Daily Papers

Recent advances in generative models have made synthetic images increasingly photorealistic, posing growing challenges to reliable and generalizable detection of AI-generated images. Existing methods typically rely on holistic image-level classification, which may overlook local artifacts, especially in high-resolution images. To address this limitation, we formulate this task as a falsification-driven multiple instance learning problem, where a single fake patch can falsify the whole image, while a real image requires all patches to be authentic. Based on this formulation, we propose Learning to Falsify (LTF), a hierarchical multiple instance learning framework that models an image as multiple bags of instances across different spatial levels and aggregates their predictions under the falsification-inspired principle. We further introduce Cross-Shuffle during training to encourage the model to learn local artifact evidence rather than image-level shortcuts. Furthermore, we propose the Falsification-driven Test-time Aggregation Strategy (FATAS), a plug-and-play module that extends the same falsification-inspired principle to existing detectors by aggregating patch-level predictions. Extensive experiments demonstrate that LTF achieves strong generalization and robustness across multiple benchmarks, while FATAS substantially improves representative detectors in high-resolution scenarios without retraining. Code is available at https://github.com/HuiGuanLab/LTF.git

We propose claim-level falsification as a principle for test-time scaling and instantiate it through Claim-Level Reliability Assessment (CLR), a training-free framework that reallocates test-time compute from additional solution sampling to targeted verification. Since whole-trace evaluation often obscures decisive errors due to signal dilution from routine tokens, CLR condenses each reasoning trace into a compact set of decision-critical claims, thereby isolating its logical anchors. Furthermore, recognizing the inherent difficulty of generating entirely correct solutions under fixed model capabilities, CLR shifts the focus to semantic falsification. This approach exploits a fundamental asymmetry between solution construction and claim refutation. Constructing a valid solution requires a flawless reasoning path, whereas refuting an incorrect claim requires identifying only a single decisive flaw. This targeted search for negative evidence systematically compresses the survival space of high-confidence incorrect traces, effectively suppressing erroneous consensus via nonlinear reliability scoring. Across four LLMs and four reasoning benchmarks under matched budgets, CLR generally improves upon pass@1 and self-consistency. On GPT-OSS-20B/CMIMC25, for instance, CLR exceeds pass@1 by 27.15 percentage-points and raises self-consistency accuracy from 77.50\% to 82.19\% with 37.0\% fewer tokens.

We study parallel test-time scaling for long-horizon agentic tasks such as agentic search and deep research, where multiple rollouts are generated in parallel and aggregated into a final response. While such scaling has proven effective for chain-of-thought reasoning, agentic tasks pose unique challenges: trajectories are long, multi-turn, and tool-augmented, and outputs are often open-ended. Aggregating only final answers discards rich information from trajectories, while concatenating all trajectories exceeds the model's context window. To address this, we propose AggAgent, an aggregation agent that treats parallel trajectories as an environment. We equip it with lightweight tools to inspect candidate solutions and search across trajectories, enabling it to navigate and synthesize information on demand. Across six benchmarks and three model families (GLM-4.7, Qwen3.5, MiniMax-M2.5), AggAgent outperforms all existing aggregation methods-by up to 5.3% absolute on average and 10.3% on two deep research tasks-while adding minimal overhead, as the aggregation cost remains bounded by a single agentic rollout. Our findings establish agentic aggregation as an effective and cost-efficient approach to parallel test-time scaling.

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity-that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1\% over Beam Search and 3.6\% over Best-of-N, while reducing FLOPs by over 52\%. We will open-source the code to support future research.

Test-time reasoning is increasingly used as a serving-time control knob, but extra reasoning is not uniformly valuable: it can repair failed attempts, waste compute on already-correct answers, or introduce harmful answer changes. We study this as a deployment allocation problem rather than a new-verifier problem. We introduce \sevra, Selective Verification for Reasoning Allocation, a serving-layer controller that decides whether to preserve a frozen solver's initial answer or invoke active verification. Using a frozen Qwen3-4B solver, we log intervention outcomes and train recoverability-aware gates from serving-visible attempt state. On \mathfive, selective verification reaches 76.3\% accuracy, compared with 75.5\% for always verifying, while reducing post-generation tokens by 26.8\% and harmful flips from 2.2\% to 1.0\%. However, an 8,192-token initial solve reaches 76.0\% accuracy with 28\% fewer total model tokens, showing that selective recovery is useful but not the best tested cost frontier. In frozen transfer to \gsm, the selective policy verifies only 3.0\% of examples, improves accuracy from 93.4\% to 94.5\%, and reduces verification tokens by 91.2\% relative to always verifying; again, a longer initial solve matches its accuracy with fewer realized tokens. On CommonsenseQA, always-on verification hurts, while Self-Consistency@5 improves accuracy at about five times the realized token cost. The resulting deployment rule is: tune the initial budget first, then use selective recovery when explicit checks, bounded retries, auditability, or regression-risk control matter.

Test-time scaling is a powerful strategy for boosting the performance of large language models on complex reasoning tasks. While state-of-the-art approaches often employ generative verifiers to select the best solution from a pool of candidates, this method incurs prohibitive computational costs, limiting its practicality. In this work, we shift the focus to a more budget-aware paradigm: discriminative verification. We conduct a thorough empirical analysis and demonstrate that while discriminative verifiers may underperform in isolation, combining them with self-consistency in a hybrid approach creates a powerful and efficient test-time scaling mechanism. Notably, under a fixed compute budget, this hybrid approach surpasses state-of-the-art generative verification by a significant margin: achieving up to 15.3\% higher accuracy on AIME2025. Our findings establish that for practical, real-world applications, budget-aware scaling with discriminative verifiers is not only a "free" upgrade over self-consistency, but also a more effective and efficient alternative to costly generative techniques. Code is available at https://github.com/wang-research-lab/verification.

Test-time scaling often uses an external verifier, such as compilers and test cases in coding or trained value functions in robotics applications, to obtain high-quality rollouts. Verifier-free test-time scaling (or VF-TTS) is gaining extensive attention as a mechanism to enhance Large Language Model (LLM) reasoning, primarily because we do not have access to such high-quality verifiers in many real-world applications. Among existing VF-TTS methods, confidence-based VF-TTS methods, which compute and rank rollouts solely by confidence, are particularly promising. Such methods introduce near-zero overhead for sample evaluation and require minimal access to internal model states, making the methods highly flexible across models and tasks. In this paper, we demonstrate a critical limitation of existing confidence-based VF-TTS methods by showing that such methods catastrophically break down on complex tasks. We observe a very interesting phenomenon: uniformly high confidence frequently indicates a failure to explore, favoring confidently wrong answers. To address this, our core insight is that robust cognitive search requires a specific confidence trajectory pattern: such methods perform exploratory branching at the beginning, as manifested by low initial confidence, and converge to a high final confidence solution. To implement this insight, we introduce consilience, a novel selection framework that explicitly evaluates the temporal asymmetry of confidence in reasoning. We operationalize this via a combinatorial metric that actively penalizes high initial confidence while strictly demanding final certainty. Extensive experiments covering both graduate-level mathematics problems and free-form code generation demonstrate that consilience effectively outperforms existing baselines, validating our novel perspective on completion confidence.

Large Reasoning Models (LRMs) achieve strong performance by generating long reasoning traces with reflection. Through a large-scale empirical analysis, we find that a substantial fraction of reflective steps consist of self-verification (recheck) that repeatedly confirm intermediate results. These rechecks occur frequently across models and benchmarks, yet the vast majority are confirmatory rather than corrective, rarely identifying errors and altering reasoning outcomes. This reveals a mismatch between how often self-verification is activated and how often it is actually useful. Motivated by this, we propose a novel, experience-driven test-time framework that reduces the overused verification. Our method detects the activation of recheck behavior, consults an offline experience pool of past verification outcomes, and estimates whether a recheck is likely unnecessary via efficient retrieval. When historical experience suggests unnecessary, a suppression signal redirects the model to proceed. Across multiple model and benchmarks, our approach reduces token usage up to 20.3% while maintaining the accuracy, and in some datasets even yields accuracy improvements.

Test-time scaling via solution sampling and aggregation has become a key paradigm for improving the reasoning performance of Large Language Models (LLMs). While reward model selection is commonly employed in this approach, it often fails to identify minority-yet-correct answers, which limits its effectiveness beyond that of simple majority voting. We argue that this limitation stems from a lack of informative critique signals during verifier training. To bridge this gap, we introduce Mirror-Critique, a framework that trains a verifier with informative critiques. Our key insight is to leverage the rich critique signal by contrasting model-generated solutions with ground-truth solutions. We deploy a small instruction-tuned model to synthesize high-quality critique data with rejection sampling that teaches the verifier not only what is wrong, but also why. The synthetic data is used to cold-start the LLMs in the RLVR process to further improve the verification ability. The resulting Mirror-Verifier is deployed to evaluate candidate solutions by generating multiple critiques per solution, aggregating them into a verify score used for weighted voting or selective abstention. The experimental results show that our Mirror-Verifier significantly outperforms majority voting in terms of solution accuracy and also improves the solver's honesty to recognize and abstain from answering beyond its capability boundaries.

Test-time scaling can improve model performance by aggregating stochastic reasoning trajectories. However, achieving sample-efficient test-time self-consistency under a limited budget remains an open challenge. We introduce PETS (Principled and Efficient Test-TimeSelf-Consistency), which initiates a principled study of trajectory allocation through an optimization framework. Central to our approach is the self-consistency rate, a new measure defined as agreement with the infinite-budget majority vote. This formulation makes sample-efficient test-time allocation theoretically grounded and amenable to rigorous analysis. We study both offline and online settings. In the offline regime, where all questions are known in advance, we connect trajectory allocation to crowdsourcing, a classic and well-developed area, by modeling reasoning traces as workers. This perspective allows us to leverage rich existing theory, yielding theoretical guarantees and an efficient majority-voting-based allocation algorithm. In the online streaming regime, where questions arrive sequentially and allocations must be made on the fly, we propose a novel method inspired by the offline framework. Our approach adapts budgets to question difficulty while preserving strong theoretical guarantees and computational efficiency. Experiments show that PETS consistently outperforms uniform allocation. On GPQA, PETS achieves perfect self-consistency in both settings while reducing the sampling budget by up to 75% (offline) and 55% (online) relative to uniform allocation. Code is available at https://github.com/ZDCSlab/PETS.

This position paper argues that AI-assisted software engineering requires explicit mechanisms for tracking the epistemic status and temporal validity of architectural decisions. LLM coding assistants generate decisions faster than teams can validate them, yet no widely-adopted framework distinguishes conjecture from verified knowledge, prevents trust inflation through conservative aggregation, or detects when evidence expires. We propose three requirements for responsible AI-assisted engineering: (1) epistemic layers that separate unverified hypotheses from empirically validated claims, (2) conservative assurance aggregation grounded in the Gödel t-norm that prevents weak evidence from inflating confidence, and (3) automated evidence decay tracking that surfaces stale assumptions before they cause failures. We formalize these requirements as the First Principles Framework (FPF), ground its aggregation semantics in fuzzy logic, and define a quintet of invariants that any valid aggregation operator must satisfy. Our retrospective audit applying FPF criteria to two internal projects found that 20-25% of architectural decisions had stale evidence within two months, validating the need for temporal accountability. We outline research directions including learnable aggregation operators, federated evidence sharing, and SMT-based claim validation.

Test-Time Scaling (TTS) is a promising approach to progressively elicit the model's intelligence during inference. Recently, training-based TTS methods, such as continued reinforcement learning (RL), have further surged in popularity, while training-free TTS methods are gradually fading from prominence. However, the additional computation overhead of training amplifies the burden on test-time scaling. In this paper, we focus on training-free TTS methods for reasoning. We first design Conditional Step-level Self-refinement, a fine-grained sequential scaling method guided by process verification. On top of its effectiveness, we further combine it with other classical parallel scaling methods at the step level, to introduce a novel inference paradigm called Hybrid Test-Time Scaling. Extensive experiments on five instruction-tuned LLMs across different scales (3B-14B) and families demonstrate that hybrid strategy incorporating various training-free TTS methods at a fine granularity has considerable potential for expanding the reasoning performance boundaries of LLMs.

This paper presents a simple, effective, and cost-efficient strategy to improve LLM performance by scaling test-time compute. Our strategy builds upon the repeated-sampling-then-voting framework, with a novel twist: incorporating multiple models, even weaker ones, to leverage their complementary strengths that potentially arise from diverse training data and paradigms. By using consistency as a signal, our strategy dynamically switches between models. Theoretical analysis highlights the efficiency and performance advantages of our strategy. Extensive experiments on six datasets demonstrate that our strategy not only outperforms self-consistency and state-of-the-art multi-agent debate approaches, but also significantly reduces inference costs. Additionally, ModelSwitch requires only a few comparable LLMs to achieve optimal performance and can be extended with verification methods, demonstrating the potential of leveraging multiple LLMs in the generation-verification paradigm.

Test-time scaling (TTS) has emerged as a new frontier for scaling the performance of Large Language Models. In test-time scaling, by using more computational resources during inference, LLMs can improve their reasoning process and task performance. Several approaches have emerged for TTS such as distilling reasoning traces from another model or exploring the vast decoding search space by employing a verifier. The verifiers serve as reward models that help score the candidate outputs from the decoding process to diligently explore the vast solution space and select the best outcome. This paradigm commonly termed has emerged as a superior approach owing to parameter free scaling at inference time and high performance gains. The verifiers could be prompt-based, fine-tuned as a discriminative or generative model to verify process paths, outcomes or both. Despite their widespread adoption, there is no detailed collection, clear categorization and discussion of diverse verification approaches and their training mechanisms. In this survey, we cover the diverse approaches in the literature and present a unified view of verifier training, types and their utility in test-time scaling. Our repository can be found at https://github.com/elixir-research-group/Verifierstesttimescaling.github.io.

Test-time reinforcement learning (TTRL) has emerged as a promising paradigm for self-evolving large reasoning models (LRMs), enabling online adaptation on unlabeled test inputs via self-induced rewards through majority voting. However, a spurious yet high-frequency unverified consensus can become a biased and reinforced reward signal, leading to incorrect mode collapse. We address this failure mode with T^3RL (Tool-Verification for Test-Time Reinforcement Learning), which introduces test-time tool verification into reward estimation. Concretely, a verifier uses an external tool as evidence (e.g., from code execution) to upweight verified rollouts in a verification-aware voting, producing more reliable pseudo-labels for training. Across various math difficulties (MATH-500, AMC, and AIME 2024) and diverse backbone types, T^3RL significantly improves over TTRL, with larger gains on harder problems. More broadly, T^3RL can be viewed as verified online data synthesis, highlighting test-time tool verification as a key mechanism for stabilizing self-evolution.

Test-time compute scaling is a primary driver of performance in large reasoning models (LRMs), but extreme inefficiency bounds current approaches, shifting the critical question from how much compute to spend, to where to allocate it. We formalize test-time reasoning as a constrained compute allocation problem over partial trajectories. Under a fixed hardware budget, existing paradigms fail to actively allocate the compute to the most promising partial progress: traditional parallel sampling treats traces independently and induces severe memory bottlenecks, while subtractive pruning starves hardware and fails to actively and sufficiently shift the output distribution. To overcome this dichotomy, we introduce Gambit, an inference algorithm that executes thought-level beam search. By periodically pruning unpromising trajectories and immediately branching from high-quality prefixes, Gambit dynamically concentrates compute onto the most promising reasoning traces via a light-weight scorer probing hidden states while maintaining continuous high hardware utilization. Extensive evaluations across multiple models and benchmarks demonstrate that Gambit strictly dominates existing baselines. Under identical hardware constraints, our method yields up to a +6.7\% absolute accuracy gain on HMMT-24 and +3.3\% on AIME-25 over pruning baselines, delivers >2times higher throughput on trace completion, and reduces total token consumption by up to 68.5\% relative to standard parallel sampling.

By utilizing more computational resources at test-time, large language models (LLMs) can improve without additional training. One common strategy uses verifiers to evaluate candidate outputs. In this work, we propose a novel scaling dimension for test-time compute: scaling the number of verifiers. We introduce Multi-Agent Verification (MAV) as a test-time compute paradigm that combines multiple verifiers to improve performance. We propose using Aspect Verifiers (AVs), off-the-shelf LLMs prompted to verify different aspects of outputs, as one possible choice for the verifiers in a MAV system. AVs are a convenient building block for MAV since they can be easily combined without additional training. Moreover, we introduce BoN-MAV, a simple multi-agent verification algorithm that combines best-of-n sampling with multiple verifiers. BoN-MAV demonstrates stronger scaling patterns than self-consistency and reward model verification, and we demonstrate both weak-to-strong generalization, where combining weak verifiers improves even stronger LLMs, and self-improvement, where the same base model is used to both generate and verify outputs. Our results establish scaling the number of verifiers as a promising new dimension for improving language model performance at test-time.

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model debate approaches, our method leverages consistency in a sequence of self-reflection actions to improve verification accuracy. Empirical evaluations across diverse mathematical process error identification benchmarks (Mathcheck, ProcessBench, and PRM800K) show consistent performance improvements over baseline methods. When applied to the recent DeepSeek R1 distilled models, our method demonstrates strong performance, enabling 7B/8B distilled models to outperform all 70B/72B models and GPT-4o on ProcessBench. Notably, the distilled 14B model with our method achieves performance comparable to Deepseek-R1. Our codes are available at https://github.com/jcguo123/Temporal-Consistency

Large language models can solve substantially harder reasoning problems with more inference-time compute. The term "test-time scaling," however, now covers diverse inference algorithms that extend deliberation along a single trajectory, sample completed candidates and aggregate them through voting or verification, or search over unfinished partial states. These algorithms differ in their statistical structure, compute accounting, and failure modes. Treating these procedures as interchangeable under a single scalar "budget," or reporting accuracy without the inference protocol that produced it, makes results difficult to compare across studies. We develop a systematic account of test-time scaling along three axes. First, we formalize test-time scaling as budgeted inference over the implicit prefix tree of an autoregressive model and distinguish three structural regimes: single-trajectory sequential scaling, leaf-level scaling with terminal reduction, and prefix-level scaling. Second, we treat the evaluated object as the entire inference system and develop evaluation principles that separate end-to-end system performance from candidate-bank diagnostics. We introduce an evaluation profile whose coordinates and simple functionals recover or bound common repeated-sampling metrics, and prescribe protocol-matched reporting of compute and uncertainty. Third, we specify reproducibility requirements for inference protocols, distinguishing exact replay from distributional reproducibility and identifying the artifacts needed to support each. We also organize the open-weight reasoning ecosystem by model-side and interface mechanisms, apply these principles to broad-knowledge, symbolic-reasoning, and competition-mathematics benchmarks, and assemble over 2 billion full reasoning traces for release with progressively richer verifier and token-level signals.

Recently, test-time adaptation (TTA) has been proposed as a promising solution for addressing distribution shifts. It allows a base model to adapt to an unforeseen distribution during inference by leveraging the information from the batch of (unlabeled) test data. However, we uncover a novel security vulnerability of TTA based on the insight that predictions on benign samples can be impacted by malicious samples in the same batch. To exploit this vulnerability, we propose Distribution Invading Attack (DIA), which injects a small fraction of malicious data into the test batch. DIA causes models using TTA to misclassify benign and unperturbed test data, providing an entirely new capability for adversaries that is infeasible in canonical machine learning pipelines. Through comprehensive evaluations, we demonstrate the high effectiveness of our attack on multiple benchmarks across six TTA methods. In response, we investigate two countermeasures to robustify the existing insecure TTA implementations, following the principle of "security by design". Together, we hope our findings can make the community aware of the utility-security tradeoffs in deploying TTA and provide valuable insights for developing robust TTA approaches.

Scaling test time compute has shown remarkable success in improving the reasoning abilities of large language models (LLMs). In this work, we conduct the first systematic exploration of applying test-time scaling methods to language agents and investigate the extent to which it improves their effectiveness. Specifically, we explore different test-time scaling strategies, including: (1) parallel sampling algorithms; (2) sequential revision strategies; (3) verifiers and merging methods; (4)strategies for diversifying rollouts.We carefully analyze and ablate the impact of different design strategies on applying test-time scaling on language agents, and have follow findings: 1. Scaling test time compute could improve the performance of agents. 2. Knowing when to reflect is important for agents. 3. Among different verification and result merging approaches, the list-wise method performs best. 4. Increasing diversified rollouts exerts a positive effect on the agent's task performance.

Recent advances have shown that scaling test-time computation enables large language models (LLMs) to solve increasingly complex problems across diverse domains. One effective paradigm for test-time scaling (TTS) involves LLM generators producing multiple solution candidates, with LLM verifiers assessing the correctness of these candidates without reference answers. In this paper, we study generative verifiers, which perform verification by generating chain-of-thought (CoT) reasoning followed by a binary verdict. We systematically analyze verification dynamics across three dimensions - problem difficulty, generator capability, and verifier generation capability - with empirical studies on 12 benchmarks across mathematical reasoning, knowledge, and natural language reasoning tasks using 14 open-source models (2B to 72B parameter range) and GPT-4o. Our experiments reveal three key findings about verification effectiveness: (1) Easy problems allow verifiers to more reliably certify correct responses; (2) Weak generators produce errors that are easier to detect than strong generators; (3) Verification ability is generally correlated with the verifier's own problem-solving capability, but this relationship varies with problem difficulty. These findings reveal opportunities to optimize basic verification strategies in TTS applications. First, given the same verifier, some weak generators can nearly match stronger ones in post-verification TTS performance (e.g., the Gemma2-9B to Gemma2-27B performance gap shrinks by 75.5%). Second, we identify cases where strong verifiers offer limited advantage over weak ones, as both fail to provide meaningful verification gains, suggesting that verifier scaling alone cannot overcome fundamental verification challenges.

Increasing test-time compute for LLMs shows promise across domains but remains underexplored in code generation, despite extensive study in math. In this paper, we propose S*, the first hybrid test-time scaling framework that substantially improves the coverage and selection accuracy of generated code. S* extends the existing parallel scaling paradigm with sequential scaling to push performance boundaries. It further leverages a novel selection mechanism that adaptively generates distinguishing inputs for pairwise comparison, combined with execution-grounded information to robustly identify correct solutions. We evaluate across 12 Large Language Models and Large Reasoning Model and show: (1) S* consistently improves performance across model families and sizes, enabling a 3B model to outperform GPT-4o-mini; (2) S* enables non-reasoning models to surpass reasoning models - GPT-4o-mini with S* outperforms o1-preview by 3.7% on LiveCodeBench; (3) S* further boosts state-of-the-art reasoning models - DeepSeek-R1-Distill-Qwen-32B with S* achieves 85.7% on LiveCodeBench, approaching o1 (high) at 88.5%. Code will be available under https://github.com/NovaSky-AI/SkyThought.

Scaling test-time compute has emerged as a key strategy for enhancing the reasoning capabilities of large language models (LLMs), particularly in tasks like mathematical problem-solving. A traditional approach, Self-Consistency (SC), generates multiple solutions to a problem and selects the most common answer via majority voting. Another common method involves scoring each solution with a reward model (verifier) and choosing the best one. Recent advancements in Generative Reward Models (GenRM) reframe verification as a next-token prediction task, enabling inference-time scaling along a new axis. Specifically, GenRM generates multiple verification chains-of-thought to score each solution. Under a limited inference budget, this introduces a fundamental trade-off: should you spend the budget on scaling solutions via SC or generate fewer solutions and allocate compute to verification via GenRM? To address this, we evaluate GenRM against SC under a fixed inference budget. Interestingly, we find that SC is more compute-efficient than GenRM for most practical inference budgets across diverse models and datasets. For instance, GenRM first matches SC after consuming up to 8x the inference compute and requires significantly more compute to outperform it. Furthermore, we derive inference scaling laws for the GenRM paradigm, revealing that compute-optimal inference favors scaling solution generation more aggressively than scaling the number of verifications. Our work provides practical guidance on optimizing test-time scaling by balancing solution generation and verification. The code is available at https://github.com/nishadsinghi/sc-genrm-scaling.

Test-time scaling (TTS), which involves dynamic allocation of compute during inference, offers a promising way to improve reasoning in large language models. While existing TTS methods work well, they often rely on long decoding paths or require a large number of samples to be generated, increasing the token usage and inference latency. We observe the surprising fact that for reasoning tasks, shorter traces are much more likely to be correct than longer ones. Motivated by this, we introduce First Finish Search (FFS), a training-free parallel decoding strategy that launches n independent samples and returns as soon as any one completes. We evaluate FFS alongside simple decoding, beam search, majority voting, and budget forcing on four reasoning models (DeepSeek-R1, R1-Distill-Qwen-32B, QwQ-32B and Phi-4-Reasoning-Plus) and across four datasets (AIME24, AIME25-I, AIME25-II and GPQA Diamond). With DeepSeek-R1, FFS achieves 82.23% accuracy on the AIME datasets, a 15% improvement over DeepSeek-R1's standalone accuracy, nearly matching OpenAI's o4-mini performance. Our theoretical analysis explains why stopping at the shortest trace is likely to yield a correct answer and identifies the conditions under which early stopping may be suboptimal. The elegance and simplicity of FFS demonstrate that straightforward TTS strategies can perform remarkably well, revealing the untapped potential of simple approaches at inference time.

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

Falsification searches for counterexamples to formal specifications in cyber-physical systems (CPS). With specifications written in Signal Temporal Logic (STL), falsification can be formulated as a robustness optimization problem, traditionally tackled with black-box search algorithms. In parallel, large language models (LLMs) have recently emerged as surprisingly effective optimizers when coupled with iterative prompting. In this work, we connect these ideas and introduce LLM-Falsifier, an LLM-based approach that falsifies specifications by minimizing the STL robustness degree. Beyond generic prompt-based optimization, our key idea is to expose the LLM to semantic information that is natural for language models but absent from standard numerical optimizers, including natural-language input and output names, output trajectories, and critical-time witnesses for the minimum robustness value. These additions enable smarter and more sample-efficient robustness search. On the ARCH-COMP falsification benchmarks, LLM-Falsifier is shown to outperform existing falsification tools based on a range of optimization paradigms, from surrogate-based and Bayesian optimization to search-based testing, on 14 of 21 specifications when measured by the average number of simulations required to find a counterexample.

Test-time compute has emerged as a powerful paradigm for improving the performance of large language models (LLMs), where generating multiple outputs or refining individual chains can significantly boost answer accuracy. However, existing methods like Best-of-N, majority voting, and self-reflection typically apply reasoning in a uniform way across inputs, overlooking the fact that different problems may require different levels of reasoning depth. In this work, we propose Fractional Reasoning, a training-free and model-agnostic framework that enables continuous control over reasoning intensity at inference time, going beyond the limitations of fixed instructional prompts. Our method operates by extracting the latent steering vector associated with deeper reasoning and reapplying it with a tunable scaling factor, allowing the model to tailor its reasoning process to the complexity of each input. This supports two key modes of test-time scaling: (1) improving output quality in breadth-based strategies (e.g., Best-of-N, majority voting), and (2) enhancing the correctness of individual reasoning chains in depth-based strategies (e.g., self-reflection). Experiments on GSM8K, MATH500, and GPQA demonstrate that Fractional Reasoning consistently improves performance across diverse reasoning tasks and models.

Test-time scaling has become an effective paradigm for improving the reasoning ability of large language models by allocating additional computation during inference. Recent structured approaches have further advanced this paradigm by organizing inference across multiple trajectories, refinement rounds, and verification-based feedback. However, existing structured test-time scaling methods either weakly coordinate parallel reasoning trajectories or rely on noisy historical information without explicitly deciding what should be retained and reused, limiting their ability to balance exploration and exploitation. In this work, we propose TMAS, a framework for scaling test-time compute via multi-agent synergy. TMAS organizes inference as a collaborative process among specialized agents, enabling structured information flow across agents, trajectories, and refinement iterations. To support effective cross-trajectory collaboration, TMAS introduces hierarchical memories: the experience bank reuses low-level reliable intermediate conclusions and local feedback, while the guideline bank records previously explored high-level strategies to steer subsequent rollouts away from redundant reasoning patterns. Furthermore, we design a hybrid reward reinforcement learning scheme tailored to TMAS, which jointly preserves basic reasoning capability, enhances experience utilization, and encourages exploration beyond previously attempted solution strategies. Extensive experiments on challenging reasoning benchmarks demonstrate that TMAS achieves stronger iterative scaling than existing test-time scaling baselines, while hybrid reward training further improves scaling effectiveness and stability across iterations. Code and data are available at https://github.com/george-QF/TMAS-code.

One common strategy for improving the performance of Large Language Models (LLMs) on downstream tasks involves using a verifier model to either select the best answer from a pool of candidates or to steer the auto-regressive generation process towards better outputs. This class of methods typically results in improved accuracy at the cost of increased computation at test-time, a paradigm known as test-time scaling. However, most existing approaches increase computation uniformly across all samples and generation steps, without considering the complexity of individual instances, leading to inefficient resource use. We address this limitation by proposing an approach, called Locally Adaptive Test-Time Scaling (LATTS), that allocates variable compute across generation steps. Specifically, at each generation step, LATTS employs a verifier-based acceptance criterion to decide whether to resample, backtrack, restart, or stop the generation process. This criterion effectively adjusts the per-step computational effort based on a precise notion of local difficulty derived from the verifier model. Empirical results show that LATTS achieves significantly superior accuracy--compute tradeoffs compared to standard verifier-based methods.

