Daily Papers

Large Language Models (LLMs) have shown promise in simulating human behavior, yet existing agents often exhibit behavioral rigidity, a flaw frequently masked by the self-referential bias of current "LLM-as-a-judge" evaluations. By evaluating against empirical ground truth, we reveal a counter-intuitive phenomenon: increasing the intensity of prompt-driven reasoning does not enhance fidelity but rather exacerbates value polarization, collapsing population diversity. To address this, we propose the Context-Value-Action (CVA) architecture, grounded in the Stimulus-Organism-Response (S-O-R) model and Schwartz's Theory of Basic Human Values. Unlike methods relying on self-verification, CVA decouples action generation from cognitive reasoning via a novel Value Verifier trained on authentic human data to explicitly model dynamic value activation. Experiments on CVABench, which comprises over 1.1 million real-world interaction traces, demonstrate that CVA significantly outperforms baselines. Our approach effectively mitigates polarization while offering superior behavioral fidelity and interpretability.

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.

Zero-Knowledge Proofs (ZKPs) are a cryptographic primitive that allows a prover to demonstrate knowledge of a secret value to a verifier without revealing anything about the secret itself. ZKPs have shown to be an extremely powerful tool, as evidenced in both industry and academic settings. In recent years, the utilization of user data in practical applications has necessitated the rapid development of privacy-preserving techniques, including ZKPs. This has led to the creation of several robust open-source ZKP frameworks. However, there remains a significant gap in understanding the capabilities and real-world applications of these frameworks. Furthermore, identifying the most suitable frameworks for the developers' specific applications and settings is a challenge, given the variety of options available. The primary goal of our work is to lower the barrier to entry for understanding and building applications with open-source ZKP frameworks. In this work, we survey and evaluate 25 general-purpose, prominent ZKP frameworks. Recognizing that ZKPs have various constructions and underlying arithmetic schemes, our survey aims to provide a comprehensive overview of the ZKP landscape. These systems are assessed based on their usability and performance in SHA-256 and matrix multiplication experiments. Acknowledging that setting up a functional development environment can be challenging for these frameworks, we offer a fully open-source collection of Docker containers. These containers include a working development environment and are accompanied by documented code from our experiments. We conclude our work with a thorough analysis of the practical applications of ZKPs, recommendations for ZKP settings in different application scenarios, and a discussion on the future development of ZKP frameworks.

Prevalent reinforcement learning~(RL) methods for fine-tuning LLM reasoners, such as GRPO or Leave-one-out PPO, abandon the learned value function in favor of empirically estimated returns. This hinders test-time compute scaling that relies on using the value-function for verification. In this work, we propose RL^V that augments any ``value-free'' RL method by jointly training the LLM as both a reasoner and a generative verifier using RL-generated data, adding verification capabilities without significant overhead. Empirically, RL^V boosts MATH accuracy by over 20\% with parallel sampling and enables 8-32times efficient test-time compute scaling compared to the base RL method. RL^V also exhibits strong generalization capabilities for both easy-to-hard and out-of-domain tasks. Furthermore, RL^V achieves 1.2-1.6times higher performance when jointly scaling parallel and sequential test-time compute with a long reasoning R1 model.

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.

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.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g. human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on the dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, the combination of the ease of learning the relatively simple RM (verifier) from the preference data, coupled with the ability of the downstream RL procedure to then filter its search space to the subset of policies (generators) that are optimal for relatively simple verifiers is what leads to the superior performance of online FT.

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.

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.

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.

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.

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.

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.

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.

Practical deployment of Multi-Agent Systems (MAS) demands strong test-time performance, motivating methods that guide inference-time search and selectively spend compute to improve quality. We present the Multi-Agent System Process Reward Model (MASPRM). It assigns per-action, per-agent values to partial inter-agent transcripts and acts as an inference-time controller. MASPRM is trained from multi-agent Monte Carlo Tree Search (MCTS) rollouts without requiring step-level human annotations, by propagating returns to local targets. At inference, MASPRM guides step-level beam search and MCTS, focusing computation on promising branches and pruning early. On GSM8K and MATH, MASPRM-guided decoding with an outcome reward model (ORM) applied to the final answer, improves exact match (EM) over a single straight-through MAS pass by +30.7 and +22.9 points, respectively. A MASPRM trained on GSM8K transfers zero-shot to MATH without retraining, adding 8.4 EM points at the same budget. MASPRM is a plug-in value model that estimates per-agent progress and complements verifier-style decoders, enabling more reliable, compute-aware multi-agent reasoning. Code: https://github.com/milad1378yz/MASPRM

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.

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.

Large language model (LLM) agents operate over long, multi-session interactions in which facts change: a user moves, a price updates, a plan is revised. Acting correctly requires using the current value of a fact and discarding values that have been superseded. We isolate this ability on real conversational data and show that it is a distinct, unsolved failure. On the knowledge-update subset of LongMemEval, replacing an agent's full context with a bounded, self-maintained memory drops accuracy from 92% to 77% even on a frontier model (gpt-5.4), a gap that is statistically significant (paired McNemar p<0.005) and persists across model scale while full-context accuracy saturates near 92%. The bottleneck is therefore memory maintenance, not comprehension, and is not closed by a stronger model. We then ask whether this is merely an undersized memory, and find it is not: as the conversation grows 24x, accuracy falls further (from 68% to 28%), and granting the agent proportionally more memory yields no detectable recovery (28% to 28%, n=25). The failure scales with the length of the conversation, not the compression ratio. We release Supersede, an open reinforcement-learning environment (on the verifiers / prime-rl stack) that turns this measurement into a training signal: agents are rewarded for answering from the current value and penalized for stale ones. Finally, we close the loop and show the gap is trainable: GRPO fine-tuning a small open model (Qwen2.5-3B) on this environment nearly doubles its held-out supersession accuracy on real, unseen conversations (9.0% to 16.7%, a single run), along a monotonic checkpoint curve indicating the learned policy, not the harness, carries the gain. To our knowledge this is the first trainable environment whose reward targets temporal fact-currency, and the first evidence the supersession gap can be trained down, not only measured.

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.

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.

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}.

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) 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.

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.

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.

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.

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.

Decentralized Finance (DeFi) has turned blockchains into financial infrastructure, allowing anyone to trade, lend, and build protocols without intermediaries, but this openness exposes pools of value controlled by code. Within five years, the DeFi ecosystem has lost over 15.75B USD to reported exploits. Many exploits arise from permissionless opportunities that any participant can trigger using only public state and standard interfaces, which we call Anyone-Can-Take (ACT) opportunities. Despite on-chain transparency, postmortem analysis remains slow and manual: investigations start from limited evidence, sometimes only a single transaction hash, and must reconstruct the exploit lifecycle by recovering related transactions, contract code, and state dependencies. We present TxRay, a Large Language Model (LLM) agentic postmortem system that uses tool calls to reconstruct live ACT attacks from limited evidence. Starting from one or more seed transactions, TxRay recovers the exploit lifecycle, derives an evidence-backed root cause, and generates a runnable, self-contained Proof of Concept (PoC) that deterministically reproduces the incident. TxRay self-checks postmortems by encoding incident-specific semantic oracles as executable assertions. To evaluate PoC correctness and quality, we develop PoCEvaluator, an independent agentic execution-and-review evaluator. On 114 incidents from DeFiHackLabs, TxRay produces an expert-aligned root cause and an executable PoC for 105 incidents, achieving 92.11% end-to-end reproduction. Under PoCEvaluator, 98.1% of TxRay PoCs avoid hard-coding attacker addresses, a +22.9pp lift over DeFiHackLabs. In a live deployment, TxRay delivers validated root causes in 40 minutes and PoCs in 59 minutes at median latency. TxRay's oracle-validated PoCs enable attack imitation, improving coverage by 15.6% and 65.5% over STING and APE.

