platform. Ablation experiments on our framework validate the effectiveness of our proposed method.

Recently, long-thought reasoning models achieve strong performance on complex reasoning tasks, but often incur substantial inference overhead, making efficiency a critical concern. Our empirical analysis reveals that the benefit of using Long-CoT varies across problems: while some problems require elaborate reasoning, others show no improvement, or even degraded accuracy. This motivates adaptive reasoning strategies that tailor reasoning depth to the input. However, prior work primarily reduces redundancy within long reasoning paths, limiting exploration of more efficient strategies beyond the Long-CoT paradigm. To address this, we propose a novel two-stage framework for adaptive and efficient reasoning. First, we construct a hybrid reasoning model by merging long and short CoT models to enable diverse reasoning styles. Second, we apply bi-level preference training to guide the model to select suitable reasoning styles (group-level), and prefer concise and correct reasoning within each style group (instance-level). Experiments demonstrate that our method significantly reduces inference costs compared to other baseline approaches, while maintaining performance. Notably, on five mathematical datasets, the average length of reasoning is reduced by more than 50%, highlighting the potential of adaptive strategies to optimize reasoning efficiency in large language models. Our code is coming soon at https://github.com/StarDewXXX/AdaR1

Recent Long-Context Language Models (LCLMs) can process hundreds of thousands of tokens in a single prompt, enabling new opportunities for knowledge-intensive multi-hop reasoning by integrating large sets of retrieved documents or, in some cases, directly all necessary information. However, simply feeding more documents into the context window fails to capture how evidence should be connected. We address this gap with thought templates, which recast reasoning as reusable thought caches, derived from prior problem solving traces, structuring how evidence is combined and guiding multi-hop inference with factual documents. To keep these templates effective, we propose an update strategy that iteratively refines templates derived from training data through natural-language feedback. Across diverse benchmarks and LCLM families, our approach delivers consistent gains over strong baselines in both retrieval-based and retrieval-free settings. Furthermore, we show that optimized templates can be distilled into smaller open-source models, demonstrating its broad applicability and transparent reasoning reuse. We refer to our framework as Thought Template Augmented LCLMs (ToTAL).

Tabular data, a fundamental data format in machine learning, is predominantly utilized in competitions and real-world applications. The performance of tabular models--such as gradient boosted decision trees and neural networks--can vary significantly across datasets due to differences in feature distributions and task characteristics. Achieving top performance on each dataset often requires specialized expert knowledge. To address this variability, practitioners often aggregate the predictions of multiple models. However, conventional aggregation strategies typically rely on static combination rules and lack instance-level adaptability. In this work, we propose an in-context ensemble framework for tabular prediction that leverages large language models (LLMs) to perform dynamic, instance-specific integration of external model predictions. Without access to raw tabular features or semantic information, our method constructs a context around each test instance using its nearest neighbors and the predictions from a pool of external models. Within this enriched context, we introduce Chain of Tabular Thoughts (CoT^2), a prompting strategy that guides LLMs through multi-step, interpretable reasoning, making still further progress toward expert-level decision-making. Experimental results show that our method outperforms well-tuned baselines and standard ensemble techniques across a wide range of tabular datasets.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

We introduce Motif-2-12.7B-Reasoning, a 12.7B parameter language model designed to bridge the gap between open-weight systems and proprietary frontier models in complex reasoning and long-context understanding. Addressing the common challenges of model collapse and training instability in reasoning adaptation, we propose a comprehensive, reproducible training recipe spanning system, data, and algorithmic optimizations. Our approach combines memory-efficient infrastructure for 64K-token contexts using hybrid parallelism and kernel-level optimizations with a two-stage Supervised Fine-Tuning (SFT) curriculum that mitigates distribution mismatch through verified, aligned synthetic data. Furthermore, we detail a robust Reinforcement Learning Fine-Tuning (RLFT) pipeline that stabilizes training via difficulty-aware data filtering and mixed-policy trajectory reuse. Empirical results demonstrate that Motif-2-12.7B-Reasoning achieves performance comparable to models with significantly larger parameter counts across mathematics, coding, and agentic benchmarks, offering the community a competitive open model and a practical blueprint for scaling reasoning capabilities under realistic compute constraints.

Over the past years, advances in artificial intelligence (AI) have demonstrated how AI can solve many perception and generation tasks, such as image classification and text writing, yet reasoning remains a challenge. This paper introduces the FLIP dataset, a benchmark for evaluating AI reasoning capabilities based on human verification tasks on the Idena blockchain. FLIP challenges present users with two orderings of 4 images, requiring them to identify the logically coherent one. By emphasizing sequential reasoning, visual storytelling, and common sense, FLIP provides a unique testbed for multimodal AI systems. Our experiments evaluate state-of-the-art models, leveraging both vision-language models (VLMs) and large language models (LLMs). Results reveal that even the best open-sourced and closed-sourced models achieve maximum accuracies of 75.5% and 77.9%, respectively, in zero-shot settings, compared to human performance of 95.3%. Captioning models aid reasoning models by providing text descriptions of images, yielding better results than when using the raw images directly, 69.6% vs. 75.2% for Gemini 1.5 Pro. Combining the predictions from 15 models in an ensemble increases the accuracy to 85.2%. These findings highlight the limitations of existing reasoning models and the need for robust multimodal benchmarks like FLIP. The full codebase and dataset will be available at https://github.com/aplesner/FLIP-Reasoning-Challenge.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic domains. However, effectively extending these capabilities into multimodal contexts-where models must integrate both visual and textual inputs-continues to be a significant challenge. Multimodal reasoning introduces complexities, such as handling conflicting information across modalities, which require models to adopt advanced interpretative strategies. Addressing these challenges involves not only sophisticated algorithms but also robust methodologies for evaluating reasoning accuracy and coherence. This paper offers a concise yet insightful overview of reasoning techniques in both textual and multimodal LLMs. Through a thorough and up-to-date comparison, we clearly formulate core reasoning challenges and opportunities, highlighting practical methods for post-training optimization and test-time inference. Our work provides valuable insights and guidance, bridging theoretical frameworks and practical implementations, and sets clear directions for future research.

With the help of in-context learning (ICL), large language models (LLMs) have achieved impressive performance across various tasks. However, the function of descriptive instructions during ICL remains under-explored. In this work, we propose an ensemble prompt framework to describe the selection criteria of multiple in-context examples, and preliminary experiments on machine translation (MT) across six translation directions confirm that this framework boosts ICL perfromance. But to our surprise, LLMs might not necessarily care what the descriptions actually say, and the performance gain is primarily caused by the ensemble format, since the framework could lead to improvement even with random descriptive nouns. We further apply this new ensemble prompt on a range of commonsense, math, logical reasoning and hallucination tasks with three LLMs and achieve promising results, suggesting again that designing a proper prompt format would be much more effective and efficient than paying effort into specific descriptions. Our code will be publicly available once this paper is published.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Existing methods on understanding the capabilities of LLMs in logical reasoning rely on binary entailment classification or synthetically derived rationales, which are not sufficient for proper investigation of model's capabilities. We present P-FOLIO, a human-annotated dataset consisting of diverse and complex reasoning chains for a set of realistic logical reasoning stories also written by humans. P-FOLIO is collected with an annotation protocol that facilitates humans to annotate well-structured natural language proofs for first-order logic reasoning problems in a step-by-step manner. The number of reasoning steps in P-FOLIO span from 0 to 20. We further use P-FOLIO to evaluate and improve large-language-model (LLM) reasoning capabilities. We evaluate LLM reasoning capabilities at a fine granularity via single-step inference rule classification, with more diverse inference rules of more diverse and higher levels of complexities than previous works. Given that a single model-generated reasoning chain could take a completely different path than the human-annotated one, we sample multiple reasoning chains from a model and use pass@k metrics for evaluating the quality of model-generated reasoning chains. We show that human-written reasoning chains significantly boost the logical reasoning capabilities of LLMs via many-shot prompting and fine-tuning. Furthermore, fine-tuning Llama3-7B on P-FOLIO improves the model performance by 10% or more on three other out-of-domain logical reasoning datasets. We also conduct detailed analysis to show where most powerful LLMs fall short in reasoning. We will release the dataset and code publicly.