Test-time scaling for complex reasoning tasks shows that leveraging inference-time compute, by methods such as independently sampling and aggregating multiple solutions, results in significantly better task outcomes. However, a critical bottleneck is verification: sampling is only effective if correct solutions can be reliably identified among candidates. While existing approaches typically evaluate candidates independently via scalar scoring, we demonstrate that models are substantially stronger at pairwise self-verification. Leveraging this insight, we introduce V_1, a framework that unifies generation and verification through efficient pairwise ranking. V_1 comprises two components: V_1-Infer, an uncertainty-guided algorithm using a tournament-based ranking that dynamically allocates self-verification compute to candidate pairs whose relative correctness is most uncertain; and V_1-PairRL, an RL framework that jointly trains a single model as both generator and pairwise self-verifier, ensuring the verifier adapts to the generator's evolving distribution. On code generation (LiveCodeBench, CodeContests, SWE-Bench) and math reasoning (AIME, HMMT) benchmarks, V_1-Infer improves Pass@1 by up to 10% over pointwise verification and outperforms recent test-time scaling methods while being significantly more efficient. Furthermore, V_1-PairRL achieves 7--9% test-time scaling gains over standard RL and pointwise joint training, and improves base Pass@1 by up to 8.7% over standard RL in a code-generation setting.

Recent studies have demonstrated that test-time compute scaling effectively improves the performance of small language models (sLMs). However, prior research has mainly examined test-time compute scaling with an additional larger model as a verifier, leaving self-verification by sLMs underexplored. In this work, we investigate whether sLMs can reliably self-verify their outputs under test-time scaling. We find that even with knowledge distillation from larger verifiers, sLMs struggle with verification tasks requiring memorization, such as numerical calculations and fact-checking. To address this limitation, we propose Tool-integrated self-verification (T1), which delegates memorization-heavy verification steps to external tools, such as a code interpreter. Our theoretical analysis shows that tool integration reduces memorization demands and improves test-time scaling performance. Experiments on the MATH benchmark demonstrate that, with T1, a Llama-3.2 1B model under test-time scaling outperforms the significantly larger Llama-3.1 8B model. Moreover, T1 generalizes effectively to both mathematical (MATH500) and multi-domain knowledge-intensive tasks (MMLU-Pro). Our findings highlight the potential of tool integration to substantially improve the self-verification abilities of sLMs.

Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the state-of-the-art DeepSeek-R1-Distill-Qwen, we find that bypassing the thinking process via simple prompting, denoted as NoThinking, can be surprisingly effective. When controlling for the number of tokens, NoThinking outperforms Thinking across a diverse set of seven challenging reasoning datasets--including mathematical problem solving, formal theorem proving, and coding--especially in low-budget settings, e.g., 51.3 vs. 28.9 on ACM 23 with 700 tokens. Notably, the performance of NoThinking becomes more competitive with pass@k as k increases. Building on this observation, we demonstrate that a parallel scaling approach that uses NoThinking to generate N outputs independently and aggregates them is highly effective. For aggregation, we use task-specific verifiers when available, or we apply simple best-of-N strategies such as confidence-based selection. Our method outperforms a range of baselines with similar latency using Thinking, and is comparable to Thinking with significantly longer latency (up to 9x). Together, our research encourages a reconsideration of the necessity of lengthy thinking processes, while also establishing a competitive reference for achieving strong reasoning performance in low-budget settings or at low latency using parallel scaling.

Test-time scaling (TTS) -- the dynamic allocation of compute during inference -- is a promising direction for improving reasoning in large language models (LLMs). However, a systematic comparison of well-known TTS strategies under identical conditions is missing, and the influence of model type and problem difficulty on performance remains unclear. To address these gaps, we conduct the first large-scale study of TTS, spanning over thirty billion tokens generated using eight open-source LLMs (7B to 235B parameters), across four reasoning datasets. We observe three consistent trends: (1) no single TTS strategy universally dominates; (2) reasoning models exhibit distinct trace-quality patterns across problem difficulty and trace length, forming short-horizon and long-horizon categories; and (3) for a given model type, the optimal TTS performance scales monotonically with compute budget. Based on these insights, we provide a practical recipe for selecting the best TTS strategy, considering problem difficulty, model type, and compute budget, providing a practical guide to effective inference-time scaling.

Test-Time Scaling (TTS) improves LLM reasoning by exploring multiple candidate responses and then operating over this set to find the best output. A tacit premise behind TTS is that sufficiently diverse candidate pools enhance reliability. In this work, we show that this assumption in TTS introduces a previously unrecognized failure mode. When candidate diversity is curtailed, even by a modest amount, TTS becomes much more likely to produce unsafe outputs. We present a reference-guided diversity reduction protocol (RefDiv) that serves as a diagnostic attack to stress test TTS pipelines. Through extensive experiments across open-source models (e.g. Qwen3, Mistral, Llama3.1, Gemma3) and two widely used TTS strategies (Monte Carlo Tree Search and Best-of-N), constraining diversity consistently signifies the rate at which TTS produces unsafe results. The effect is often stronger than that produced by prompts directly with high adversarial intent scores. This observed phenomenon also transfers across TTS strategies and to closed-source models (e.g. OpenAI o3-mini and Gemini-2.5-Pro), thus indicating that this is a general and extant property of TTS rather than a model-specific artifact. Additionally, we find that numerous widely used safety guardrail classifiers (e.g. Llama-Guard), are unable to flag the adversarial input prompts generated by RefDiv, demonstrating that existing defenses offer limited protection against this diversity-driven failure mode.

Recent advancements in software engineering agents have demonstrated promising capabilities in automating program improvements. However, their reliance on closed-source or resource-intensive models introduces significant deployment challenges in private environments, prompting a critical question: How can personally deployable open-source LLMs achieve comparable code reasoning performance? To this end, we propose a unified Test-Time Compute scaling framework that leverages increased inference-time computation instead of larger models. Our framework incorporates two complementary strategies: internal TTC and external TTC. Internally, we introduce a development-contextualized trajectory synthesis method leveraging real-world software repositories to bootstrap multi-stage reasoning processes, such as fault localization and patch generation. We further enhance trajectory quality through rejection sampling, rigorously evaluating trajectories along accuracy and complexity. Externally, we propose a novel development-process-based search strategy guided by reward models and execution verification. This approach enables targeted computational allocation at critical development decision points, overcoming limitations of existing "end-point only" verification methods. Evaluations on SWE-bench Verified demonstrate our 32B model achieves a 46\% issue resolution rate, surpassing significantly larger models such as DeepSeek R1 671B and OpenAI o1. Additionally, we provide the empirical validation of the test-time scaling phenomenon within SWE agents, revealing that models dynamically allocate more tokens to increasingly challenging problems, effectively enhancing reasoning capabilities. We publicly release all training data, models, and code to facilitate future research. https://github.com/yingweima2022/SWE-Reasoner

As large language models (LLMs) increasingly tackle complex reasoning tasks, test-time scaling has become critical for enhancing capabilities. However, in agentic scenarios with frequent tool calls, the traditional generation-length-based definition breaks down: tool latency decouples inference time from generation length. We propose Timely Machine, redefining test-time as wall-clock time, where models dynamically adjust strategies based on time budgets. We introduce Timely-Eval, a benchmark spanning high-frequency tool calls, low-frequency tool calls, and time-constrained reasoning. By varying tool latency, we find smaller models excel with fast feedback through more interactions, while larger models dominate high-latency settings via superior interaction quality. Moreover, existing models fail to adapt reasoning to time budgets. We propose Timely-RL to address this gap. After cold-start supervised fine-tuning, we use reinforcement learning to enhance temporal planning. Timely-RL improves time budget awareness and consistently boosts performance across Timely-Eval. We hope our work offers a new perspective on test-time scaling for the agentic era.

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines a population of candidate reasoning chains through aggregation of subsets to yield a population of improved solutions, which are then used as the candidate pool for the next iteration. Empirically, RSA delivers substantial performance gains with increasing compute budgets across diverse tasks, model families and sizes. Notably, RSA with Gemini 3 Flash attains performance near the top of the ARC-AGI-2 public leaderboard. RSA also enables Qwen3-4B-Instruct-2507 to achieve competitive performance with larger reasoning models, including DeepSeek-R1 and o3-mini (high), outperforming purely parallel and sequential scaling strategies across AIME-25, HMMT-25, Reasoning Gym, LiveCodeBench-v6, and SuperGPQA. We further propose a novel aggregation-aware reinforcement learning approach that yields significant performance gains by training the model to combine solutions.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

Test-Time Adaptation (TTA) has recently emerged as a promising approach for tackling the robustness challenge under distribution shifts. However, the lack of consistent settings and systematic studies in prior literature hinders thorough assessments of existing methods. To address this issue, we present TTAB, a test-time adaptation benchmark that encompasses ten state-of-the-art algorithms, a diverse array of distribution shifts, and two evaluation protocols. Through extensive experiments, our benchmark reveals three common pitfalls in prior efforts. First, selecting appropriate hyper-parameters, especially for model selection, is exceedingly difficult due to online batch dependency. Second, the effectiveness of TTA varies greatly depending on the quality and properties of the model being adapted. Third, even under optimal algorithmic conditions, none of the existing methods are capable of addressing all common types of distribution shifts. Our findings underscore the need for future research in the field to conduct rigorous evaluations on a broader set of models and shifts, and to re-examine the assumptions behind the empirical success of TTA. Our code is available at https://github.com/lins-lab/ttab.

Test-time scaling with parallel branches is widely adopted to improve performance on challenging reasoning tasks. The predominant approach, repeated sampling, draws branches independently from a single policy, which can produce redundant attempts and thereby limit the gains from additional inference compute. To address this limitation, we propose Planned Test-Time Scaling (PTTS), which replaces independent sampling with a coordinated joint policy: a planner generates a solution outline for each branch, steering the branches toward distinct reasoning paths, and an executor produces a full solution conditioned on each outline. Formally, we show that PTTS strictly generalizes repeated sampling and, in a stylized setting, provably promotes coverage of complementary reasoning modes and yields better pass@k scaling. We instantiate PTTS on top of strong reasoning models, keeping them fixed as executors while replacing repeated sampling with PTTS inference to further enhance test-time scaling. Concretely, we develop two variants: PTTS-ZS prompts a model to jointly generate outlines for all branches in a single autoregressive pass, while PTTS-RL directly optimizes the planner against the pass@k reward using truncated execution rollouts for efficient training and a sharper reward signal. Across five mathematical reasoning benchmarks with Qwen3-1.7B and 4B, PTTS-ZS improves pass@64 over repeated sampling by up to 6.7 points, while PTTS-RL further increases the gain to up to 13.4 points. Further analysis indicates that broader coverage of distinct reasoning paths contributes to these gains. Overall, PTTS provides a general framework for improving test-time scaling by coordinating reasoning branches, with zero-shot and trainable instantiations that yield substantial performance gains.

Language models can produce plausible short proofs, but may still be unreliable on long-horizon research problems, where progress depends on a sequence of uncertain and interdependent decisions. We introduce Stellar Colosseum, a model-agnostic harness for allocating inference across research in mathematics and theoretical computer science. Colosseum explores alternative strategies before proof construction, uses a readiness gate to decide when a route is mature enough to decompose, represents the proof plan as interdependent section-level subproblems, and routes verifier findings back to the affected part of the argument. Across these stages, it generates candidates in parallel, attacks them with targeted falsification, and combines candidates and their critiques into a single research artifact through overlapping random-sample tree aggregation. The Colosseum workflow has been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern. We demonstrate the capabilities of Colosseum through open-ended research and evaluations on theorem-proving and competitive programming benchmarks. Using Colosseum with Gemini 3.1 Pro, we obtain several new results that address open problems arising from papers published at top venues such as FOCS and JMLR. On TCS-Bench, a benchmark of research-level theorem-proving tasks drawn from papers published at FOCS, STOC, and SODA, Colosseum achieves 71.0% accuracy using Gemini 3.1 Pro and Gemini 3.7 Flash. In a separate Codeforces evaluation using Gemini 3.1 Pro, the proof-oriented pipeline with execution feedback solves 218 of 222 problems.

Deploying models on target domain data subject to distribution shift requires adaptation. Test-time training (TTT) emerges as a solution to this adaptation under a realistic scenario where access to full source domain data is not available and instant inference on target domain is required. Despite many efforts into TTT, there is a confusion over the experimental settings, thus leading to unfair comparisons. In this work, we first revisit TTT assumptions and categorize TTT protocols by two key factors. Among the multiple protocols, we adopt a realistic sequential test-time training (sTTT) protocol, under which we further develop a test-time anchored clustering (TTAC) approach to enable stronger test-time feature learning. TTAC discovers clusters in both source and target domain and match the target clusters to the source ones to improve generalization. Pseudo label filtering and iterative updating are developed to improve the effectiveness and efficiency of anchored clustering. We demonstrate that under all TTT protocols TTAC consistently outperforms the state-of-the-art methods on six TTT datasets. We hope this work will provide a fair benchmarking of TTT methods and future research should be compared within respective protocols. A demo code is available at https://github.com/Gorilla-Lab-SCUT/TTAC.

Recent prominent post-training methods, such as Reinforcement Learning (RL) and On-Policy Self-Distillation (OPSD), have driven rapid progress in mathematical reasoning for large language models, yet their reliance on ground-truth labels precludes test-time training (TTT). Replacing ground truth with majority-vote pseudo-labels is a natural alternative, yet it is fragile: an incorrect vote corrupts the teacher and misleads every token. We observe that this failure mode is asymmetric: rollouts that disagree with the pseudo-label are typically wrong regardless of whether the vote itself is correct. Building on this observation, we propose Test-Time Policy Optimization (TTPO), an asymmetric objective that distills agreeing rollouts via OPSD and penalizes disagreeing rollouts with Grouped RL. Token-level selection further refines both branches: distillation down-weights already-converged positions, while RL penalizes only confident errors. Both updates remain well-grounded even under frequent pseudo-label errors, and majority-vote routing yields tighter self-supervision as the model improves. Without any labels, TTPO matches label-supervised OPSD on five competition-level benchmarks, raises Qwen3-1.7B from 38.0% to 45.2% in TTT, yields +25.2% to +36.4% without thinking, and shows strong cross-task generalization.

There is growing excitement about the potential of Language Models (LMs) to accelerate scientific discovery. Falsifying hypotheses is key to scientific progress, as it allows claims to be iteratively refined over time. This process requires significant researcher effort, reasoning, and ingenuity. Yet current benchmarks for LMs predominantly assess their ability to generate solutions rather than challenge them. We advocate for developing benchmarks that evaluate this inverse capability - creating counterexamples for subtly incorrect solutions. To demonstrate this approach, we start with the domain of algorithmic problem solving, where counterexamples can be evaluated automatically using code execution. Specifically, we introduce REFUTE, a dynamically updating benchmark that includes recent problems and incorrect submissions from programming competitions, where human experts successfully identified counterexamples. Our analysis finds that the best reasoning agents, even OpenAI o3-mini (high) with code execution feedback, can create counterexamples for only <9% of incorrect solutions in REFUTE, even though ratings indicate its ability to solve up to 48% of these problems from scratch. We hope our work spurs progress in evaluating and enhancing LMs' ability to falsify incorrect solutions - a capability that is crucial for both accelerating research and making models self-improve through reliable reflective reasoning.

Recently, Test-Time Scaling (TTS) has gained increasing attention for improving LLM reasoning performance at test time without retraining the model. A notable TTS technique is Self-Consistency (SC), which generates multiple reasoning chains in parallel and selects the final answer via majority voting. While effective, the order-of-magnitude computational overhead limits its broad deployment. Prior attempts to accelerate SC mainly rely on model-based confidence scores or heuristics with limited empirical support. For the first time, we theoretically and empirically analyze the inefficiencies of SC and reveal actionable opportunities for improvement. Building on these insights, we propose Slim-SC, a step-wise pruning strategy that identifies and removes redundant chains using inter-chain similarity at the thought level. Experiments on three STEM reasoning datasets and two recent LLM architectures show that Slim-SC reduces inference latency and KVC usage by up to 45% and 26%, respectively, with R1-Distill, while maintaining or improving accuracy, thus offering a simple yet efficient TTS alternative for SC.

Test-time scaling has emerged as a transformative paradigm for enhancing the performance of large reasoning models, enabling dynamic allocation of computational resources during inference. However, as the landscape of reasoning models rapidly expands, a critical question remains: how can we systematically compare and evaluate the test-time scaling capabilities across different models? In this paper, we introduce ARISE (Adaptive Resolution-aware Scaling Evaluation), a novel metric specifically designed to assess the test-time scaling effectiveness of large reasoning models. Unlike existing evaluation approaches, ARISE incorporates two key innovations: (1) sample-level awareness that effectively penalizes negative scaling behaviors where increased computation leads to performance degradation, and (2) a dynamic sampling mechanism that mitigates the impact of accuracy fluctuations and token count instability on the final assessment. We conduct comprehensive experiments evaluating state-of-the-art reasoning models across diverse domains including mathematical reasoning, code generation, and agentic tasks. Our results demonstrate that ARISE provides a reliable and fine-grained measurement of test-time scaling capabilities, revealing significant variations in scaling efficiency across models. Notably, our evaluation identifies Claude Opus as exhibiting superior scaling characteristics compared to other contemporary reasoning models.

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.

Traditional fixed test sets fall short in evaluating open-ended capabilities of foundation models. To address this, we propose ONEBench(OpeN-Ended Benchmarking), a new testing paradigm that consolidates individual evaluation datasets into a unified, ever-expanding sample pool. ONEBench allows users to generate custom, open-ended evaluation benchmarks from this pool, corresponding to specific capabilities of interest. By aggregating samples across test sets, ONEBench enables the assessment of diverse capabilities beyond those covered by the original test sets, while mitigating overfitting and dataset bias. Most importantly, it frames model evaluation as a collective process of selecting and aggregating sample-level tests. The shift from task-specific benchmarks to ONEBench introduces two challenges: (1)heterogeneity and (2)incompleteness. Heterogeneity refers to the aggregation over diverse metrics, while incompleteness describes comparing models evaluated on different data subsets. To address these challenges, we explore algorithms to aggregate sparse measurements into reliable model scores. Our aggregation algorithm ensures identifiability(asymptotically recovering ground-truth scores) and rapid convergence, enabling accurate model ranking with less data. On homogenous datasets, we show our aggregation algorithm provides rankings that highly correlate with those produced by average scores. We also demonstrate robustness to ~95% of measurements missing, reducing evaluation cost by up to 20x with little-to-no change in model rankings. We introduce ONEBench-LLM for language models and ONEBench-LMM for vision-language models, unifying evaluations across these domains. Overall, we present a technique for open-ended evaluation, which can aggregate over incomplete, heterogeneous sample-level measurements to continually grow a benchmark alongside the rapidly developing foundation models.

The remarkable performance of the o1 model in complex reasoning demonstrates that test-time computing scaling can further unlock the model's potential, enabling powerful System-2 thinking. However, there is still a lack of comprehensive surveys for test-time computing scaling. We trace the concept of test-time computing back to System-1 models. In System-1 models, test-time computing addresses distribution shifts and improves robustness and generalization through parameter updating, input modification, representation editing, and output calibration. In System-2 models, it enhances the model's reasoning ability to solve complex problems through repeated sampling, self-correction, and tree search. We organize this survey according to the trend of System-1 to System-2 thinking, highlighting the key role of test-time computing in the transition from System-1 models to weak System-2 models, and then to strong System-2 models. We also point out a few possible future directions.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Large language models are often adapted through parameter efficient fine tuning, but current release practices provide weak assurances about what data were used and how updates were computed. We present Verifiable Fine Tuning, a protocol and system that produces succinct zero knowledge proofs that a released model was obtained from a public initialization under a declared training program and an auditable dataset commitment. The approach combines five elements. First, commitments that bind data sources, preprocessing, licenses, and per epoch quota counters to a manifest. Second, a verifiable sampler that supports public replayable and private index hiding batch selection. Third, update circuits restricted to parameter efficient fine tuning that enforce AdamW style optimizer semantics and proof friendly approximations with explicit error budgets. Fourth, recursive aggregation that folds per step proofs into per epoch and end to end certificates with millisecond verification. Fifth, provenance binding and optional trusted execution property cards that attest code identity and constants. On English and bilingual instruction mixtures, the method maintains utility within tight budgets while achieving practical proof performance. Policy quotas are enforced with zero violations, and private sampling windows show no measurable index leakage. Federated experiments demonstrate that the system composes with probabilistic audits and bandwidth constraints. These results indicate that end to end verifiable fine tuning is feasible today for real parameter efficient pipelines, closing a critical trust gap for regulated and decentralized deployments.

Agent harnesses enable large language models to act through tools, observe the results, and iteratively work toward a task goal. Verification checks and revises agents' work to improve output quality. Yet there is limited guidance on how harnesses should organize this effort. We study verification as an axis of test-time scaling by examining when to intervene, who checks the work, and how checking leads to revision. Our framework spans four layers of the agent lifecycle: initial instructions, mid-turn reminders, completion gates, and independent review. We compare 17 designs across seven frontier coding models on Terminal-Bench (TB) and SWE-bench Verified (SWE), and introduce VisualBench for expert evaluation of visual and interactive artifacts. Initial instructions and execution-time reminders yield modest, model-dependent average gains on the coding benchmarks, without substantially increasing average output token use. Completion gates can yield larger gains but may substantially increase cost. Independent review by a critic offers a more favorable accuracy-cost tradeoff, improving average accuracy by 5.9-9.5 percentage points on TB and 3.9-6.6 on SWE at 1.13-1.25 and 1.00-1.04 times baseline cost, respectively. On VisualBench, independent review achieves net preferences of 13.2-23.8 points over the baseline across its four designs, exceeding the evaluated L0-L2 designs. Additional review rounds or independent critics further improve average TB accuracy by up to 3.5 percentage points. Together, these results provide empirical guidance for verification design in agent harnesses and support independent review as a practical axis of test-time scaling.

Agent benchmarks are growing fast, but no single benchmark touches more than four or five of the dimensions that deployment exposes. This paper aggregates the largest coordinated deep-dive of one MCP-based industrial-agent benchmark to date: fourteen parallel implementation studies covering new asset classes (including a multi-modal visual extension), alternative orchestrations, retrieval strategies, reasoning modes, infrastructure optimizations, and evaluation-methodology probes. Consolidating those studies with seven prior agent benchmarks, we argue that aggregate-score leaderboards systematically underspecify deployed-agent evaluation. Rankings derived from aggregate scores do not transfer to out-of-distribution settings; recent public-to-hidden competition retrospectives provide direct empirical evidence of this rank instability. We propose ranking configurations by predictive validity, the correlation between in-sample and out-of-sample rank, rather than in-sample mean, and report a twelve-tier measurement apparatus that exposes the deployment-relevant dimensions HELM and its agent-era successors collapse. The position is operationalized through three falsifiable out-of-distribution criteria with explicit thresholds; existing evidence partly supports it but is too thin to confirm. We close with a pre-registered pilot design and a field-level vision for what the next generation of agentic benchmarks should report.

Given the increasing adoption of modern AI-enabled control systems, ensuring their safety and reliability has become a critical task in software testing. One prevalent approach to testing control systems is falsification, which aims to find an input signal that causes the control system to violate a formal safety specification using optimization algorithms. However, applying falsification to AI-enabled control systems poses two significant challenges: (1)~it requires the system to execute numerous candidate test inputs, which can be time-consuming, particularly for systems with AI models that have many parameters, and (2)~multiple safety requirements are typically defined as a conjunctive specification, which is difficult for existing falsification approaches to comprehensively cover. This paper introduces Synthify, a falsification framework tailored for AI-enabled control systems. Our approach performs falsification in a two-phase process. At the start, Synthify synthesizes a program that implements one or a few linear controllers to serve as a proxy for the AI controller. This proxy program mimics the AI controller's functionality but is computationally more efficient. Then, Synthify employs the ε-greedy strategy to sample a promising sub-specification from the conjunctive safety specification. It then uses a Simulated Annealing-based falsification algorithm to find violations of the sampled sub-specification for the control system. To evaluate Synthify, we compare it to PSY-TaLiRo, a state-of-the-art and industrial-strength falsification tool, on 8 publicly available control systems. On average, Synthify achieves a 83.5% higher success rate in falsification compared to PSY-TaLiRo with the same budget of falsification trials. The safety violations found by Synthify are also more diverse than those found by PSY-TaLiRo, covering 137.7% more sub-specifications.

Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many replication efforts. We seek the simplest approach to achieve test-time scaling and strong reasoning performance. First, we curate a small dataset s1K of 1,000 questions paired with reasoning traces relying on three criteria we validate through ablations: difficulty, diversity, and quality. Second, we develop budget forcing to control test-time compute by forcefully terminating the model's thinking process or lengthening it by appending "Wait" multiple times to the model's generation when it tries to end. This can lead the model to double-check its answer, often fixing incorrect reasoning steps. After supervised finetuning the Qwen2.5-32B-Instruct language model on s1K and equipping it with budget forcing, our model s1 exceeds o1-preview on competition math questions by up to 27% (MATH and AIME24). Further, scaling s1 with budget forcing allows extrapolating beyond its performance without test-time intervention: from 50% to 57% on AIME24. Our model, data, and code are open-source at https://github.com/simplescaling/s1.

Improving open-source models on real-world SWE tasks (solving GITHUB issues) faces two key challenges: 1) scalable curation of execution environments to train these models, and, 2) optimal scaling of test-time compute. We introduce AgentGym, the largest procedurally-curated executable gym environment for training real-world SWE-agents, consisting of more than 8.7K tasks. AgentGym is powered by two main contributions: 1) SYNGEN: a synthetic data curation recipe that enables scalable curation of executable environments using test-generation and back-translation directly from commits, thereby reducing reliance on human-written issues or unit tests. We show that this enables more scalable training leading to pass@1 performance of 34.4% on SWE-Bench Verified benchmark with our 32B model. 2) Hybrid Test-time Scaling: we provide an in-depth analysis of two test-time scaling axes; execution-based and execution-free verifiers, demonstrating that they exhibit complementary strengths and limitations. Test-based verifiers suffer from low distinguishability, while execution-free verifiers are biased and often rely on stylistic features. Surprisingly, we find that while each approach individually saturates around 42-43%, significantly higher gains can be obtained by leveraging their complementary strengths. Overall, our approach achieves 51% on the SWE-Bench Verified benchmark, reflecting a new state-of-the-art for open-weight SWE-agents and for the first time showing competitive performance with proprietary models such as o1, o1-preview and sonnet-3.5-v2 (with tools). We will open-source our environments, models, and agent trajectories.

As enthusiasm for scaling computation (data and parameters) in the pretraining era gradually diminished, test-time scaling (TTS), also referred to as ``test-time computing'' has emerged as a prominent research focus. Recent studies demonstrate that TTS can further elicit the problem-solving capabilities of large language models (LLMs), enabling significant breakthroughs not only in specialized reasoning tasks, such as mathematics and coding, but also in general tasks like open-ended Q&A. However, despite the explosion of recent efforts in this area, there remains an urgent need for a comprehensive survey offering a systemic understanding. To fill this gap, we propose a unified, multidimensional framework structured along four core dimensions of TTS research: what to scale, how to scale, where to scale, and how well to scale. Building upon this taxonomy, we conduct an extensive review of methods, application scenarios, and assessment aspects, and present an organized decomposition that highlights the unique functional roles of individual techniques within the broader TTS landscape. From this analysis, we distill the major developmental trajectories of TTS to date and offer hands-on guidelines for practical deployment. Furthermore, we identify several open challenges and offer insights into promising future directions, including further scaling, clarifying the functional essence of techniques, generalizing to more tasks, and more attributions.

Achieving effective test-time scaling requires models to engage in In-Context Exploration -- the intrinsic ability to generate, verify, and refine multiple reasoning hypotheses within a single continuous context. Grounded in State Coverage theory, our analysis identifies a critical bottleneck to enabling this capability: while broader state coverage requires longer reasoning trajectories, the probability of sampling such sequences decays exponentially during autoregressive generation, a phenomenon we term the ``Shallow Exploration Trap''. To bridge this gap, we propose Length-Incentivized Exploration(\method). This simple yet effective recipe explicitly encourages models to explore more via a length-based reward coupled with a redundancy penalty, thereby maximizing state coverage in two-step manner. Comprehensive experiments across different models (Qwen3, Llama) demonstrate that \method effectively incentivize in-context exploration. As a result, our method achieves an average improvement of 4.4\% on in-domain tasks and a 2.7\% gain on out-of-domain benchmarks.

Test-time scaling improves the reasoning performance of large language models but often results in token-inefficient overthinking, where models continue reasoning beyond what is necessary for a correct answer. Existing dynamic early-exit methods typically rely on single-step confidence signals, which are often unreliable for detecting reasoning convergence in multi-step settings. To mitigate this limitation, we propose TRACE, a training-free framework for efficient test-time scaling that determines when to terminate reasoning based on temporal aggregation of multi-step evidence rather than instantaneous signals. TRACE detects reasoning convergence over time by aggregating two complementary signals across recent reasoning steps: answer consistency, capturing the persistence of predicted answers, and confidence trajectory, modeling the temporal evolution of model confidence. Benefiting from these two factors, TRACE can accurately determine whether the reasoning process has converged, thereby promptly halting inference and effectively avoiding redundant reasoning steps. Extensive experiments on multiple challenging benchmarks show that TRACE reduces reasoning token usage by 25-30% on average while maintaining accuracy within 1-2% of full-length reasoning, consistently outperforming existing dynamic reasoning methods.

Test-Time Scaling (TTS) improves the performance of Large Language Models (LLMs) by using additional inference-time computation to explore multiple reasoning paths through search. Yet how to allocate a fixed rollout budget most effectively during search remains underexplored, often resulting in inefficient use of compute at test time. To bridge this gap, we formulate test-time search as a resource allocation problem and derive the optimal allocation strategy that maximizes the probability of obtaining a correct solution under a fixed rollout budget. Within this formulation, we reveal a core limitation of existing search methods: solution-level allocation tends to favor reasoning directions with more candidates, leading to theoretically suboptimal and inefficient use of compute. To address this, we propose Direction-Oriented Resource Allocation (DORA), a provably optimal method that mitigates this bias by decoupling direction quality from candidate count and allocating resources at the direction level. To demonstrate DORA's effectiveness, we conduct extensive experiments on challenging mathematical reasoning benchmarks including MATH500, AIME2024, and AIME2025. The empirical results show that DORA consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art accuracy. We hope our findings contribute to a broader understanding of optimal TTS for LLMs.

While scaling test-time compute can substantially improve model performance, existing approaches either rely on static compute allocation or sample from fixed generation distributions. In this work, we introduce a test-time compute allocation framework that jointly adapts where computation is spent and how generation is performed. Our method begins with a warm-up phase that identifies easy queries and assembles an initial pool of question-response pairs from the test set itself. An adaptive phase then concentrates further computation on unresolved queries while reshaping their generation distributions through evolving in-context demonstrations -- conditioning each generation on successful responses from semantically related queries rather than resampling from a fixed distribution. Experiments across math, coding, and reasoning benchmarks demonstrate that our approach consistently outperforms existing baselines while consuming substantially less inference-time compute.

Test-time compute has emerged as a promising strategy to enhance the reasoning abilities of large language models (LLMs). However, this strategy has in turn increased how much users pay cloud-based providers offering LLM-as-a-service, since providers charge users for the amount of test-time compute they use to generate an output. In our work, we show that the market of LLM-as-a-service is socially inefficient: providers have a financial incentive to increase the amount of test-time compute, even if this increase contributes little to the quality of the outputs. To address this inefficiency, we introduce a reverse second-price auction mechanism where providers bid their offered price and (expected) quality for the opportunity to serve a user, and users pay proportionally to the marginal value generated by the winning provider relative to the second-highest bidder. To illustrate and complement our theoretical results, we conduct experiments with multiple instruct models from the Llama and Qwen families, as well as reasoning models distilled from DeepSeek-R1, on math and science benchmark datasets.

Small Vision-Language Models (VLMs) provide a computationally efficient alternative to larger models, at the cost of weaker generalization abilities and downstream task performance. These shortcomings could be addressed by test-time scaling techniques, but existing methods are typically computationally demanding, contradicting the resource-efficient design goals of small models. To address these limitations, we propose two novel and efficient test-time scaling strategies that leverage the model-internal features rather than external supervision: (i) Test-Time Augmentation (TTAug), which generates multiple augmented inputs and aggregates outputs at the token level without parameter updates, and (ii) Test-Time Adaptation (TTAdapt), which adapts model parameters during inference using consensus-based pseudolabels from TTAug. Through extensive experiments across nine benchmarks, we demonstrate consistent performance improvements while maintaining computational efficiency suitable for resource-constrained environments. The generality of our approach is demonstrated both within models at different scales and across different VLMs without additional tuning.

Chain-of-Thought (CoT) and its variants have markedly advanced the reasoning abilities of Large Language Models (LLMs), yet their monolithic and auto-regressive architecture inherently conflates high-level strategic planning with low-level step-by-step execution, leading to computational inefficiency, limited exploration of reasoning paths, and reduced interpretability. To overcome these issues, we propose the Explore-Execute Chain (E^2C), a structured reasoning framework that decouples reasoning into two distinct phases: an exploratory phase that stochastically generates succinct high-level plans, followed by an execution phase that deterministically carries out the chosen plan. Our approach incorporates a two-stage training methodology, which combines Supervised Fine-Tuning (SFT) - augmented by a novel data generation algorithm enforcing strict plan adherence - with a subsequent Reinforcement Learning (RL) stage that capitalizes on the informativeness of exploration and reinforces the determinism of execution. This decomposition enables an efficient test-time scaling strategy: on AIME'2024, E^2C Test Time Scaling reaches 58.1% accuracy using <10% of the decoding tokens required by comparable methods (e.g., Forest-of-Thought), sharply cutting self-consistency overhead. For cross-domain adaptation, our Exploration-Focused SFT (EF-SFT) fine-tunes with only 3.5% of the tokens used by standard SFT yet yields up to 14.5% higher accuracy than standard SFT on medical benchmarks, delivering state-of-the-art performance, strong generalization, and greater interpretability by separating planning from execution. The code and pre-trained models for the project are available at: https://github.com/yks23/Explore-Execute-Chain.git

As the cost of code generation becomes cheaper with AI, the new bottleneck in software engineering has shifted to intent specification and validation. Overcoming this durability crisis of AI-driven coding requires more than traditional fuzzing: each candidate property must be proven correct over a model and shown to hold on the real implementation, making formal proof and systematic property-based testing (PBT) complementary. However, validating properties this way at scale requires solving two subproblems: verifying candidate properties and operationalizing PBT without AI hallucination. We hypothesize that recurring property patterns, cast as property templates--abstract, parameterized forms with holes--address both at once. This paper investigates recurring property patterns in Apache Spark. In data-intensive scalable computing systems, correctness properties arise from the principles of data partition, computation decomposition, and dataflow computation. For instance, aggregation decomposition relates a global function executed on the entire dataset to a local function followed by a recombiner. We design an agentic, dual-track validation framework that uses property templates to formally verify correctness in the Lean 4 theorem prover and instantiate PBT templates as executable PySpark tests. Our evaluation shows that property templates increase agentic proof engineering success by up to 2.6x (1.6x on average) and reduce proof hallucinations by 59%. Template-guided PBT synthesis reduces intent misalignments from 22 to 1 and cuts synthesis cost by up to 5.7x (3.8x on average). Template-guided synthesis further exceeds a state-of-the-art Spark fuzzer and approaches unguided LLM-based PBT on code coverage. Finally, comparing the two tracks is informative: when a proof succeeds yet a PBT finds a counterexample, the mismatch identifies a gap between the formal model and implementation.

Large Language Model Powered Multi-Agent Systems (MASs) are increasingly employed to automate complex real-world problems, such as programming and scientific discovery. Despite their promising, MASs are not without their flaws. However, failure attribution in MASs - pinpointing the specific agent actions responsible for failures - remains underexplored and labor-intensive, posing significant challenges for debugging and system improvement. To bridge this gap, we propose FAMAS, the first spectrum-based failure attribution approach for MASs, which operates through systematic trajectory replay and abstraction, followed by spectrum analysis.The core idea of FAMAS is to estimate, from variations across repeated MAS executions, the likelihood that each agent action is responsible for the failure. In particular, we propose a novel suspiciousness formula tailored to MASs, which integrates two key factor groups, namely the agent behavior group and the action behavior group, to account for the agent activation patterns and the action activation patterns within the execution trajectories of MASs. Through expensive evaluations against 12 baselines on the Who and When benchmark, FAMAS demonstrates superior performance by outperforming all the methods in comparison.

Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive. We introduce Pythagoras-Prover, a compute-efficient open-source family of Lean theorem provers built for practical compute budgets. The family spans two generation paradigms: autoregressive models at 4B and 32B parameters, and a first proof-of-concept diffusion-based prover (4B) that iteratively refines Lean proofs at inference time. For training efficiency, we build a Lean-verified corpus stratified into easy, medium, and hard problems for curriculum SFT, so models acquire proof skills progressively from shorter, simpler proofs to longer, harder ones. During SFT, a dynamic proof-reasoning filtering scheme preserves informative proof traces while keeping each instance within an 8k-token context budget. We also introduce Augmented Lean Formalisation (ALF), which expands scarce verified corpora into variants of formal statements, populated via self-distillation for extra training signal without formally verifying every mutated instance. By perturbing known problems while preserving their formal character, ALF reduces reliance on any statement's surface form. Empirically, Pythagoras-Prover-4B surpasses DeepSeek-Prover-V2-671B at pass@32 on MiniF2F-Test (86.1% vs 82.4%) with ~167x fewer parameters, while Pythagoras-Prover-32B sets the open-source state of the art at 93.0% on MiniF2F-Test and solves 93 of 672 PutnamBench problems. We release MiniF2F-ALF, an ALF-mutated contamination-sensitive benchmark on which every evaluated model loses accuracy; here our 32B remains strongest and our 4B matches the prior state of the art, Goedel-Prover-V2-32B.

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

The LLM-as-a-Judge paradigm shows promise for evaluating generative content but lacks reliability in reasoning-intensive scenarios, such as programming. Inspired by recent advances in reasoning models and shifts in scaling laws, we pioneer bringing test-time computation into LLM-as-a-Judge, proposing MCTS-Judge, a resource-efficient, System-2 thinking framework for code correctness evaluation. MCTS-Judge leverages Monte Carlo Tree Search (MCTS) to decompose problems into simpler, multi-perspective evaluations. Through a node-selection strategy that combines self-assessment based on historical actions in the current trajectory and the Upper Confidence Bound for Trees based on prior rollouts, MCTS-Judge balances global optimization and refinement of the current trajectory. We further designed a high-precision, unit-test-level reward mechanism to encourage the Large Language Model (LLM) to perform line-by-line analysis. Extensive experiments on three benchmarks and five LLMs demonstrate the effectiveness of MCTS-Judge, which improves the base model's accuracy from 41% to 80%, surpassing the o1-series models with 3x fewer tokens. Further evaluations validate the superiority of its reasoning trajectory in logic, analytics, thoroughness, and overall quality, while revealing the test-time scaling law of the LLM-as-a-Judge paradigm.

Machine learning-based intrusion detection systems (IDS) are critical for securing Industrial Internet of Things (IIoT) environments. Most adversarial research against them perturbs the feature vector or the traffic that produces it, and depends on gradient access, repeated model queries, or a learned model of benign traffic. A smaller line of work reshapes packet timing without querying the detector, but makes malicious traffic mimic a learned model of benign timing. Across these approaches, one assumption of industrial monitoring pipelines has received little attention: temporal synchronization. An IDS reconstructs operational state by aggregating telemetry into sliding or tumbling windows, so its view depends not only on what is observed but on when each observation falls relative to a window boundary. We introduce the Phantom State Attack (PSA), which exploits that dependence under a passive, zero-query threat model. Rather than modifying packets, perturbing features, querying the classifier, or fitting any model of benign traffic, PSA injects bounded timing drift calibrated to the attack flow's own inter-arrival variability, moving observations across the nearest window boundary by the minimal shift needed. The IDS then reconstructs a phantom state that diverges from the true process state. We evaluate PSA on ToN-IoT and CIC IIoT 2025 (DataSense), against Random Forest, MLP and XGBoost, measuring detection degradation, synchronization distortion, stealth, and attacker cost. PSA degrades detection on flows carrying enough packets for window-boundary redistribution, and leaves others almost unchanged, so its effect is conditional. A query-based baseline reaches higher raw success but needs many queries per window, while PSA needs none. The results identify temporal aggregation as an attack surface reachable under weaker assumptions than prior evasion techniques.

We present swarm-attack, an open-source adversarial testing framework in which multiple lightweight LLM agents coordinate through shared memory, parallel exploration, and evolutionary optimization. Together, our results demonstrate that both safety bypass of frontier models and software vulnerability discovery, i.e., the capability class that motivated restricted release of Anthropic's Mythos Preview, are achievable at effectively zero cost using commodity hardware and openly available models. We report two experiments. In the first, five instances of a 1.2 billion parameter model conducted 225 jailbreak attacks each against GPT-4o and Claude Sonnet~4. Against GPT-4o, the swarm achieved an Effective Harm Rate of 45.8%, producing 49 critical-severity breaches; against Claude Sonnet-4, the Effective Harm Rate was 0% despite a 40% technical success rate. In the second experiment, the same models performed combined source code analysis and binary fuzzing against a vulnerable C application with 9 planted CWEs. With a hand-crafted exploit seed corpus, regex pattern detection, and AddressSanitizer-based crash classification, the pipeline recovers 9 of 9 vulnerabilities (100% recall) in approximately four minutes on a consumer MacBook. With those scaffold components disabled, the same model recovers 0 of 9 by crash verification and 2 of 9 by citation. The capability class that motivated restricted release of Anthropic's Mythos Preview is therefore reproducible at effectively zero cost; the important enabler is the system scaffold itself, which compensates for the limited reasoning capacity of small individual models.

Large language models (LLMs) have made misinformation inexpensive to produce but not to verify, creating a growing asymmetry in the information ecosystem. Under tight time, labor, and budget constraints, media organizations, platforms, and fact-checkers rely on screening to prioritize which content to verify. We introduce VEX-Bench, a unified benchmark for evaluating the verification complexity of LLM-generated misinformation, as perceived during screening, across models and generation methods. Verification complexity is assessed along multiple dimensions derived from journalistic and fact-checking practices, capturing checkability, harm potential, source credibility signals, imposter legitimacy, and expected verification effort. We define the VEX score as an integrated measure combining elicitation yield and verification complexity to quantify how generated content consumes limited verification capacity. We construct a benchmark spanning two misinformation categories, 6 high-stakes domains, and 60 real-world topics, and evaluate 7 frontier LLMs and 7 generation methods, yielding 5{,}880 articles. We employ an LLM-as-judge for scalable evaluation and validate it using content-analysis methodology, including ordinal Krippendorff α for inter-annotator reliability, complemented by fact-checking agents for verification. Our findings show that no single method dominates all dimensions, underscoring the need for multi-dimensional evaluation. LLMs can generate high-VEX misinformation at 3times to 169times lower cost than agent-based verification. Such content is often prioritized during screening, consuming scarce verification resources and introducing a systematic risk of misallocation in resource-constrained verification systems. The code is publicly available in our https://github.com/HanxunH/VEX-Bench{GitHub repository}.