A rule-based logic solver resolves every instance in our benchmark in under 50 microseconds with 100% accuracy; the best frontier language model reaches 65% at best and drops to 23.5% under rendering-robust evaluation (worst case over four surface renderings). We introduce DeFAb (Defeasible Abduction Benchmark), a dataset and generation pipeline that converts four decades of publicly funded knowledge bases into formally grounded instances for defeasible abduction: constructing hypotheses that explain anomalies by overriding defaults while preserving unrelated expectations. Because every hypothesis must pass polynomial-time checks for valid derivation, conservativity, and minimality, DeFAb makes logical rigor the instrument for measuring creativity and theoretical reasoning, scoring the disciplined construction of theory revisions rather than fluent but theory-destroying prose. The pipeline pairs taxonomic hierarchies (OpenCyc, YAGO, Wikidata) with behavioral property graphs (ConceptNet, UMLS) to produce 372,648+ instances across 33.75M materialized rules from 18 sources, in three levels with polynomial-time verifiable gold standards. Four frontier models do not reliably internalize defeasible reasoning: rendering-robust Level 2 accuracy is 7.8-23.5%; chain-of-thought variance (~36 pp) exceeds any inter-model gap; and a matched contamination control isolates a +19.4 pp Level 3 gap. We further release DeFAb-Hard (a 235-instance Level 3 difficulty variant; best model 53.3% vs 100% symbolic) and CONJURE (a kernel-verified transformative-creativity variant of 560 Lean 4/Mathlib instances whose gold answers are definitions the proof kernel did not previously contain, judge-free verifier; a pilot finds zero novel concepts). The same verifier doubles as an exact reward for preference optimization (DPO, RLVR/GRPO). Released under MIT at https://huggingface.co/datasets/PatrickAllenCooper/DeFAb.

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.

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

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.

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.

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.

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.

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.

Large language models (LLMs) have exhibited impressive capabilities across a myriad of tasks, yet they occasionally yield undesirable outputs. We posit that these limitations are rooted in the foundational autoregressive architecture of LLMs, which inherently lacks mechanisms for differentiating between desirable and undesirable results. Drawing inspiration from the dual-process theory of human cognition, we introduce LLM2, a novel framework that combines an LLM (System 1) with a process-based verifier (System 2). Within LLM2, the LLM is responsible for generating plausible candidates, while the verifier provides timely process-based feedback to distinguish desirable and undesirable outputs. The verifier is trained with a pairwise comparison loss on synthetic process-supervision data generated through our token quality exploration strategy. Empirical results on mathematical reasoning benchmarks substantiate the efficacy of LLM2, exemplified by an accuracy enhancement from 50.3 to 57.8 (+7.5) for Llama3-1B on GSM8K. Furthermore, when combined with self-consistency, LLM2 achieves additional improvements, boosting major@20 accuracy from 56.2 to 70.2 (+14.0).

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.

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.

Existing fraud detection methods predominantly rely on transcribed text, suffering from ASR errors and missing crucial acoustic cues like vocal tone and environmental context. This limits their effectiveness against complex deceptive strategies. To address these challenges, we first propose SAFE-QAQ, an end-to-end comprehensive framework for audio-based slow-thinking fraud detection. First, the SAFE-QAQ framework eliminates the impact of transcription errors on detection performance. Secondly, we propose rule-based slow-thinking reward mechanisms that systematically guide the system to identify fraud-indicative patterns by accurately capturing fine-grained audio details, through hierarchical reasoning processes. Besides, our framework introduces a dynamic risk assessment framework during live calls, enabling early detection and prevention of fraud. Experiments on the TeleAntiFraud-Bench demonstrate that SAFE-QAQ achieves dramatic improvements over existing methods in multiple key dimensions, including accuracy, inference efficiency, and real-time processing capabilities. Currently deployed and analyzing over 70,000 calls daily, SAFE-QAQ effectively automates complex fraud detection, reducing human workload and financial losses. Code: https://anonymous.4open.science/r/SAFE-QAQ.

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.

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.

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.

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.

The Internet of Value (IoV) is a heterogeneous, partially-trusted network in which the dominant marginal risk is composite (route, sentiment, liquidity, and the policy a system is willing to commit to) rather than a property of any single chain. We argue that a risk primitive adequate for this regime is a composition of five engines: a prediction engine over price, liquidity, volatility, and route health; a Bittensor verification subnet that decentralises and economically scores prediction outputs; a sentiment-fusion engine over text, on-chain flow, and grey-literature feeds; an agentic engine under constitutional, role-bound action constraints; and an API-risk and scenario engine that converts forecasts into pre-committed action programs in the sense of Monte-Carlo scenario generation. We anchor the architecture in two empirical artefacts: a 27-hour policy-constrained liquidity stress-response experiment on Solana, and a 168-hour prediction-router calibration arc reported with explicit class-imbalance honesty. The case study supports deployability; the validator-loss decomposition is stated formally and is falsifiable.

In Reinforcement Learning with Verifiable Rewards (RLVR), constructing a robust advantage baseline is critical for policy gradients, effectively guiding the policy model to reinforce desired behaviors. Recent research has introduced Generalist Value Models (such as V_0), which achieve pre-trained value estimation by explicitly encoding model capabilities in-context, eliminating the need to synchronously update the value model alongside the policy model. In this paper, we propose V_{0.5}, which adaptively fuses the baseline predicted by such value model (acting as a prior) with the empirical mean derived from sparse rollouts. This constructs a robust baseline that balances computational efficiency with extremely low variance. Specifically, we introduce a real-time statistical testing and dynamic budget allocation. This balances the high variance caused by sparse sampling against the systematic bias (or hallucinations) inherent in the value model's prior. By constructing a hypothesis test to evaluate the prior's reliability in real-time, the system dynamically allocates additional rollout budget on demand. This mechanism minimizes the baseline estimator's Mean Squared Error (MSE), guaranteeing stable policy gradients, even under extreme sparsity with a group size of 4. Extensive evaluations across six mathematical reasoning benchmarks demonstrate that V_{0.5} significantly outperforms GRPO and DAPO, achieving faster convergence and over some 10% performance improvement.