Deep iterative chain-of-thought (CoT) reasoning enables LLMs to tackle complex tasks by progressively activating relevant pre-trained knowledge. However, it faces challenges in ensuring continual improvement and determining a stopping criterion. In this paper, we investigate whether the relevant knowledge that contributes directly to solving the given question can be activated from the initial reasoning path, thus circumventing the need for iterative refinement. Our experiments reveal that increasing the diversity of initial reasoning paths can achieve comparable or superior performance, a concept we term breadth reasoning. However, existing breadth reasoning approaches, such as self-consistency, offer limited diversity. To address this limitation, we propose a simple yet effective method that enhances reasoning breadth by integrating contextual exploration with reduced sampling randomness. Extensive experiments demonstrate that our approach significantly outperforms deep iterative reasoning. Our code is provided in https://github.com/zongqianwu/breadth.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

Mixture-of-Experts (MoE) architectures within Large Reasoning Models (LRMs) have achieved impressive reasoning capabilities by selectively activating experts to facilitate structured cognitive processes. Despite notable advances, existing reasoning models often suffer from cognitive inefficiencies like overthinking and underthinking. To address these limitations, we introduce a novel inference-time steering methodology called Reinforcing Cognitive Experts (RICE), designed to improve reasoning performance without additional training or complex heuristics. Leveraging normalized Pointwise Mutual Information (nPMI), we systematically identify specialized experts, termed ''cognitive experts'' that orchestrate meta-level reasoning operations characterized by tokens like ''<think>''. Empirical evaluations with leading MoE-based LRMs (DeepSeek-R1 and Qwen3-235B) on rigorous quantitative and scientific reasoning benchmarks demonstrate noticeable and consistent improvements in reasoning accuracy, cognitive efficiency, and cross-domain generalization. Crucially, our lightweight approach substantially outperforms prevalent reasoning-steering techniques, such as prompt design and decoding constraints, while preserving the model's general instruction-following skills. These results highlight reinforcing cognitive experts as a promising, practical, and interpretable direction to enhance cognitive efficiency within advanced reasoning models.

In this work, we aim to develop an MLLM that understands and solves questions by learning to create each intermediate step of the reasoning involved till the final answer. To this end, we propose Collective Monte Carlo Tree Search (CoMCTS), a new learning-to-reason method for MLLMs, which introduces the concept of collective learning into ``tree search'' for effective and efficient reasoning-path searching and learning. The core idea of CoMCTS is to leverage collective knowledge from multiple models to collaboratively conjecture, search and identify effective reasoning paths toward correct answers via four iterative operations including Expansion, Simulation and Error Positioning, Backpropagation, and Selection. Using CoMCTS, we construct Mulberry-260k, a multimodal dataset with a tree of rich, explicit and well-defined reasoning nodes for each question. With Mulberry-260k, we perform collective SFT to train our model, Mulberry, a series of MLLMs with o1-like step-by-step Reasoning and Reflection capabilities. Extensive experiments demonstrate the superiority of our proposed methods on various benchmarks. Code will be available at https://github.com/HJYao00/Mulberry

Reasoning-enhanced large language models (RLLMs), whether explicitly trained for reasoning or prompted via chain-of-thought (CoT), have achieved state-of-the-art performance on many complex reasoning tasks. However, we uncover a surprising and previously overlooked phenomenon: explicit CoT reasoning can significantly degrade instruction-following accuracy. Evaluating 15 models on two benchmarks: IFEval (with simple, rule-verifiable constraints) and ComplexBench (with complex, compositional constraints), we consistently observe performance drops when CoT prompting is applied. Through large-scale case studies and an attention-based analysis, we identify common patterns where reasoning either helps (e.g., with formatting or lexical precision) or hurts (e.g., by neglecting simple constraints or introducing unnecessary content). We propose a metric, constraint attention, to quantify model focus during generation and show that CoT reasoning often diverts attention away from instruction-relevant tokens. To mitigate these effects, we introduce and evaluate four strategies: in-context learning, self-reflection, self-selective reasoning, and classifier-selective reasoning. Our results demonstrate that selective reasoning strategies, particularly classifier-selective reasoning, can substantially recover lost performance. To our knowledge, this is the first work to systematically expose reasoning-induced failures in instruction-following and offer practical mitigation strategies.

Large language models (LLMs) have demonstrated remarkable reasoning abilities in complex tasks, often relying on Chain-of-Thought (CoT) reasoning. However, due to their autoregressive token-level generation, the reasoning process is largely constrained to local decision-making and lacks global planning. This limitation frequently results in redundant, incoherent, or inaccurate reasoning, which significantly degrades overall performance. Existing approaches, such as tree-based algorithms and reinforcement learning (RL), attempt to address this issue but suffer from high computational costs and often fail to produce optimal reasoning trajectories. To tackle this challenge, we propose Plan-Then-Action Enhanced Reasoning with Group Relative Policy Optimization PTA-GRPO, a two-stage framework designed to improve both high-level planning and fine-grained CoT reasoning. In the first stage, we leverage advanced LLMs to distill CoT into compact high-level guidance, which is then used for supervised fine-tuning (SFT). In the second stage, we introduce a guidance-aware RL method that jointly optimizes the final output and the quality of high-level guidance, thereby enhancing reasoning effectiveness. We conduct extensive experiments on multiple mathematical reasoning benchmarks, including MATH, AIME2024, AIME2025, and AMC, across diverse base models such as Qwen2.5-7B-Instruct, Qwen3-8B, Qwen3-14B, and LLaMA3.2-3B. Experimental results demonstrate that PTA-GRPO consistently achieves stable and significant improvements across different models and tasks, validating its effectiveness and generalization.

Large reasoning models (e.g., R1, o3) have demonstrated remarkable mathematical problem-solving abilities. However, the high reported accuracy of these advanced models on popular datasets, reliance on purely numerical evaluation and potential benchmark leakage, often masks their true reasoning shortcomings. To address this, we propose leveraging the inherent rigor and methodological complexity of mathematical proofs as a diagnostic tool to expose these hidden failures. Specifically, we introduce the RFMDataset (Reveal Failure Modes), a collection of 200 diverse mathematical proof problems, and thoroughly evaluate advanced models' performance on it. Our in-depth analysis of their failures uncovers 10 fine-grained error types, which shows fundamental limitations in current large reasoning models: 1) large reasoning models grapple profoundly with mathematical proofs, with some generating entirely correct proofs for less than 20% of problems and failing even on basic ones; 2) models exhibit a diverse spectrum of reasoning failures, prominently demonstrating the lack of guarantees for the correctness and rigor of single-step reasoning; and 3) models show hallucination and incompleteness during the reasoning process. Our findings reveal that models' self-reflection is insufficient to resolve the current logical dilemmas, necessitating formalized and fine-grained logical training.

Chain-of-Thought (CoT) prompting has been shown to improve Large Language Model (LLM) performance on various tasks. With this approach, LLMs appear to produce human-like reasoning steps before providing answers (a.k.a., CoT reasoning), which often leads to the perception that they engage in deliberate inferential processes. However, some initial findings suggest that CoT reasoning may be more superficial than it appears, motivating us to explore further. In this paper, we study CoT reasoning via a data distribution lens and investigate if CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. Thus, its effectiveness is fundamentally bounded by the degree of distribution discrepancy between the training data and the test queries. With this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To investigate each dimension, we design DataAlchemy, an isolated and controlled environment to train LLMs from scratch and systematically probe them under various distribution conditions. Our results reveal that CoT reasoning is a brittle mirage that vanishes when it is pushed beyond training distributions. This work offers a deeper understanding of why and when CoT reasoning fails, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their tendency to produce excessively long reasoning traces, which are often filled with redundant content (e.g., repeated definitions), over-analysis of simple problems, and superficial exploration of multiple reasoning paths for harder tasks. This inefficiency introduces significant challenges for training, inference, and real-world deployment (e.g., in agent-based systems), where token economy is critical. In this survey, we provide a comprehensive overview of recent efforts aimed at improving reasoning efficiency in LRMs, with a particular focus on the unique challenges that arise in this new paradigm. We identify common patterns of inefficiency, examine methods proposed across the LRM lifecycle, i.e., from pretraining to inference, and discuss promising future directions for research. To support ongoing development, we also maintain a real-time GitHub repository tracking recent progress in the field. We hope this survey serves as a foundation for further exploration and inspires innovation in this rapidly evolving area.

A very simple way to improve the performance of almost any machine learning algorithm is to train many different models on the same data and then to average their predictions. Unfortunately, making predictions using a whole ensemble of models is cumbersome and may be too computationally expensive to allow deployment to a large number of users, especially if the individual models are large neural nets. Caruana and his collaborators have shown that it is possible to compress the knowledge in an ensemble into a single model which is much easier to deploy and we develop this approach further using a different compression technique. We achieve some surprising results on MNIST and we show that we can significantly improve the acoustic model of a heavily used commercial system by distilling the knowledge in an ensemble of models into a single model. We also introduce a new type of ensemble composed of one or more full models and many specialist models which learn to distinguish fine-grained classes that the full models confuse. Unlike a mixture of experts, these specialist models can be trained rapidly and in parallel.

Scaling up test-time compute, by generating multiple independent solutions and selecting or aggregating among them, has become a central paradigm for improving large language models (LLMs) on challenging reasoning tasks. While most prior work relies on simple majority voting or reward model ranking to aggregate solutions, these approaches may only yield limited benefits. In this work, we propose to learn aggregation as an explicit reasoning skill: given a set of candidate solutions, we train an aggregator model to review, reconcile, and synthesize a final, correct answer using reinforcement learning from verifiable rewards. A key ingredient is careful balancing of easy and hard training examples, allowing the model to learn both to recover minority-but-correct answers as well as easy majority-correct answers. Empirically, we find our method, AggLM, outperforms both strong rule-based and reward-model baselines, across multiple benchmarks. Furthermore, it generalizes effectively to solutions from differing models, including stronger ones than contained in the training data, all while requiring substantially fewer tokens than majority voting with larger numbers of solutions.

Recent works have shown that chain-of-thought (CoT) prompting can elicit language models to solve complex reasoning tasks, step-by-step. However, prompt-based CoT methods are dependent on very large models such as GPT-3 175B which are prohibitive to deploy at scale. In this paper, we use these large models as reasoning teachers to enable complex reasoning in smaller models and reduce model size requirements by several orders of magnitude. We propose Fine-tune-CoT, a method that generates reasoning samples from very large teacher models to fine-tune smaller models. We evaluate our method on a wide range of public models and complex tasks. We find that Fine-tune-CoT enables substantial reasoning capability in small models, far outperforming prompt-based baselines and even the teacher model in many tasks. Additionally, we extend our method by leveraging the teacher model's ability to generate multiple distinct rationales for each original sample. Enriching the fine-tuning data with such diverse reasoning results in a substantial performance boost across datasets, even for very small models. We conduct ablations and sample studies to understand the emergence of reasoning capabilities of student models. Our code implementation and data are available at https://github.com/itsnamgyu/reasoning-teacher.

Difficult problems, which often result in long reasoning traces, are widely recognized as key factors for enhancing the performance of reasoning models. However, such high-challenge problems are scarce, limiting the size of available datasets. In this paper, we propose a simple method to decouple the reliance on problem difficulty. First, we empirically demonstrate that reasoning length, rather than problem difficulty, primarily influences the performance of trained models. Second, we identify a scaling law on reasoning length, showing that model performance increases in a log-linear fashion as the reasoning data length grows. Finally, we introduce a straightforward technique to generate reasoning data of arbitrary length, and show that synthesized data is effective for training reasoning models. After fine-tuning the Qwen2.5-32B-Instruct language model on our Long1K dataset, we present our model, Long1K-32B, which achieves remarkable performance with only 1,000 training samples, achieving 95.6\% accuracy on MATH, and 71.1\% on GPQA outperforming DeepSeek-R1-Distill-Qwen-32B. The model, code, and dataset are all open-sourced, available at https://huggingface.co/ZTss/LONG1.

In this paper, we introduce Knowledge-Orthogonal Reasoning (KOR), which minimizes the impact of domain-specific knowledge for a more accurate evaluation of models' reasoning abilities in out-of-distribution scenarios. Based on this concept, we propose the Knowledge-Orthogonal Reasoning Benchmark (KOR-Bench), encompassing five task categories: Operation, Logic, Cipher, Puzzle, and Counterfactual. KOR-Bench emphasizes the effectiveness of models in applying new rule descriptions to solve novel rule-driven questions, revealing that top-performing models like Claude-3.5-Sonnet and GPT-4o only achieve 58.96% and 58.00% accuracy, respectively. We conduct thorough analyses to identify bottlenecks in the Cipher task using Stepwise Prompting, discovering that two rounds of Self-Correction yield optimal results. Complex Task Processing evaluates model performance across three integrated tasks, while we also explore the impact of Tricks on the Puzzle task and visualize rule-focused attention to enhance our understanding of model behavior. We aim for KOR-Bench to be a valuable resource for enhancing models' reasoning capabilities and fostering further research in this field.

We introduce Phi-4-reasoning, a 14-billion parameter reasoning model that achieves strong performance on complex reasoning tasks. Trained via supervised fine-tuning of Phi-4 on carefully curated set of "teachable" prompts-selected for the right level of complexity and diversity-and reasoning demonstrations generated using o3-mini, Phi-4-reasoning generates detailed reasoning chains that effectively leverage inference-time compute. We further develop Phi-4-reasoning-plus, a variant enhanced through a short phase of outcome-based reinforcement learning that offers higher performance by generating longer reasoning traces. Across a wide range of reasoning tasks, both models outperform significantly larger open-weight models such as DeepSeek-R1-Distill-Llama-70B model and approach the performance levels of full DeepSeek-R1 model. Our comprehensive evaluations span benchmarks in math and scientific reasoning, coding, algorithmic problem solving, planning, and spatial understanding. Interestingly, we observe a non-trivial transfer of improvements to general-purpose benchmarks as well. In this report, we provide insights into our training data, our training methodologies, and our evaluations. We show that the benefit of careful data curation for supervised fine-tuning (SFT) extends to reasoning language models, and can be further amplified by reinforcement learning (RL). Finally, our evaluation points to opportunities for improving how we assess the performance and robustness of reasoning models.

Long chain-of-thought (CoT) is an essential ingredient in effective usage of modern large language models, but our understanding of the reasoning strategies underlying these capabilities remains limited. While some prior works have attempted to categorize CoTs using predefined strategy types, such approaches are constrained by human intuition and fail to capture the full diversity of model behaviors. In this work, we introduce the CoT Encyclopedia, a bottom-up framework for analyzing and steering model reasoning. Our method automatically extracts diverse reasoning criteria from model-generated CoTs, embeds them into a semantic space, clusters them into representative categories, and derives contrastive rubrics to interpret reasoning behavior. Human evaluations show that this framework produces more interpretable and comprehensive analyses than existing methods. Moreover, we demonstrate that this understanding enables performance gains: we can predict which strategy a model is likely to use and guide it toward more effective alternatives. Finally, we provide practical insights, such as that training data format (e.g., free-form vs. multiple-choice) has a far greater impact on reasoning behavior than data domain, underscoring the importance of format-aware model design.

Large language models (LLMs) excel in complex tasks through advanced prompting techniques like Chain-of-Thought (CoT) and Tree-of-Thought (ToT), but their reliance on manually crafted, task-specific prompts limits adaptability and efficiency. We introduce Mixture of Reasoning (MoR), a training framework that embeds diverse reasoning strategies into LLMs for autonomous, task-adaptive reasoning without external prompt engineering. MoR has two phases: Thought Generation, creating reasoning chain templates with models like GPT-4o, and SFT Dataset Construction, pairing templates with benchmark datasets for supervised fine-tuning.Our experiments show that MoR significantly enhances performance, with MoR150 achieving 0.730 (2.2% improvement) using CoT prompting and 0.734 (13.5% improvement) compared to baselines. MoR eliminates the need for task-specific prompts, offering a generalizable solution for robust reasoning across diverse tasks.

With the release of R1, a publicly available large reasoning model (LRM), researchers commonly train new LRMs by training language models on R1's long chain-of-thought (CoT) inferences. While prior works show that LRMs' capabilities can be reproduced through direct distillation, the continued reliance on the existing models (e.g., R1) remains a critical limitation in advancing the field. As a first step toward independent LRM development, this paper explores the possibility of constructing a long CoT dataset with LLMs that are not trained for inference-time scaling. To this end, we present the Long CoT Collection, a dataset of 100K CoT rationales annotated using existing short CoT LLMs. We develop a pipeline that induces o1's novel reasoning strategies into short CoT LLMs, enabling them to think longer and introducing controllability over the thought budget to better manage the overthinking problem. Our extensive analyses validate that our dataset achieves quality comparable to--or slightly below--R1. Furthermore, our experiments demonstrate that training on our dataset not only strengthens general reasoning skills, but also provides a strong foundation for reinforcement learning--models initialized on our data achieve 2-3x larger gains with RLVR.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Large Language Models (LLMs) have exhibited an impressive capability to perform reasoning tasks, especially if they are encouraged to generate a sequence of intermediate steps. Reasoning performance can be improved by suitably combining multiple LLM responses, generated either in parallel in a single query, or via sequential interactions with LLMs throughout the reasoning process. Existing strategies for combination, such as self-consistency and progressive-hint-prompting, make inefficient usage of the LLM responses. We present Hint Marginalization, a novel and principled algorithmic framework to enhance the reasoning capabilities of LLMs. Our approach can be viewed as an iterative sampling strategy for forming a Monte Carlo approximation of an underlying distribution of answers, with the goal of identifying the mode the most likely answer. Empirical evaluation on several benchmark datasets for arithmetic reasoning demonstrates the superiority of the proposed approach.

Numerous crucial tasks in real-world decision-making rely on machine learning algorithms with calibrated uncertainty estimates. However, modern methods often yield overconfident and uncalibrated predictions. Various approaches involve training an ensemble of separate models to quantify the uncertainty related to the model itself, known as epistemic uncertainty. In an explicit implementation, the ensemble approach has high computational cost and high memory requirements. This particular challenge is evident in state-of-the-art neural networks such as transformers, where even a single network is already demanding in terms of compute and memory. Consequently, efforts are made to emulate the ensemble model without actually instantiating separate ensemble members, referred to as implicit ensembling. We introduce LoRA-Ensemble, a parameter-efficient deep ensemble method for self-attention networks, which is based on Low-Rank Adaptation (LoRA). Initially developed for efficient LLM fine-tuning, we extend LoRA to an implicit ensembling approach. By employing a single pre-trained self-attention network with weights shared across all members, we train member-specific low-rank matrices for the attention projections. Our method exhibits superior calibration compared to explicit ensembles and achieves similar or better accuracy across various prediction tasks and datasets.

Software issue resolution is a critical challenge in software engineering and has garnered increasing attention in recent years. With the rapid advancement of large language models (LLMs), substantial progress has been made in addressing real-world software engineering tasks. Recent studies have introduced ensemble reasoning techniques to enhance the performance of LLM-based issue resolution. However, existing prompting-based methods still face limitations in effectively exploring large ensemble spaces and lack the capacity for repository-level understanding, both of which constrain their overall effectiveness. In this paper, we propose Trae Agent, the first agent-based ensemble reasoning approach for repository-level issue resolution. Trae Agent formulates our goal as an optimal solution search problem and addresses two key challenges, i.e., large ensemble spaces and repository-level understanding, through modular agents for generation, pruning, and selection. We conduct extensive experiments using three leading LLMs on the widely-adopted SWE-bench benchmark, comparing Trae Agent against four state-of-the-art ensemble reasoning techniques. Experimental results demonstrate that Trae Agent consistently achieves superior performance, with an average improvement of 10.22% over all baselines in terms of Pass@1. Trae Agent has achieved first place on the SWE-bench Verified leaderboard, with a notable Pass@1 score of 75.20%. We are pleased to release Trae Agent as an open-source project to support the research community, with all resources available at https://github.com/bytedance/trae-agent.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex tasks. Recent advancements in Large Reasoning Models (LRMs), such as OpenAI o1 and DeepSeek-R1, have further improved performance in System-2 reasoning domains like mathematics and programming by harnessing supervised fine-tuning (SFT) and reinforcement learning (RL) techniques to enhance the Chain-of-Thought (CoT) reasoning. However, while longer CoT reasoning sequences improve performance, they also introduce significant computational overhead due to verbose and redundant outputs, known as the "overthinking phenomenon". In this paper, we provide the first structured survey to systematically investigate and explore the current progress toward achieving efficient reasoning in LLMs. Overall, relying on the inherent mechanism of LLMs, we categorize existing works into several key directions: (1) model-based efficient reasoning, which considers optimizing full-length reasoning models into more concise reasoning models or directly training efficient reasoning models; (2) reasoning output-based efficient reasoning, which aims to dynamically reduce reasoning steps and length during inference; (3) input prompts-based efficient reasoning, which seeks to enhance reasoning efficiency based on input prompt properties such as difficulty or length control. Additionally, we introduce the use of efficient data for training reasoning models, explore the reasoning capabilities of small language models, and discuss evaluation methods and benchmarking.

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they often suffer from overthinking, expending redundant computational steps on simple problems, or underthinking, failing to explore sufficient reasoning paths despite inherent capabilities. These issues lead to inefficiencies and potential inaccuracies, limiting practical deployment in resource-constrained settings. Existing methods to mitigate overthinking, such as suppressing reflective keywords or adjusting reasoning length, may inadvertently induce underthinking, compromising accuracy. Therefore, we propose ReBalance, a training-free framework that achieves efficient reasoning with balanced thinking. ReBalance leverages confidence as a continuous indicator of reasoning dynamics, identifying overthinking through high confidence variance and underthinking via consistent overconfidence. By aggregating hidden states from a small-scale dataset into reasoning mode prototypes, we compute a steering vector to guide LRMs' reasoning trajectories. A dynamic control function modulates this vector's strength and direction based on real-time confidence, pruning redundancy during overthinking, and promoting exploration during underthinking. Extensive experiments conducted on four models ranging from 0.5B to 32B, and across nine benchmarks in math reasoning, general question answering, and coding tasks demonstrate that ReBalance effectively reduces output redundancy while improving accuracy, offering a general, training-free, and plug-and-play strategy for efficient and robust LRM deployment. Code is available at https://github.com/yu-lin-li/ReBalance .

Deep Ensembles are a simple, reliable, and effective method of improving both the predictive performance and uncertainty estimates of deep learning approaches. However, they are widely criticised as being computationally expensive, due to the need to deploy multiple independent models. Recent work has challenged this view, showing that for predictive accuracy, ensembles can be more computationally efficient (at inference) than scaling single models within an architecture family. This is achieved by cascading ensemble members via an early-exit approach. In this work, we investigate extending these efficiency gains to tasks related to uncertainty estimation. As many such tasks, e.g. selective classification, are binary classification, our key novel insight is to only pass samples within a window close to the binary decision boundary to later cascade stages. Experiments on ImageNet-scale data across a number of network architectures and uncertainty tasks show that the proposed window-based early-exit approach is able to achieve a superior uncertainty-computation trade-off compared to scaling single models. For example, a cascaded EfficientNet-B2 ensemble is able to achieve similar coverage at 5% risk as a single EfficientNet-B4 with <30% the number of MACs. We also find that cascades/ensembles give more reliable improvements on OOD data vs scaling models up. Code for this work is available at: https://github.com/Guoxoug/window-early-exit.

It is impossible today to pretend that the practice of machine learning is compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how scenarios involving multiple data distributions are best served by representations that are both richer than those obtained by regularizing for the best in-distribution performance, and richer than those obtained under the influence of the implicit sparsity bias of common stochastic gradient procedures. This contribution investigates the use of very high dropout rates instead of ensembles to obtain such rich representations. Although training a deep network from scratch using such dropout rates is virtually impossible, fine-tuning a large pre-trained model under such conditions is not only possible but also achieves out-of-distribution performances that exceed those of both ensembles and weight averaging methods such as model soups. This result has practical significance because the importance of the fine-tuning scenario has considerably grown in recent years. This result also provides interesting insights on the nature of rich representations and on the intrinsically linear nature of fine-tuning a large network using a comparatively small dataset.

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.

We propose a novel speculative decoding method tailored for multi-sample reasoning scenarios, such as self-consistency and Best-of-N sampling. Our method exploits the intrinsic consensus of parallel generation paths to synthesize high-quality draft tokens without requiring auxiliary models or external databases. By dynamically analyzing structural patterns across parallel reasoning paths through a probabilistic aggregation mechanism, it identifies consensus token sequences that align with the decoding distribution. Evaluations on mathematical reasoning benchmarks demonstrate a substantial improvement in draft acceptance rates over baselines, while reducing the latency in draft token construction. This work establishes a paradigm shift for efficient multi-sample inference, enabling seamless integration of speculative decoding with sampling-based reasoning techniques.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

We present the surprising finding that a language model's reasoning capabilities can be improved by training on synthetic datasets of chain-of-thought (CoT) traces from more capable models, even when all of those traces lead to an incorrect final answer. Our experiments show this approach can yield better performance on reasoning tasks than training on human-annotated datasets. We hypothesize that two key factors explain this phenomenon: first, the distribution of synthetic data is inherently closer to the language model's own distribution, making it more amenable to learning. Second, these `incorrect' traces are often only partially flawed and contain valid reasoning steps from which the model can learn. To further test the first hypothesis, we use a language model to paraphrase human-annotated traces -- shifting their distribution closer to the model's own distribution -- and show that this improves performance. For the second hypothesis, we introduce increasingly flawed CoT traces and study to what extent models are tolerant to these flaws. We demonstrate our findings across various reasoning domains like math, algorithmic reasoning and code generation using MATH, GSM8K, Countdown and MBPP datasets on various language models ranging from 1.5B to 9B across Qwen, Llama, and Gemma models. Our study shows that curating datasets that are closer to the model's distribution is a critical aspect to consider. We also show that a correct final answer is not always a reliable indicator of a faithful reasoning process.

This work introduces Symbolic-Aided Chain-of-Thought (CoT), an improved approach to standard CoT, for logical reasoning in large language models (LLMs). The key idea is to integrate lightweight symbolic representations into few-shot prompts, structuring the inference steps with a consistent strategy to make reasoning patterns more explicit within a non-iterative reasoning process. By incorporating these symbolic structures, our method preserves the generalizability of standard prompting techniques while enhancing the transparency, interpretability, and analyzability of LLM logical reasoning. Extensive experiments on four well-known logical reasoning benchmarks -- ProofWriter, FOLIO, ProntoQA, and LogicalDeduction, which cover diverse reasoning scenarios -- demonstrate the effectiveness of the proposed approach, particularly in complex reasoning tasks that require navigating multiple constraints or rules. Notably, Symbolic-Aided CoT consistently improves LLMs' reasoning capabilities across various model sizes and significantly outperforms conventional CoT on three out of four datasets, ProofWriter, ProntoQA, and LogicalDeduction.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Ensembling multiple models has always been an effective approach to push the limits of existing performance and is widely used in classification tasks by simply averaging the classification probability vectors from multiple classifiers to achieve better accuracy. However, in the thriving open-source Large Language Model (LLM) community, ensembling methods are rare and typically limited to ensembling the full-text outputs of LLMs, such as selecting the best output using a ranker, which leads to underutilization of token-level probability information. In this paper, we treat the Generation of each token by LLMs as a Classification (GaC) for ensembling. This approach fully exploits the probability information at each generation step and better prevents LLMs from producing early incorrect tokens that lead to snowballing errors. In experiments, we ensemble state-of-the-art LLMs on several benchmarks, including exams, mathematics and reasoning, and observe that our method breaks the existing community performance ceiling. Furthermore, we observed that most of the tokens in the answer are simple and do not affect the correctness of the final answer. Therefore, we also experimented with ensembling only key tokens, and the results showed better performance with lower latency across benchmarks.

Combining pre-trained expert models offers substantial potential for scalable multimodal reasoning, but building a unified framework remains challenging due to the increasing diversity of input modalities and task complexity. For instance, medical diagnosis requires precise reasoning over structured clinical tables, while financial forecasting depends on interpreting plot-based data to make informed predictions. To tackle this challenge, we introduce MEXA, a training-free framework that performs modality- and task-aware aggregation of multiple expert models to enable effective multimodal reasoning across diverse and distinct domains. MEXA dynamically selects expert models based on the input modality and the task-specific reasoning demands (i.e., skills). Each expert model, specialized in a modality task pair, generates interpretable textual reasoning outputs. MEXA then aggregates and reasons over these outputs using a Large Reasoning Model (LRM) to produce the final answer. This modular design allows flexible and transparent multimodal reasoning across diverse domains without additional training overhead. We extensively evaluate our approach on diverse multimodal benchmarks, including Video Reasoning, Audio Reasoning, 3D Understanding, and Medical QA. MEXA consistently delivers performance improvements over strong multimodal baselines, highlighting the effectiveness and broad applicability of our expert-driven selection and aggregation in diverse multimodal reasoning tasks.

Recent advances in synergizing large reasoning models (LRMs) with retrieval-augmented generation (RAG) have shown promising results, yet two critical challenges remain: (1) reasoning models typically operate from a single, unchallenged perspective, limiting their ability to conduct deep, self-correcting reasoning over external documents, and (2) existing training paradigms rely excessively on outcome-oriented rewards, which provide insufficient signal for shaping the complex, multi-step reasoning process. To address these issues, we propose an Reasoner-Verifier framework named Adversarial Reasoning RAG (ARR). The Reasoner and Verifier engage in reasoning on retrieved evidence and critiquing each other's logic while being guided by process-aware advantage that requires no external scoring model. This reward combines explicit observational signals with internal model uncertainty to jointly optimize reasoning fidelity and verification rigor. Experiments on multiple benchmarks demonstrate the effectiveness of our method.

The paradigm shift in large language models (LLMs) from instinctive responses to chain-of-thought (CoT) reasoning has fueled two prevailing assumptions: (1) reasoning capabilities only emerge in sufficiently large models, and (2) such capabilities require training on massive datasets. While the first assumption has already been challenged by recent sub-billion-parameter reasoning models such as Qwen3-0.6B and DeepSeek distilled variants, the second remains largely unquestioned. In this work, we revisit the necessity of scaling to extremely large corpora (>10T tokens) for reasoning emergence. By carefully curating and resampling open-source datasets that we identify as beneficial under our designed metrics, we demonstrate that strong reasoning abilities can emerge with far less data. Specifically, we show that only ~2T tokens of high-quality data are sufficient, and pre-training with 4.2T tokens on the dataset resampled from these ~2T tokens, followed by a established post-training procedure, enables the development of MobileLLM-R1, a series of sub-billion-parameter reasoning models that substantially outperform prior models trained on fully open-sourced data. For example, MobileLLM-R1-950M achieves an AIME score of 15.5, compared to just 0.6 for OLMo-2-1.48B and 0.3 for SmolLM-2-1.7B. Remarkably, despite being trained on only 11.7% of the tokens compared to Qwen3's proprietary 36T-token corpus for pretraining, MobileLLM-R1-950M matches or surpasses Qwen3-0.6B across multiple reasoning benchmarks. To facilitate further research in this direction, we have released the complete training recipe, data sources, data mixing ratio, and model checkpoints, together with the key insights obtained throughout this study.

Hierarchical reasoning model (HRM) achieves extraordinary performance on various reasoning tasks, significantly outperforming large language model-based reasoners. To understand the strengths and potential failure modes of HRM, we conduct a mechanistic study on its reasoning patterns and find three surprising facts: (a) Failure of extremely simple puzzles, e.g., HRM can fail on a puzzle with only one unknown cell. We attribute this failure to the violation of the fixed point property, a fundamental assumption of HRM. (b) "Grokking" dynamics in reasoning steps, i.e., the answer is not improved uniformly, but instead there is a critical reasoning step that suddenly makes the answer correct; (c) Existence of multiple fixed points. HRM "guesses" the first fixed point, which could be incorrect, and gets trapped there for a while or forever. All facts imply that HRM appears to be "guessing" instead of "reasoning". Leveraging this "guessing" picture, we propose three strategies to scale HRM's guesses: data augmentation (scaling the quality of guesses), input perturbation (scaling the number of guesses by leveraging inference randomness), and model bootstrapping (scaling the number of guesses by leveraging training randomness). On the practical side, by combining all methods, we develop Augmented HRM, boosting accuracy on Sudoku-Extreme from 54.5% to 96.9%. On the scientific side, our analysis provides new insights into how reasoning models "reason".

Large language models demonstrate a remarkable capability for learning to solve new tasks from a few examples. The prompt template, or the way the input examples are formatted to obtain the prompt, is an important yet often overlooked aspect of in-context learning. In this work, we conduct a comprehensive study of the template format's influence on the in-context learning performance. We evaluate the impact of the prompt template across models (from 770M to 70B parameters) and 4 standard classification datasets. We show that a poor choice of the template can reduce the performance of the strongest models and inference methods to a random guess level. More importantly, the best templates do not transfer between different setups and even between models of the same family. Our findings show that the currently prevalent approach to evaluation, which ignores template selection, may give misleading results due to different templates in different works. As a first step towards mitigating this issue, we propose Template Ensembles that aggregate model predictions across several templates. This simple test-time augmentation boosts average performance while being robust to the choice of random set of templates.

Large Reasoning Models (LRMs) have achieved remarkable success, yet they often suffer from producing unnecessary and verbose reasoning chains. We identify a core aspect of this issue as "invalid thinking" -- models tend to repeatedly double-check their work after having derived the correct answer. To address this specific inefficiency, we move beyond the general principles of Efficacy and Efficiency to propose two new, fine-grained principles: Brevity, which advocates for eliminating redundancy, and Sufficiency, which ensures critical reasoning steps are preserved. Guided by these principles, we introduce LC-R1, a post-training method based on Group Relative Policy Optimization (GRPO). LC-R1 employs a novel combination of a Length Reward for overall conciseness and a Compress Reward that is specifically designed to remove the invalid portion of the thinking process. Extensive experiments on multiple reasoning benchmarks demonstrate that LC-R1 achieves a significant reduction in sequence length (~50%) with only a marginal (~2%) drop in accuracy, achieving a favorable trade-off point on the Pareto frontier that prioritizes high compression. Our analysis further validates the robustness of LC-R1 and provides valuable insights for developing more powerful yet computationally efficient LRMs. Our code is released at https://github.com/zxiangx/LC-R1.

Large language models have achieved remarkable capabilities across domains, yet mechanisms underlying sophisticated reasoning remain elusive. Recent reasoning models outperform comparable instruction-tuned models on complex cognitive tasks, attributed to extended computation through longer chains of thought. Here we show that enhanced reasoning emerges not from extended computation alone, but from simulating multi-agent-like interactions -- a society of thought -- which enables diversification and debate among internal cognitive perspectives characterized by distinct personality traits and domain expertise. Through quantitative analysis and mechanistic interpretability methods applied to reasoning traces, we find that reasoning models like DeepSeek-R1 and QwQ-32B exhibit much greater perspective diversity than instruction-tuned models, activating broader conflict between heterogeneous personality- and expertise-related features during reasoning. This multi-agent structure manifests in conversational behaviors, including question-answering, perspective shifts, and the reconciliation of conflicting views, and in socio-emotional roles that characterize sharp back-and-forth conversations, together accounting for the accuracy advantage in reasoning tasks. Controlled reinforcement learning experiments reveal that base models increase conversational behaviors when rewarded solely for reasoning accuracy, and fine-tuning models with conversational scaffolding accelerates reasoning improvement over base models. These findings indicate that the social organization of thought enables effective exploration of solution spaces. We suggest that reasoning models establish a computational parallel to collective intelligence in human groups, where diversity enables superior problem-solving when systematically structured, which suggests new opportunities for agent organization to harness the wisdom of crowds.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Recent advancements in long-context modeling have enhanced language models (LMs) for complex tasks across multiple NLP applications. Despite this progress, we find that these models struggle with multi-hop reasoning and exhibit decreased performance in the presence of noisy contexts. In this paper, we introduce Reasoning with Attributions, a novel approach that prompts LMs to supply attributions for each assertion during their reasoning. We validate our approach through experiments on three multi-hop datasets, employing both proprietary and open-source models, and demonstrate its efficacy and resilience. Furthermore, we explore methods to augment reasoning capabilities via fine-tuning and offer an attribution-annotated dataset and a specialized training strategy. Our fine-tuned model achieves competitive performance on multi-hop reasoning benchmarks, closely paralleling proprietary LMs such as ChatGPT and Claude-instant.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Large Language Models (LLMs) have shown remarkable capabilities in general natural language processing tasks but often fall short in complex reasoning tasks. Recent studies have explored human-like problem-solving strategies, such as self-correct, to push further the boundary of single-model reasoning ability. In this work, we let a single model "step outside the box" by engaging multiple models to correct each other. We introduce a multi-agent collaboration strategy that emulates the academic peer review process. Each agent independently constructs its own solution, provides reviews on the solutions of others, and assigns confidence levels to its reviews. Upon receiving peer reviews, agents revise their initial solutions. Extensive experiments on three different types of reasoning tasks show that our collaboration approach delivers superior accuracy across all ten datasets compared to existing methods. Further study underscores the effectiveness of integrating confidence in reviews, demonstrates the superiority of feedback exchange over mere solution sharing, and highlights the role of capability and diversity in fostering successful collaboration.

We present Phi-4-reasoning-vision-15B, a compact open-weight multimodal reasoning model, and share the motivations, design choices, experiments, and learnings that informed its development. Our goal is to contribute practical insight to the research community on building smaller, efficient multimodal reasoning models and to share the result of these learnings as an open-weight model that is good at common vision and language tasks and excels at scientific and mathematical reasoning and understanding user interfaces. Our contributions include demonstrating that careful architecture choices and rigorous data curation enable smaller, open-weight multimodal models to achieve competitive performance with significantly less training and inference-time compute and tokens. The most substantial improvements come from systematic filtering, error correction, and synthetic augmentation -- reinforcing that data quality remains the primary lever for model performance. Systematic ablations show that high-resolution, dynamic-resolution encoders yield consistent improvements, as accurate perception is a prerequisite for high-quality reasoning. Finally, a hybrid mix of reasoning and non-reasoning data with explicit mode tokens allows a single model to deliver fast direct answers for simpler tasks and chain-of-thought reasoning for complex problems.

A central question in artificial intelligence is the extent to which machine learning models comprehend mathematics. To address this, we propose a novel framework for measuring mathematical reasoning that moves beyond standard benchmarks to diagnose specific failure points. Our method first generates structured, step-by-step reasoning from gpt-3.5-turbo on the GSM8K dataset. We then use a more capable analyst model, gpt-4o-mini, to categorize errors and, crucially, perform an unsupervised clustering of every reasoning sentence to identify emergent "reasoning modes." This analysis reveals a cognitive profile with a stark, nonhuman-like brittleness: while the model achieves near-perfect accuracy on procedural modes like sequential calculation, its performance on modes requiring combinatorial reasoning with restrictions plummets. By identifying and quantifying the reliability of these distinct reasoning skills, our work provides a more granular method to evaluate mathematical comprehension and offers a precise roadmap for developing new capabilities and more reliable future applications.

Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens, incurring extraneous inference costs. Upon examination of the output distribution of current LLMs, we find evidence on their latent ability to reason more concisely, relative to their default behavior. To elicit this capability, we propose simple fine-tuning methods which leverage self-generated concise reasoning paths obtained by best-of-N sampling and few-shot conditioning, in task-specific settings. Our combined method achieves a 30% reduction in output tokens on average, across five model families on GSM8K and MATH, while maintaining average accuracy. By exploiting the fundamental stochasticity and in-context learning capabilities of LLMs, our self-training approach robustly elicits concise reasoning on a wide range of models, including those with extensive post-training. Code is available at https://github.com/TergelMunkhbat/concise-reasoning

Understanding the mathematical reasoning capabilities of Large Language Models (LLMs) is a central topic in the study of artificial intelligence. This new domain necessitates the creation of datasets of reasoning tasks for both training and benchmarking the performance of LLMs. To this end, we introduce the Karp dataset: The first dataset composed of detailed proofs of NP-completeness reductions. The reductions vary in difficulty, ranging from simple exercises of undergraduate courses to more challenging reductions from academic papers. We compare the performance of state-of-the-art models on this task and demonstrate the effect of fine-tuning with the Karp dataset on reasoning capacity.

Chain-of-Thought and Program-Aided Language Models represent two distinct reasoning methods, each with its own strengths and weaknesses. We demonstrate that it is possible to combine the best of both worlds by using different models for different problems, employing a large language model (LLM) to perform model selection. Through a theoretical analysis, we discover that the performance improvement is determined by the differences between the combined methods and the success rate of choosing the correct model. On eight reasoning datasets, our proposed approach shows significant improvements. Furthermore, we achieve new state-of-the-art results on GSM8K and SVAMP with accuracies of 96.5% and 93.7%, respectively. Our code is publicly available at https://github.com/XuZhao0/Model-Selection-Reasoning.

Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the premise. While reasoning LLMs have demonstrated strong performance on logical and mathematical tasks, their behavior on such open-ended, non-deterministic inferences remains largely unexplored. We introduce ProbCOPA, a dataset of 210 handcrafted probabilistic inferences in English, each annotated for inference likelihood by 25--30 human participants. We find that human responses are graded and varied, revealing probabilistic judgments of the inferences in our dataset. Comparing these judgments with responses from eight state-of-the-art reasoning LLMs, we show that models consistently fail to produce human-like distributions. Finally, analyzing LLM reasoning chains, we find evidence of a common reasoning pattern used to evaluate such inferences. Our findings reveal persistent differences between humans and LLMs, and underscore the need to evaluate reasoning beyond deterministic settings.

Large Language Models (LLMs) exhibit impressive reasoning abilities, yet their reliance on structured step-by-step processing reveals a critical limitation. While human cognition fluidly adapts between intuitive, heuristic (System 1) and analytical, deliberative (System 2) reasoning depending on the context, LLMs lack this dynamic flexibility. This rigidity can lead to brittle and unreliable performance when faced with tasks that deviate from their trained patterns. To address this, we create a dataset of 2,000 samples with valid System 1 and System 2 answers, explicitly align LLMs with these reasoning styles, and evaluate their performance across reasoning benchmarks. Our results reveal an accuracy-efficiency trade-off: System 2-aligned models excel in arithmetic and symbolic reasoning, while System 1-aligned models perform better in commonsense tasks. A mechanistic analysis of model responses shows that System 1 models employ more definitive answers, whereas System 2 models demonstrate greater uncertainty. Interpolating between these extremes produces a monotonic transition in reasoning accuracy, preserving coherence. This work challenges the assumption that step-by-step reasoning is always optimal and highlights the need for adapting reasoning strategies based on task demands.

We introduce Rank1, the first reranking model trained to take advantage of test-time compute. Rank1 demonstrates the applicability within retrieval of using a reasoning language model (i.e. OpenAI's o1, Deepseek's R1, etc.) for distillation in order to rapidly improve the performance of a smaller model. We gather and open-source a dataset of more than 600,000 examples of R1 reasoning traces from queries and passages in MS MARCO. Models trained on this dataset show: (1) state-of-the-art performance on advanced reasoning and instruction following datasets; (2) work remarkably well out of distribution due to the ability to respond to user-input prompts; and (3) have explainable reasoning chains that can be given to users or RAG-based systems. Further, we demonstrate that quantized versions of these models retain strong performance while using less compute/memory. Overall, Rank1 shows that test-time compute allows for a fundamentally new type of explainable and performant reranker model for search.

We introduce Vibe Reasoning, a human-AI collaborative paradigm for solving complex mathematical problems. Our key insight is that frontier AI models already possess the knowledge required to solve challenging problems -- they simply do not know how, what, or when to apply it. Vibe Reasoning transforms AI's latent potential into manifested capability through generic meta-prompts, agentic grounding, and model orchestration. We demonstrate this paradigm through IMO 2025 Problem 6, a combinatorial optimization problem where autonomous AI systems publicly reported failures. Our solution combined GPT-5's exploratory capabilities with Gemini 3 Pro's proof strengths, leveraging agentic workflows with Python code execution and file-based memory, to derive both the correct answer (2112) and a rigorous mathematical proof. Through iterative refinement across multiple attempts, we discovered the necessity of agentic grounding and model orchestration, while human prompts evolved from problem-specific hints to generic, transferable meta-prompts. We analyze why capable AI fails autonomously, how each component addresses specific failure modes, and extract principles for effective vibe reasoning. Our findings suggest that lightweight human guidance can unlock frontier models' mathematical reasoning potential. This is ongoing work; we are developing automated frameworks and conducting broader evaluations to further validate Vibe Reasoning's generality and effectiveness.

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

Chain-of-Thought (CoT) reasoning enables Large Language Models (LLMs) to solve complex reasoning tasks by generating intermediate reasoning steps. However, most existing approaches focus on hard token decoding, which constrains reasoning within the discrete vocabulary space and may not always be optimal. While recent efforts explore continuous-space reasoning, they often suffer from catastrophic forgetting, limiting their applicability to state-of-the-art LLMs that already perform well in zero-shot settings with a proper instruction. To address this challenge, we propose a novel approach for continuous-space reasoning that does not require modifying the underlying LLM. Specifically, we employ a lightweight assistant model to generate instance-specific soft thought tokens speculatively as the initial chain of thoughts, which are then mapped into the LLM's representation space via a projection module. Experimental results on five reasoning benchmarks demonstrate that our method enhances LLM reasoning performance through supervised, parameter-efficient fine-tuning.

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due to sparse and fragmented training data. To address this issue, we propose CodeI/O, a novel approach that systematically condenses diverse reasoning patterns inherently embedded in contextually-grounded codes, through transforming the original code into a code input-output prediction format. By training models to predict inputs/outputs given code and test cases entirely in natural language as Chain-of-Thought (CoT) rationales, we expose them to universal reasoning primitives -- like logic flow planning, state-space searching, decision tree traversal, and modular decomposition -- while decoupling structured reasoning from code-specific syntax and preserving procedural rigor. Experimental results demonstrate CodeI/O leads to consistent improvements across symbolic, scientific, logic, math & numerical, and commonsense reasoning tasks. By matching the existing ground-truth outputs or re-executing the code with predicted inputs, we can verify each prediction and further enhance the CoTs through multi-turn revision, resulting in CodeI/O++ and achieving higher performance. Our data and models are available at https://github.com/hkust-nlp/CodeIO.

Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions provided are not consistent with how LMs are trained, process information, and generate new tokens. To illustrate this incommensurability we assume the view that transformer-based LMs implement an implicit finite-order Markov kernel mapping contexts to conditional token distributions. In this view, reasoning-like outputs correspond to statistical regularities and approximate statistical invariances in the learned kernel rather than the implementation of explicit logical mechanisms. This view is illustrative of the claim that LMs are "statistical pattern matchers"" and not genuine reasoners and provides a perspective that clarifies why reasoning-like outputs arise in LMs without any guarantees of logical consistency. This distinction is fundamental to how epistemic uncertainty is evaluated in LMs. We invite a discussion on the importance of how the computational processes of the systems we build and analyze in NLP research are described.

Large Language Models (LLMs) have shown remarkable abilities across various language tasks, but solving complex reasoning problems remains a challenge. While existing methods like Chain-of-Thought (CoT) and Tree-of-Thought (ToT) enhance reasoning by decomposing problems or structuring prompts, they typically perform a single pass of reasoning and may fail to revisit flawed paths, compromising accuracy. To address this, we propose a novel reasoning framework called Forest-of-Thought (FoT), which integrates multiple reasoning trees to leverage collective decision-making for solving complex logical problems. FoT utilizes sparse activation strategies to select the most relevant reasoning paths, improving both efficiency and accuracy. Additionally, we introduce a dynamic self-correction strategy that enables real-time error correction and learning from past mistakes, as well as consensus-guided decision making strategies to optimize correctness and computational resources. Experimental results demonstrate that the FoT framework, combined with these strategies, significantly enhances the reasoning capabilities of LLMs, enabling them to solve complex tasks with greater precision and efficiency.

We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on well-defined tasks with complete information. However, LLMs continue to struggle with making accurate and well-calibrated probabilistic predictions under uncertainty or partial information. While incorporating uncertainty into model predictions often boosts performance, obtaining reliable estimates of that uncertainty remains understudied. In particular, LLM probability estimates tend to be coarse and biased towards more frequent numbers. Through a combination of human and synthetic data creation and assessment, scaling to larger models, and better supervision, we propose a set of strong and precise probability estimation models. We conduct systematic evaluations across tasks that rely on conditional probability estimation and show that our approach consistently outperforms existing fine-tuned and prompting-based methods by a large margin.

Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks while benefiting from better computational scalability. However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model. We propose AutoDEUQ, an automated approach for generating an ensemble of deep neural networks. Our approach leverages joint neural architecture and hyperparameter search to generate ensembles. We use the law of total variance to decompose the predictive variance of deep ensembles into aleatoric (data) and epistemic (model) uncertainties. We show that AutoDEUQ outperforms probabilistic backpropagation, Monte Carlo dropout, deep ensemble, distribution-free ensembles, and hyper ensemble methods on a number of regression benchmarks.

It is well known that ensemble methods often provide enhanced performance in reinforcement learning. In this paper, we explore this concept further by using group-aided training within the distributional reinforcement learning paradigm. Specifically, we propose an extension to categorical reinforcement learning, where distributional learning targets are implicitly based on the total information gathered by an ensemble. We empirically show that this may lead to much more robust initial learning, a stronger individual performance level, and good efficiency on a per-sample basis.

This work addresses the challenge of democratizing advanced Large Language Models (LLMs) by compressing their mathematical reasoning capabilities into sub-billion parameter Small Language Models (SLMs) without compromising performance. We introduce Equation-of-Thought Distillation (EoTD), a novel technique that encapsulates the reasoning process into equation-based representations to construct an EoTD dataset for fine-tuning SLMs. Additionally, we propose the Mix Thoughts Distillation (MTD) framework to enhance the reasoning performance of SLMs. This involves creating a reasoning dataset with multiple thought processes and using it for fine-tuning. Our experimental findings demonstrate that EoTD significantly boosts the reasoning abilities of SLMs, while MTD enables these models to achieve state-of-the-art reasoning performance.

Recently, large language models (LLMs) have demonstrated outstanding reasoning capabilities on mathematical and coding tasks. However, their application to financial tasks-especially the most fundamental task of stock movement prediction-remains underexplored. We study a three-class classification problem (up, hold, down) and, by analyzing existing reasoning responses, observe that: (1) LLMs follow analysts' opinions rather than exhibit a systematic, independent analytical logic (CoTs). (2) LLMs list summaries from different sources without weighing adversarial evidence, yet such counterevidence is crucial for reliable prediction. It shows that the model does not make good use of its reasoning ability to complete the task. To address this, we propose Reflective Evidence Tuning (RETuning), a cold-start method prior to reinforcement learning, to enhance prediction ability. While generating CoT, RETuning encourages dynamically constructing an analytical framework from diverse information sources, organizing and scoring evidence for price up or down based on that framework-rather than on contextual viewpoints-and finally reflecting to derive the prediction. This approach maximally aligns the model with its learned analytical framework, ensuring independent logical reasoning and reducing undue influence from context. We also build a large-scale dataset spanning all of 2024 for 5,123 A-share stocks, with long contexts (32K tokens) and over 200K samples. In addition to price and news, it incorporates analysts' opinions, quantitative reports, fundamental data, macroeconomic indicators, and similar stocks. Experiments show that RETuning successfully unlocks the model's reasoning ability in the financial domain. Inference-time scaling still works even after 6 months or on out-of-distribution stocks, since the models gain valuable insights about stock movement prediction.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

Cognitive textual and visual reasoning tasks, such as puzzles, series, and analogies, demand the ability to quickly reason, decipher, and evaluate patterns both textually and spatially. While LLMs and VLMs, through extensive training on large amounts of human-curated data, have attained a high level of pseudo-human intelligence in some common sense reasoning tasks, they still struggle with more complex reasoning tasks that require cognitive understanding. In this work, we introduce a new dataset, NTSEBench, designed to evaluate the cognitive multi-modal reasoning and problem-solving skills of large models. The dataset comprises 2,728 multiple-choice questions comprising of a total of 4,642 images across 26 categories sampled from the NTSE examination conducted nationwide in India, featuring both visual and textual general aptitude questions that do not rely on rote learning. We establish baselines on the dataset using state-of-the-art LLMs and VLMs. To facilitate a comparison between open source and propriety models, we propose four distinct modeling strategies to handle different modalities (text and images) in the dataset instances.

We envision a continuous collaborative learning system where groups of LLM agents work together to solve reasoning problems, drawing on memory they collectively build to improve performance as they gain experience. This work establishes the foundations for such a system by studying the interoperability of chain-of-thought reasoning styles, multi-agent collaboration, and memory banks. Extending beyond the identical agents of self-consistency, we introduce varied-context agents with diverse exemplars and a summarizer agent in place of voting. We generate frozen and continuously learned memory banks of exemplars and pair them with fixed, random, and similarity-based retrieval mechanisms. Our systematic study reveals where various methods contribute to reasoning performance of two LLMs on three grounded reasoning tasks, showing that random exemplar selection can often beat more principled approaches, and in some tasks, inclusion of any exemplars serves only to distract both weak and strong models.

Large Language Models (LLMs) have achieved impressive performance on complex reasoning tasks with Chain-of-Thought (CoT) prompting. However, conventional CoT relies on reasoning steps explicitly verbalized in natural language, introducing inefficiencies and limiting its applicability to abstract reasoning. To address this, there has been growing research interest in latent CoT reasoning, where inference occurs within latent spaces. By decoupling reasoning from language, latent reasoning promises richer cognitive representations and more flexible, faster inference. Researchers have explored various directions in this promising field, including training methodologies, structural innovations, and internal reasoning mechanisms. This paper presents a comprehensive overview and analysis of this reasoning paradigm. We begin by proposing a unified taxonomy from four perspectives: token-wise strategies, internal mechanisms, analysis, and applications. We then provide in-depth discussions and comparative analyses of representative methods, highlighting their design patterns, strengths, and open challenges. We aim to provide a structured foundation for advancing this emerging direction in LLM reasoning. The relevant papers will be regularly updated at https://github.com/EIT-NLP/Awesome-Latent-CoT.

This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We then study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for a class of network models including instances of Transformers, random features models, and diagonal linear networks, a min-degree-interpolator (MDI) is learned on the unseen. We also provide evidence that other instances with larger learning rates or mean-field networks reach leaky MDIs. These findings lead to two implications: (1) we provide an explanation to the length generalization problem (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports.

Deep Ensembles (DE) are a prominent approach for achieving excellent performance on key metrics such as accuracy, calibration, uncertainty estimation, and out-of-distribution detection. However, hardware limitations of real-world systems constrain to smaller ensembles and lower-capacity networks, significantly deteriorating their performance and properties. We introduce Packed-Ensembles (PE), a strategy to design and train lightweight structured ensembles by carefully modulating the dimension of their encoding space. We leverage grouped convolutions to parallelize the ensemble into a single shared backbone and forward pass to improve training and inference speeds. PE is designed to operate within the memory limits of a standard neural network. Our extensive research indicates that PE accurately preserves the properties of DE, such as diversity, and performs equally well in terms of accuracy, calibration, out-of-distribution detection, and robustness to distribution shift. We make our code available at https://github.com/ENSTA-U2IS/torch-uncertainty.

Recent advances in reasoning models have demonstrated significant improvements in accuracy, particularly for complex tasks such as mathematical reasoning, by employing detailed and comprehensive reasoning processes. However, generating these lengthy reasoning sequences is computationally expensive and time-consuming. To address this inefficiency, we leverage the inherent parallelizability of certain tasks to accelerate the reasoning process. Specifically, when multiple parallel reasoning branches exist, we decode multiple tokens per step using a specialized attention mask, processing them within a single sequence, avoiding additional memory usage. Experimental results show that our method achieves over 100% speedup in decoding time while maintaining the answer quality.

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

AI researchers and practitioners increasingly apply large language models (LLMs) to what we call reasoning-intensive regression (RiR), i.e. deducing subtle numerical properties from text. Unlike standard language regression tasks, e.g. for sentiment or similarity, RiR often appears instead in ad-hoc problems like rubric-based scoring or domain-specific retrieval, where much deeper analysis of text is required while only limited task-specific training data and computation are available. We cast three realistic problems as RiR tasks to establish an initial benchmark, and use that to test our hypothesis that prompting frozen LLMs and finetuning Transformer encoders via gradient descent will both often struggle in RiR. We then propose MENTAT, a simple and lightweight method that combines batch-reflective prompt optimization with neural ensemble learning. MENTAT achieves up to 65% improvement over both baselines, though substantial room remains for future advances in RiR.

Leveraging the autonomous decision-making capabilities of large language models (LLMs) demonstrates superior performance in reasoning tasks. Despite the successes of iterative or recursive retrieval-augmented generation (RAG), they often are trapped in a single solution space when confronted with complex tasks. In this paper, we propose a novel thinking pattern in RAG which integrates system analysis with efficient reasoning actions, significantly activating intrinsic reasoning capabilities and expanding the solution space of specific tasks via Monte Carlo Tree Search (MCTS), dubbed AirRAG. Specifically, our approach designs five fundamental reasoning actions that are expanded to a wide tree-based reasoning spaces using MCTS. The extension also uses self-consistency verification to explore potential reasoning paths and implement inference scaling. In addition, computationally optimal strategies are used to apply more inference computation to key actions to achieve further performance improvements. Experimental results demonstrate the effectiveness of AirRAG through considerable performance gains over complex QA datasets. Furthermore, AirRAG is flexible and lightweight, making it easy to integrate with other advanced technologies.

Recent breakthroughs in large language models (LLMs), particularly in reasoning capabilities, have propelled Retrieval-Augmented Generation (RAG) to unprecedented levels. By synergizing retrieval mechanisms with advanced reasoning, LLMs can now tackle increasingly complex problems. This paper presents a systematic review of the collaborative interplay between RAG and reasoning, clearly defining "reasoning" within the RAG context. It construct a comprehensive taxonomy encompassing multi-dimensional collaborative objectives, representative paradigms, and technical implementations, and analyze the bidirectional synergy methods. Additionally, we critically evaluate current limitations in RAG assessment, including the absence of intermediate supervision for multi-step reasoning and practical challenges related to cost-risk trade-offs. To bridge theory and practice, we provide practical guidelines tailored to diverse real-world applications. Finally, we identify promising research directions, such as graph-based knowledge integration, hybrid model collaboration, and RL-driven optimization. Overall, this work presents a theoretical framework and practical foundation to advance RAG systems in academia and industry, fostering the next generation of RAG solutions.

We present Logics-STEM, a state-of-the-art reasoning model fine-tuned on Logics-STEM-SFT-Dataset, a high-quality and diverse dataset at 10M scale that represents one of the largest-scale open-source long chain-of-thought corpora. Logics-STEM targets reasoning tasks in the domains of Science, Technology, Engineering, and Mathematics (STEM), and exhibits exceptional performance on STEM-related benchmarks with an average improvement of 4.68% over the next-best model at 8B scale. We attribute the gains to our data-algorithm co-design engine, where they are jointly optimized to fit a gold-standard distribution behind reasoning. Data-wise, the Logics-STEM-SFT-Dataset is constructed from a meticulously designed data curation engine with 5 stages to ensure the quality, diversity, and scalability, including annotation, deduplication, decontamination, distillation, and stratified sampling. Algorithm-wise, our failure-driven post-training framework leverages targeted knowledge retrieval and data synthesis around model failure regions in the Supervised Fine-tuning (SFT) stage to effectively guide the second-stage SFT or the reinforcement learning (RL) for better fitting the target distribution. The superior empirical performance of Logics-STEM reveals the vast potential of combining large-scale open-source data with carefully designed synthetic data, underscoring the critical role of data-algorithm co-design in enhancing reasoning capabilities through post-training. We make both the Logics-STEM models (8B and 32B) and the Logics-STEM-SFT-Dataset (10M and downsampled 2.2M versions) publicly available to support future research in the open-source community.