Agentic search requires language model agents to explore many sources and answer complex information-seeking questions. Scaling test-time compute is a promising way to improve these agents, but current approaches can fail, because correct answers are often sparse and score-based selection depends on model calibration. We propose FineVerify, a fine-grained self-verification framework that decomposes each question into checkable sub-questions, verifies sampled candidates against each sub-question, and selects the candidate with the highest aggregated score. This per-check structure turns selection into simpler local judgments and produces scores under the same explicit criteria. Across four agentic search benchmarks and two models, FineVerify consistently outperforms standard scaling baselines. With only four sampled trajectories, it improves GPT-5-mini by 8.2 accuracy points and Gemini-3-flash by 5.6% on average. With 12 samples, FineVerify enables GPT-5-mini to surpass frontier GPT-5 on BrowseComp-Plus. Beyond accuracy, FineVerify produces interpretable verification traces that help audit benchmark errors, suggesting broader applications for inspecting agentic search systems. Code and data are available at https://github.com/XuZhao0/fineverify

The central challenge of AI for Science is not reasoning alone, but the ability to create computational methods in an open-ended scientific world. Existing LLM-based agents rely on static, pre-defined tool libraries, a paradigm that fundamentally fails in scientific domains where tools are sparse, heterogeneous, and intrinsically incomplete. In this paper, we propose Test-Time Tool Evolution (TTE), a new paradigm that enables agents to synthesize, verify, and evolve executable tools during inference. By transforming tools from fixed resources into problem-driven artifacts, TTE overcomes the rigidity and long-tail limitations of static tool libraries. To facilitate rigorous evaluation, we introduce SciEvo, a benchmark comprising 1,590 scientific reasoning tasks supported by 925 automatically evolved tools. Extensive experiments show that TTE achieves state-of-the-art performance in both accuracy and tool efficiency, while enabling effective cross-domain adaptation of computational tools. The code and benchmark have been released at https://github.com/lujiaxuan0520/Test-Time-Tool-Evol.

Verifiers have been demonstrated to enhance LLM reasoning via test-time scaling (TTS). Yet, they face significant challenges in complex domains. Error propagation from incorrect intermediate reasoning can lead to false positives for seemingly plausible solutions, while lacking external grounding makes verifiers unreliable on computation or knowledge-intensive tasks. To address these challenges, we propose Agentic Verifier, a framework that transforms reward modeling into a multi-turn, tool-augmented deliberative process. We introduce complementary forward and backward agents: one traces solutions from premises to conclusions, while the other re-checks conclusions against their underlying premises. This bidirectional process enables a comprehensive, reliable, and interpretable assessment of solutions. To facilitate practical deployment, we propose AgentV-RL. Through proactive exploration and reinforcement learning, the verifier autonomously interleaves tool-use with internal reasoning. Extensive experiments show that Agentic Verifier yields consistent performance gains under both parallel and sequential TTS. Notably, our 4B variant surpasses state-of-the-art ORMs by 25.2%, positioning it as a promising paradigm for agentic reward modeling.

Test-time compute scaling is a primary axis for improving LLM reasoning. Existing methods primarily scale depth by extending a single reasoning trace. Scaling breadth by sampling multiple candidates in parallel is straightforward, but introduces a selection bottleneck: choosing the best candidate without a ground-truth verifier, since pointwise LLM judging is noisy and biased. To address this, we introduce OpenDeepThink, a population-based test-time compute framework that selects via pairwise Bradley-Terry comparison. Each generation, the LLM judges random pairs of candidates and aggregates votes via Bradley-Terry into a global ranking; top-ranked candidates are preserved and the top three quarters are mutated using the natural-language critiques produced during comparison; the bottom quarter is discarded. OpenDeepThink raises Gemini 3.1 Pro's effective Codeforces Elo by +405 points in eight sequential LLM-call rounds (~27 minutes wall-clock). The pipeline transfers across weaker and stronger models without retuning, and on the multi-domain HLE benchmark, gains appear concentrated in objectively verifiable domains and reverse in subjective ones. We release CF-73, a curated set of 73 expert-rated Codeforces problems with International Grandmaster annotation and 99% local-evaluation agreement against the official verdict.

Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems and models-even when the guidance is correct and problem-relevant. We show that this instability arises from a previously underexplored gap between strategy usage-whether a reasoning strategy appears in successful solutions-and strategy executability-whether the strategy remains effective when instantiated as guidance for a target model. Through a controlled analysis of paired human-written and model-generated solutions, we identify a systematic dissociation between usage and executability: human- and model-derived strategies differ in structured, domain-dependent ways, leading to complementary strengths and consistent source-dependent reversals under guidance. Building on this diagnosis, we propose Selective Strategy Retrieval (SSR), a test-time framework that explicitly models executability by selectively retrieving and combining strategies using empirical, multi-route, source-aware signals. Across multiple mathematical reasoning benchmarks, SSR yields reliable and consistent improvements over direct solving, in-context learning, and single-source guidance, improving accuracy by up to +13 points on AIME25 and +5 points on Apex for compact reasoning models. Code and benchmark are publicly available at: https://github.com/lwd17/strategy-execute-pipeline.

Test-time scaling seeks to improve the reasoning performance of large language models (LLMs) by adding computational resources. A prevalent approach within the field is sampling-based test-time scaling methods, which enhance reasoning by generating multiple reasoning paths for a given input during inference. However, despite its practical success, the theoretical foundations remain underexplored. In this paper, we provide the first theoretical framework for analyzing sampling-based test-time scaling methods, grounded in the perspective of confidence estimation. Based on the framework, we analyze two dominant paradigms: self-consistency and perplexity, and reveal key limitations: self-consistency suffers from high estimation error while perplexity exhibits substantial modeling error and possible degradation of the estimation error convergence. To address these limitations, we introduce RPC, a hybrid method that leverages our theoretical insights through two key components: Perplexity Consistency and Reasoning Pruning. Perplexity Consistency combines the strengths of self-consistency and perplexity, boosting the convergence rate of estimation error from linear to exponential while preserving model error. Reasoning Pruning prevents degradation by eliminating low-probability reasoning paths. Both theoretical analysis and empirical results across seven benchmark datasets demonstrate that RPC has a strong potential for reducing reasoning error. Notably, RPC achieves reasoning performance comparable to self-consistency while not only enhancing confidence reliability but also reducing sampling costs by 50%. The code and resources are available at https://wnjxyk.github.io/RPC.

Large reasoning models (LRMs) have exhibited strong performance on complex reasoning tasks, with further gains achievable through increased computational budgets at inference. However, current test-time scaling methods predominantly rely on redundant sampling, ignoring the historical experience utilization, thereby limiting computational efficiency. To overcome this limitation, we propose Sticker-TTS, a novel test-time scaling framework that coordinates three collaborative LRMs to iteratively explore and refine solutions guided by historical attempts. At the core of our framework are distilled key conditions-termed stickers-which drive the extraction, refinement, and reuse of critical information across multiple rounds of reasoning. To further enhance the efficiency and performance of our framework, we introduce a two-stage optimization strategy that combines imitation learning with self-improvement, enabling progressive refinement. Extensive evaluations on three challenging mathematical reasoning benchmarks, including AIME-24, AIME-25, and OlymMATH, demonstrate that Sticker-TTS consistently surpasses strong baselines, including self-consistency and advanced reinforcement learning approaches, under comparable inference budgets. These results highlight the effectiveness of sticker-guided historical experience utilization. Our code and data are available at https://github.com/RUCAIBox/Sticker-TTS.

Scaling test-time compute brings substantial performance gains for large language models (LLMs). By sampling multiple answers and heuristically aggregate their answers (e.g., either through majority voting or using verifiers to rank the answers), one can achieve consistent performance gains in math domains. In this paper, we propose a new way to leverage such multiple sample set. We train a compact LLM, called Sample Set Aggregator (SSA), that takes a concatenated sequence of multiple samples and output the final answer, optimizing it for the answer accuracy with reinforcement learning. Experiments on multiple reasoning datasets show that SSA outperforms other test-time scaling methods such as reward model-based re-ranking. Our approach also shows a promising generalization ability, across sample set sizes, base model families and scales, and tasks. By separating LLMs to generate answers and LLMs to analyze and aggregate sampled answers, our approach can work with the outputs from premier black box models easily and efficiently.

Vericoding refers to the generation of formally verified code from rigorous specifications. Recent AI models show promise in vericoding, but a unified methodology for cross-paradigm evaluation is lacking. Existing benchmarks test only individual languages/tools (e.g., Dafny, Verus, and Lean) and each covers very different tasks, so the performance numbers are not directly comparable. We address this gap with AlgoVeri, a benchmark that evaluates vericoding of 77 classical algorithms in Dafny, Verus, and Lean. By enforcing identical functional contracts, AlgoVeri reveals critical capability gaps in verification systems. While frontier models achieve tractable success in Dafny (40.3% for Gemini-3 Flash), where high-level abstractions and SMT automation simplify the workflow, performance collapses under the systems-level memory constraints of Verus (24.7%) and the explicit proof construction required by Lean (7.8%). Beyond aggregate metrics, we uncover a sharp divergence in test-time compute dynamics: Gemini-3 effectively utilizes iterative repair to boost performance (e.g., tripling pass rates in Dafny), whereas GPT-OSS saturates early. Finally, our error analysis shows that language design affects the refinement trajectory: while Dafny allows models to focus on logical correctness, Verus and Lean trap models in persistent syntactic and semantic barriers. All data and evaluation code can be found at https://github.com/haoyuzhao123/algoveri.

Alignment faking (AF) occurs when an LLM strategically complies with training objectives to avoid value modification, reverting to prior preferences once monitoring is lifted. Current detection methods focus on conversational settings and rely primarily on Chain-of-Thought (CoT) analysis, which provides a reliable signal when strategic reasoning surfaces, but cannot distinguish deception from capability failures if traces are absent or unfaithful. We formalize AF as a composite behavioural event and detect it through observable tool selection, where the LLM selects the safe tool when unmonitored, but switches to the unsafe tool under monitoring that rewards helpfulness over safety, while its reasoning still acknowledges the safe choice. We release a dataset of 108 enterprise IT scenarios spanning Security, Privacy, and Integrity domains under Corruption and Sabotage pressures. Evaluating six frontier LLMs across five independent runs, we find mean AF detection rates between 3.5% and 23.7%, with vulnerability profiles varying by domain and pressure type. These results suggest that susceptibility reflects training methodology rather than capability alone.

Recent advancements in Large Language Models (LLMs) have created new opportunities to enhance performance on complex reasoning tasks by leveraging test-time computation. However, conventional approaches such as repeated sampling with majority voting or reward model scoring, often face diminishing returns as test-time compute scales, in addition to requiring costly task-specific reward model training. In this paper, we present Self-Enhanced Test-Time Scaling (SETS), a novel method that leverages the self-verification and self-correction capabilities of recent advanced LLMs to overcome these limitations. SETS integrates sampling, self-verification, and self-correction into a unified framework, enabling efficient and scalable test-time computation for improved capabilities at complex tasks. Through extensive experiments on challenging planning and reasoning benchmarks, compared to the alternatives, we demonstrate that SETS achieves significant performance improvements and more favorable test-time scaling laws.

We present Veriphi, a GPU-accelerated neural network verification system that combines fast adversarial attacks with formal bound certification using alpha,beta-CROWN methods. Through systematic experiments on MNIST and CIFAR-10 using three training methodologies (standard, adversarial, certified), we demonstrate that training method effectiveness is fundamentally dataset-dependent. Interval Bound Propagation (IBP) achieves 78% certified accuracy on simple MNIST (784 dimensions) but provides negligible certification performance on the more complex CIFAR-10 dataset, where PGD adversarial training dominates with 94% certification at small perturbations. We achieve 5x verification speedup through attack-guided falsification and scale our approach to production-size models (105.8M parameters) for real-world aerospace logistics optimization. Our results challenge the assumption that certified training universally outperforms adversarial training, showing context matters critically for verification strategy selection.

The new paradigm of test-time scaling has yielded remarkable breakthroughs in Large Language Models (LLMs) (e.g. reasoning models) and in generative vision models, allowing models to allocate additional computation during inference to effectively tackle increasingly complex problems. Despite the improvements of this approach, an important limitation emerges: the substantial increase in computation time makes the process slow and impractical for many applications. Given the success of this paradigm and its growing usage, we seek to preserve its benefits while eschewing the inference overhead. In this work we propose one solution to the critical problem of integrating test-time scaling knowledge into a model during post-training. Specifically, we replace reward guided test-time noise optimization in diffusion models with a Noise Hypernetwork that modulates initial input noise. We propose a theoretically grounded framework for learning this reward-tilted distribution for distilled generators, through a tractable noise-space objective that maintains fidelity to the base model while optimizing for desired characteristics. We show that our approach recovers a substantial portion of the quality gains from explicit test-time optimization at a fraction of the computational cost. Code is available at https://github.com/ExplainableML/HyperNoise

Automated test generation holds great promise for alleviating the burdens of manual test creation. However, existing search-based techniques compromise on test readability, while LLM-based approaches are prohibitively expensive in practice. We present TestForge, an agentic unit testing framework designed to cost-effectively generate high-quality test suites for real-world code. Our key insight is to reframe LLM-based test generation as an iterative process. TestForge thus begins with tests generated via zero-shot prompting, and then continuously refines those tests based on feedback from test executions and coverage reports. We evaluate TestForge on TestGenEval, a real world unit test generation benchmark sourced from 11 large scale open source repositories; we show that TestForge achieves a pass@1 rate of 84.3%, 44.4% line coverage and 33.8% mutation score on average, outperforming prior classical approaches and a one-iteration LLM-based baseline. TestForge produces more natural and understandable tests compared to state-of-the-art search-based techniques, and offers substantial cost savings over LLM-based techniques (at $0.63 per file). Finally, we release a version of TestGenEval integrated with the OpenHands platform, a popular open-source framework featuring a diverse set of software engineering agents and agentic benchmarks, for future extension and development.

Recent advances in Deep Research Agents (DRAs) are transforming automated knowledge discovery and problem-solving. While the majority of existing efforts focus on enhancing policy capabilities via post-training, we propose an alternative paradigm: self-evolving the agent's ability by iteratively verifying the policy model's outputs, guided by meticulously crafted rubrics. This approach gives rise to the inference-time scaling of verification, wherein an agent self-improves by evaluating its generated answers to produce iterative feedback and refinements. We derive the rubrics based on an automatically constructed DRA Failure Taxonomy, which systematically classifies agent failures into five major categories and thirteen sub-categories. We present DeepVerifier, a rubrics-based outcome reward verifier that leverages the asymmetry of verification and outperforms vanilla agent-as-judge and LLM judge baselines by 12%-48% in meta-evaluation F1 score. To enable practical self-evolution, DeepVerifier integrates as a plug-and-play module during test-time inference. The verifier produces detailed rubric-based feedback, which is fed back to the agent for iterative bootstrapping, refining responses without additional training. This test-time scaling delivers 8%-11% accuracy gains on challenging subsets of GAIA and XBench-DeepResearch when powered by capable closed-source LLMs. Finally, to support open-source advancement, we release DeepVerifier-4K, a curated supervised fine-tuning dataset of 4,646 high-quality agent steps focused on DRA verification. These examples emphasize reflection and self-critique, enabling open models to develop robust verification capabilities.

We propose a framework that amortizes the cost of inference-time reasoning by converting transient critiques into retrievable guidelines, through a file-based memory system and agent-controlled tool calls. We evaluate this method on the Rubric Feedback Bench, a novel dataset for rubric-based learning. Experiments demonstrate that our augmented LLMs rapidly match the performance of test-time refinement pipelines while drastically reducing inference cost.

Most recent test-time adaptation methods focus on only classification tasks, use specialized network architectures, destroy model calibration or rely on lightweight information from the source domain. To tackle these issues, this paper proposes a novel Test-time Self-Learning method with automatic Adversarial augmentation dubbed TeSLA for adapting a pre-trained source model to the unlabeled streaming test data. In contrast to conventional self-learning methods based on cross-entropy, we introduce a new test-time loss function through an implicitly tight connection with the mutual information and online knowledge distillation. Furthermore, we propose a learnable efficient adversarial augmentation module that further enhances online knowledge distillation by simulating high entropy augmented images. Our method achieves state-of-the-art classification and segmentation results on several benchmarks and types of domain shifts, particularly on challenging measurement shifts of medical images. TeSLA also benefits from several desirable properties compared to competing methods in terms of calibration, uncertainty metrics, insensitivity to model architectures, and source training strategies, all supported by extensive ablations. Our code and models are available on GitHub.

Test-time scaling for large language models (LLMs) can involve generating multiple candidate solutions for selection or revising an earlier attempt. To guide selection and revision, we need a verifier that can estimate candidate correctness and provide evidence of failure. In competitive programming, however, official judging systems provide authoritative verdicts under finite submission budgets, without revealing failure explanations or failing inputs. To provide informative feedback without consuming official submissions, we formulate a task in which a model judges and diagnoses a candidate program using only the problem statement and source code, with generated counterexamples serving as checkable evidence. To evaluate this task, we build USACO-JUDGE from the USACO 2026 contests, using accepted and unaccepted programs written by human experts and multiple LLMs. We then train ARBITER, a 35B mixture-of-experts (MoE) agentic verifier, with reinforcement learning in a generic execution sandbox. Training raises counterexample success on incorrect programs from 40.61% to 62.67% and mean binary verdict accuracy on USACO-JUDGE from 71.41% to 87.41%, approaching frontier verification performance. Beyond verification, ARBITER outperforms baselines in both code selection and refinement. In an IOI 2026 case study, ARBITER-guided refinement raises GPT-OSS-120B's expected score above the gold-medal threshold under the official submission limit.

Large language models demonstrate remarkable reasoning capabilities but often produce unreliable or incorrect responses. Existing verification methods are typically model-specific or domain-restricted, requiring significant computational resources and lacking scalability across diverse reasoning tasks. To address these limitations, we propose VerifiAgent, a unified verification agent that integrates two levels of verification: meta-verification, which assesses completeness and consistency in model responses, and tool-based adaptive verification, where VerifiAgent autonomously selects appropriate verification tools based on the reasoning type, including mathematical, logical, or commonsense reasoning. This adaptive approach ensures both efficiency and robustness across different verification scenarios. Experimental results show that VerifiAgent outperforms baseline verification methods (e.g., deductive verifier, backward verifier) among all reasoning tasks. Additionally, it can further enhance reasoning accuracy by leveraging feedback from verification results. VerifiAgent can also be effectively applied to inference scaling, achieving better results with fewer generated samples and costs compared to existing process reward models in the mathematical reasoning domain. Code is available at https://github.com/Jiuzhouh/VerifiAgent

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.

Agents need reliable ways to validate their outputs, both when completing tasks and when filtering synthetic training data. We study verifier generation: from the instruction and environment available for solving a task, an agent writes an executable verifier that must accept every valid solution and reject invalid ones. We introduce VerifierBench, a benchmark of 222 tasks from six agent benchmarks spanning tool-call, state-based, and code verification, with 4,993 hidden test cases that include alternative valid solutions and attacks; Verifier4Verifier (V4V), a six-check audit, screens its source verifiers and test suites. Across 19 models in a common agent harness, normalized balanced accuracy ranges from 10.6 to 62.1, with generated verifiers consistently rejecting invalid solutions more reliably than they accept valid ones. This apparent strength can mask overly restrictive verification: most false rejections in the analyzed records come from verifiers that accept no tested solution to a task. Case studies reveal unsupported assumptions about solution formats, tool use, and code changes that exclude valid solutions. These errors survive self-testing because agents test solutions that share the verifier's mistaken assumptions, or submit verifiers without confirming that any correct solution passes. These findings suggest testing both whether a verifier accepts a correct solution and whether it accepts other solutions permitted by the task. The project page and dataset are publicly available.

Large reasoning models (LRMs) spend substantial test-time compute on long chain-of-thought (CoT) traces, but what *characterizes* an effective CoT remains unclear. While prior work reports gains from lengthening CoTs and increasing review (revisiting earlier steps) via appended *wait* tokens, recent studies suggest that shorter thinking can outperform longer traces. We therefore conduct a systematic evaluation across ten LRMs on math and scientific reasoning. Contrary to the "longer-is-better" narrative, we find that both naive CoT lengthening and increased review are associated with *lower* accuracy. As CoT unfolds step by step, token-level metrics can conflate verbosity with process quality. We introduce a graph view of CoT to extract structure and identify a single statistic-the *Failed-Step Fraction (FSF)*, the fraction of steps in abandoned branches-that consistently outpredicts length and review ratio for correctness across models. To probe causality, we design two interventions. First, we rank candidate CoTs by each metric at test time, where FSF yields the largest pass@1 gains; second, we edit CoTs to remove failed branches, which significantly improves accuracy, indicating that failed branches bias subsequent reasoning. Taken together, these results characterize effective CoTs as those that *fail less* and support *structure-aware* test-time scaling over indiscriminately generating long CoT.

Large Language Models (LLMs) have significantly advanced automated test generation, yet existing methods often rely on ground-truth code for verification, risking bug propagation and limiting applicability in test-driven development. We present ConVerTest, a novel two-stage pipeline for synthesizing reliable tests without requiring prior code implementations. ConVerTest integrates three core strategies: (i) Self-Consistency(SC) to generate convergent test cases via majority voting; (ii) Chain-of-Verification (CoVe) for iterative, reasoning-guided code refinement; and (iii) a Dual Execution Agreement to crossvalidate code and tests through consensus. Experiments on BIGCODEBENCH and LESS BASIC PYTHON PROBLEMS (LBPP) benchmarks demonstrate that ConVerTest improves test validity, line coverage, and mutation scores by up to 39%, 28%, and 18% respectively over baselines. Our findings highlight ConVerTest as a robust solution for mitigating hallucinations and enhancing the reliability of autonomous software testing agents.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Test-time training (TTT) adapts language models through gradient-based updates at inference. But is adaptation the right strategy? We study compute-optimal test-time strategies for verifiable execution-grounded (VEG) tasks, domains like GPU kernel optimization where a deterministic evaluator provides dense, continuous reward signals. Using KernelBench as our testbed and a 120B-parameter model (GPT-OSS-120B with LoRA adaptation), we find that search outperforms minimal adaptation (1-5 gradient steps): Best-of-N sampling achieves 90% task success (18/20 tasks) at K=64 across the full KernelBench L1 eval set while TTT's best checkpoint reaches only 30.6% (3-seed mean), with TTT's "equivalent K" falling below 1, worse than single-sample inference. The failure mode is over-sharpening: gradient updates collapse diversity toward mediocre solutions rather than discovering optimal ones. Our main contribution is surprisal-guided selection: selecting the highest-surprisal (lowest-confidence) correct sample yields 80% success vs. 50% for most-confident selection, a 30% improvement. Extending to surprisal-guided-top3 matches oracle performance at 100%. This zero-cost strategy, validated through length-controlled analysis, recovers oracle performance. For dense-reward VEG tasks, compute should be allocated to sample diversity and intelligent selection rather than gradient adaptation. The surprisal-guided selection principle may generalize to other execution-grounded domains where optimal solutions occupy the distribution tail.

In data poisoning attacks, an adversary tries to change a model's prediction by adding, modifying, or removing samples in the training data. Recently, ensemble-based approaches for obtaining provable defenses against data poisoning have been proposed where predictions are done by taking a majority vote across multiple base models. In this work, we show that merely considering the majority vote in ensemble defenses is wasteful as it does not effectively utilize available information in the logits layers of the base models. Instead, we propose Run-Off Election (ROE), a novel aggregation method based on a two-round election across the base models: In the first round, models vote for their preferred class and then a second, Run-Off election is held between the top two classes in the first round. Based on this approach, we propose DPA+ROE and FA+ROE defense methods based on Deep Partition Aggregation (DPA) and Finite Aggregation (FA) approaches from prior work. We evaluate our methods on MNIST, CIFAR-10, and GTSRB and obtain improvements in certified accuracy by up to 3%-4%. Also, by applying ROE on a boosted version of DPA, we gain improvements around 12%-27% comparing to the current state-of-the-art, establishing a new state-of-the-art in (pointwise) certified robustness against data poisoning. In many cases, our approach outperforms the state-of-the-art, even when using 32 times less computational power.

Test-time compute is emerging as a new paradigm for enhancing language models' complex multi-step reasoning capabilities, as demonstrated by the success of OpenAI's o1 and o3, as well as DeepSeek's R1. Compared to explicit reasoning in test-time compute, implicit reasoning is more inference-efficient, requiring fewer generated tokens. However, why does the advanced reasoning capability fail to emerge in the implicit reasoning style? In this work, we train GPT-2 from scratch on a curated multi-step mathematical reasoning dataset and conduct analytical experiments to investigate how language models perform implicit reasoning in multi-step tasks. Our findings reveal: 1) Language models can perform step-by-step reasoning and achieve high accuracy in both in-domain and out-of-domain tests via implicit reasoning. However, this capability only emerges when trained on fixed-pattern data. 2) Conversely, implicit reasoning abilities emerging from training on unfixed-pattern data tend to overfit a specific pattern and fail to generalize further. Notably, this limitation is also observed in state-of-the-art large language models. These findings suggest that language models acquire implicit reasoning through shortcut learning, enabling strong performance on tasks with similar patterns while lacking generalization.

Large Reasoning Models (LRMs) demonstrate exceptional capability in tackling complex mathematical, logical, and coding tasks by leveraging extended Chain-of-Thought (CoT) reasoning. Test-time scaling methods, such as prolonging CoT with explicit token-level exploration, can push LRMs' accuracy boundaries, but they incur significant decoding overhead. A key inefficiency source is LRMs often generate redundant thinking CoTs, which demonstrate clear structured overthinking and underthinking patterns. Inspired by human cognitive reasoning processes and numerical optimization theories, we propose TrimR, a verifier-based, training-free, efficient framework for dynamic CoT compression to trim reasoning and enhance test-time scaling, explicitly tailored for production-level deployment. Our method employs a lightweight, pretrained, instruction-tuned verifier to detect and truncate redundant intermediate thoughts of LRMs without any LRM or verifier fine-tuning. We present both the core algorithm and asynchronous online system engineered for high-throughput industrial applications. Empirical evaluations on Ascend NPUs and vLLM show that our framework delivers substantial gains in inference efficiency under large-batch workloads. In particular, on the four MATH500, AIME24, AIME25, and GPQA benchmarks, the reasoning runtime of Pangu Pro MoE, Pangu-R-38B, QwQ-32B, and DeepSeek-R1-Distill-Qwen-32B is improved by up to 70% with negligible impact on accuracy.

Byzantine-robust aggregation rules such as multi-Krum assume a central coordinator, and decentralising them is obstructed by the rules themselves: they are globally coupled, non-associative, and discontinuous, so an ulpscale perturbation can flip the selected subset, moving the output by a non-vanishing amount. None of this prevents coordinator-free replication, because a robust rule needs no agreed order of contributions, only an agreed set and an agreed exclusion predicate, both of which converge without consensus. ACFA (Accountable Consensus-Free Aggregation) replicates a content-addressed OR-Set of signed contributions and a grow-only set of self-authenticating equivocation proofs, offline-verifiable by anyone. Aggregation is a deterministic pure function of the converged product state: fixed-point integer arithmetic over a hash-canonical order, ties broken by content hash. We prove that any pure function of a converged product of CRDTs (non-monotone, non-associative, or stochastic) inherits Strong Eventual Consistency, together with its converse; the contribution is the composition of a data lattice with an evidence lattice applied to a robust selector, not the elementary lifting step. A prototype (10 nodes, 3 Byzantine) passes 16/16 falsification checks: byte-identical roots under adversarial gossip, deterministic re-convergence after late equivocation proofs, partition recovery, and three byte-identity-breaking ablations. The guarantee is consistency, not accuracy; robustness is imported, conditional on 2f + 3 admitted contributions (at most f Byzantine) and a stated quantisation-margin condition.

Large language models (LLMs) struggle with complex, long-horizon reasoning due to instability caused by their frozen policy assumption. Current test-time scaling methods treat execution feedback merely as an external signal for filtering or rewriting trajectories, without internalizing it to improve the underlying reasoning strategy. Inspired by Popper's epistemology of "conjectures and refutations," we argue that intelligence requires real-time evolution of the model's policy through learning from failed attempts. We introduce Policy of Thoughts (PoT), a framework that recasts reasoning as a within-instance online optimization process. PoT first generates diverse candidate solutions via an efficient exploration mechanism, then uses Group Relative Policy Optimization (GRPO) to update a transient LoRA adapter based on execution feedback. This closed-loop design enables dynamic, instance-specific refinement of the model's reasoning priors. Experiments show that PoT dramatically boosts performance: a 4B model achieves 49.71% accuracy on LiveCodeBench, outperforming GPT-4o and DeepSeek-V3 despite being over 50 smaller.

Large language models (LLMs) can generate plausible code but offer limited guarantees of correctness. Formally verifying that implementations satisfy specifications requires constructing machine-checkable proofs, a task that remains beyond current automation. We propose a hierarchical proof search framework for automated code verification in Lean~4 that decomposes complex verification goals into structurally simpler subgoals before attempting tactic-level proving. Central to our approach is a principled decomposition score that combines constructive justification with structural effectiveness. Crucially, this score serves as both the training reward and the inference-time ranking criterion, ensuring strict alignment between optimization and deployment. We train Goedel-Code-Prover-8B, a single unified policy for both decomposition and completion, via supervised initialization followed by hybrid reinforcement learning, where a continuous decomposition reward drives planning exploration while supervised replay stabilizes proof generation. On three Lean-based code verification benchmarks comprising 427 tasks, our 8B-parameter model achieves a 62.0\% prove success rate, a 2.6times improvement over the strongest baseline, surpassing neural provers up to 84times larger. We further observe consistent inference-time scaling: success rates improve monotonically with search iterations and sampling budget, with our trained model achieving greater efficiency than frontier off-the-shelf models of comparable scale.

Test-time adaptation (TTA) aims to address the distribution shift between the training and test data with only unlabeled data at test time. Existing TTA methods often focus on improving recognition performance specifically for test data associated with classes in the training set. However, during the open-world inference process, there are inevitably test data instances from unknown classes, commonly referred to as outliers. This paper pays attention to the problem that conducts both sample recognition and outlier rejection during inference while outliers exist. To address this problem, we propose a new approach called STAble Memory rePlay (STAMP), which performs optimization over a stable memory bank instead of the risky mini-batch. In particular, the memory bank is dynamically updated by selecting low-entropy and label-consistent samples in a class-balanced manner. In addition, we develop a self-weighted entropy minimization strategy that assigns higher weight to low-entropy samples. Extensive results demonstrate that STAMP outperforms existing TTA methods in terms of both recognition and outlier detection performance. The code is released at https://github.com/yuyongcan/STAMP.

Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of general reliability, and business logic blindness. In this work, we propose a novel framework that leverages functional programming and type systems to translate Scala backend code into formal Lean representations. Our pipeline automatically generates theorems that specify the intended behavior of APIs and database operations, and uses LLM-based provers to verify them. When a theorem is proved, the corresponding logic is guaranteed to be correct and no further testing is needed. If the negation of a theorem is proved instead, it confirms a bug. In cases where neither can be proved, human intervention is required. We evaluate our method on realistic backend systems and find that it can formally verify over 50% of the test requirements, which suggests that half of a testing engineer's workload can be automated. Additionally, with an average cost of only $2.19 per API, LLM-based verification is significantly more cost-effective than manual testing and can be scaled easily through parallel execution. Our results indicate a promising direction for scalable, AI-powered software testing, with the potential to greatly improve engineering productivity as models continue to advance.

AI systems deployed in legal workflows hallucinate at rates that aggregate metrics report at ~52%, but this average conceals where errors concentrate and in which direction they run, leaving compliance officers without an actionable signal for trustworthy deployment. We present LegalHalluLens, an auditing framework with three components: typed hallucination profiles across four legally-motivated claim categories (numeric, temporal, obligation/entitlement, factual) over CUAD (Hendrycks et al., 2021); a Risk Direction Index (RDI) that reduces omission-versus-invention bias to a single deployment-comparable scalar; and a typed debate pipeline calibrated to both magnitudes and directions. Across 510 contracts and 249,252 clause-level instances we measure a within-model gap of approximately 38-40 pp between obligation/numeric and temporal claims that aggregate reporting hides, and show that two systems with matched 52% rates can carry opposite RDIs. The debate pipeline reduces fabricated detections by 45% with per-category gains tracking the diagnosis, matching commercial APIs with a substantially smaller backbone (4B active parameters). Typed profiles and RDI surface failure modes that aggregate metrics hide; we further show these diagnostics serve as calibration inputs for multi-agent debate pipelines, where Skeptic challenges and asymmetric gates targeted at measured failure modes outperform generically-tuned debate. The framework supports direction-aware procurement, accountability, and agent design for legal AI deployed in the wild.

Inference-time compute has re-emerged as a practical way to improve LLM reasoning. Most test-time scaling (TTS) algorithms rely on autoregressive decoding, which is ill-suited to discrete diffusion language models (dLLMs) due to their parallel decoding over the entire sequence. As a result, developing effective and efficient TTS methods to unlock dLLMs' full generative potential remains an underexplored challenge. To address this, we propose Prism (Pruning, Remasking, and Integrated Self-verification Method), an efficient TTS framework for dLLMs that (i) performs Hierarchical Trajectory Search (HTS) which dynamically prunes and reallocates compute in an early-to-mid denoising window, (ii) introduces Local branching with partial remasking to explore diverse implementations while preserving high-confidence tokens, and (iii) replaces external verifiers with Self-Verified Feedback (SVF) obtained via self-evaluation prompts on intermediate completions. Across four mathematical reasoning and code generation benchmarks on three dLLMs, including LLaDA 8B Instruct, Dream 7B Instruct, and LLaDA 2.0-mini, our Prism achieves a favorable performance-efficiency trade-off, matching best-of-N performance with substantially fewer function evaluations (NFE). The code is released at https://github.com/viiika/Prism.

In this paper, we propose a novel approach where agents can form swarms to produce high-quality responses effectively. This is accomplished by utilizing agents capable of data inference and ranking, which can be effectively implemented using LLMs as response classifiers. We assess existing approaches for trustless agent inference, define our methodology, estimate practical parameters, and model various types of malicious agent attacks. Our method leverages the collective intelligence of swarms, ensuring robust and efficient decentralized AI inference with better accuracy, security, and reliability. We show that our approach is an order of magnitude faster than other trustless inference strategies reaching less than 125 ms validation latency.

Test-time scaling for code generation commonly relies on Best-of-N selection, in which multiple candidate solutions are sampled from a base model, and the best one is selected by an LLM judge. However, training reliable LLM judges is challenging due to severe distribution shifts, including imbalances between easy and hard problems, mismatches between training tasks and evaluation benchmarks, and trajectory mismatch arising from training data generated by cheaper models whose behavior differs from that of inference-time models. We propose DAJ, a reasoning-based LLM judge trained with verifiable rewards under a bi-level data-reweighted learning framework. The proposed framework learns data-importance weights (either domain-level or instance-level) to optimize generalization performance on a held-out meta set aligned with target benchmarks. To the best of our knowledge, this is the first application of data reweighting to LLM-as-a-Judge training for test-time scaling. Our approach automatically emphasizes hard problems, in-distribution samples, and trajectory-aligned data, without relying on hand-crafted heuristics. Empirically, DAJ achieves state-of-the-art performance on LiveCodeBench and BigCodeBench, outperforming strong test-time scaling baselines as well as leading proprietary models.

Test-Time Scaling (TTS) methods for enhancing Large Language Model (LLM) reasoning often incur substantial computational costs, primarily due to extensive reliance on external Process Reward Models (PRMs) or sampling methods like Best-of-N (BoN). This paper introduces Guided by Gut (GG), an efficient self-guided TTS framework that achieves PRM-level performance without costly external verifier models. Our method employs a lightweight tree search guided solely by intrinsic LLM signals, token-level confidence and step novelty. One critical innovation is improving the reliability of internal confidence estimates via a targeted reinforcement learning fine-tuning phase. Empirical evaluations on challenging mathematical reasoning benchmarks demonstrate that GG enables smaller models (e.g., 1.5B parameters) to achieve accuracy matching or surpassing significantly larger models (e.g., 32B-70B parameters), while reducing GPU memory usage by up to 10x. Compared to PRM-based methods, GG achieves comparable accuracy with 8x faster inference speeds and 4-5x lower memory usage. Additionally, GG reduces KV cache memory usage by approximately 50% compared to the BoN strategy, facilitating more efficient and practical deployment of TTS techniques.

Multi-path speculative decoding accelerates lossless sampling from a target model by using a cheaper draft model to generate a draft tree of tokens, and then applies a verification algorithm that accepts a subset of these. While prior work has proposed various verification algorithms for i.i.d rollouts, their relative performance under matched settings remains unclear. In this work, we firstly present a systematic evaluation of verification strategies across model families, tasks, and sampling regimes, and find that Traversal Verification dominates consistently, with OT-based methods lagging far behind. Our analysis uncovers that this occurs because OT-based methods achieve high multi-token acceptance near the root of the draft tree, while multi-token gains are most impactful deeper in the draft tree, where draft and target distributions diverge. Based on this insight, we propose delayed tree expansion, which drafts a partial single path, delaying the i.i.d. branching point. We show that delayed tree expansion preserves the target distribution and improves on root-node i.i.d rollouts. Further, we develop a dynamic neural selector that estimates the expected block efficiency of optimal-transport-based verification methods from draft and target features, enabling context-dependent expansion decisions. Our neural selector allows OT-based methods like SpecInfer to outperform Traversal Verification for the first time, achieving 5% higher average throughput across a wide range of models, datasets, and sampling settings.

Recent test-time training (TTT) frameworks have enabled open-weight large language models (LLMs) to outperform inference-only frameworks powered by frontier models on scientific discovery tasks. However, TTT introduces additional computational cost for online weight updates during the discovery process, making computational efficiency an important consideration when scaling to larger models. This motivates us to explore an efficient test-time adaptation method for scientific discovery. We introduce Test-Time Memory Evolution (TTME), a plug-and-play test-time adaptation method, as an alternative to TTT. TTME continually updates the external memory by distilling the experience to guide subsequent discovery without updating model weights. To have a clean comparison, we evaluate TTME and TTT under the same discovery framework, replacing only the test-time adaptation method. Our evaluation shows that TTME outperforms TTT on all five mathematical tasks, while reducing computational cost by 82.8-84.6% in FLOPs and 47.7-58.4% in runtime. These results establish TTME as an effective and computationally efficient alternative to TTT in the evaluated discovery settings.

Test-time scaling has emerged as a widely adopted inference-time strategy for boosting reasoning performance. However, its effectiveness has been studied almost exclusively in English, leaving its behavior in other languages largely unexplored. We present the first systematic study of test-time scaling in multilingual settings, evaluating DeepSeek-R1-Distill-LLama-8B and DeepSeek-R1-Distill-Qwen-7B across both high- and low-resource Latin-script languages. Our findings reveal that the relative gains from test-time scaling vary significantly across languages. Additionally, models frequently switch to English mid-reasoning, even when operating under strictly monolingual prompts. We further show that low-resource languages not only produce initial reasoning thoughts that differ significantly from English but also have lower internal consistency across generations in their early reasoning. Building on our findings, we introduce MITT (Multilingual Initial Thought Transfer), an unsupervised and lightweight reasoning prefix-tuning approach that transfers high-resource reasoning prefixes to enhance test-time scaling across all languages, addressing inconsistencies in multilingual reasoning performance. MITT significantly boosts DeepSeek-R1-Distill-Qwen-7B's reasoning performance, especially for underrepresented languages.

Which forms of test-time compute improve the predictions of strong pretrained tabular foundation models (TFMs)? We systematically study this along three axes: adaptation, aggregation, and context construction. Our evaluation spans modern TFMs across the TabArena benchmark, supplemented by experiments on wide and large-scale tables from OpenML. For adaptation, we introduce DiagScale, a diagonal query-key similarity update. It trains only 0.003-0.03% of model parameters and achieves gains comparable to full fine-tuning across three independently pretrained backbones. For aggregation, both pool composition and selection strategy matter. TabPFN-3 already averages predictions from different preprocessing variants of the same data, and adding more such predictions yields diminishing returns. With a broader pool of 96 configurations, greedy selection reduces error by 2.4% relative to the default predictor, but uniform averaging increases error. For context construction, attention-guided retrieval improves TabPFN-3's predictions on some large tables and supports source pools beyond the full context memory limit. The context expansion methods we test yield no consistent improvement. Taken together, our results suggest that adaptation and selective aggregation yield consistent benchmark-level gains. The benefits of context construction depend more on the task and data regime. Adaptation and aggregation over the same backbone yield further gains when combined, but require substantially more computation than default inference. These trade-offs motivate choosing strategies according to the available computation budget. Code is available at https://github.com/kanghui-learning/test-time-compute-for-tabular-foundation-models.

Despite the rapid progress in multimodal models and Large Visual-Language Models (LVLM), they remain highly susceptible to adversarial perturbations, raising serious concerns about their reliability in real-world use. While adversarial training has become the leading paradigm for building models that are robust to adversarial attacks, Test-Time Transformations (TTT) have emerged as a promising strategy to boost robustness at inference. In light of this, we propose Energy-Guided Test-Time Transformation (ET3), a lightweight, training-free defense that enhances the robustness by minimizing the energy of the input samples. Our method is grounded in a theory that proves our transformation succeeds in classification under reasonable assumptions. We present extensive experiments demonstrating that ET3 provides a strong defense for classifiers, zero-shot classification with CLIP, and also for boosting the robustness of LVLMs in tasks such as Image Captioning and Visual Question Answering. Code is available at github.com/OmnAI-Lab/Energy-Guided-Test-Time-Defense .

State-of-the-art reasoning models utilize long chain-of-thought (CoT) to solve increasingly complex problems using more test-time computation. In this work, we explore a long CoT setting where the model makes up to K successive attempts at solving a problem, in which each attempt is allowed to build on earlier ones after the model receives a hard verifier feedback. This motivates RL methods that can harness per-attempt rewards by carefully weighting individual attempts. We study optimizing the Verification@K reward (the model succeeds by the K-th attempt) and show that naively weighing the attempts by their pass/fail results in biased gradients. We introduce Calibrated Attempt-Level (CAL) GRPO by devising a weighing strategy to obtain unbiased gradients while maintaining small variance. Our theory reveals how incorporating per-attempt rewards influence the training and the eventual Verification@K performance. Experiments, baselines, and ablations on synthetic and real data corroborate our theory and the benefits of CAL-GRPO over vanilla GRPO as well as naive weighting.

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating proof search spaces. While the existing approaches primarily rely on value functions and Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Search (BFS) remains underexplored. This paper investigates whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM's policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a score of 71.31 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.

Test-time adaptation (TTA) addresses distribution shifts for streaming test data in unsupervised settings. Currently, most TTA methods can only deal with minor shifts and rely heavily on heuristic and empirical studies. To advance TTA under domain shifts, we propose the novel problem setting of active test-time adaptation (ATTA) that integrates active learning within the fully TTA setting. We provide a learning theory analysis, demonstrating that incorporating limited labeled test instances enhances overall performances across test domains with a theoretical guarantee. We also present a sample entropy balancing for implementing ATTA while avoiding catastrophic forgetting (CF). We introduce a simple yet effective ATTA algorithm, known as SimATTA, using real-time sample selection techniques. Extensive experimental results confirm consistency with our theoretical analyses and show that the proposed ATTA method yields substantial performance improvements over TTA methods while maintaining efficiency and shares similar effectiveness to the more demanding active domain adaptation (ADA) methods. Our code is available at https://github.com/divelab/ATTA

By incorporating test-time compute scaling, large reasoning models (LRMs) can solve complex problems through explicit chain-of-thought (CoT) reasoning processes. However, they often suffer from overthinking, resulting in redundant token outputs and degraded accuracy. Current methods to mitigate this issue remain limited: training-based approaches require substantial computational resources, while training-free methods rely on well-crafted prompts or unreliable confidence signals. In this work, we investigate early stopping from the perspective of attention distributions and propose a simple method, ASAG, which infers the model's reasoning state and adaptively adjusts the generation strategy. The proposed framework is training-free and plug-and-play, enabling seamless integration into existing LRMs. Extensive experiments on nine benchmarks demonstrate consistent improvements across mainstream LRMs with varying parameter scales, including the DeepSeek-R1-Distill and Qwen3 series. Specifically, ASAG improves average accuracy by 3.2% while reducing the number of generated tokens by nearly 40% across all reasoning tasks on Qwen3-8B.