Artificial Intelligence (AI) is starting to transform the research process as we know it by automating the discovery of new solutions. Given a task, the typical AI-driven approach is (i) to generate a set of diverse solutions, and then (ii) to verify these solutions and select one that solves the problem. Crucially, this approach assumes the existence of a reliable verifier, i.e., one that can accurately determine whether a solution solves the given problem. We argue that systems research, long focused on designing and evaluating new performance-oriented algorithms, is particularly well-suited for AI-driven solution discovery. This is because system performance problems naturally admit reliable verifiers: solutions are typically implemented in real systems or simulators, and verification reduces to running these software artifacts against predefined workloads and measuring performance. We term this approach as AI-Driven Research for Systems (ADRS), which iteratively generates, evaluates, and refines solutions. Using penEvolve, an existing open-source ADRS instance, we present case studies across diverse domains, including load balancing for multi-region cloud scheduling, Mixture-of-Experts inference, LLM-based SQL queries, and transaction scheduling. In multiple instances, ADRS discovers algorithms that outperform state-of-the-art human designs (e.g., achieving up to 5.0x runtime improvements or 50% cost reductions). We distill best practices for guiding algorithm evolution, from prompt design to evaluator construction, for existing frameworks. We then discuss the broader implications for the systems community: as AI assumes a central role in algorithm design, we argue that human researchers will increasingly focus on problem formulation and strategic guidance. Our results highlight both the disruptive potential and the urgent need to adapt systems research practices in the age of AI.

We propose Reinforcement Learning with Explicit Human Values (RLEV), a method that aligns Large Language Model (LLM) optimization directly with quantifiable human value signals. While Reinforcement Learning with Verifiable Rewards (RLVR) effectively trains models in objective domains using binary correctness rewards, it overlooks that not all tasks are equally significant. RLEV extends this framework by incorporating human-defined value signals directly into the reward function. Using exam-style data with explicit ground-truth value labels, RLEV consistently outperforms correctness-only baselines across multiple RL algorithms and model scales. Crucially, RLEV policies not only improve value-weighted accuracy but also learn a value-sensitive termination policy: concise for low-value prompts, thorough for high-value ones. We demonstrate this behavior stems from value-weighted gradient amplification on end-of-sequence tokens. Ablation studies confirm the gain is causally linked to value alignment. RLEV remains robust under noisy value signals, such as difficulty-based labels, demonstrating that optimizing for an explicit utility function offers a practical path to aligning LLMs with human priorities.

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.

Agreement Technologies refer to open computer systems in which autonomous software agents interact with one another, typically on behalf of humans, in order to come to mutually acceptable agreements. With the advance of AI systems in recent years, it has become apparent that such agreements, in order to be acceptable to the involved parties, must remain aligned with ethical principles and moral values. However, this is notoriously difficult to ensure, especially as different human users (and their software agents) may hold different value systems, i.e. they may differently weigh the importance of individual moral values. Furthermore, it is often hard to specify the precise meaning of a value in a particular context in a computational manner. Methods to estimate value systems based on human-engineered specifications, e.g. based on value surveys, are limited in scale due to the need for intense human moderation. In this article, we propose a novel method to automatically learn value systems from observations and human demonstrations. In particular, we propose a formal model of the value system learning problem, its instantiation to sequential decision-making domains based on multi-objective Markov decision processes, as well as tailored preference-based and inverse reinforcement learning algorithms to infer value grounding functions and value systems. The approach is illustrated and evaluated by two simulated use cases.

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

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.

Aligning Large Language Models (LLMs) with human values has attracted increasing attention since it provides clarity, transparency, and the ability to adapt to evolving scenarios. In this paper, we introduce a Controlled Value Vector Activation (ConVA) method that directly aligns the internal values of LLMs by interpreting how a value is encoded in their latent representations and modifies relevant activations to ensure consistent values in LLMs. To ensure an accurate and unbiased interpretation, we propose a context-controlled value vector identification method. To consistently control values without sacrificing model performance, we introduce a gated value vector activation method for effective and minimum degree of value control. Experiments show that our method achieves the highest control success rate across 10 basic values without hurting LLM performance and fluency, and ensures target values even with opposite and potentially malicious input prompts. Source code and data are available at~ https://github.com/hr-jin/ConVA.

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.

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.

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.

Detecting AI risks becomes more challenging as stronger models emerge and find novel methods such as Alignment Faking to circumvent these detection attempts. Inspired by how risky behaviors in humans (i.e., illegal activities that may hurt others) are sometimes guided by strongly-held values, we believe that identifying values within AI models can be an early warning system for AI's risky behaviors. We create LitmusValues, an evaluation pipeline to reveal AI models' priorities on a range of AI value classes. Then, we collect AIRiskDilemmas, a diverse collection of dilemmas that pit values against one another in scenarios relevant to AI safety risks such as Power Seeking. By measuring an AI model's value prioritization using its aggregate choices, we obtain a self-consistent set of predicted value priorities that uncover potential risks. We show that values in LitmusValues (including seemingly innocuous ones like Care) can predict for both seen risky behaviors in AIRiskDilemmas and unseen risky behaviors in HarmBench.

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.

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.

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.

Automated code generation with large language models has gained significant traction, but there remains no guarantee on the correctness of generated code. We aim to use formal verification to provide mathematical guarantees that the generated code is correct. However, generating formally verified code with LLMs is hindered by the scarcity of training data and the complexity of formal proofs. To tackle this challenge, we introduce AlphaVerus, a self-improving framework that bootstraps formally verified code generation by iteratively translating programs from a higher-resource language and leveraging feedback from a verifier. AlphaVerus operates in three phases: exploration of candidate translations, Treefinement -- a novel tree search algorithm for program refinement using verifier feedback, and filtering misaligned specifications and programs to prevent reward hacking. Through this iterative process, AlphaVerus enables a LLaMA-3.1-70B model to generate verified code without human intervention or model finetuning. AlphaVerus shows an ability to generate formally verified solutions for HumanEval and MBPP, laying the groundwork for truly trustworthy code-generation agents.

As reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant paradigm for scaling reasoning capabilities in LLMs, a new failure mode emerges: LLMs gaming verifiers. We study this phenomenon on inductive reasoning tasks, where models must induce and output logical rules. We find that RLVR-trained models systematically abandon rule induction. Instead of learning generalizable patterns (e.g., ``trains carrying red cars go east''), they enumerate instance-level labels, producing outputs that pass verifiers without capturing the relational patterns required by the task. We show that this behavior is not a failure of understanding but a form of reward hacking: imperfect verifiers that check only extensional correctness admit false positives. To detect such shortcuts, we introduce Isomorphic Perturbation Testing (IPT), which evaluates a single model output under both extensional and isomorphic verification, where the latter enforces invariance under logically isomorphic tasks. While genuine rule induction remains invariant, shortcut strategies fail. We find that shortcut behavior is specific to RLVR-trained reasoning models (e.g., GPT-5, Olmo3) and absent in non-RLVR models (e.g., GPT-4o, GPT-4.5, Ministral). Moreover, shortcut prevalence increases with task complexity and inference-time compute. In controlled training experiments, extensional verification directly induces shortcut strategies, while isomorphic verification eliminates them. These results show that RLVR can incentivize reward hacking not only through overt manipulation but also by exploiting what the verifier fails to enforce.

For humans to trust the fluent generations of large language models (LLMs), they must be able to verify their correctness against trusted, external sources. Recent efforts aim to increase verifiability through citations of retrieved documents or post-hoc provenance. However, such citations are prone to mistakes that further complicate their verifiability. To address these limitations, we tackle the verifiability goal with a different philosophy: we trivialize the verification process by developing models that quote verbatim statements from trusted sources in pre-training data. We propose Quote-Tuning, which demonstrates the feasibility of aligning LLMs to leverage memorized information and quote from pre-training data. Quote-Tuning quantifies quoting against large corpora with efficient membership inference tools, and uses the amount of quotes as an implicit reward signal to construct a synthetic preference dataset for quoting, without any human annotation. Next, the target model is aligned to quote using preference optimization algorithms. Experimental results show that Quote-Tuning significantly increases the percentage of LLM generation quoted verbatim from high-quality pre-training documents by 55% to 130% relative to untuned models while maintaining response quality. Further experiments demonstrate that Quote-Tuning generalizes quoting to out-of-domain data, is applicable in different tasks, and provides additional benefits to truthfulness. Quote-Tuning not only serves as a hassle-free method to increase quoting but also opens up avenues for improving LLM trustworthiness through better verifiability.

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.

Reliable verifiable data has become a key driver of capability gains in modern language models, enabling stable reinforcement learning with verifiable rewards and effective distillation that transfers competence across math, coding, and agentic tasks. Yet constructing generalizable synthetic verifiable data remains difficult due to hallucination-prone generation, and weak or trivial verification artifacts that fail to separate strong from weak solutions. Existing approaches often rely on task-specific heuristics or post-hoc filters that do not transfer across domains and lack a principled, universal evaluator of verifiability. In this work, we introduce an evolutionary, task-agnostic, strategy-guided, executably-checkable data synthesis framework that, from minimal seed supervision, jointly synthesizes problems, diverse candidate solutions, and verification artifacts, and iteratively discovers strategies via a consistency-based evaluator that enforces agreement between human-annotated and strategy-induced checks. This pipeline upgrades filtering into principled synthesis: it reliably assembles coherent, verifiable training instances and generalizes without domain-specific rules. Our experiments demonstrate the effectiveness of the proposed approach under both RLVR and model distillation training paradigms. The results show that training with our synthesized data yields significant improvements on both the LiveCodeBench and AgentBench-OS tasks, highlighting the robust generalization of our framework.

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/.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Speculative decoding (SD) addresses the high inference costs of LLMs by having lightweight drafters generate candidates for large verifiers to validate in parallel. Existing draft-verify methods use binary decisions: accept or fully recompute. Yet we find that many rejected tokens can be verified correctly by a slim submodel derived from the full verifier via intra-model routing, instead of the full verifier. This motivates our slim-verifier to handle tokens requiring moderate verification resources, reducing expensive large-model calls. We propose Verification via Intra-Model Routing for Speculative Decoding (VIA-SD), a multi-tier framework using a routed slim-verifier. Draft tokens are processed hierarchically: direct acceptance for high-confidence cases, slim-verifier regeneration for medium-confidence cases, and full-model verification for uncertain cases. Across four representative tasks and multiple model families, VIA-SD reduces rejection rates by 0.10-0.22 and delivers 10-20% speedups over strong SD baselines, while achieving 2.5-3x acceleration over non-drafting decoding. Moreover, VIA-SD is compatible with existing SD frameworks without modifying their training procedures. Our results suggest multi-tier SD as a general paradigm for scalable and efficient LLM inference. Project page: https://zju-xyc.github.io/VIA-SD-Project-Page/

Retrieval-enhanced methods have become a primary approach in fact verification (FV); it requires reasoning over multiple retrieved pieces of evidence to verify the integrity of a claim. To retrieve evidence, existing work often employs off-the-shelf retrieval models whose design is based on the probability ranking principle. We argue that, rather than relevance, for FV we need to focus on the utility that a claim verifier derives from the retrieved evidence. We introduce the feedback-based evidence retriever(FER) that optimizes the evidence retrieval process by incorporating feedback from the claim verifier. As a feedback signal we use the divergence in utility between how effectively the verifier utilizes the retrieved evidence and the ground-truth evidence to produce the final claim label. Empirical studies demonstrate the superiority of FER over prevailing baselines.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising approach for training reasoning language models (RLMs) by leveraging supervision from verifiers. Although verifier implementation is easier than solution annotation for many tasks, existing synthetic data generation methods remain largely solution-centric, while verifier-based methods rely on a few hand-crafted procedural environments. In this work, we scale RLVR by introducing ReSyn, a pipeline that generates diverse reasoning environments equipped with instance generators and verifiers, covering tasks such as constraint satisfaction, algorithmic puzzles, and spatial reasoning. A Qwen2.5-7B-Instruct model trained with RL on ReSyn data achieves consistent gains across reasoning benchmarks and out-of-domain math benchmarks, including a 27\% relative improvement on the challenging BBEH benchmark. Ablations show that verifier-based supervision and increased task diversity both contribute significantly, providing empirical evidence that generating reasoning environments at scale can enhance reasoning abilities in RLMs

Large Language Models (LLMs) have made unprecedented breakthroughs, yet their increasing integration into everyday life might raise societal risks due to generated unethical content. Despite extensive study on specific issues like bias, the intrinsic values of LLMs remain largely unexplored from a moral philosophy perspective. This work delves into ethical values utilizing Moral Foundation Theory. Moving beyond conventional discriminative evaluations with poor reliability, we propose DeNEVIL, a novel prompt generation algorithm tailored to dynamically exploit LLMs' value vulnerabilities and elicit the violation of ethics in a generative manner, revealing their underlying value inclinations. On such a basis, we construct MoralPrompt, a high-quality dataset comprising 2,397 prompts covering 500+ value principles, and then benchmark the intrinsic values across a spectrum of LLMs. We discovered that most models are essentially misaligned, necessitating further ethical value alignment. In response, we develop VILMO, an in-context alignment method that substantially enhances the value compliance of LLM outputs by learning to generate appropriate value instructions, outperforming existing competitors. Our methods are suitable for black-box and open-source models, offering a promising initial step in studying the ethical values of LLMs.

Autonomous GUI agents face two fundamental challenges: early stopping, where agents prematurely declare success without verifiable evidence, and repetitive loops, where agents cycle through the same failing actions without recovery. We present VLAA-GUI, a modular GUI agentic framework built around three integrated components that guide the system on when to Stop, Recover, and Search. First, a mandatory Completeness Verifier enforces UI-observable success criteria and verification at every finish step -- with an agent-level verifier that cross-examines completion claims with decision rules, rejecting those lacking direct visual evidence. Second, a mandatory Loop Breaker provides multi-tier filtering: switching interaction mode after repeated failures, forcing strategy changes after persistent screen-state recurrence, and binding reflection signals to strategy shifts. Third, an on-demand Search Agent searches online for unfamiliar workflows by directly querying a capable LLM with search ability, returning results as plain text. We additionally integrate a Coding Agent for code-intensive actions and a Grounding Agent for precise action grounding, both invoked on demand when required. We evaluate VLAA-GUI across five top-tier backbones, including Opus 4.5, 4.6 and Gemini 3.1 Pro, on two benchmarks with Linux and Windows tasks, achieving top performance on both (77.5% on OSWorld and 61.0% on WindowsAgentArena). Notably, three of the five backbones surpass human performance (72.4%) on OSWorld in a single pass. Ablation studies show that all three proposed components consistently improve a strong backbone, while a weaker backbone benefits more from these tools when the step budget is sufficient. Further analysis also shows that the Loop Breaker nearly halves wasted steps for loop-prone models.

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.

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.

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.

Reinforcement learning with verifiable rewards has become a central tool for improving the reasoning ability of large language models, but current methods face a trade-off between simplicity and credit assignment. Group-relative methods such as GRPO avoid training a critic, but typically assign a trajectory-level advantage to every token. Actor-critic methods provide denser learning signals, but require a learned value function with its own training instability. We introduce VIMPO, a critic-free policy optimization method that derives a policy-implied value function from the optimality conditions of KL-regularized reinforcement learning. For autoregressive generation, the resulting value recurrence can be written in terms of policy-reference log-ratios and anchored by the terminal condition that no future reward remains at the end of a trajectory. This gives a simple value loss that incorporates outcome-level verifiable rewards without training a critic. The same derivation also yields a critic-free actor advantage, allowing VIMPO to separate reward incorporation through the value loss from policy improvement through a PPO-style actor update. On mathematical RLVR benchmarks, VIMPO improves over GRPO across MATH-500, AIME 2024, AIME 2025, and OlympiadBench, with especially larger gains on competition-style evaluations. Under noisy rewards, VIMPO retains a consistent advantage over GRPO, suggesting that policy-implied value optimization can provide finer credit assignment while preserving the practical simplicity of critic-free training.

It is tempting to assume any task solvable by a short program can be taught to a model as its chain-of-thought: write the steps out, fine-tune, and the model follows. This paper shows the assumption fails for an identifiable class of procedures. The testbed is nine reasoning tasks, each from a deterministic generator; public and hidden splits share generators, so held-out data proxies test accuracy. I reverse-engineer the generators into Python solvers, render them as chain-of-thought, and distill into a rank-<= 32 LoRA over a 30B (3.5B-active) Nemotron model. Forward-computable tasks install readily: lookup/arithmetic and an 8-bit boolean task transfer (>= 0.99 and 0.68). Cryptarithm does not: distilling its backtracking search holds at 0.01-0.07 across eleven chain-of-thought designs, RL from verifiable rewards, and self-training, even though a search solver answers 71% of instances. This is not a capability gap. The model does the arithmetic on 97-100% of lines and ranks the correct cipher in its top eight on 71%; it cannot carry the search forward as a left-to-right derivation. Fine-tuning learns the shape of a verifiable elimination step while its verdicts become unconditional templates, correct only 16-57% of the time ("verdict-as-token"). The ceiling holds across backbones from 3B to 671B and across fine-tuning and prompting; a controlled intervention isolates the cause: revealing the cipher key, which turns the derivation forward, lifts the same instances from 0.03 to 0.57. When a procedure's only solution is search over information-free structure, no faithful forward chain-of-thought exists to imitate. The task becomes learnable only by removing the search, precomputing its combinatorial core into a catalog and reducing the trace to recall plus verification; the 1st-place solution reaches Private LB 0.92 this way. What distills is memorization and verification, not search.

Large language models (LLMs) have recently achieved notable success in code-generation benchmarks such as HumanEval and LiveCodeBench. However, a detailed examination reveals that these evaluation suites often comprise only a limited number of homogeneous test cases, resulting in subtle faults going undetected. This not only artificially inflates measured performance but also compromises accurate reward estimation in reinforcement learning frameworks utilizing verifiable rewards (RLVR). To address these critical shortcomings, we systematically investigate the test-case generation (TCG) task by proposing multi-dimensional metrics designed to rigorously quantify test-suite thoroughness. Furthermore, we introduce a human-LLM collaborative method (SAGA), leveraging human programming expertise with LLM reasoning capability, aimed at significantly enhancing both the coverage and the quality of generated test cases. In addition, we develop a TCGBench to facilitate the study of the TCG task. Experiments show that SAGA achieves a detection rate of 90.62% and a verifier accuracy of 32.58% on TCGBench. The Verifier Accuracy (Verifier Acc) of the code generation evaluation benchmark synthesized by SAGA is 10.78% higher than that of LiveCodeBench-v6. These results demonstrate the effectiveness of our proposed method. We hope this work contributes to building a scalable foundation for reliable LLM code evaluation, further advancing RLVR in code generation, and paving the way for automated adversarial test synthesis and adaptive benchmark integration.

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.

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.

The widespread adoption of deep neural networks (DNNs) requires efficient techniques for verifying their safety. DNN verifiers are complex tools, which might contain bugs that could compromise their soundness and undermine the reliability of the verification process. This concern can be mitigated using proofs: artifacts that are checkable by an external and reliable proof checker, and which attest to the correctness of the verification process. However, such proofs tend to be extremely large, limiting their use in many scenarios. In this work, we address this problem by minimizing proofs of unsatisfiability produced by DNN verifiers. We present algorithms that remove facts which were learned during the verification process, but which are unnecessary for the proof itself. Conceptually, our method analyzes the dependencies among facts used to deduce UNSAT, and removes facts that did not contribute. We then further minimize the proof by eliminating remaining unnecessary dependencies, using two alternative procedures. We implemented our algorithms on top of a proof producing DNN verifier, and evaluated them across several benchmarks. Our results show that our best-performing algorithm reduces proof size by 37%-82% and proof checking time by 30%-88%, while introducing a runtime overhead of 7%-20% to the verification process itself.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

Reinforcement Learning (RL) has become a powerful tool for enhancing the reasoning abilities of large language models (LLMs) by optimizing their policies with reward signals. Yet, RL's success relies on the reliability of rewards, which are provided by verifiers. In this paper, we expose and analyze a widespread problem--false negatives--where verifiers wrongly reject correct model outputs. Our in-depth study of the Big-Math-RL-Verified dataset reveals that over 38% of model-generated responses suffer from false negatives, where the verifier fails to recognize correct answers. We show, both empirically and theoretically, that these false negatives severely impair RL training by depriving the model of informative gradient signals and slowing convergence. To mitigate this, we propose tinyV, a lightweight LLM-based verifier that augments existing rule-based methods, which dynamically identifies potential false negatives and recovers valid responses to produce more accurate reward estimates. Across multiple math-reasoning benchmarks, integrating TinyV boosts pass rates by up to 10% and accelerates convergence relative to the baseline. Our findings highlight the critical importance of addressing verifier false negatives and offer a practical approach to improve RL-based fine-tuning of LLMs. Our code is available at https://github.com/uw-nsl/TinyV.

Reinforcement learning with verifiable rewards (RLVR) for Large Reasoning Models hinges on baseline estimation for variance reduction, but existing approaches pay a heavy price: PPO requires a policy-model scale critic, while GRPO needs multiple rollouts per prompt to keep its empirical group mean stable. We introduce Policy Optimization with Internal State Value Estimation), which obtains a baseline at negligible cost by using the policy model's internal signals already computed during the policy forward pass. A lightweight probe predicts the expected verifiable reward from the hidden states of the prompt and generated trajectory, as well as token-entropy statistics, and is trained online alongside the policy. To preserve gradient unbiasedness despite using trajectory-conditioned features, we introduce a cross-rollout construction that predicts each rollout's value from an independent rollout's internal states. Because POISE estimates prompt value using only a single rollout, it enables higher prompt diversity for a fixed compute budget during training. This reduces gradient variance for more stable learning and also eliminates the compute overhead of sampling costs for detecting zero-advantage prompts. On Qwen3-4B and DeepSeek-R1-Distill-Qwen-1.5B across math reasoning benchmarks, POISE matches DAPO while requiring less compute. Moreover, its value estimator shows similar performance to a separate LLM-scale value model and generalizes to various verifiable tasks. By leveraging the model's own internal representations, POISE enables more stable and efficient policy optimization.

The advent of pre-trained code language models (CodeLMs) has lead to significant progress in language-to-code generation. State-of-the-art approaches in this area combine CodeLM decoding with sample pruning and reranking using test cases or heuristics based on the execution results. However, it is challenging to obtain test cases for many real-world language-to-code applications, and heuristics cannot well capture the semantic features of the execution results, such as data type and value range, which often indicates the correctness of the program. In this work, we propose LEVER, a simple approach to improve language-to-code generation by learning to verify the generated programs with their execution results. Specifically, we train verifiers to determine whether a program sampled from the CodeLM is correct or not based on the natural language input, the program itself and its execution results. The sampled programs are reranked by combining the verification score with the CodeLM generation probability, and marginalizing over programs with the same execution results. On four datasets across the domains of table QA, math QA and basic Python programming, LEVER consistently improves over the base CodeLMs (4.6% to 10.9% with code-davinci-002) and achieves new state-of-the-art results on all of them.

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.

Fact verification is essential for ensuring the reliability of LLM applications. In this study, we evaluate 12 pre-trained LLMs and one specialized fact-verifier, including frontier LLMs and open-weight reasoning LLMs, using a collection of examples from 14 fact-checking benchmarks. We share three findings intended to guide future development of more robust fact verifiers. First, we highlight the importance of addressing annotation errors and ambiguity in datasets, demonstrating that approximately 16\% of ambiguous or incorrectly labeled data substantially influences model rankings. Neglecting this issue may result in misleading conclusions during comparative evaluations, and we suggest using a systematic pipeline utilizing LLM-as-a-judge to help identify these issues at scale. Second, we discover that frontier LLMs with few-shot in-context examples, often overlooked in previous works, achieve top-tier performance. We therefore recommend future studies include comparisons with these simple yet highly effective baselines. Lastly, despite their effectiveness, frontier LLMs incur substantial costs, motivating the development of small, fine-tuned fact verifiers. We show that these small models still have room for improvement, particularly on instances that require complex reasoning. Encouragingly, we demonstrate that augmenting training with synthetic multi-hop reasoning data significantly enhances their capabilities in such instances. We release our code, model, and dataset at https://github.com/just1nseo/verifying-the-verifiers

We introduce our Leanabell-Prover-V2, a 7B large language models (LLMs) that can produce formal theorem proofs in Lean 4, with verifier-integrated Long Chain-of-Thoughts (CoT). Following our previous work Leanabell-Prover-V1, we continual to choose to posttrain existing strong prover models for further performance improvement. In our V2 version, we mainly upgrade the Reinforcement Learning (RL) with feedback provided by the Lean 4 verifier. Crucially, verifier feedback, such as indicating success or detailing specific errors, allows the LLM to become ``self-aware'' of the correctness of its own reasoning process and learn to reflexively correct errors. Leanabell-Prover-V2 directly optimizes LLM reasoning trajectories with multi-turn verifier interactions, together with feedback token masking for stable RL training and a simple reward strategy. Experiments show that Leanabell-Prover-V2 improves performance by 3.2% (pass@128) with Kimina-Prover-Preview-Distill-7B and 2.0% (pass@128) with DeepSeek-Prover-V2-7B on the MiniF2F test set. The source codes, curated data and models are available at: https://github.com/Leanabell-LM/Leanabell-Prover-V2.

Speculative sampling (SpS) has been successful in accelerating the decoding throughput of auto-regressive large language models by leveraging smaller draft models. SpS strictly enforces the generated distribution to match that of the verifier LLM. This is unnecessarily restrictive as slight variations of the verifier's distribution, such as sampling with top-k or temperature, would also be acceptable. Typical acceptance sampling (TAS) alleviates this issue by accepting more tokens using entropy-based heuristics. However, this approach distorts the verifier distribution, potentially degrading output quality when the verifier encodes critical information. In this work, we formalize the speculative sampling algorithm through the lens of constrained optimization. Based on this formulation, we propose Cactus (constrained acceptance speculative sampling), a method that guarantees controlled divergence from the verifier distribution and increasing acceptance rates. Empirical results across a wide range of benchmarks confirm the effectiveness of our approach.

Finetuning specialized generative evaluators has emerged as a popular paradigm to meet the increasing demand for scalable evaluation during both training and test-time. However, recent work has largely focused on applying new methodology, such as reinforcement learning (RL), to training evaluators, shying away from large-scale, data-driven development. In this work, we focus on data scaling, curating a set of 2.5M samples spanning five unique evaluation tasks (pairwise, step-level, reference-free and reference-based verification, and single rating) and multiple domains focused on reasoning evaluation. With our data, we train Foundational Automatic Reasoning Evaluators (FARE), a family of 8B and 20B (with 3.6B active) parameter evaluators, with a simple iterative rejection-sampling supervised finetuning (SFT) approach. FARE-8B challenges larger specialized RL-trained evaluators and FARE-20B sets the new standard for open-source evaluators, surpassing specialized 70B+ evaluators. Beyond static benchmarks, we evaluate FARE in real-world tasks: As inference-time rerankers, FARE-20B achieves near-oracle performance on MATH. As verifiers in RL training, FARE improves the downstream RL-trained model performance by up to 14.1% vs. string-matching verifiers. When initialized from FARE, a continually-finetuned FARE-Code outperforms gpt-oss-20B by 65% on evaluating test-case quality.

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.

The proliferation of large language models (LLMs) requires robust evaluation of their alignment with local values and ethical standards, especially as existing benchmarks often reflect the cultural, legal, and ideological values of their creators. LocalValueBench, introduced in this paper, is an extensible benchmark designed to assess LLMs' adherence to Australian values, and provides a framework for regulators worldwide to develop their own LLM benchmarks for local value alignment. Employing a novel typology for ethical reasoning and an interrogation approach, we curated comprehensive questions and utilized prompt engineering strategies to probe LLMs' value alignment. Our evaluation criteria quantified deviations from local values, ensuring a rigorous assessment process. Comparative analysis of three commercial LLMs by USA vendors revealed significant insights into their effectiveness and limitations, demonstrating the critical importance of value alignment. This study offers valuable tools and methodologies for regulators to create tailored benchmarks, highlighting avenues for future research to enhance ethical AI development.

While large language models (LLMs) are trained to align with human values, their generations may still violate safety constraints. A growing line of work addresses this problem by modifying the model's sampling policy at decoding time using a safety reward. However, existing decoding-time steering methods often intervene unnecessarily, modifying generations that would have been safe under the base model. Such unnecessary interventions are undesirable, as they can distort key properties of the base model such as helpfulness, fluency, style, and coherence. We propose a new test-time steering method designed to reduce such unnecessary interventions while improving the safety of unsafe responses. Our approach filters tokens using a value-based safety criterion and provides an explicit bound on the probability of false interventions. A single threshold hyperparameter controls this bound, allowing practitioners to trade off higher rates of unnecessary intervention for better output safety. Across multiple datasets and experiments, we show that our value-filtered decoding method outperforms existing baselines, achieving better trade-offs between safety, helpfulness, and similarity to the base model.

The integration of machine learning (ML) systems into critical industries such as healthcare, finance, and cybersecurity has transformed decision-making processes, but it also brings new challenges around trust, security, and accountability. As AI systems become more ubiquitous, ensuring the transparency and correctness of AI-driven decisions is crucial, especially when they have direct consequences on privacy, security, or fairness. Verifiable AI, powered by Zero-Knowledge Machine Learning (zkML), offers a robust solution to these challenges. zkML enables the verification of AI model inferences without exposing sensitive data, providing an essential layer of trust and privacy. However, traditional zkML systems typically require deep cryptographic expertise, placing them beyond the reach of most ML engineers. In this paper, we introduce JSTprove, a specialized zkML toolkit, built on Polyhedra Network's Expander backend, to enable AI developers and ML engineers to generate and verify proofs of AI inference. JSTprove provides an end-to-end verifiable AI inference pipeline that hides cryptographic complexity behind a simple command-line interface while exposing auditable artifacts for reproducibility. We present the design, innovations, and real-world use cases of JSTprove as well as our blueprints and tooling to encourage community review and extension. JSTprove therefore serves both as a usable zkML product for current engineering needs and as a reproducible foundation for future research and production deployments of verifiable AI.

Program verifiers play a central role in training coding agents, including selecting trajectories for supervised fine-tuning (SFT) and providing rewards for reinforcement learning (RL). Standard execution-based verification requires running unit tests inside per-repository environments such as Docker images, incurring substantial environment setup costs. We propose Dockerless, an environment-free agentic patch verifier that evaluates generated code patches without executing them. Rather than simply matching candidate patches to references, Dockerless judges patch correctness using evidence gathered through agentic repository exploration. On a verifier evaluation benchmark, Dockerless outperforms the strongest open-source verifier by 14.3 AUC points. Using Dockerless as both the SFT trajectory filter and the RL reward enables a fully environment-free post-training pipeline. The resulting model reaches 62.0%, 50.0%, and 35.2% resolve rate on SWE-bench Verified, Multilingual, and Pro, respectively. It surpasses the Qwen3.5-9B baseline by 2.4, 8.7, and 2.9 points, matching environment-based post-training.

Speculative decoding accelerates LLM inference by drafting a tree of candidate continuations and verifying it in one target forward. Existing drafters fall into two camps with opposite weaknesses. Autoregressive drafters such as EAGLE-3 preserve dependence along each draft path but call the drafter once per tree depth, making drafting a non-trivial share of per-iteration latency. Parallel drafters cut drafter calls by predicting multiple future positions in one forward, but each position is predicted without seeing the others, producing paths the verifier rejects. In this paper, we propose SpecBlock, a block-iterative drafter that combines path dependence with cheap drafting. Each drafter forward produces K dependent positions and we call this a block. The draft tree grows through repeated block expansions. Two mechanisms explicitly carry path dependence to keep later draft positions accurate. Within each block, a layer-wise shift carries the previous position's hidden state into every decoder layer. Across blocks, each new block can start from any position of the previous block, inheriting its hidden state to extend the path. To spend verifier budget where acceptance is likely, a co-trained rank head replaces the fixed top-k tree by allocating per-position branching during drafting. To avoid training the drafter on prefixes it never produces at inference, a valid-prefix mask drops the loss at later positions once an earlier one is wrong. Beyond static drafting, a cost-aware bandit at deployment uses free verifier feedback to update the drafter selectively, only when the expected throughput gain exceeds the update cost. Experiments show that SpecBlock improves mean speedup by 8-13% over EAGLE-3 at 44-52% of its drafting cost, and cost-aware adaptation extends this lead to 11-19%.

Reinforcement learning with verifiable rewards (RLVR) is a practical and scalable approach to enhancing large language models in areas such as math, code, and other structured tasks. Two questions motivate this paper: how much of the reported gains survive under strictly parity-controlled evaluation, and whether RLVR is cost-free or exacts a measurable tax. We argue that progress is real, but gains are often overstated due to three forces - an RLVR tax, evaluation pitfalls, and data contamination. Using a partial-prompt contamination audit and matched-budget reproductions across base and RL models, we show that several headline gaps shrink or vanish under clean, parity-controlled evaluation. We then propose a tax-aware training and evaluation protocol that co-optimizes accuracy, grounding, and calibrated abstention and standardizes budgeting and provenance checks. Applied to recent RLVR setups, this protocol yields more reliable estimates of reasoning gains and, in several cases, revises prior conclusions. Our position is constructive: RLVR is valuable and industry-ready; we advocate keeping its practical benefits while prioritizing reliability, safety, and measurement.

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.

AI coding agents are increasingly used to write real-world software, but ensuring that their outputs are correct remains a fundamental challenge. Formal verification offers a promising path: an agent generates code together with a machine-checked proof, guaranteeing that the code satisfies a formal specification. However, there is no guarantee that the formal spec itself matches the user's intent. In this work, we study specification autoformalization: whether LLM agents can translate informal programming problems into faithful formal specifications. We introduce Verus-SpecBench, a benchmark of 581 spec-writing tasks derived from Codeforces problems targeting Verus, a verifier for Rust, and Verus-SpecGym, an agentic environment in which models interact with Verus, bash, & the filesystem to develop these specs. The central challenge is evaluation: expert-written reference specs are expensive to write, & LLM judges can miss subtle mistakes. We address this by (a) extending Verus's exec_spec mechanism so that generated specs can be executed as Rust code, & (b) testing them against official Codeforces tests & adversarial cases extracted from Codeforces "hacks", which are edge cases written by competitors to break incorrect solutions. On Verus-SpecBench, the strongest model, Gemini 3.1 Pro, solves 77.8% of tasks, other frontier models solve 51.1--57.8% & OSS models reach only 21.5--25.5%. Our analysis of failure modes shows that model-generated specs can omit important input assumptions, accept incorrect outputs, & reject valid ones. We also find that LLM-as-a-judge evaluation misses 26% of the failures our evaluator catches. Overall, our results suggest that spec autoformalization is within reach for frontier agents but remains brittle even on problems where they can already generate correct code. The code, data, & logs can be found at https://github.com/formal-verif-is-cool/verus-spec-gym

Data trading is essential to accelerate the development of data-driven machine learning pipelines. The central problem in data trading is to estimate the utility of a seller's dataset with respect to a given buyer's machine learning task, also known as data valuation. Typically, data valuation requires one or more participants to share their raw dataset with others, leading to potential risks of intellectual property (IP) violations. In this paper, we tackle the novel task of preemptively protecting the IP of datasets that need to be shared during data valuation. First, we identify and formalize two kinds of novel IP risks in visual datasets: data-item (image) IP and statistical (dataset) IP. Then, we propose a novel algorithm to convert the raw dataset into a sanitized version, that provides resistance to IP violations, while at the same time allowing accurate data valuation. The key idea is to limit the transfer of information from the raw dataset to the sanitized dataset, thereby protecting against potential intellectual property violations. Next, we analyze our method for the likely existence of a solution and immunity against reconstruction attacks. Finally, we conduct extensive experiments on three computer vision datasets demonstrating the advantages of our method in comparison to other baselines.

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.

Code verifiers play a critical role in post-verification for LLM-based code generation, yet existing supervised fine-tuning methods suffer from data scarcity, high failure rates, and poor inference efficiency. While reinforcement learning (RL) offers a promising alternative by optimizing models through execution-driven rewards without labeled supervision, our preliminary results show that naive RL with only functionality rewards fails to generate effective unit tests for difficult branches and samples. We first theoretically analyze showing that branch coverage, sample difficulty, syntactic and functional correctness can be jointly modeled as RL rewards, where optimizing these signals can improve the reliability of unit-test-based verification. Guided by this analysis, we design syntax- and functionality-aware rewards and further propose branch- and sample-difficulty--aware RL using exponential reward shaping and static analysis metrics. With this formulation, CVeDRL achieves state-of-the-art performance with only 0.6B parameters, yielding up to 28.97% higher pass rate and 15.08% higher branch coverage than GPT-3.5, while delivering over 20times faster inference than competitive baselines. Code is available at https://github.com/LIGHTCHASER1/CVeDRL.git

Test-time scaling has shown considerable success in improving the performance of language models on complex reasoning tasks without requiring fine-tuning. However, current strategies such as self-reflection primarily focus on logical or structural refinement. They do not leverage the guiding potential of affective feedback. Inspired by psychological research showing that emotions can modulate cognitive performance, we introduce HEART--a novel framework that uses emotionally-driven prompts for iterative self-correction. HEART provides feedback on a model's incorrect response using a curated set of concise, emotionally charged phrases based on the six universal emotions categorized by Dr. Paul Ekman. By systematically varying the emotional tone of the feedback across iterations, our method guides the model to escape flawed reasoning paths and explore more promising alternatives. We evaluate our framework on challenging reasoning benchmarks including OlympiadBench, Humanity's Last Exam, and SimpleQA. Our results reveal a significant new phenomenon: when guided by an oracle verifier, this affective iteration protocol unlocks significantly deeper reasoning, leading to consistent and substantial increases in accuracy over state-of-the-art baselines with the same verifier. However, we also identify a critical bottleneck for practical deployment. In a verifier-free setting, it struggles to harness these gains consistently, highlighting as a key challenge for future work. Our findings suggest that the next frontier in machine reasoning may lie not just in refining logic, but also in understanding and leveraging the `HEART' of the models.

The deployment of autonomous AI agents in sensitive domains, such as healthcare, introduces critical risks to safety, security, and privacy. These agents may deviate from user objectives, violate data handling policies, or be compromised by adversarial attacks. Mitigating these dangers necessitates a mechanism to formally guarantee that an agent's actions adhere to predefined safety constraints, a challenge that existing systems do not fully address. We introduce VeriGuard, a novel framework that provides formal safety guarantees for LLM-based agents through a dual-stage architecture designed for robust and verifiable correctness. The initial offline stage involves a comprehensive validation process. It begins by clarifying user intent to establish precise safety specifications. VeriGuard then synthesizes a behavioral policy and subjects it to both testing and formal verification to prove its compliance with these specifications. This iterative process refines the policy until it is deemed correct. Subsequently, the second stage provides online action monitoring, where VeriGuard operates as a runtime monitor to validate each proposed agent action against the pre-verified policy before execution. This separation of the exhaustive offline validation from the lightweight online monitoring allows formal guarantees to be practically applied, providing a robust safeguard that substantially improves the trustworthiness of LLM agents.

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.

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

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.

Reinforcement Learning (RL) has enabled Large Language Models (LLMs) to achieve remarkable reasoning in domains like mathematics and coding, where verifiable rewards provide clear signals. However, extending this paradigm to financial decision is challenged by the market's stochastic nature: rewards are verifiable but inherently noisy, causing standard RL to degenerate into reward hacking. To address this, we propose Trade-R1, a model training framework that bridges verifiable rewards to stochastic environments via process-level reasoning verification. Our key innovation is a verification method that transforms the problem of evaluating reasoning over lengthy financial documents into a structured Retrieval-Augmented Generation (RAG) task. We construct a triangular consistency metric, assessing pairwise alignment between retrieved evidence, reasoning chains, and decisions to serve as a validity filter for noisy market returns. We explore two reward integration strategies: Fixed-effect Semantic Reward (FSR) for stable alignment signals, and Dynamic-effect Semantic Reward (DSR) for coupled magnitude optimization. Experiments on different country asset selection demonstrate that our paradigm reduces reward hacking, with DSR achieving superior cross-market generalization while maintaining the highest reasoning consistency.

Generative Pre-trained Transformer (GPT) models have exhibited exciting progress in capabilities, capturing the interest of practitioners and the public alike. Yet, while the literature on the trustworthiness of GPT models remains limited, practitioners have proposed employing capable GPT models for sensitive applications to healthcare and finance - where mistakes can be costly. To this end, this work proposes a comprehensive trustworthiness evaluation for large language models with a focus on GPT-4 and GPT-3.5, considering diverse perspectives - including toxicity, stereotype bias, adversarial robustness, out-of-distribution robustness, robustness on adversarial demonstrations, privacy, machine ethics, and fairness. Based on our evaluations, we discover previously unpublished vulnerabilities to trustworthiness threats. For instance, we find that GPT models can be easily misled to generate toxic and biased outputs and leak private information in both training data and conversation history. We also find that although GPT-4 is usually more trustworthy than GPT-3.5 on standard benchmarks, GPT-4 is more vulnerable given jailbreaking system or user prompts, potentially due to the reason that GPT-4 follows the (misleading) instructions more precisely. Our work illustrates a comprehensive trustworthiness evaluation of GPT models and sheds light on the trustworthiness gaps. Our benchmark is publicly available at https://decodingtrust.github.io/.

Reinforcement learning with verifiable rewards (RLVR) succeeds in reasoning tasks (e.g., math and code) by checking the final verifiable answer (i.e., a verifiable dot signal). However, extending this paradigm to open-ended generation is challenging because there is no unambiguous ground truth. Relying on single-dot supervision often leads to inefficiency and reward hacking. To address these issues, we propose reinforcement learning with verifiable reference-based rewards (RLVRR). Instead of checking the final answer, RLVRR extracts an ordered linguistic signal from high-quality references (i.e, reward chain). