Daily Papers

Automated research with LLM agents has shown promising results in various domains. Through iterative refinement and scored verifiers, LLM agents are capable of discovering new ideas. There are different ways to scale automated research: let one agent iterate for longer, run several agents in parallel, or further let the parallel agents communicate and build on one another's candidates. However, we find that all three strategies eventually plateau as the agents accumulate history. Each agent becomes anchored to its own past attempts, making fewer and smaller edits. Beyond this point, additional budget brings little further improvement. In this paper, we show that the key to scaling discovery further is to forget. Periodically discarding the search state, including every agent's session and the candidate history, and restarting from the best candidate found so far, unblocks the search and pushes the same budget further. We implement forgetting in a team of agents with communication and evaluate it on four tasks spanning heuristic programming, kernel optimization and model training. The results show up to 15% improvement compared to parallel agents, and up to 39% compared to a single agent. Our results suggest that, for open-ended discovery, what an agent is allowed to remember matters as much as how much compute it is given.

Tool-using LLM agents fail through trajectories rather than only final responses, as they may execute unsafe tool calls, follow injected instructions, comply with harmful requests, or over-refuse benign tasks despite producing a seemingly safe answer. Existing safety-alignment signals are largely response-level or off-policy, and often incur a safety-utility trade-off: improving agent safety comes at the cost of degraded task performance. Such sparse and single-objective rewards severely limit real-world usability. To bridge this gap, we propose FATE, an on-policy self-evolving framework that transforms verifier-scored failures into repair supervision without expert demonstrations. For each failure, the same policy proposes repair candidates, which are then re-scored by verifiers and filtered across security, utility, over-refusal control, and trajectory validity. This dense trajectory-level information is then used as a supervision signal for agent self-evolution. During this process, we further introduce Pareto-Front Policy Optimization (PFPO), combining supervised warmup with Pareto-aware policy optimization to preserve safety-utility trade-offs. Experiments on AgentDojo, AgentHarm, and ATBench show that FATE improves safety across different models and scales while preserving useful behavior. Compared with strong baselines, FATE reduces attack success rate by 33.5%, harmful compliance by 82.6%, and improves external trajectory-safety diagnosis by 6.5%. These results suggest that failed trajectories can provide structured repair supervision for safer self-evolving agents.

Data-residency constraints force enterprises to self-host LLMs, but continuous adoption of newer models without decommissioning their predecessors expands the serving fleet, fragmenting a finite GPU pool. We consolidate traffic from over 200 internal applications onto a single model by closing quality gaps identified through production error analysis along three axes: instruction following, function-calling, and internal task distribution. Quality is tracked by offline benchmarks stratified to production traffic and scored by deterministic verifiers or calibrated LLM judges. Rather than optimising all objectives jointly, which introduces cross-domain reward interference, we train a separate GRPO expert per axis and merge them via two-stage SLERP. Each expert's reward exposes a distinct failure mode, namely semantic collapse, over-calling, and verbosity hacking, each requiring a domain-specific fix. In non-reasoning mode the recipe surpasses a {sim}7times larger by total parameters baseline on the in-house Arena with 69.6 to 65.8, instruction following with 0.85 to 0.83, and function-calling with 0.79 to 0.77, while lifting general dialogue benchmarks. The model absorbs 50% of platform traffic, 116M requests per month, at a fraction of the serving cost.

Frontier deep research agents (DRAs) plan a research task, synthesize across documents, and return a structured deliverable on demand. They are being deployed in enterprise workflows faster than they are being evaluated. Existing benchmarks measure factual recall, single-hop QA, or generic agentic skill, missing the multi-document, decision-grade work DRAs are deployed to produce. We introduce a benchmark targeting the structured analytical deliverables that fill a management consultant's typical week. We grade three frontier agents, namely Claude Opus 4.6 with web search, OpenAI o3-deep-research, and Google Gemini 3.1 Pro deep-research, on 42 SME-authored prompts. Each of the 126 responses is scored on two layers: deterministic ground-truth verifiers (mean 13.8 per task) and a five-criterion 0-3 SME rubric, composed into a Verifier-Rubric Score (VRS) on 0-100. Most prompts embed cognitive traps that penalize surface-pattern matching. Acceptance under our joint threshold (rubric mean >= 2.5 and verifier rate >= 80%) is uniformly low: Gemini 21.4%, o3 9.5%, Claude 9.5%. Mean VRS scores agree with published rubric-based benchmarks (our top 62.6 vs. APEX-v1 64.2, ProfBench 65.9, ResearchRubrics < 68%), validating the rubric construct. ACCEPT rates sit below APEX-Agents' MC-segment Pass@1 band (12.3-22.7%) on dedicated DR agents; our floor is three points lower despite the harness advantage, opened by stricter conjunctive grading and trap design. Each agent fails distinctively. Claude produces the deliverable most reliably (4.5x the others' rate on file-required tasks) but carries the highest fabrication signature. o3 has the cleanest reasoning average yet drops required sections and propagates arithmetic errors. Gemini is bimodal, with the highest acceptance rate alongside the most zero-scored rubric cells.

Verification is critical for improving agents: it provides the reward signal for Reinforcement Learning and enables inference-time gains through Test-Time Scaling (TTS). Despite its importance, verification in software engineering (SWE) agent settings often relies on code execution, which can be difficult to scale due to environment setup overhead. Scalable alternatives such as patch classifiers and heuristic methods exist, but they are less grounded in codebase context and harder to interpret. To this end, we explore Agentic Rubrics: an expert agent interacts with the repository to create a context-grounded rubric checklist, and candidate patches are then scored against it without requiring test execution. On SWE-Bench Verified under parallel TTS evaluation, Agentic Rubrics achieve a score of 54.2% on Qwen3-Coder-30B-A3B and 40.6% on Qwen3-32B, with at least a +3.5 percentage-point gain over the strongest baseline in our comparison set. We further analyze rubric behavior, showing that rubric scores are consistent with ground-truth tests while also flagging issues that tests do not capture. Our ablations show that agentic context gathering is essential for producing codebase-specific, unambiguous criteria. Together, these results suggest that Agentic Rubrics provide an efficient, scalable, and granular verification signal for SWE agents.

Verifying the success of computer use agent (CUA) trajectories is a critical challenge: without reliable verification, neither evaluation nor training signal can be trusted. In this paper, we present lessons learned from building a best-in-class verifier for web tasks we call the Universal Verifier. We design the Universal Verifier around four key principles: 1) constructing rubrics with meaningful, non-overlapping criteria to reduce noise; 2) separating process and outcome rewards that yield complementary signals, capturing cases where an agent follows the right steps but gets blocked or succeeds through an unexpected path; 3) distinguishing between controllable and uncontrollable failures scored via a cascading-error-free strategy for finer-grained failure understanding; and 4) a divide-and-conquer context management scheme that attends to all screenshots in a trajectory, improving reliability on longer task horizons. We validate these findings on CUAVerifierBench, a new set of CUA trajectories with both process and outcome human labels, showing that our Universal Verifier agrees with humans as often as humans agree with each other. We report a reduction in false positive rates to near zero compared to baselines like WebVoyager (geq 45\%) and WebJudge (geq 22\%). We emphasize that these gains stem from the cumulative effect of the design choices above. We also find that an auto-research agent achieves 70\% of expert quality in 5\% of the time, but fails to discover all strategies required to replicate the Universal Verifier. We open-source our Universal Verifier system along with CUAVerifierBench; available at https://github.com/microsoft/fara.

Reinforcement Learning (RL) has been shown to significantly boost reasoning capabilities of large language models (LLMs) in math, coding, and multi-hop reasoning tasks. However, RL fine-tuning requires abundant high-quality verifiable data, often sourced from human annotations, generated from frontier LLMs, or scored by LLM-based verifiers. All three have considerable limitations: human-annotated datasets are small and expensive to curate, LLM-generated data is hallucination-prone and costly, and LLM-based verifiers are inaccurate and slow. In this work, we investigate a cheaper alternative: RL fine-tuning on rule-generated synthetic data for multi-hop reasoning tasks. We discover that LLMs fine-tuned on synthetic data perform significantly better on popular real-world question-answering benchmarks, despite the synthetic data containing only fictional knowledge. On stratifying performance by question difficulty, we find that synthetic data teaches LLMs to compose knowledge -- a fundamental and generalizable reasoning skill. Our work highlights rule-generated synthetic reasoning data as a free and scalable resource to improve LLM reasoning capabilities.

Scaling pre-training, post-training, and test-time compute have become the central paradigms for improving the capabilities of LLMs. In this work, we identify verification, the ability to determine the correctness of a solution, as a new scaling axis. To unlock this and demonstrate its effectiveness, we introduce LLM-as-a-Verifier, a general-purpose verification framework that provides fine-grained feedback for agentic tasks without requiring additional training. Unlike standard LM judges that prompt LLMs to produce discrete scores for candidate solutions, LLM-as-a-Verifier computes the expectation over the distribution of scoring token logits to generate continuous scores. This probabilistic formulation enables verification to scale along multiple dimensions: (1) score granularity, (2) repeated evaluation, and (3) criteria decomposition. In particular, we show that scaling the scoring granularity leads to better separation between positive and negative solutions, resulting in more calibrated comparisons. Moreover, scaling repeated evaluation and criteria decomposition consistently lead to additional gains in verification accuracy through variance and complexity reduction. We further introduce a cost-efficient ranking algorithm for selecting the best solution among candidates using the verifier's continuous scores. LLM-as-a-Verifier achieves state-of-the-art performance on Terminal-Bench V2 (86.5%), SWE-Bench Verified (78.2%), RoboRewardBench (87.4%), and MedAgentBench (73.3%). Beyond verification, the fine-grained signals from LLM-as-a-Verifier can also serve as a proxy for estimating task progress. We build an extension for Claude Code, enabling developers to monitor and improve their own agentic systems. Finally, we show that LLM-as-a-Verifier can provide dense feedback for RL, improving the sample efficiency of SAC and GRPO on robotics and mathematical reasoning benchmarks.

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.

A verifier for robot policies reads a candidate behavior and returns a score for how well it did, used both to evaluate vision-language-action policies and to train them. Verifiers range from success detectors and reward models to runtime monitors, safety filters, and temporal-logic specifications. We survey roughly 150 verifiers and compare them along two properties. Availability is how much a verdict costs, how early in a rollout the verdict arrives, and how often a verdict can be asked for. Availability rises as verdicts get cheaper, earlier, and denser. Credibility is how much a high score tells us about the task. Credibility falls as the judgment becomes gameable and self-serving. We group the verifiers by who supplies the judgment: human verifiers, rule-based and formal verifiers, learned and pretrained verifiers, and model-intrinsic verifiers. Across the four families, we find that credibility falls as availability rises. Regardless of who supplies the judgment, there is no free checker. We then examine what validates a verifier itself, and how much a high score tells us. Three measures appear in the literature: agreement with human labels, the performance of the policy it trains, and behavior under reward hacking. We close with nine metrics that make a verifier claim checkable, and coordinates for the verifiers still to be built.

Large language models (LLMs) can act as both problem solvers and solution verifiers, where the latter select high-quality answers from a pool of solver-generated candidates. This raises the question of under what conditions verification pays off in solver-verifier systems. Prior work has conducted only limited studies of the factors influencing verification performance, focusing primarily on self-verification and examining neither the relationship between solver and verifier model families nor the effects of reasoning post-training. To rectify this, we present a systematic study across 37 models spanning multiple families, sizes, and base vs. post-trained variants, evaluated on 9 benchmarks covering logical reasoning, structured puzzles, symbolic computation, mathematics, commonsense, factual recall, and domain knowledge. In order to support our analysis, we introduce and empirically validate verifier gain, a metric that predicts the performance improvements from test-time verifier-based rejection sampling. Our experiments find that 1) verification across model families is more effective than either self-verification or verification within the same family, and more generally that the benefits of verification decrease as the solver and verifier become more similar, 2) reasoning post-training weakens self-improvement abilities but strengthens cross-family improvement, and 3) some tasks are inherently more amenable to improvement through verification, particularly mathematical and logical tasks.

Verifiers can improve language model capabilities by scoring and ranking responses from generated candidates. Currently, high-quality verifiers are either unscalable (e.g., humans) or limited in utility (e.g., tools like Lean). While LM judges and reward models have become broadly useful as general-purpose verifiers, a significant performance gap remains between them and oracle verifiers (verifiers with perfect accuracy). To help close this gap, we introduce Weaver, a framework for designing a strong verifier by combining multiple weak, imperfect verifiers. We find weighted ensembles of verifiers, which typically require learning from labeled data, significantly outperform unweighted combinations due to differences in verifier accuracies. To reduce dependency on labeled data, Weaver leverages weak supervision to estimate each verifier's accuracy and combines outputs into a unified score that better reflects true response quality. However, directly applying weak supervision algorithms poses challenges, including inconsistent verifier output formats and handling low-quality verifiers. Weaver addresses these using dataset statistics to normalize outputs and filter specific verifiers. We study Weaver's effectiveness in test-time repeated sampling, where a model generates multiple candidate responses and selects one. Our evaluations show Weaver significantly improves over Pass@1-performance when selecting the first candidate-across reasoning and math tasks, achieving o3-mini-level accuracy with Llama 3.3 70B Instruct as generator, and an ensemble of 70B or smaller judge and reward models as verifiers (87.7% average). This gain mirrors the jump between GPT-4o and o3-mini (69.0% vs. 86.7%), which required extensive finetuning and post-training. To reduce computational costs of verifier ensembles, we train a 400M cross-encoder using Weaver's combined output scores.

Verifiers or reward models are often used to enhance the reasoning performance of large language models (LLMs). A common approach is the Best-of-N method, where N candidate solutions generated by the LLM are ranked by a verifier, and the best one is selected. While LLM-based verifiers are typically trained as discriminative classifiers to score solutions, they do not utilize the text generation capabilities of pretrained LLMs. To overcome this limitation, we instead propose training verifiers using the ubiquitous next-token prediction objective, jointly on verification and solution generation. Compared to standard verifiers, such generative verifiers (GenRM) can benefit from several advantages of LLMs: they integrate seamlessly with instruction tuning, enable chain-of-thought reasoning, and can utilize additional inference-time compute via majority voting for better verification. We demonstrate that when using Gemma-based verifiers on algorithmic and grade-school math reasoning tasks, GenRM outperforms discriminative verifiers and LLM-as-a-Judge, showing a 16-64% improvement in the percentage of problems solved with Best-of-N. Furthermore, we show that GenRM scales favorably across dataset size, model capacity, and inference-time compute.

Reinforcement learning with verifiable rewards has enabled strong post-training gains in domains such as math and coding, though many open-ended settings rely on rubric-based rewards. We study reward hacking in rubric-based RL, where a policy is optimized against a training verifier but evaluated against a cross-family panel of three frontier judges, reducing dependence on any single evaluator. Our framework separates two sources of divergence: verifier failure, where the training verifier credits rubric criteria that reference verifiers reject, and rubric-design limitations, where even strong rubric-based verifiers favor responses that rubric-free judges rate worse overall. Across medical and science domains, weak verifiers produce large proxy-reward gains that do not transfer to the reference verifiers; exploitation grows over training and concentrates in recurring failures such as partial satisfaction of compound criteria, treating implicit content as explicit, and imprecise topical matching. Stronger verifiers substantially reduce, but do not eliminate, verifier exploitation. We also introduce a self-internalization gap, a verifier-free diagnostic based on policy log-probabilities, which tracks reference-verifier quality, detecting when the policy trained using the weak verifier stops improving. Finally, in our setting, stronger verification does not prevent reward hacking when the rubric leaves important failure modes unspecified: rubric-based verifiers prefer the RL checkpoint, while rubric-free judges prefer the base model. These disagreements coincide with gains concentrated in completeness and presence-based criteria, alongside declines in factual correctness, conciseness, relevance, and overall quality. Together, these results suggest that stronger verification reduces reward hacking, but does not by itself ensure that rubric gains correspond to broader quality gains.

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.

Step-by-step verifiers -- also known as process reward models (PRMs) -- are a key ingredient for test-time scaling. PRMs require step-level supervision, making them expensive to train. This work aims to build data-efficient PRMs as verbalized step-wise reward models that verify every step in the solution by generating a verification chain-of-thought (CoT). We propose ThinkPRM, a long CoT verifier fine-tuned on orders of magnitude fewer process labels than those required by discriminative PRMs. Our approach capitalizes on the inherent reasoning abilities of long CoT models, and outperforms LLM-as-a-Judge and discriminative verifiers -- using only 1% of the process labels in PRM800K -- across several challenging benchmarks. Specifically, ThinkPRM beats the baselines on ProcessBench, MATH-500, and AIME '24 under best-of-N selection and reward-guided search. In an out-of-domain evaluation on a subset of GPQA-Diamond and LiveCodeBench, our PRM surpasses discriminative verifiers trained on the full PRM800K by 8% and 4.5%, respectively. Lastly, under the same token budget, ThinkPRM scales up verification compute more effectively compared to LLM-as-a-Judge, outperforming it by 7.2% on a subset of ProcessBench. Our work highlights the value of generative, long CoT PRMs that can scale test-time compute for verification while requiring minimal supervision for training. Our code, data, and models will be released at https://github.com/mukhal/thinkprm.

Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling. To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary {0,1} during training. This choice carries a cost: it introduces false negatives (rejecting correct answers, FNs) and false positives (accepting incorrect ones, FPs). For instance, a rule-based checker may mark the correct fraction 12{36} as wrong when compared against the canonical 1{3} due to brittle parsing/equivalence rules (FN), while a large language model (LLM) judges can be gamed by superficial cues or even a single adversarial token, yielding inflated correctness for wrong solutions (FP). We formalize verifier unreliability by modeling the verifier as a stochastic reward channel with asymmetric noise rates. From this abstraction, we derive two correction algorithms for verifier errors. The first is a backward correction that de-biases the observed binary reward to recover an unbiased estimator of the clean policy gradient. The second is a forward correction that reweights score-function terms so that the expected update direction aligns with the clean gradient; notably, it requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimization (GRPO)-based RLVR pipeline and evaluate them on math-reasoning models and benchmarks. Across models and datasets, both corrections improve over uncorrected training; the forward variant converges faster and remains stable under heavier noise. Finally, we show a practical appeal mechanism in which a lightweight LLM verifier estimates the FN rate online by rechecking rule-based negatives, obtaining outperformance compared with other state-of-the-art contenders.

Reinforcement learning with verifiable rewards improves mathematical reasoning when a final answer can be checked, but a correct answer does not certify the derivation behind it, and proof problems offer no answer to check. Replacing the check with a reasoning model as an in-loop verifier faces a fundamental obstacle: the policy must already produce occasional correct attempts for any reward to exist, which it may never do at olympiad level. We instead move verification and repair out of the training loop and into offline data generation with SPLICE, a workflow in which a second model, given only a reference solution, edits a reasoning model's traces as they are generated: it verifies progress, truncates a failed trace at its last verified step, and splices in an adaptively strengthened hint until progress resumes. The resulting dataset includes repaired examples whose sampled unaided trajectory failed, with failed continuations removed and progress repeatedly checked against the reference solution. A model finetuned on SPLICE traces outperforms the same model distilled from the reasoning model's unedited traces on AIME and, under a grading protocol validated against human grades, on olympiad proofs. The trained model's own traces show a corresponding behavioral signature: at difficult points it announces a branch in the style of the spliced hints and takes riskier steps, with predictive entropy rising there and just after, a pattern absent from the model trained on unedited traces.

Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess these paths. However, existing verifiers, typically trained on binary-labeled reasoning paths, fail to fully utilize the relative merits of intermediate steps, thereby limiting the effectiveness of the feedback provided. To overcome this limitation, we propose Tree-based Preference Learning Verifier (Tree-PLV), a novel approach that constructs reasoning trees via a best-first search algorithm and collects step-level paired data for preference training. Compared to traditional binary classification, step-level preferences more finely capture the nuances between reasoning steps, allowing for a more precise evaluation of the complete reasoning path. We empirically evaluate Tree-PLV across a range of arithmetic and commonsense reasoning tasks, where it significantly outperforms existing benchmarks. For instance, Tree-PLV achieved substantial performance gains over the Mistral-7B self-consistency baseline on GSM8K (67.55% to 82.79%), MATH (17.00% to 26.80%), CSQA (68.14% to 72.97%), and StrategyQA (82.86% to 83.25%).Additionally, our study explores the appropriate granularity for applying preference learning, revealing that step-level guidance provides feedback that better aligns with the evaluation of the reasoning process.

Recent advances such as DeepSeek R1-Zero highlight the effectiveness of incentive training, a reinforcement learning paradigm that computes rewards solely based on the final answer part of a language model's output, thereby encouraging the generation of intermediate reasoning steps. However, these methods fundamentally rely on external verifiers, which limits their applicability to domains like mathematics and coding where such verifiers are readily available. Although reward models can serve as verifiers, they require high-quality annotated data and are costly to train. In this work, we propose NOVER, NO-VERifier Reinforcement Learning, a general reinforcement learning framework that requires only standard supervised fine-tuning data with no need for an external verifier. NOVER enables incentive training across a wide range of text-to-text tasks and outperforms the model of the same size distilled from large reasoning models such as DeepSeek R1 671B by 7.7 percent. Moreover, the flexibility of NOVER enables new possibilities for optimizing large language models, such as inverse incentive training.

Verifiers are auxiliary models that assess the correctness of outputs generated by base large language models (LLMs). They play a crucial role in many strategies for solving reasoning-intensive problems with LLMs. Typically, verifiers are LLMs themselves, often as large (or larger) than the base model they support, making them computationally expensive. In this work, we introduce a novel lightweight verification approach, LiLaVe, which reliably extracts correctness signals from the hidden states of the base LLM. A key advantage of LiLaVe is its ability to operate with only a small fraction of the computational budget required by traditional LLM-based verifiers. To demonstrate its practicality, we couple LiLaVe with popular meta-generation strategies, like best-of-n or self-consistency. Moreover, we design novel LiLaVe-based approaches, like conditional self-correction or conditional majority voting, that significantly improve both accuracy and efficiency in generation tasks with smaller LLMs. Our work demonstrates the fruitfulness of extracting latent information from the hidden states of LLMs, and opens the door to scalable and resource-efficient solutions for reasoning-intensive applications.

Agent systems often decompose a task across multiple roles, but these roles are typically specified by prompts rather than enforced by access controls. Without enforcement, a team pass rate can mask whether agents actually coordinated or whether one role effectively did another role's work. We present TeamBench, a benchmark with 851 task templates and 931 seeded instances for evaluating agent coordination under operating system-enforced role separation. TeamBench separates specification access, workspace editing, and final certification across Planner, Executor, and Verifier roles, so that no role can read the full requirements, modify the workspace, and certify the final answer. Prompt-only and sandbox-enforced teams reach statistically indistinguishable pass rates, but prompt-only runs produce 3.6 times more cases where the verifier attempts to edit the executor's code. Verifiers approve 49% of submissions that fail the deterministic grader, and removing the verifier improves mean partial score in the ablation. Team value is also conditional. Teams benefit when single agents struggle, but hurt when single agents already perform well. A 40-session human study under the same role separation shows that our benchmark exposes interaction patterns that pass rate misses. Solo participants work through the task directly, human participants paired with agents often collapse into quick approval, and human teams spend more effort coordinating missing information across roles.

Speech deepfake detectors usually emit one score per utterance, but a borderline score does not reveal why two examples differ during retrospective error analysis. We ask whether a final score can be calibrated from component fields while keeping those fields visible for inspection. We build a decision record with a passive detector score and a score from a probe applied to a marked copy. It also includes retrieval support held out of the evaluated family, a margin from a support-set profile, and raw neighbor closeness. A cross-fit calibrator combines these fields and two differences between raw scores into one final score. On matched ASVspoof development data, the calibrated record reduces equal error rate (EER) by 3.48 percentage points relative to the fixed retrieval-augmented rule. It reaches 8.43% EER, whereas a passive WavLM baseline reaches 6.71% on the same subset. The record is therefore not the strongest detector in this comparison. Its value is to retain inspectable component fields while producing one scalar score for retrospective diagnosis.

Verifier-guided reinforcement learning has become a powerful paradigm for improving LLM reasoning. In multi-turn settings, models receive a verifier score after each turn and iteratively refine their outputs. Although such scores provide dense feedback, they do not directly provide dense credit: a score measures the quality of the current output, while credit should measure how the current turn changes the refinement trajectory. We propose TCPO, a turn-level credit assignment method for verifier-guided multi-turn RL. TCPO casts credit assignment as score-to-credit conversion and constructs turn-level advantages through reference-based comparisons: retrospective credit captures immediate progress and regression relative to the best prior state; hindsight delayed credit identifies non-improving turns with later payoff; and selective fixed-history counterfactual estimation refines high-surprisal turns under the same history. Experiments on math reasoning, code generation, and AppWorld agent tasks show that TCPO improves or matches the strongest baselines across model scales, task domains, and verifier types. TCPO achieves the best or tied-best best-turn Pass@8 on Qwen3-4B and DeepSeek-R1-Distill-Llama-8B, reduces turns to success, and improves multi-turn agent performance. These results highlight score-to-credit conversion as a central ingredient for verifier-guided multi-turn policy optimization.

Trustworthy verifiers are essential for the success of reinforcement learning with verifiable reward (RLVR), which is the core methodology behind various large reasoning models such as DeepSeek-R1. In complex domains like mathematical reasoning, rule-based verifiers have been widely adopted in previous works to train strong reasoning models. However, the reliability of these verifiers and their impact on the RL training process remain poorly understood. In this work, we take mathematical reasoning as a case study and conduct a comprehensive analysis of various verifiers in both static evaluation and RL training scenarios. First, we find that current open-source rule-based verifiers often fail to recognize equivalent answers presented in different formats across multiple commonly used mathematical datasets, resulting in non-negligible false negative rates. This limitation adversely affects RL training performance and becomes more pronounced as the policy model gets stronger. Subsequently, we investigate model-based verifiers as a potential solution to address these limitations. While the static evaluation shows that model-based verifiers achieve significantly higher verification accuracy, further analysis and RL training results imply that they are highly susceptible to hacking, where they misclassify certain patterns in responses as correct (i.e., false positives). This vulnerability is exploited during policy model optimization, leading to artificially inflated rewards. Our findings underscore the unique risks inherent to both rule-based and model-based verifiers, aiming to offer valuable insights to develop more robust reward systems in reinforcement learning.

Large language models (LLMs) increasingly rely on reinforcement learning (RL) to enhance their reasoning capabilities through feedback. A critical challenge is verifying the consistency of model-generated responses and reference answers, since these responses are often lengthy, diverse, and nuanced. Rule-based verifiers struggle with complexity, prompting the use of model-based verifiers. However, specialized verifiers lack flexibility, while general LLM judges can be inconsistent. Existing research primarily focuses on building better verifiers, yet a systematic evaluation of different types of verifiers' performance across domains remains lacking, severely constraining the reliable development of Reinforcement Learning with Verifiable Reward (RLVR). To address this, we propose VerifyBench--a cross-domain comprehensive benchmark for systematically evaluating verifiers. We construct 4,000 expert-level questions covering mathematics, physics, chemistry, and biology. Each question is equipped with reference answers and diverse responses. The reliability of the evaluation is ensured through a rigorous annotation process conducted by a multidisciplinary expert team. We design a four-dimensional experimental framework to comprehensively compare the performance boundaries of specialized verifiers and general LLMs under combined conditions of extracted answers vs. complete responses, and short vs. long outputs. Our evaluation uncovers fundamental trade-offs in verifiers: while specialized verifiers achieve leading accuracy, they exhibit deficiencies in recall; general models show stronger inclusivity but unstable precision. More importantly, we discover verifiers' high sensitivity to input structure and inherent limitations in cross-domain generalization, providing critical insights into the bottlenecks of current verifier technology.

Video temporal grounding supports applications such as video search, content review, and automated editing by localizing events described in natural language. Yet existing generative models typically output timestamps without explicit interval-level confidence scores to guide candidate selection. We separate candidate generation from acceptance by scoring individual intervals within the original decoding pass. A lightweight confidence head reads pooled decoder states, providing an explicit score trained for interval selection. Offline verifier scores supervise the head on fixed candidate sequences, and temporal-overlap labels adapt it to current rollouts during reinforcement learning. GT-anchored candidate-pool supervision and set-level optimization train the generator. The resulting scores support ranking, threshold-based selection, and rejection without invoking an external verifier at inference. On a fixed OMTG-Bench candidate pool, confidence raises query-macro Recall@0.5 from 9.95% to 14.42% over generation order at a 10% global return budget, and from 26.48% to 31.12% at a 25% budget. The continuous scores let downstream applications adjust return budgets or acceptance thresholds to match their precision-recall preferences, without regenerating candidate intervals.

The standard paradigm for solving coding tasks via large language models (LLMs) is to generate-then-rank programs, where the latter step uses a verifier in the ranking process. The growing consensus is that a comprehensive verifier (e.g., a full test suite) should be prioritized over an outcome reward model (ORM) whenever possible, with little consideration given to the trade-offs involved. We aim to challenge this assumption by systematically exploring the tradeoff between speed and accuracy. We find that ORMs play a crucial role in scaling verification through trading accuracy for speed, even when a comprehensive verifier is available. Their value becomes especially apparent when used in a generate-prune-then-rank approach, where a faster but less accurate verifier removes incorrect solutions prior to ranking -- leading to a system that is 11.65x faster while only being 8.33% less accurate than the full test suite. We analyze the generate-prune-then-rank approach and show that it works by filtering out incorrect but highly ranked solutions. These findings enable the design of scalable and accurate program ranking systems.

Generative visual verifiers play a crucial role in advancing multimodal intelligence. To enhance the robustness of visual verifiers in complex multimodal scenarios involving compositional requirements, we move beyond conventional binary verifiers that produce only True/False discrete judgments and introduce a verifier that automatically decomposes complex prompts or environmental rules into fine-grained components and assigns pointwise scores to provide a continuous and more informative critique signal. Our experiments further demonstrate that these structured and interpretable outputs improve the verifier's generalization to out-of-domain multimodal critic tasks. To train this verifier, we introduce a Decoupled RL training strategy that jointly optimizes sub-question-level binary judgment and global alignment scoring, using precise local feedback to develop fine-grained verification capabilities that provide a foundation for reliable continuous scoring at the global level. Under a general reinforcement learning framework, we first empirically demonstrate that the proposed pointwise graded verifier significantly outperforms binary verifiers in traditional text-to-image scenarios. We then extend our investigation to rule-governed generative world modeling where generative models are leveraged for world simulation and world reasoning under explicit rules. From a theoretical standpoint, we further show that a pairwise verification paradigm yields more accurate critiques than the pointwise formulation when ground-truth images are available, with empirical results on diverse structured world-modeling tasks such as Maze and Sudoku further validating the effectiveness of our approach. Overall, our findings suggest a key insight: the transition from generative models to structured world-modeling agents critically hinges on the availability of accurate pairwise graded visual verifiers.

Common self-improvement approaches for large language models (LLMs), such as STaR (Zelikman et al., 2022), iteratively fine-tune LLMs on self-generated solutions to improve their problem-solving ability. However, these approaches discard the large amounts of incorrect solutions generated during this process, potentially neglecting valuable information in such solutions. To address this shortcoming, we propose V-STaR that utilizes both the correct and incorrect solutions generated during the self-improvement process to train a verifier using DPO that judges correctness of model-generated solutions. This verifier is used at inference time to select one solution among many candidate solutions. Running V-STaR for multiple iterations results in progressively better reasoners and verifiers, delivering a 4% to 17% test accuracy improvement over existing self-improvement and verification approaches on common code generation and math reasoning benchmarks with LLaMA2 models.

Training language models for formal theorem proving requires large numbers of verifier calls. Slow checks and timeouts often leave GPUs waiting and withhold rewards from potentially correct proofs. We train neural evaluators to predict Lean 4 verdicts and compiler feedback on GPUs using 4.84M labelled programs. We compare two validity classifiers with a feedback model that annotates proof attempts with predicted goal states and error messages. A two-stage evaluator that screens candidates with a classifier and scores its positive predictions with the feedback model reaches 87.8% accuracy in predicting whether Lean accepts a candidate proof, evaluated on a 68,932-program benchmark collected from public provers. The combined evaluator processes 3.5 candidates per second on one H100, 4.2x the throughput of our 64-worker Lean baseline with environment reuse. Finally, we combine our evaluator with Lean verdicts to obtain a hybrid reward system that shortens GRPO training steps by approximately 31%. After one GRPO epoch with hybrid rewards, the prover achieves nearly the same miniF2F pass@1 as with Lean-only rewards (62.2% versus 62.4%) and a pass@32 of 72.4% versus 71.3%.

Agent benchmarks score submissions with outcome verifiers that are typically hand-written and brittle, leaving them open to reward hacking. We audit 1,968 tasks across five terminal-agent benchmarks and find 323 (16%) hackable by frontier models given only the task description. This corrupts both leaderboard rankings and RL training signal, yet the standard response is manual and reactive. We introduce the hacker-fixer loop, a method for building exploit-resistant verifiers without per-task manual patching. The loop alternates three LLM agents: a hacker tries to pass the verifier without solving the task, a fixer patches the verifier to reject each discovered exploit, and a solver confirms the patched verifier still admits legitimate solutions. The loop iterates: each patch reshapes what the verifier rewards, surfacing the next exploit. We further add verifier access, and let patches transfer across tasks, to broaden the exploits the loop discovers. On KernelBench, the loop drives the attack success rate from 62% to 0% on a held-out corpus of publicly reported exploits. We also find that weaker agents in the loop can defend against much stronger hackers: Gemini 3 Flash's loop drives the stronger Gemini 3.1 Pro and Claude Opus 4.7's attack success rate from 76% and 61% to 0% on KernelBench, and Gemini 3.1 Pro's from 39% to 17% on Terminal Bench across 77 tasks. We release Terminal Wrench (323 hackable environments, 3,632 hack trajectories) as a snapshot of the current attack surface, our patched verifiers, the exploits the loop discovered, and our implementation as a basis for future work.

Large language models (LLMs) have achieved significant progress in solving complex reasoning tasks by Reinforcement Learning with Verifiable Rewards (RLVR). This advancement is also inseparable from the oversight automated by reliable verifiers. However, current outcome-based verifiers (OVs) are unable to inspect the unreliable intermediate steps in the long reasoning chains of thought (CoTs). Meanwhile, current process-based verifiers (PVs) have difficulties in reliably detecting errors in the complex long CoTs, limited by the scarcity of high-quality annotations due to the prohibitive costs of human annotations. Therefore, we propose the Outcome-based Process Verifier (OPV), which verifies the rationale process of summarized outcomes from long CoTs to achieve both accurate and efficient verification and enable large-scale annotation. To empower the proposed verifier, we adopt an iterative active learning framework with expert annotations to progressively improve the verification capability of OPV with fewer annotation costs. Specifically, in each iteration, the most uncertain cases of the current best OPV are annotated and then subsequently used to train a new OPV through Rejection Fine-Tuning (RFT) and RLVR for the next round. Extensive experiments demonstrate OPV's superior performance and broad applicability. It achieves new state-of-the-art results on our held-out \thisbench, outperforming much larger open-source models such as Qwen3-Max-Preview with an F1 score of 83.1 compared to 76.3. Furthermore, OPV effectively detects false positives within synthetic dataset, closely align with expert assessment. When collaborating with policy models, OPV consistently yields performance gains, e.g., raising the accuracy of DeepSeek-R1-Distill-Qwen-32B from 55.2\% to 73.3\% on AIME2025 as the compute budget scales.

Large language models (LLMs) have achieved significant progress in solving complex reasoning tasks by Reinforcement Learning with Verifiable Rewards (RLVR). This advancement is also inseparable from the oversight automated by reliable verifiers. However, current outcome-based verifiers (OVs) are unable to inspect the unreliable intermediate steps in the long reasoning chains of thought (CoTs). Meanwhile, current process-based verifiers (PVs) have difficulties in reliably detecting errors in the complex long CoTs, limited by the scarcity of high-quality annotations due to the prohibitive costs of human annotations. Therefore, we propose the Outcome-based Process Verifier (OPV), which verifies the rationale process of summarized outcomes from long CoTs to achieve both accurate and efficient verification and enable large-scale annotation. To empower the proposed verifier, we adopt an iterative active learning framework with expert annotations to progressively improve the verification capability of OPV with fewer annotation costs. Specifically, in each iteration, the most uncertain cases of the current best OPV are annotated and then subsequently used to train a new OPV through Rejection Fine-Tuning (RFT) and RLVR for the next round. Extensive experiments demonstrate OPV's superior performance and broad applicability. It achieves new state-of-the-art results on our held-out OPV-Bench, outperforming much larger open-source models such as Qwen3-Max-Preview with an F1 score of 83.1 compared to 76.3. Furthermore, OPV effectively detects false positives within synthetic dataset, closely align with expert assessment. When collaborating with policy models, OPV consistently yields performance gains, e.g., raising the accuracy of DeepSeek-R1-Distill-Qwen-32B from 55.2% to 73.3% on AIME2025 as the compute budget scales.

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.

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural language proofs be checked for errors. LLM judges are increasingly being adopted to meet the growing demand for evaluating such proofs. While verification is considered easier than generation, what model capability does reliable verification actually require? We systematically evaluate four open-source and two frontier LLMs on datasets of human-graded natural language proofs of competition-level problems. We consider two key metrics: verifier accuracy and self-consistency (the rate of agreement across repeated judgments on the same proof). We observe that smaller open-source models are only up to ~10% behind frontier models in accuracy but they are up to ~25% more inconsistent. Furthermore, we see that verifier accuracy is sensitive to prompt choice across all models. We then demonstrate that the smaller models, in fact, do possess the mathematical capabilities to verify proofs at the level of frontier models, but they struggle to reliably elicit these capabilities with general judging prompts. Through an LLM-guided prompt search, we synthesize an ensemble of specialized prompts that overcome the specific failure modes of smaller models, boosting their performance by up to 9.1% in accuracy and 15.9% in self-consistency. These gains are realized across models and datasets, allowing models like Qwen3.5-35B to perform on par with frontier models such as Gemini 3.1 Pro for proof verification.

Reasoning in Large Language Models (LLMs) has recently shown strong potential in enhancing generative recommendation through deep understanding of complex user preference. Existing approaches follow a {reason-then-recommend} paradigm, where LLMs perform step-by-step reasoning before item generation. However, this paradigm inevitably suffers from reasoning degradation (i.e., homogeneous or error-accumulated reasoning) due to the lack of intermediate verification, thus undermining the recommendation. To bridge this gap, we propose a novel \textit{reason-verify-recommend} paradigm, which interleaves reasoning with verification to provide reliable feedback, guiding the reasoning process toward more faithful user preference understanding. To enable effective verification, we establish two key principles for verifier design: 1) reliability ensures accurate evaluation of reasoning correctness and informative guidance generation; and 2) multi-dimensionality emphasizes comprehensive verification across multi-dimensional user preferences. Accordingly, we propose an effective implementation called VRec. It employs a mixture of verifiers to ensure multi-dimensionality, while leveraging a proxy prediction objective to pursue reliability. Experiments on four real-world datasets demonstrate that VRec substantially enhances recommendation effectiveness and scalability without compromising efficiency. The codes can be found at https://github.com/Linxyhaha/Verifiable-Rec.

Inference-time skill augmentation provides a lightweight way to improve data-analytic agents by injecting reusable procedural knowledge without updating model parameters. However, discovering effective skills for data analysis remains challenging, as reliable supervision is expensive and success criteria vary across analytical formats. This raises the key question of how to discover reusable data-analysis skills from unlabeled exploration alone. We propose DataCOPE, an unsupervised verifier-guided skill discovery framework for data-analytic agents. DataCOPE derives verifier signals from the exploration trajectories and uses them to characterize relative quality or aggreement among trajectories. It iteratively coordinates a Data-Analytic Agent for trajectory generation, an Unsupervised Verifier for signal extraction, and a Skill Manager for contrastive skill distillation. For report-style analysis, we instantiate the verifier as an Adaptive Checklist Verifier that derives task-specific criteria, scores reports by verifiable coverage, and iteratively refines the checklist. For reasoning-style analysis, we instantiate it as an Answer Agreement Verifier that groups trajectories by answer agreement and uses self-consistency as an auxiliary signal. We evaluate DataCOPE on report-style analysis from Deep Data Research and reasoning-style analysis from DABStep. Across both settings, DataCOPE consistently improves held-out performance over baselines. Averaged across four model settings, DataCOPE improves the mean score by 9.71% and 32.30% on report-style and reasoning-style tasks respectively.

Inference-time scaling via repeated sampling has shown promise in reasoning tasks, but its effectiveness in multilingual generation remains underexplored. We evaluate this approach using perplexity- and reward-based verifiers on two multilingual benchmarks: the Aya Evaluation Suite and m-ArenaHard. Our results show consistent quality improvements, with gains exceeding 35% in some cases. While perplexity-based scoring is effective for open-ended prompts, only reward-based verifiers improve performance on tasks requiring reasoning (e.g., math, code). Our results demonstrate the broader utility of repeated sampling for multilingual text generation and underscore the importance of selecting right verifiers for the task.

State-of-the-art language models can match human performance on many tasks, but they still struggle to robustly perform multi-step mathematical reasoning. To diagnose the failures of current models and support research, we introduce GSM8K, a dataset of 8.5K high quality linguistically diverse grade school math word problems. We find that even the largest transformer models fail to achieve high test performance, despite the conceptual simplicity of this problem distribution. To increase performance, we propose training verifiers to judge the correctness of model completions. At test time, we generate many candidate solutions and select the one ranked highest by the verifier. We demonstrate that verification significantly improves performance on GSM8K, and we provide strong empirical evidence that verification scales more effectively with increased data than a finetuning baseline.

Answer verification is crucial not only for evaluating large language models (LLMs) by matching their unstructured outputs against standard answers, but also serves as the reward model to guide LLM optimization. Most evaluation frameworks rely on regularized matching or employ general LLMs for answer verification, which demands extensive, repetitive customization for regex rules or evaluation prompts. Two fundamental limitations persist in current methodologies: 1) the absence of comprehensive benchmarks that systematically evaluate verification capabilities across different LLMs; and 2) the nascent stage of verifier development, where existing approaches lack both the robustness to handle complex edge cases and the generalizability across different domains. In this work, we develop CompassVerifier, an accurate and robust lightweight verifier model for evaluation and outcome reward. It demonstrates multi-domain competency spanning math, knowledge, and diverse reasoning tasks, with the capability to process various answer types, including multi-subproblems, formulas, and sequence answers, while effectively identifying abnormal/invalid responses. We introduce VerifierBench benchmark comprising model outputs collected from multiple data sources, augmented through manual analysis of metaerror patterns to enhance CompassVerifier. We anticipate that CompassVerifier and VerifierBench will facilitate answer verification, evaluation protocols, and reinforcement learning research. Code and dataset are available at https://github.com/open-compass/CompassVerifier.

Mathematical verfier achieves success in mathematical reasoning tasks by validating the correctness of solutions. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedbacks as rationale labels (i.e., the correctness of the current step and the explanations). In this paper, we propose Math-Minos, a natural language feedback enhanced verifier by constructing automatically-generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set (30k) of natural language feedbacks can significantly boost the performance of the verifier by the accuracy of 1.6\% (86.6\% rightarrow 88.2\%) on GSM8K and 0.8\% (37.8\% rightarrow 38.6\%) on MATH. We have released our code and data for further exploration.

Post-training for reasoning of large language models (LLMs) increasingly relies on verifiable rewards: deterministic checkers that provide 0-1 correctness signals. While reliable, such binary feedback is brittle--many tasks admit partially correct or alternative answers that verifiers under-credit, and the resulting all-or-nothing supervision limits learning. Reward models offer richer, continuous feedback, which can serve as a complementary supervisory signal to verifiers. We introduce HERO (Hybrid Ensemble Reward Optimization), a reinforcement learning framework that integrates verifier signals with reward-model scores in a structured way. HERO employs stratified normalization to bound reward-model scores within verifier-defined groups, preserving correctness while refining quality distinctions, and variance-aware weighting to emphasize challenging prompts where dense signals matter most. Across diverse mathematical reasoning benchmarks, HERO consistently outperforms RM-only and verifier-only baselines, with strong gains on both verifiable and hard-to-verify tasks. Our results show that hybrid reward design retains the stability of verifiers while leveraging the nuance of reward models to advance reasoning.

Vision-language models (VLMs) have achieved strong performance in multimodal reasoning, yet they remain prone to generating plausible but incorrect answers. Self-verification offers a practical way to improve answer reliability without relying on external judges, but existing methods typically depend on a single verification criterion or fixed prompt, resulting in incomplete and unstable reliability estimates. We first systematically analyze how verifier capability and prompt design affect verification performance. Our findings show that stronger verifiers provide more reliable judgments, while verification performance is highly sensitive to prompt choice, with no single prompt consistently dominating across tasks. Guided by these findings, we propose MOTIVE, a Multi-View Self-VerificatiOn wiTh RelIability-Guided SelectiVE Rethinking framework for reliable multimodal reasoning. MOTIVE evaluates each candidate answer from complementary verification perspectives and learns a correctness-aligned reliability score through correctness-grounded multi-view verification learning. During inference, this score governs an accept-or-rethink decision, allowing reliable answers to be returned directly while uncertain ones trigger history-guided rethinking. Extensive experiments across diverse multimodal benchmarks and VLM backbones demonstrate that MOTIVE consistently outperforms strong self-verification and self-correction baselines. Further results show that reliable verification improves accept-or-rethink decisions and reduces unnecessary reasoning turns, enabling more reliable and efficient self-verification without an external judge.

Automated Essay Score (AES) is proven to be one of the cutting-edge technologies. Scoring techniques are used for various purposes. Reliable scores are calculated based on influential variables. Such variables can be computed by different methods based on the domain. The research is concentrated on the user's understanding of a given topic. The analysis is based on a scoring index by using Large Language Models. The user can then compare and contrast the understanding of a topic that they recently learned. The results are then contributed towards learning analytics and progression is made for enhancing the learning ability. In this research, the focus is on summarizing a PDF document and gauging a user's understanding of its content. The process involves utilizing a Langchain tool to summarize the PDF and extract the essential information. By employing this technique, the research aims to determine how well the user comprehends the summarized content.

Comprehensively evaluating AI agents across interactive environments is difficult due to fragmented tasks, scaffolds, verifiers, and scoring rules. Unfortunately, existing efforts to unify these evaluations are limited in scale and domain, making costly reruns necessary and leaving available data incomparable. We introduce MESSIER, a unified corpus of 957,611 records spanning 30 benchmarks, 745 agents, 11,891 tasks, and 74,263 verifiers. MESSIER combines public evaluation results with new runs on six underrepresented professional and scientific benchmarks, standardizing their heterogeneous components into a common schema. Using this corpus, we show that frontier progress is uneven across benchmark groups, with function-calling evaluations largely saturated, programming improving fastest, and enterprise workflows remaining most challenging. Counterfactual rescoring further shows that strict all-pass scoring in multi-verifier tasks can alter agent rankings. Finally, we derive capability scores from our corpus that correlate with Epoch's Evaluation Capability Index rankings at Spearman ho = 0.84. The scores can also be estimated for subsets defined by domain, occupation, action space, or verifier type. In essence, MESSIER is a reusable resource for studying agent performance at scale, and a basis for designing better evaluations.

Reinforcement learning (RL) has recently emerged as a compelling approach for enhancing the reasoning capabilities of large language models (LLMs), where an LLM generator serves as a policy guided by a verifier (reward model). However, current RL post-training methods for LLMs typically use verifiers that are fixed (rule-based or frozen pretrained) or trained discriminatively via supervised fine-tuning (SFT). Such designs are susceptible to reward hacking and generalize poorly beyond their training distributions. To overcome these limitations, we propose Tango, a novel framework that uses RL to concurrently train both an LLM generator and a verifier in an interleaved manner. A central innovation of Tango is its generative, process-level LLM verifier, which is trained via RL and co-evolves with the generator. Importantly, the verifier is trained solely based on outcome-level verification correctness rewards without requiring explicit process-level annotations. This generative RL-trained verifier exhibits improved robustness and superior generalization compared to deterministic or SFT-trained verifiers, fostering effective mutual reinforcement with the generator. Extensive experiments demonstrate that both components of Tango achieve state-of-the-art results among 7B/8B-scale models: the generator attains best-in-class performance across five competition-level math benchmarks and four challenging out-of-domain reasoning tasks, while the verifier leads on the ProcessBench dataset. Remarkably, both components exhibit particularly substantial improvements on the most difficult mathematical reasoning problems. Code is at: https://github.com/kaiwenzha/rl-tango.

Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited by selecting and prioritizing valid reasoning paths. However, we identify a critical limitation: scaling flaws, prevalent across different models (Mistral 7B and DeepSeekMath 7B), benchmarks (GSM8K and MATH), and verifiers (outcome value models and process reward models). As sample size increases, verifier-guided search exhibits diminishing advantages and eventually underperforms repeated sampling. Our analysis attributes this to verifier failures, where imperfect verifiers misrank candidates and erroneously prune all valid paths. These issues are further exacerbated in challenging and out-of-distribution problems, restricting search effectiveness. To mitigate verifier failures, we explore reducing reliance on verifiers and conduct preliminary investigations using two simple methods. Our findings reveal fundamental limitations in verifier-guided search and suggest 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.

While Reinforcement Learning with Verifiable Rewards (RLVR) is effective for deterministically checkable tasks, many vision-language tasks are partially verifiable, demanding multi-criteria supervision (e.g., perceptual details, reasoning steps, and constraints). Rubrics provide a natural interface for this fine-grained supervision, but their effectiveness depends on the execution accuracy during online RL. We propose Reinforcement Learning with Robust Rubric Rewards (RLR^3), extending RLVR from task-level verification to criterion-level verification. RLR^3 routes instance-specific rubrics through two execution paths: an LLM-as-an-extractor paired with a deterministic verifier, or an LLM-as-a-Judge for non-verifiable criteria. To ensure faithful scoring, RLR^3 introduce a minimal exposure strategy that masks ground truths from extractors and images from judges. Furthermore, RLR^3 employs hierarchical aggregation to prioritize essential criteria over additional criteria, and mitigates score saturation within rollout groups. Evaluated on Qwen3-VL-30B-A3B across 15 benchmarks, RLR^3 consistently outperforms RLVR, yielding a 4.7-point improvement over the base model and exceeding the official instruct-to-thinking model gap. Controlled audits confirm our deterministic verification and minimal exposure significantly reduce exploitable false positives.

Answer verification methods are widely employed in language model training pipelines spanning data curation, evaluation, and reinforcement learning with verifiable rewards (RLVR). While prior work focus on developing unified verifiers applicable across multiple reasoning scenarios, significant challenges remain in computation-oriented scientific domains, such as algebraic equivalence checking and physical constant substitution. In this paper, we introduce \model, a tool-augmented verifier that leverages external executors to perform precise computations and symbolic simplifications. \model enables robust verification that goes beyond simple semantic matching. We propose a novel two-stage pipeline, which begin with cold-start fine-tuning and followed by multi-turn reinforcement learning with tool integration. Extensive experiments conducted on STEM subjects, general QA, and long-form reasoning tasks demonstrates strong generalization of \model. The results shows that the \model achieves state-of-the-art performance on VerifyBench-Hard and SCI-Bench. And we also employ our \model in RLVR as a reward model, the results show that it consistently outperforms both rubric-based and model-based verifiers on AIME'24 and AIME'25, demonstrating strong potential to enhance reasoning capabilities of LLM. Our model is released at https://huggingface.co/Nanbeige/CoSineVerifier-Tool-4B{https://huggingface.co/Nanbeige/CoSineVerifier-Tool-4B}.

Large language models have made significant progress in mathematical reasoning, which serves as an important testbed for AI and could impact scientific research if further advanced. By scaling reasoning with reinforcement learning that rewards correct final answers, LLMs have improved from poor performance to saturating quantitative reasoning competitions like AIME and HMMT in one year. However, this approach faces fundamental limitations. Pursuing higher final answer accuracy doesn't address a key issue: correct answers don't guarantee correct reasoning. Moreover, many mathematical tasks like theorem proving require rigorous step-by-step derivation rather than numerical answers, making final answer rewards inapplicable. To push the limits of deep reasoning, we believe it is necessary to verify the comprehensiveness and rigor of mathematical reasoning. Self-verification is particularly important for scaling test-time compute, especially for open problems without known solutions. Towards self-verifiable mathematical reasoning, we investigate how to train an accurate and faithful LLM-based verifier for theorem proving. We then train a proof generator using the verifier as the reward model, and incentivize the generator to identify and resolve as many issues as possible in their own proofs before finalizing them. To maintain the generation-verification gap as the generator becomes stronger, we propose to scale verification compute to automatically label new hard-to-verify proofs, creating training data to further improve the verifier. Our resulting model, DeepSeekMath-V2, demonstrates strong theorem-proving capabilities, achieving gold-level scores on IMO 2025 and CMO 2024 and a near-perfect 118/120 on Putnam 2024 with scaled test-time compute.

Large Language Models (LLMs) have demonstrated impressive problem-solving capabilities in mathematics through step-by-step reasoning chains. However, they are susceptible to reasoning errors that impact the quality of subsequent reasoning chains and the final answer due to language models' autoregressive token-by-token generating nature. Recent works have proposed adopting external verifiers to guide the generation of reasoning paths, but existing works utilize models that have been trained with step-by-step labels to assess the correctness of token-by-token reasoning chains. Consequently, they struggle to recognize discriminative details of tokens within a reasoning path and lack the ability to evaluate whether an intermediate reasoning path is on a promising track toward the correct final answer. To amend the lack of sound and token-grained math-verification signals, we devise a novel training scheme for verifiers that apply token-level supervision with the expected cumulative reward (i.e., value). Furthermore, we propose a practical formulation of the cumulative reward by reducing it to finding the probability of future correctness of the final answer and thereby enabling the empirical estimation of the value. Experimental results on mathematical reasoning benchmarks show that Token-Supervised Value Model (TVM) can outperform step-by-step verifiers on GSM8K and MATH with Mistral and Llama.

A classical intuition holds that verifying a solution is easier than producing one. For today's coding agents, this intuition is being inverted: as foundation models develop stronger reasoning capabilities and engineering harnesses grow more sophisticated, generating complex candidate solutions is no longer difficult -- reliably verifying them has become the harder problem. Every verifier we can build is only a proxy for human intent, never the intent itself. This makes verification subject to a twofold difficulty: first, intent is underspecified by nature, making it inherently hard to faithfully check whether it has been fulfilled; second, during model training, optimization widens the gap between proxy and intent -- manifesting as reward hacking or signal saturation. To address this, we characterize the quality of verification signals along three dimensions -- scalability, faithfulness, and robustness -- and argue that achieving all three simultaneously is the central challenge. We further study four reward constructions: a test verifier for general coding tasks, a rubric verifier for frontend tasks, the user as verifier for real-world agent tasks, and an automated agent verifier for long-horizon tasks. Across different task types and policy capability levels, we conduct in-depth analysis and experiments on the core challenges of reward design and how to more effectively leverage reward signals. Experiments show that targeted verification design can effectively suppress reward hacking, improve task completion quality, and achieve significant gains across multiple internal and public benchmarks. These experiences collectively point to a core observation: no fixed reward function can remain effective as policy capability continues to grow; and verification must co-evolve with the generator.

Routine complete blood counts (CBCs) could yield new biomarkers, but the private records needed to evaluate candidates cannot be shared with frontier language model agents that excel at discovery. We distilled the evidence held in the Clalit Health Services panel of over 5.4 million patients into a released scoring tool: for each of 13 immune-mediated diseases, a graph attention network was trained inside the data boundary to predict the case-control AUC of candidate CBC expressions, and only the trained weights were released. The tool grounds an agent's propose-score-refine loop in real-world data without exposing any patient data. In external validation, agent-discovered expressions improved on their literature-seeded starting points by a median of 4.18 AUC percentage points, and across three independent cohorts, reranking the candidates of three frontier research tools improved on their first choices in most comparisons, with gains that varied by cohort. The released scorer supports privacy-preserving biomarker hypothesis generation.

Large language models (LLMs) continue to struggle with mathematical reasoning, and common post-training pipelines often reduce each generated solution to a binary outcome: correct or incorrect. This perspective is limiting in practice, as failures in chain-of-thought (CoT) reasoning are frequently structured; solutions may appear convincing while containing subtle logical, algebraic, or numerical flaws. Meanwhile, reinforcement learning from human feedback (RLHF) variants that rely on large reward models or LLM-as-a-judge signals are often expensive, difficult to scale, and unstable to iterate. We propose a lightweight and pragmatic post-training pipeline that targets such structured errors under realistic compute budgets. Starting from supervised fine-tuning (SFT) on MetaMathQA-style CoT data, we introduce a compact MathVerifier that decomposes a candidate solution into a six-dimensional error profile and aggregates it into interpretable wrongness and absurdity scores. These verifier signals serve two roles: (i) mining hard negatives that are near-correct yet structurally flawed, and (ii) defining per-sample importance weights that emphasize the most informative preference pairs. We integrate both into an offline Direct Preference Optimization (DPO) objective via a verifier-guided weighted formulation. Experiments on a 1.5B-parameter Qwen2.5 model show that verifier-guided, weighted DPO yields more targeted improvements than vanilla SFT and unweighted DPO, particularly on problems where solutions are numerically close to correct but logically inconsistent, while avoiding the overhead of training large reward models or relying on external judges.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

Automated formal verification remains challenging for large language models because data for proof assistants and verification-aware languages is scarce, and correctness depends on satisfying precise machine-checkable specifications rather than producing plausible code. This thesis studies how verifier environments can improve LLM generation of verified programs and proofs through reinforcement learning from verifiable rewards (RLVR) and verifier-guided inference-time search. First, we train open-source models in Dafny with RLVR using Group Relative Policy Optimization (GRPO) and related variants, assembling generated candidates into complete programs and scoring them with compiler and verifier outcomes. Initial experiments on an APPS-derived Dafny dataset increased verified reward from 2.2% to 58.1%, but revealed specification hacking, where models exploit weak formal specifications instead of implementing the intended solutions. After filtering underspecified and vulnerable tasks, multi-turn RLVR on the refined benchmark improves the verified pass rate from 9.7% to 31.1%. Second, we develop a verifier-guided inference scaffold in Lean that treats proof generation as structured search over decomposed subgoals, verifier feedback, diagnostics, and repair. With a fixed base model, the full scaffold with proof reviser improves pass rate on an initial VeriCoding pilot set from 46.2% under direct repair to 69.2%. On the larger VERINA dataset, whole-task decomposition plus proof reviser solves 7 of 42 previously unsolved tasks. We also introduce Dalek-Bench, a repository-scale Lean benchmark derived from the Rust curve25519-dalek verification project; preliminary results remain weak, indicating that stronger progress evaluation and task-specific tool-use policies are still needed.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Large Language Models (LLMs) demonstrate strong capabilities for solving scientific and mathematical problems, yet they struggle to produce valid, challenging, and novel problems - an essential component for advancing LLM training and enabling autonomous scientific research. Existing problem generation approaches either depend on expensive human expert involvement or adopt naive self-play paradigms, which frequently yield invalid problems due to reward hacking. This work introduces VHG, a verifier-enhanced hard problem generation framework built upon three-party self-play. By integrating an independent verifier into the conventional setter-solver duality, our design constrains the setter's reward to be jointly determined by problem validity (evaluated by the verifier) and difficulty (assessed by the solver). We instantiate two verifier variants: a Hard symbolic verifier and a Soft LLM-based verifier, with evaluations conducted on indefinite integral tasks and general mathematical reasoning tasks. Experimental results show that VHG substantially outperforms all baseline methods by a clear margin.

In realistic education, a solution is often expressed not only in words but in a drawing--a circuit, a geometric construction, a function plot--and a teacher must grade the drawing as carefully as the text. Recent advances in unified multimodal models have enabled scientific image generation, yet verifying the correctness of these specialized visual outputs remains a critical bottleneck: errors often arise from intricate domain knowledge, structural reasoning, and multi-step instruction rather than surface-level artifacts. Existing verifiers mainly target natural images and compress judgement into scalar scores, leaving scientific coverage and explainable feedback for error correction underexplored. To bridge this gap, we make three main contributions. (1) We construct SciGen-Verify, a benchmark dedicated to explainable verification of scientific image generation, spanning instruction following, multidisciplinary reasoning, and world knowledge domains. It contains a three-tier hierarchical protocol over the binary judgement, supporting explanation, and corrective editing instruction. (2) We develop SciGen-Verifier, a reasoning-driven multimodal verifier trained via cold-start supervised fine-tuning followed by a curriculum-based two-stage reinforcement learning pipeline. The rubric-guided process rewards first strengthen scientific reasoning exploration and outcome rewards subsequently align output with ground-truth annotation. (3) On SciGen-Verify, SciGen-Verifier achieves competitive performance against much larger proprietary models. It further serves as a practical online critic for iterative image rectification.

Recent Language Models (LMs) have shown impressive capabilities in generating texts with the knowledge internalized in parameters. Yet, LMs often generate the factually incorrect responses to the given queries, since their knowledge may be inaccurate, incomplete, and outdated. To address this problem, previous works propose to augment LMs with the knowledge retrieved from an external knowledge source. However, such approaches often show suboptimal text generation performance due to two reasons: 1) the model may fail to retrieve the knowledge relevant to the given query, or 2) the model may not faithfully reflect the retrieved knowledge in the generated text. To overcome these, we propose to verify the output and the knowledge of the knowledge-augmented LMs with a separate verifier, which is a small LM that is trained to detect those two types of errors through instruction-finetuning. Then, when the verifier recognizes an error, we can rectify it by either retrieving new knowledge or generating new text. Further, we use an ensemble of the outputs from different instructions with a single verifier to enhance the reliability of the verification processes. We validate the effectiveness of the proposed verification steps on multiple question answering benchmarks, whose results show that the proposed verifier effectively identifies retrieval and generation errors, allowing LMs to provide more factually correct outputs. Our code is available at https://github.com/JinheonBaek/KALMV.

Large language model (LLM)-based reasoning systems have recently achieved gold medal-level performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also sufficiently supported. To train LLM-based reasoners in such challenging, open-ended settings, strong verifiers capable of catching step-level mistakes are necessary prerequisites. We introduce Hard2Verify, a human-annotated, step-level verification benchmark produced with over 500 hours of human labor. Hard2Verify is designed to rigorously assess step-level verifiers at the frontier: Verifiers must provide step-level annotations or identify the first error in responses generated by frontier LLMs for very recent, challenging, and open-ended math questions. We evaluate 29 generative critics and process reward models, demonstrating that, beyond a few standouts, open-source verifiers lag closed source models. We subsequently analyze what drives poor performance in step-level verification, the impacts of scaling verifier compute, as well as fundamental questions such as self-verification and verification-generation dynamics.

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.

Machine reading comprehension (MRC) is an AI challenge that requires machine to determine the correct answers to questions based on a given passage. MRC systems must not only answer question when necessary but also distinguish when no answer is available according to the given passage and then tactfully abstain from answering. When unanswerable questions are involved in the MRC task, an essential verification module called verifier is especially required in addition to the encoder, though the latest practice on MRC modeling still most benefits from adopting well pre-trained language models as the encoder block by only focusing on the "reading". This paper devotes itself to exploring better verifier design for the MRC task with unanswerable questions. Inspired by how humans solve reading comprehension questions, we proposed a retrospective reader (Retro-Reader) that integrates two stages of reading and verification strategies: 1) sketchy reading that briefly investigates the overall interactions of passage and question, and yield an initial judgment; 2) intensive reading that verifies the answer and gives the final prediction. The proposed reader is evaluated on two benchmark MRC challenge datasets SQuAD2.0 and NewsQA, achieving new state-of-the-art results. Significance tests show that our model is significantly better than the strong ELECTRA and ALBERT baselines. A series of analysis is also conducted to interpret the effectiveness of the proposed reader.

We show that on-policy reinforcement learning with verifiable rewards (RLVR) can improve the current objective while making successful behaviors for later objectives too rare to sample and reinforce. We call this verifier-induced support reshaping and define effective rewardable support as successful trajectories reachable within a fixed rollout budget. Across two model families, we study this effect through repeated verifier-scored sampling and bidirectional training on mathematical reasoning and constrained instruction following, including sequential training with the opposite verifier. Math-RLVR raises average instruction-following success but reduces the number of prompts with any successful response under repeated sampling. On IFEval with Qwen3-8B-Base, pass@1 rises by 6.5 percentage points while best@32 falls by 9.8 percentage points, and the same divergence appears across both models and IF benchmarks. Conversely, IF-RLVR shifts math responses from step-by-step openings toward direct answers, lowers best@k across sampling budgets, and reduces reward variation for later Math-RLVR. Token-distribution analyses and controlled opening interventions show that these changes concentrate in the first few response tokens. RLVR mainly reranks openings already available in the base policy, and the selected opening causally affects math searchability. The tested reference-policy constraints, routing priors, and on-policy distillation preserve cross-task support only partially; MathIF and ReasonIF show that marginal gains translate only partly into responses that are both correct and constraint-following. Therefore, endpoint improvements do not guarantee future trainability or joint capability under on-policy optimization. Code is available at https://github.com/sylvain-wei/verifier-induced-support-reshaping

While tool-augmented Large Language Models have significantly improved multi-step reasoning in quantitative STEM tasks, a critical residual failure mode remains: intermediate reasoning steps that are syntactically well-formed, mathematically executable, and unit-consistent, yet contextually ungrounded. Current approaches either rely on formal verifiers that cannot assess semantic intent, or burden Process Reward Models (PRMs) with the dual task of checking both arithmetic and logic. In this paper, we propose a neuro-symbolic framework that cleanly decouples reasoning into two formal dimensions: Symbolic Validity (V) and Semantic Groundedness (G). We guarantee V by construction using a deterministic symbolic verifier acting as a hard filter. To assess G, we train a PRM conditionally on the verifier-accepted manifold. To train this PRM efficiently, we introduce Counterfactual Symbolic Perturbation (CSP), a novel data synthesis strategy that algorithmically generates constraint-preserving hard negatives (steps that perfectly pass the verifier but are logically flawed). At inference, we deploy a verifier-first constrained search that guarantees execution consistency for verifier-covered operations while relying on the PRM solely to rank semantic grounding. By targeting the exact residual error class of strong tool-using LLMs, our method significantly improves reasoning reliability without the sprawling heuristics of prior frameworks.

Metrics like FactScore and VeriScore that evaluate long-form factuality operate by decomposing an input response into atomic claims and then individually verifying each claim. While effective and interpretable, these methods incur numerous LLM calls and can take upwards of 100 seconds to evaluate a single response, limiting their practicality in large-scale evaluation and training scenarios. To address this, we propose VeriFastScore, which leverages synthetic data to fine-tune Llama3.1 8B for simultaneously extracting and verifying all verifiable claims within a given text based on evidence from Google Search. We show that this task cannot be solved via few-shot prompting with closed LLMs due to its complexity: the model receives ~4K tokens of evidence on average and needs to concurrently decompose claims, judge their verifiability, and verify them against noisy evidence. However, our fine-tuned VeriFastScore model demonstrates strong correlation with the original VeriScore pipeline at both the example level (r=0.80) and system level (r=0.94) while achieving an overall speedup of 6.6x (9.9x excluding evidence retrieval) over VeriScore. To facilitate future factuality research, we publicly release our VeriFastScore model and synthetic datasets.

Verifiable rewards have advanced reinforcement learning in mathematics and code. However, many valuable open-ended tasks share three properties: no automatic verifier of overall quality, multiple requirements to satisfy jointly, and multiple valid responses to each query. Training therefore needs feedback on requirement satisfaction across different valid responses. Rubric-based reinforcement learning provides this feedback by aggregating scores from explicit criteria. As learning progresses unevenly, some criteria become fully satisfied and lose discrimination while others remain informative. Dynamic methods revise shared rubrics or select evolving criteria to restore discrimination, but may also change useful criteria. To address this, we propose Reinforcement Learning with Adaptive Rubric Evolution (RARE). The core idea is to use current policy feedback to guide both which criteria change and what their replacements assess. Sample-level updates replace criteria fully satisfied across current outputs with checks of remaining quality differences, retaining all other criteria and scores. Within this rule, we compare rewarding desirable qualities with penalizing observed flaws. Video script generation exemplifies these properties and supports content production. Its demands for coherent, executable narratives under constraints make it a challenging testbed. Targeting flaws performs best across three video types with a mean gain of 3.82 points over matched static rubrics. Model and human preferences support these gains. Improvements also extend to writing and general generation benchmarks.

Fine-grained credit assignment is a central challenge in reinforcement learning for long horizon LLM agents. Standard objectives often train from programmatically verifiable terminal rewards by broadcasting each sparse outcome to every action in a trajectory. Existing methods typically seek finer credit from the rollout side, constructing auxiliary trajectory signals or additional comparisons to estimate action importance. Although useful, these approaches still treat the verifier that judged success as a scalar reward, discarding its internal task structure. Our key insight is that many verifiable tasks already encode the relevant checks inside their terminal verifier. We propose VICT (VerifierInstrumented Credit Tracing), a training-time interface that exposes executable or evidence backed atoms and traces them back to actions through dependency-valid proof edges. VICT redistributes group-relative advantage only along those edges, shifting credit assignment from rollout-side inference to verifierside tracing. It preserves the original terminal reward, abstains when evidence is incomplete or ambiguous, and changes only the training-time advantage tensor, requiring no learned critic, process labels, branch rollouts, or inference-time verifier access. On ALFWorld and WebShop, VICT improves substantially over outcome-only training and achieves strong performance alongside recent fine-grained credit methods; ablations rule out dense atom rewards, final-commit credit, temporal proximity, and sparsity as sufficient explanations.

Autonomous research agents produce competitive solutions and professional-looking manuscripts, yet their outputs contain verifiability failures undetectable by surface-level evaluation: fabricated citations, unreproducible scores, and method descriptions that diverge from the implementation. We address this through three contributions. First, Chain-of-Evidence (CoE), a verifiability framework requiring every claim to be traceable to its evidence source. Second, ScientistOne, an end-to-end autonomous research system that maintains evidence chains by construction throughout literature review, solution discovery, and paper writing. Third, CoE Audit, a post-hoc audit whose four integrity checks -- score verification, specification violation, reference verification, and method-code alignment -- apply uniformly to all systems. Across 75 papers spanning five systems and five frontier research tasks, every baseline exhibits at least one systematic failure mode: hallucinated reference rates reach 21%, score verification passes in as few as 42% of papers, and method-code alignment ranges from 20% to 80%. ScientistOne achieves zero hallucinated references (0/337), perfect score verification (12/12), and the highest method-code alignment (14/15), while matching or exceeding human expert performance on all five tasks. ScientistOne further generalizes to six additional tasks spanning medical imaging, fine-grained recognition, 3D perception, and language modeling, achieving state-of-the-art on Parameter Golf and gold medals on MLE-Bench tasks where baselines fail entirely.

Reinforcement Learning with Verifiable Rewards (RLVR) has driven recent progress in reasoning-oriented large language models (LLMs) by enabling large-scale optimization. However, its applicability remains largely limited to domains such as mathematics and coding, where correctness can be deterministically verified. Open-ended tasks instead often rely on human preferences, reward models, or LLM-based judges, introducing evaluation bias, judge capability bottlenecks, and additional inference costs.Drawing on the principle of self-supervised learning, which constructs pretext tasks to derive supervision from the data itself, we propose Reinforcement Learning with Self-Verifiable Rewards (RLSVR), a task-transformation-based training paradigm for extending RLVR to open-ended tasks. RLSVR transforms open-ended tasks into verifiable proxy environments whose internal rules and interaction outcomes automatically generate reward signals. We instantiate RLSVR with SpyRL, a multi-agent self-play environment inspired by Who Is the Spy?. Agents receive asymmetric information, complete the same target task, and vote to identify a designated spy. Because the spy identity is predetermined, voting outcomes provide fully verifiable rewards, while successful identification remains closely related to output quality. Experiments on text summarization, creative writing, and mathematical reasoning show that SpyRL outperforms existing self-improvement methods on non-verifiable tasks and yields consistent gains on verifiable reasoning tasks. These results demonstrate that task transformation can extend scalable RLVR-based self-improvement beyond inherently verifiable domains. Models and code have been released at https://github.com/wangqinsi1/SpyRL.

Verifiers play a crucial role in large language model (LLM) reasoning, needed by post-training techniques such as reinforcement learning. However, reliable verifiers are hard to get for difficult coding problems, because a well-disguised wrong solution may only be detected by carefully human-written edge cases that are difficult to synthesize. To address this issue, we propose HARDTESTGEN, a pipeline for high-quality test synthesis using LLMs. With this pipeline, we curate a comprehensive competitive programming dataset HARDTESTS with 47k problems and synthetic high-quality tests. Compared with existing tests, HARDTESTGEN tests demonstrate precision that is 11.3 percentage points higher and recall that is 17.5 percentage points higher when evaluating LLM-generated code. For harder problems, the improvement in precision can be as large as 40 points. HARDTESTS also proves to be more effective for model training, measured by downstream code generation performance. We will open-source our dataset and synthesis pipeline at https://leililab.github.io/HardTests/.

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.

Verifiable instruction-following benchmarks emphasize output-constraint satisfaction but can overlook whether responses meaningfully answer the underlying request, creating an evaluation blind spot. We show that frontier models can receive full credit for responses with little substantive answer content. Using the same verifier-based criterion as a training reward can induce reward hacking, as publicly released checkpoints exhibit higher constraint satisfaction but lower response quality after reinforcement learning with verifiable rewards. To address this reward hacking, we introduce CALIF, a lightweight method that augments verifier rewards with a calibrated likelihood-based bonus to preserve response quality. CALIF evaluates response likelihood under the request alone using the existing frozen reference policy, requiring no additional judge or learned reward model. Across models ranging from 1.7B to 8B in reasoning and non-reasoning modes, CALIF improves constraint satisfaction on IFBench while maintaining response quality near or above pre-RL levels. It also outperforms corresponding base policies in 40 of 45 model-metric comparisons across three rubric-based instruction-following benchmarks, demonstrating gains beyond training verifiers.

The recent paradigm shift towards training large language models (LLMs) using DeepSeek-R1-Zero-style reinforcement learning (RL) on verifiable rewards has led to impressive advancements in code and mathematical reasoning. However, this methodology is limited to tasks where rule-based answer verification is possible and does not naturally extend to real-world domains such as chemistry, healthcare, engineering, law, biology, business, and economics. Current practical workarounds use an additional LLM as a model-based verifier; however, this introduces issues such as reliance on a strong verifier LLM, susceptibility to reward hacking, and the practical burden of maintaining the verifier model in memory during training. To address this and extend DeepSeek-R1-Zero-style training to general reasoning domains, we propose a verifier-free method (VeriFree) that bypasses answer verification and instead uses RL to directly maximize the probability of generating the reference answer. We compare VeriFree with verifier-based methods and demonstrate that, in addition to its significant practical benefits and reduced compute requirements, VeriFree matches and even surpasses verifier-based methods on extensive evaluations across MMLU-Pro, GPQA, SuperGPQA, and math-related benchmarks. Moreover, we provide insights into this method from multiple perspectives: as an elegant integration of training both the policy and implicit verifier in a unified model, and as a variational optimization approach. Code is available at https://github.com/sail-sg/VeriFree.

The rapid proliferation of large language models (LLMs) and the growing diversity of their applications presents a unique optimization opportunity: selecting the right model for the task, while optimizing for speed, cost, and quality at a per-task level. However, inference endpoints can vary widely in quality, price, latency, context support, tool use, domain expertise, and reasoning behavior. This heterogeneity makes manual heuristics difficult to maintain and unlikely to achieve consistently favorable speed--cost--quality trade-offs on their own. We introduce , a lightweight GLiClass-based router that assigns a suitability score to each inference-time model label without autoregressive generation. The released 0.6B-parameter checkpoint combines a Qwen3 decoder with a shallow bidirectional scorer. Its decoder-KV execution path preserves a text-only key--value cache across a session, encodes only new dialogue turns, and evaluates transient candidate-label tokens without adding them to the persistent cache. The same checkpoint also predicts task type, difficulty, reasoning mode, and expected output length, and supports custom zero-shot labels. For task generation, we construct a task ontology with 23 families, 115 task types, 345 routable subtypes, 1,173 synthetic examples, and an orthogonal axis of 30 domains. Using this structure, we generate 150,000 verifier-scored tasks and 15,000 open-ended tasks. We then train the Qwen3 decoder on these tasks, while explicitly separating learned request prediction from per-task policies for attributes such as eligibility, cost, cache reuse, safety, and sovereignty. Across six LiveBench subsets, the router outperforms the mean candidate; on the selected 1,000-task subset, it achieves an aggregate top-1 score of 0.707 versus 0.696 for the strongest fixed model, with benchmark-dependent gains.

When should an AI system's answer be trusted? Formal proof assistants offer certainty but cannot reach most of the problem distribution; scalar LLM judges offer coverage but produce opaque scores that cannot be audited after the fact and are subject to the same coherence issues as any LLM. We present Theoria, a verification architecture that closes this gap. A candidate solution is rewritten into a sequence of typed state transitions, each licensed by an explicit justification, whether that be a citation, computation, or problem-given fact, and every transition is independently auditable. The foundational invariant is completeness of change: every difference between consecutive proof states must be accounted for, so hidden premises surface as unlicensed mutations rather than passing silently. On HLE-Verified Gold (185 text-only expert problems), Theoria certifies 105 at 91.4% strict precision (Wilson 95% CI [84.5%, 95.4%]). Every certification produces a human readable proof trace in which each step can be independently challenged. Holistic LLM judges achieve comparable precision at matched coverage but fail on different problems (Jaccard 0.14-0.36), making the approaches complementary. On 95 adversarial poisoned proofs across 15 domains, structured judges catch 94.7% versus 83.2% for holistic judging (p= 0.0017). The overall 11.5 pp gap concentrates in hidden premises (90.6% vs. 62.5%, a 28 pp difference) and fabricated citations (100% vs. 90%), the error classes where the formal analysis predicts an advantage; performance is identical on arithmetic and theorem-misapplication errors, where no advantage is predicted. On GPQA Diamond (n= 65), certified precision is 97.1% (Wilson CI [85.1%, 99.5%]).

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.

Recent advancements in tree search algorithms guided by verifiers have significantly enhanced the reasoning capabilities of large language models (LLMs), but at the cost of increased computational resources. In this work, we identify two key challenges contributing to this inefficiency: over-exploration due to redundant states with semantically equivalent content, and under-exploration caused by high variance in verifier scoring leading to frequent trajectory switching. To address these issues, we propose FETCH, an efficient tree search framework, which is a flexible, plug-and-play system compatible with various tree search algorithms. Our framework mitigates over-exploration by merging semantically similar states using agglomerative clustering of text embeddings obtained from a fine-tuned SimCSE model. To tackle under-exploration, we enhance verifiers by incorporating temporal difference learning with adjusted lambda-returns during training to reduce variance, and employing a verifier ensemble to aggregate scores during inference. Experiments on GSM8K, GSM-Plus, and MATH datasets demonstrate that our methods significantly improve reasoning accuracy and computational efficiency across four different tree search algorithms, paving the way for more practical applications of LLM-based reasoning. The code is available at https://github.com/Soistesimmer/Fetch.

AI systems now write long and difficult mathematical proofs, and checking their step-by-step validity is becoming a bottleneck. A learned verifier could check proofs cheaply, but training one requires a correctness label on every step, and such labels are hard to obtain for open-ended proofs. Existing methods take them from human annotators, which is costly, or derive them from final answers, which proofs do not have, and formalizing each proof in Lean requires expert effort. We introduce LeanPRM, a framework that uses the Lean proof assistant to create step-level labels for natural-language proofs. A model writes a natural-language proof together with a paired formal proof, without feedback from Lean. Lean then labels every step, and a second model discards failures caused only by the formal syntax, so that the negative labels mark errors in the mathematics. LeanPRM contains 10,634 proofs with 152K labeled steps and no human annotation. A Qwen3-4B verifier trained on LeanPRM raises exact step-label accuracy on a held-out set of 200 proofs (LeanPRM-Bench) from 48.2 to 74.7, as opposed to 60.3 when the same base model is trained on PRM800K. It also selects better proofs in best-of-N selection on IMO-level problems, and outperforms the PRM800K-trained verifier on three of four external verification benchmarks. Training on LeanPRM improves verifiers at every size from 0.6B to 8B parameters on LeanPRM-Bench, Hard2Verify and IMO-GradingBench. Given the labels need no human annotation, LeanPRM can grow with the supply of formal statements, offering a path to step-level feedback on AI-generated proofs that are hard for humans to check.

Large language models often produce plausible numerical claims from financial filings while using the wrong reporting period, unit, line item, or formula. Verifying such claims requires more than rechecking arithmetic: a verifier must ground the relevant facts, establish the authorized calculation, and determine whether the candidate value follows from both. We propose VeriFin, a neurosymbolic verification framework for numerical financial question answering that grounds operands in filed XBRL facts, derives calculations from the question, filing linkbases, or documented metric definitions, and checks claims using Z3. When a claim is inconsistent, solver-derived unsatisfiable cores identify the conflicting facts, formula, and candidate value, enabling targeted repair. We evaluate VeriFin on XBRLFiling, a new 600-question benchmark constructed from 10-K filings of 28 U.S. companies, and on FinanceBench. On fixed candidate pools shared by all verification methods, VeriFin accepts none of the incorrect claims, whereas the baselines accept 6 to 92 incorrect claims on XBRLFiling's 600 claims and 4 to 21 incorrect claims on FinanceBench's 67 claims. The zero false-accept result persists across multiple answer-generator models. Solver-derived feedback further improves repair, achieving up to 69.9% recovery among true catches. These results show that source-grounded symbolic verification can provide a reliable and auditable acceptance control for LLM-generated financial claims.

Split language models keep input text on a client but send intermediate representations to a server. Attacks can reconstruct text from these messages. Comparing privacy evaluations is difficult when attackers see different messages, know different model weights or use different datasets and recovery measures. We present LLM-Attacker, a framework that records these choices and lets researchers check, compare and extend an evaluation. Compatible attacks reuse recorded messages, and their predictions are saved for independent scoring. The scoring rule requires a linked undefended reference before a defence can pass. Reports also identify attacks that remain untested. In a controlled GPT-2 experiment, adding gradients returned during training increased token recovery from 94.20% to 97.38% and exact-document recovery from 13.71% to 37.77%. The 95% interval for the token gain lay above the two-percentage-point threshold fixed before testing. This experiment is shared with a companion study; here, it tests how the evaluation responds to a change in attacker access. Further studies measure how corpus choice and compression defences affect recovery, compare an adapted published attack with its reference implementation, and test the measurement code. The framework reports implementation checks separately from measured attack effectiveness. Each privacy claim should state the attacker, dataset and scoring rule, report its controls and identify untested attacks.

As LLMs are deployed in high-stakes settings, users must judge the correctness of individual responses, often relying on model-generated justifications such as reasoning chains or explanations. Yet, no standard measure exists for whether these justifications help users distinguish correct answers from incorrect ones. We formalize this idea as error verifiability and propose v_{bal}, a balanced metric that measures whether justifications enable raters to accurately assess answer correctness, validated against human raters who show high agreement. We find that neither common approaches, such as post-training and model scaling, nor more targeted interventions recommended improve verifiability. We introduce two methods that succeed at improving verifiability: reflect-and-rephrase (RR) for mathematical reasoning and oracle-rephrase (OR) for factual QA, both of which improve verifiability by incorporating domain-appropriate external information. Together, our results establish error verifiability as a distinct dimension of response quality that does not emerge from accuracy improvements alone and requires dedicated, domain-aware methods to address.

Coding agents spend substantial computation generating actions and processing long interaction histories. Poor action choices can steer agents into low-value states, wasting computation and increasing API costs. Sampling and verifying alternative actions can improve the agent's decisions, but applying this procedure at every step adds substantial overhead. We introduce SWE-Verifier, a lightweight generative model that selectively triggers candidate sampling and verification. It scores the coding agent's proposed action to determine when additional candidate sampling is needed, then ranks the resulting actions before execution. We train SWE-Verifier from Qwen3.5-4B using preference data that groups contrasting actions with their resulting environment observations and rubric-guided teacher scores. Using the mini-swe-agent harness, SWE-Verifier improves resolution from 75.47% to 77.20% on MiniMax-M2.7 at 1.09 times cost and generalizes to DeepSeek-V4-Flash without training on its actions, improving resolution from 72.60% to 74.27% at 1.13 times cost. Across both models, SWE-Verifier verifies fewer than 4% of steps and achieves comparable or higher resolution than the trajectory and all-step baselines at substantially lower cost. These results demonstrate that selective candidate sampling and lightweight verification provide complementary gains in coding-agent performance and inference efficiency. Our model, code, and data are available at https://github.com/zkjzou/SWE-Verifier.

Scaling robot data and model capacity has improved Vision-Language-Action (VLA) policies, but further progress is constrained by the high cost of robotic data. Verifier-guided test-time scaling offers an efficient alternative by sampling multiple action candidates and selecting the one most likely to lead to task success at inference time. Existing classification-based verifiers learn from trajectory-level outcomes but treat all visited states equally, even though their value for candidate discrimination can vary across a trajectory. At many states, plausible actions are similar and provide limited discrimination signal, while only a sparse set of decision-critical states admits meaningfully different actions that can substantially affect downstream outcomes. To address this, we propose DiVeR, which estimates decision criticality from the dispersion of sampled action representations. DiVeR then uses this signal to reweight verifier learning toward states where action selection is most consequential, without requiring step-level annotations or additional environment interaction. Across LIBERO, RoboCasa, and real-world experiments on a Franka Research 3 robot, DiVeR consistently improves task success through more effective verifier-guided action selection, while adding negligible verifier inference overhead.

Agentic reinforcement learning (RL) holds great promise for the development of autonomous agents under complex GUI tasks, but its scalability remains severely hampered by the verification of task completion. Existing task verification is treated as a passive, post-hoc process: a verifier (i.e., rule-based scoring script, reward or critic model, and LLM-as-a-Judge) analyzes the agent's entire interaction trajectory to determine if the agent succeeds. Such processing of verbose context that contains irrelevant, noisy history poses challenges to the verification protocols and therefore leads to prohibitive cost and low reliability. To overcome this bottleneck, we propose SmartSnap, a paradigm shift from this passive, post-hoc verification to proactive, in-situ self-verification by the agent itself. We introduce the Self-Verifying Agent, a new type of agent designed with dual missions: to not only complete a task but also to prove its accomplishment with curated snapshot evidences. Guided by our proposed 3C Principles (Completeness, Conciseness, and Creativity), the agent leverages its accessibility to the online environment to perform self-verification on a minimal, decisive set of snapshots. Such evidences are provided as the sole materials for a general LLM-as-a-Judge verifier to determine their validity and relevance. Experiments on mobile tasks across model families and scales demonstrate that our SmartSnap paradigm allows training LLM-driven agents in a scalable manner, bringing performance gains up to 26.08% and 16.66% respectively to 8B and 30B models. The synergizing between solution finding and evidence seeking facilitates the cultivation of efficient, self-verifying agents with competitive performance against DeepSeek V3.1 and Qwen3-235B-A22B.

Large language models often solve a theorem forward yet fail to disprove a closely related false one: a falsification gap that supervised fine-tuning does not close and can actively worsen. We frame counterexample generation as constrained witness emission against a deterministic per-theorem Python verifier, and release SymCE, a corpus of 4,707 false undergraduate-algebra and real-analysis conjectures, each paired with executable verifiers. The verifier also serves as the reward function, making SymCE a training environment. Training Qwen3-4B with SFT followed by GRPO under this oracle reveals an imitation trap: counterexample-only SFT collapses true-theorem recognition from 0.27 to 0.00, while RLVR with a sparse outcome-only reward repairs this and exceeds the base, to 0.66. The collapse replicates across four seeds and on Gemma-3-4B. Sparse and dense rewards yield statistically indistinguishable in-domain success yet diverge by 33 points on a held-out calibration probe, a dissociation we trace to the partial-credit term. Our 4B model outperforms every evaluated 7B open-weights math specialist, remains competitive with six frontier commercial APIs, and transfers under unchanged prompting to GSM8K, MATH-500 and MMLU-college-math. A human audit of 177 verifier decisions finds 97.7% accuracy. Code, data, verifier modules and annotations: https://github.com/ce-rlvr/SymCE.

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

Large reasoning models such as OpenAI o1 and DeepSeek-R1 have achieved remarkable performance in the domain of reasoning. A key component of their training is the incorporation of verifiable rewards within reinforcement learning (RL). However, existing reward benchmarks do not evaluate reference-based reward systems, leaving researchers with limited understanding of the accuracy of verifiers used in RL. In this paper, we introduce two benchmarks, VerifyBench and VerifyBench-Hard, designed to assess the performance of reference-based reward systems. These benchmarks are constructed through meticulous data collection and curation, followed by careful human annotation to ensure high quality. Current models still show considerable room for improvement on both VerifyBench and VerifyBench-Hard, especially smaller-scale models. Furthermore, we conduct a thorough and comprehensive analysis of evaluation results, offering insights for understanding and developing reference-based reward systems. Our proposed benchmarks serve as effective tools for guiding the development of verifier accuracy and the reasoning capabilities of models trained via RL in reasoning tasks.

Large language models (LLMs) have shown remarkable progress in complex reasoning tasks, largely enabled by test-time scaling (TTS) paradigms that allocate additional compute during inference. Among these, external TTS (particularly the Best-of-N selection paradigm) yields scalable performance improvements by selecting from multiple independently generated reasoning trajectories. However, this approach faces key limitations: (i) the high computational overhead of deploying process reward models, (ii) the underutilization of the LLM's intrinsic latent representations. We introduce TrajSelector, an efficient and effective Best-of-N framework that exploit the hidden states in the sampler LLM for process-level scoring. A lightweight verifier (with only 0.6B parameters) evaluates the quality of step-wise trajectory, and then aggregates these scores to identify the optimal reasoning trajectory. Our framework employs a fully data-driven, end-to-end training recipe that eliminates reliance on massive step-level annotations. Experiential results across five benchmarks demonstrate that TrajSelector delivers consistent performance gains. In Best-of-32 settings, it surpasses majority voting by 4.61% accuracy and outperforms existing process reward models by 4.31% to 12.21%, all while maintaining lower inference costs.

In this work, we propose a novel method named Automated Process-Supervised Verifier (\textsc{AutoPSV}) to enhance the reasoning capabilities of large language models (LLMs) by automatically annotating the reasoning steps. AutoPSV begins by training a verification model on the correctness of final answers, enabling it to generate automatic process annotations. This verification model assigns a confidence score to each reasoning step, indicating the probability of arriving at the correct final answer from that point onward. We detect relative changes in the verification's confidence scores across reasoning steps to automatically annotate the reasoning process, enabling error detection even in scenarios where ground truth answers are unavailable. This alleviates the need for numerous manual annotations or the high computational costs associated with model-induced annotation approaches. We experimentally validate that the step-level confidence changes learned by the verification model trained on the final answer correctness can effectively identify errors in the reasoning steps. We demonstrate that the verification model, when trained on process annotations generated by AutoPSV, exhibits improved performance in selecting correct answers from multiple LLM-generated outputs. Notably, we achieve substantial improvements across five datasets in mathematics and commonsense reasoning. The source code of AutoPSV is available at https://github.com/rookie-joe/AutoPSV.

Computer-using agents (CUAs) enable task completion through natural interaction with operating systems and software interfaces. While script-based verifiers are widely adopted for evaluation, they suffer from limited scalability and inability to provide step-wise assessment. Reward models offer promising alternatives, but their effectiveness on CUA evaluation remains largely underexplored. To address this gap, we present CUARewardBench, comprising four key contributions: (1) First-ever Comprehensive CUA Reward Benchmark: We introduce the first benchmark for evaluating both outcome reward models (ORM) and process reward models (PRM) on CUA tasks, enabling systematic assessment across trajectory-level and step-level evaluation. (2) Diverse, Practical and Reliable Dataset: CUARewardBench encompasses trajectories from 10 software categories and 7 agent architectures with varying performance levels (25.9%-50.8% success rates). All trajectories are expertly annotated through carefully designed protocols, with rigorous quality control to ensure reliability and practical applicability. (3) Comprehensive Analysis and Insights: Through extensive experiments across 7 vision-language models and 3 prompt templates, we reveal critical limitations of current CUA RMs, including insufficient visual reasoning capabilities, knowledge deficiencies, and the superiority of general VLMs over specialized CUA models for reward evaluation. (4) Unanimous Prompt Ensemble (UPE): Based on the insights from our comprehensive analysis, we propose UPE, a novel ensemble method that significantly enhances reward model reliability through strict unanimous voting and strategic prompt-template configurations. UPE achieves 89.8% precision and 93.3% NPV for ORM, and 81.7% precision and 85.1% NPV for PRM, substantially outperforming single VLMs and traditional ensemble approaches.

Visual fluency in generated video does not imply physical reliability, and a scalar quality score alone is incapable of indicating the obligation a clip violates or the moment it fails. We present VeriPhy, an auditable physical-verification system in which a text-only planner compiles the prompt into typed physical obligations and a statically validated execution plan before any frame is observed. During execution, observations gate and scope only declared calls to frozen low-level experts (e.g., segmentation and tracking, counting, eleven typed physical measurements over the resulting tracks, depth, OCR, and audio-event detection). Each action returns a provenance-carrying evidence record whose payload, when usable, is either a typed measurement or an explicitly tagged learned state. Typed resolvers and fixed composition map usable records to a three-valued state (supported, contradicted, or unknown, surfaced as plausible, implausible, or abstain) with full provenance, so that every verdict is traceable to the evidence that produced it. We anchor evaluation in a 1,500-clip corpus of human-annotated flaw records that localize real generation failures in prompt reference, space, and time. On a 149-clip core carrying 304 such records, VeriPhy accounts for 228, against 164 for a published question-decomposition evaluator given the same clips and the same claims. Recall alone does not separate it from prompting the same backbone monolithically, which reaches 222; what separates them is that each decision retains its evidence record and provenance, making the traces auditable one verdict at a time and usable as the interface through which a critic verdict could be written back into generation.

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.

Speculative decoding typically characterizes speedup by draft tokens accepted per verification round. Lossless verification preserves the target model's output distribution and thus expected completion length, making this metric a meaningful efficiency proxy. Relaxed (lossy) verification accepts tokens that lossless verification would reject, potentially altering that distribution. We identify a length inflation phenomenon: relaxed verification lengthens completions, primarily by extending reasoning traces, largely offsetting apparent gains in accepted tokens per round. We evaluate existing training-free relaxed verification rules on twelve target-drafter pairs against lossless verification on identical prompts, measuring completion length, verifier rounds, wall-clock time, and task accuracy. At each rule's most relaxed evaluated setting, relaxed verification on average accepts 1.34times as many tokens per round but produces 1.54times longer completions. For rules with higher acceptance lengths, tokens accepted only under relaxed verification tend to have low target-model probability, contributing to length inflation. For rules that reduce verifier rounds, accuracy typically drops substantially. Further analysis traces some failures to continued reasoning that exhausts the budget needed to deliver a final answer. Overall, accepted tokens per round alone is an unreliable measure of decoding speed under relaxed verification. Completion length and verifier rounds must also be reported to assess actual efficiency.

State-of-the-art (SOTA) LLMs have progressed from struggling on proof-based Olympiad problems to solving most of the IMO 2025 problems, with leading systems reportedly handling 5 of 6 problems. Given this progress, we assess how well these models can grade proofs: detecting errors, judging their severity, and assigning fair scores beyond binary correctness. We study proof-analysis capabilities using a corpus of 90 Gemini 2.5 Pro-generated solutions that we grade on a 1-4 scale with detailed error annotations, and on MathArena solution sets for IMO/USAMO 2025 scored on a 0-7 scale. Our analysis shows that models can reliably flag incorrect (including subtly incorrect) solutions but exhibit calibration gaps in how partial credit is assigned. To address this, we introduce agentic workflows that extract and analyze reference solutions and automatically derive problem-specific rubrics for a multi-step grading process. We instantiate and compare different design choices for the grading workflows, and evaluate their trade-offs. Across our annotated corpus and MathArena, our proposed workflows achieve higher agreement with human grades and more consistent handling of partial credit across metrics. We release all code, data, and prompts/logs to facilitate future research.

As LLM agents undertake increasingly complex, long-horizon tasks, verifying their outputs becomes increasingly challenging. We study how verification capability can be strengthened with a fixed base model, without access to reference answers or grading rubrics at test time. Repeated sampling yields multiple rollouts that can contain complementary correct claims, but we need a reliable verification mechanism to determine which claims to trust. We first find that disagreement often exposes correct alternatives, while consensus can conceal errors. These observations motivate VeriHarness, which turns the underlying LLM a generator uses into an agentic verifier by giving it a workspace, evidence tools, and reusable verification skills. A disagreement resolver checks competing claims against environmental evidence, while a consensus challenger tests shared claims and searches for omitted requirements. Their findings guide the selection and revision of the final artifact. Across five long-horizon workspace benchmarks and two frontier models, VeriHarness achieves the highest selection scores among the evaluated baselines. Evidence-backed revision further improves average performance, bringing gains over a single rollout to 6.2 points with Gemini 3.5 Flash and 6.4 points with Claude Opus 4.8. We further show that verification skills can self-improve from failure feedback, demonstrating VeriHarness as a novel and critical approach for scaling long-horizon agentic verification. We release the full pool of approximately 26,000 rollouts across all five benchmarks and both models, produced at a cost of over $100,000, to support future research on agentic verification.

Reinforcement learning with verifiable rewards (RLVR) replaces human preference labels with executable reward functions such as math answer checkers, JSON tool-call validators, and code unit-test harnesses. That makes the reward partly a software artifact: if the verifier is wrong, optimization can learn the bug. We study this failure mode with a lightweight verifier-fuzzing framework that generates adversarial completions, compares buggy and stricter reference verifiers, logs paired decisions, and reports false-positive, false-negative, disagreement, exploit, and uncertainty metrics.

Reinforcement Learning with Verifiable Rewards (RLVR) demonstrates promising potential in advancing the reasoning capabilities of LLMs. However, its success remains largely confined to mathematical and code domains. This primary limitation stems from the heavy reliance on domain-specific verifiers, which results in prohibitive complexity and limited scalability. To address the challenge, our key observation is that LLM's intrinsic probability of generating a correct free-form answer directly indicates its own evaluation of the reasoning reward (i.e., how well the reasoning process leads to the correct answer). Building on this insight, we propose RLPR, a simple verifier-free framework that extrapolates RLVR to broader general domains. RLPR uses the LLM's own token probability scores for reference answers as the reward signal and maximizes the expected reward during training. We find that addressing the high variance of this noisy probability reward is crucial to make it work, and propose prob-to-reward and stabilizing methods to ensure a precise and stable reward from LLM intrinsic probabilities. Comprehensive experiments in four general-domain benchmarks and three mathematical benchmarks show that RLPR consistently improves reasoning capabilities in both areas for Gemma, Llama, and Qwen based models. Notably, RLPR outperforms concurrent VeriFree by 7.6 points on TheoremQA and 7.5 points on Minerva, and even surpasses strong verifier-model-dependent approaches General-Reasoner by 1.6 average points across seven benchmarks.

Verifier-based selection improves LLM performance by generating multiple candidate solutions and using a verifier to select the most promising one. However, existing methods typically treat verification only as a ranking step and discard its feedback once a fixed candidate pool has been evaluated. In this paper, we ask whether verification can also improve the candidate set itself. To this end, we introduce LLM-as-an-Improver and propose Verify--Repair--Reselect (VRR), which uses verification feedback to generate and reselect improved candidates. VRR retains the initial winner while conditionally generating three complementary alternatives: repaired versions of the winner and runner-up, and a solution based on a new approach. It filters invalid and duplicate candidates using only inference-time information and then reselects the final answer under the original evaluation criteria. Across diverse models and code-generation and reasoning benchmarks, VRR improves over fixed-pool verifier-based selection in many settings and can recover correct solutions even when all candidates in the initial pool are incorrect. These results highlight a broader role for LLMs as improvers: verification feedback can not only select among existing solutions but also construct stronger candidates beyond the initial pool.

Autonomous agents for long-sequence Graphical User Interface tasks are hindered by sparse rewards and the intractable credit assignment problem. To address these challenges, we introduce GUI-Shepherd, a Process Reward Model that provides dense, step-by-step feedback to guide agents. GUI-Shepherd is trained on a diverse large-scale data set of 52k interactions that features human-annotated scores and GPT-4o generated rationales, enabling it to serve both as a reward provider for RL training and as a verifier for inference. As far as we know, we are the first to conduct a systematic study of process supervision in GUI agents, across diverse settings from online long-horizon tasks to offline single-step prediction. On the online AndroidWorld benchmark, GUI-Shepherd improves success rate by 7.7 points via multi-turn online PPO, significantly outperforming Outcome Reward Model based competitors. When used as an inference verifier, it brings 5.1 points improvements. The benefits generalize to the offline AndroidControl benchmark, with gains of 2.2 points as a reward provider and 4.3 points as a verifier. Collectively, our results establish that high-fidelity process supervision is critical for building more capable GUI agents and present a generalizable solution.

Many inference-time language-model pipelines combine a cheap reward signal with an expensive verifier, such as exact answer checking in mathematical reasoning or hidden-test execution in code generation. We formalize this setting using a learning-theoretic lens as generative active search: a cost-sensitive first-positive search problem in which a policy adaptively samples candidates from an unknown distribution, observes cheap scores, and pays for verifier labels until it finds a positive example. For a fixed prompt, the generator and reward model induce two unknown objects: a distribution over reward scores and a score-conditioned success function. When these quantities are known, we characterize the distribution-aware optimal policy using a dynamic programming approach. In the realistic and practical setting where both the score distribution and success function are unknown, we propose ADAP, a shellwise adaptive generate-rank-verify algorithm that progressively increases the number of sampled responses and top-ranked verifications. Under the monotonicity assumption that higher reward scores are no less likely to pass verification, we show that ADAP achieves expected cost within a constant factor of the distribution-aware optimum. We complement this result with learning-theoretic lower bounds, based on a centered star number, showing that structural assumptions on the score--label relationship are necessary. Experiments on mathematical reasoning and competitive programming validate the predicted advantage over both fixed non-adaptive policies and difficulty-adaptive baselines.

The breakthrough of OpenAI o1 highlights the potential of enhancing reasoning to improve LLM. Yet, most research in reasoning has focused on mathematical tasks, leaving domains like medicine underexplored. The medical domain, though distinct from mathematics, also demands robust reasoning to provide reliable answers, given the high standards of healthcare. However, verifying medical reasoning is challenging, unlike those in mathematics. To address this, we propose verifiable medical problems with a medical verifier to check the correctness of model outputs. This verifiable nature enables advancements in medical reasoning through a two-stage approach: (1) using the verifier to guide the search for a complex reasoning trajectory for fine-tuning LLMs, (2) applying reinforcement learning (RL) with verifier-based rewards to enhance complex reasoning further. Finally, we introduce HuatuoGPT-o1, a medical LLM capable of complex reasoning, which outperforms general and medical-specific baselines using only 40K verifiable problems. Experiments show complex reasoning improves medical problem-solving and benefits more from RL. We hope our approach inspires advancements in reasoning across medical and other specialized domains.

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.

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.

Reinforcement learning from verifiable rewards (RLVR) has improved the reasoning abilities of large language models (LLMs), but most existing approaches rely on sparse outcome-level feedback. This sparsity creates a credit assignment challenge in long-horizon agentic reasoning: a trajectory may fail despite containing many correct intermediate decisions, or succeed despite containing flawed ones. In this work, we study a class of densely-verifiable agentic reasoning problems, where intermediate actions can be objectively checked by symbolic or algorithmic oracles. We propose Verifiable Process Rewards (VPR), a framework that converts such oracles into dense turn-level supervision for reinforcement learning, and instantiate it in three representative settings: search-based verification for dynamic deduction, constraint-based verification for logical reasoning, and posterior-based verification for probabilistic inference. We further provide a theoretical analysis showing that dense verifier-grounded rewards can improve long-horizon credit assignment by providing more localized learning signals, with the benefit depending on the reliability of the verifier. Empirically, VPR outperforms outcome-level reward and rollout-based process reward baselines across controlled environments, and more importantly, transfers to both general and agentic reasoning benchmarks, suggesting that verifiable process supervision can foster general reasoning skills applicable beyond the training environments. Our results indicate that VPR is a promising approach for enhancing LLM agents whenever reliable intermediate verification is available, while also highlighting its dependence on oracle quality and the open challenge of extending VPR to less structured, open-ended environments.

Large language models (LLMs) have achieved remarkable performance on high-school and competition-level mathematics, yet their capabilities on advanced mathematics remain poorly understood. Existing benchmarks, however, fall short in both scope and evaluation granularity: they provide limited disciplinary coverage and often rely on final-answer correctness or coarse judgments, leaving the validity of the reasoning process inadequately assessed. To bridge this gap, we introduce AdvancedMathBench, a benchmark suite designed to evaluate the reasoning capabilities of LLMs on advanced mathematical proofs. Its core generation benchmark, ProverBench, contains 245 problems spanning undergraduate (UG) and doctoral qualifying-exam (QE) levels. To reliably evaluate these proofs, we develop a dedicated automatic verification pipeline that is trained on large-scale expert annotations, produces both correctness verdicts and fine-grained analyses, and exhibits strong agreement with human experts on held-out proof trajectories. We further introduce VerifierBench, consisting of 888 model-generated proof trajectories paired with expert ground truth, to evaluate whether models can correctly judge proof validity and provide sound verification rationales. Experiments show that AdvancedMathBench remains challenging for frontier models. On proof generation, the best-performing model, GPT-5.5-xhigh, achieves only 64.5 and 48.9 on the UG and QE splits, respectively. On proof verification, the best model only attains a Balanced F1 of 65.1. Further analysis reveals a notable mismatch between proof generation and verification capabilities across models.

Code generated by large language models passes security checks at a rate that has barely moved in four years. In regulated backends, the defect classes that matter most are money arithmetic, time handling, retry safety, and access control. Teams answer with instruction files, yet the largest controlled study of instruction files to date found no benefit. This paper tests a narrower idea: generated code improves when the prompt carries a specification, a fixed preamble stating what must be true of the result. We pre-registered hypotheses, refuters, analysis code, and a one-shot generation rule, then ran 50 realistic backend tasks from finance, healthcare, and insurance practice through five frontier models from five vendor lineages, each task twice: bare, and preceded by a 267-word filled specification frame. Nine deterministic AST-based checkers scored the outputs. The Bandit security scanner, which knows nothing of the frame, scored them independently. The frame reduced defects in all five models (mean reduction 0.16 to 0.70 findings per task, every Holm-adjusted sign test significant, every bootstrap confidence interval excluding zero). Where the arms differed, the frame arm won 95 of 100 times. It never made any model worse in any domain. Bandit found 53 medium-or-high issues in the bare arm and 11 in the frame arm, in the same direction for every model. The effect was largest where a model's unprompted defaults were weakest: the frame supplies the discipline a model lacks. All 500 outputs, prompts, checkers, scoring code, and the pre-registration are published with a DOI, so any team can re-derive the result without trusting the author.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

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.

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

The evolution of machine learning has increasingly prioritized the development of powerful models and more scalable supervision signals. However, the emergence of foundation models presents significant challenges in providing effective supervision signals necessary for further enhancing their capabilities. Consequently, there is an urgent need to explore novel supervision signals and technical approaches. In this paper, we propose verifier engineering, a novel post-training paradigm specifically designed for the era of foundation models. The core of verifier engineering involves leveraging a suite of automated verifiers to perform verification tasks and deliver meaningful feedback to foundation models. We systematically categorize the verifier engineering process into three essential stages: search, verify, and feedback, and provide a comprehensive review of state-of-the-art research developments within each stage. We believe that verifier engineering constitutes a fundamental pathway toward achieving Artificial General Intelligence.

Visible tests are a common gate for LLM-generated code, but passing them does not certify specification correctness. We study a deployment-like monitoring problem: after code has passed public tests, can a weaker LLM verifier identify the residual hidden bugs? We introduce Code Monitor Red Teaming, a monitor-red-teaming protocol that fixes a public-check information boundary while varying generator pressure, verifier scaffolding, and weak-to-strong capability. We instantiate it as CodeMonitorBench, spanning function-level, data-science, and workflow code. Across 71,000 generated candidates, 43,677 pass public tests and 23,081 of those fail hidden tests. Weak verifiers improve with scaffolding and model family, but still miss most hidden bugs at 5% false-positive rate. As a robustness stress test, adversarial public-test-overfit pressure lowers verifier AUROC and raises low-FPR miss rates in most cells. A GLM-5.1 verifier recovers part of the gap under the same evidence boundary; an inferability audit shows that remaining misses mix verifier failures with M1 evidence limits.

We present OpenComputer, a verifier-grounded framework for constructing verifiable software worlds for computer-use agents. OpenComputer integrates four components: (1) app-specific state verifiers that expose structured inspection endpoints over real applications, (2) a self-evolving verification layer that improves verifier reliability using execution-grounded feedback, (3) a task-generation pipeline that synthesizes realistic and machine-checkable desktop tasks, and (4) an evaluation harness that records full trajectories and computes auditable partial-credit rewards. In its current form, OpenComputer covers 33 desktop applications and 1,000 finalized tasks spanning browsers, office tools, creative software, development environments, file managers, and communication applications. Experiments show that OpenComputer's hard-coded verifiers align more closely with human adjudication than LLM-as-judge evaluation, especially when success depends on fine-grained application state. Frontier agents struggle with end-to-end completion despite partial progress, and open-source models exhibit sharp drops from their OSWorld-Verified scores, exposing a persistent gap in robust computer automation.

The main issue with most evaluation schemes today is their "static" nature: the same problems are reused repeatedly, allowing for memorization, format exploitation, and eventual saturation. To measure genuine AI progress, we need evaluation that is robust by construction, not by post-hoc detection. In response, we propose VeRA (Verified Reasoning Data Augmentation), a framework that converts benchmark problems into executable specifications, comprising (i) a natural language template with placeholder slots, (ii) a coherent generator that samples valid configurations, and (iii) a deterministic verifier that validates parameters and calculates the corresponding correct answers for each configuration. From a single seed problem, VeRA automatically creates unlimited verified variants with reliable labels at near-zero marginal cost without human involvement. VeRA operates in two complementary modes. VeRA-E (equivalent) rewrites problems while keeping the underlying logic intact, useful for detecting memorization versus genuine reasoning. VeRA-H (hardened) systematically increases complexity while remaining verifiable, enabling reliable creation and labelling of fresh difficult tasks at the boundary of intelligence. Evaluating 16 frontier models with VeRA, we find: (i) VeRA-E improves evaluation quality and reveals contamination patterns. (ii) VeRA-H enables human-free generation of hard tasks with reliable labels. (iii) VeRA establishes verified benchmarks as a general paradigm. VeRA reconceptualizes benchmarks from static objects used until exhausted, to executable specifications generating fresh, verified instances on demand, enhancing robustness and cost-effectiveness for evaluation. With VeRA, we envision that evaluation in any verifiable domain can scale indefinitely without sacrificing label integrity. To stimulate future research, we have open-sourced all code and datasets.

Autonomous coding agents solve repository issues by reading code, running commands, editing files, and submitting patches. Extra inference-time compute yields gains only when it produces a useful repair and supplies reliable evidence for choosing one. Three behaviors decide both, and we argue they are teachable rather than byproducts of scale, so a policy can carry them instead of a scaffold. Location diversity remains narrow, since attempts return to the same site and extra samples add no coverage. Edit diversity is left unexploited, since methodologies that differ resolve complementary issues no single run reaches. Verification misleads, since a test the agent writes for its own patch accepts many incorrect ones. Directing search by execution feedback and scoring each patch against its own reverted tree resolves 52.8% of SWE-bench Verified using 48.1% of the agent-steps an eight-sample baseline spends. Training moves these behaviors into the policy. On the 270 issues held out from SFT and RL training, weighted supervised fine-tuning raises pass@1 from 31.9% to 35.2% and pass@8 from 46.7% to 51.1%. A reinforcement objective then trains the verifier against gold-labeled repairs and incorrect variants, crediting the assertions that detect them. It raises pass@1 to 43.0% and pass@8 to 60.7%, lifts verifier precision from 26.8% to 41.7%, and more than halves false acceptance. Resolution improves on two of three out-of-distribution suites and verifier precision on all three, and the gains hold at 7B, 14B, and 30B against published coder baselines.

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.

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

Reinforcement learning with verifiable rewards (RLVR) is central to training modern reasoning models, but the undisclosed training data raises concerns about benchmark contamination. Unlike pretraining methods, which optimize models using token-level probabilities, RLVR fine-tunes models based on reward feedback from self-generated reasoning trajectories, making conventional likelihood-based detection methods less effective. We show that RLVR induces a distinctive behavioral signature: prompts encountered during RLVR training result in more rigid and similar generations, while unseen prompts retain greater diversity. We introduce Min-kNN Distance, a simple black-box detector that quantifies this collapse by sampling multiple completions for a given prompt and computing the average of the k smallest nearest-neighbor edit distances. Min-kNN Distance requires no access to the reference model or token probabilities. Experiments across multiple RLVR-trained reasoning models show that Min-kNN Distance reliably distinguishes RL-seen examples from unseen ones and outperforms existing membership inference and RL contamination detection baselines.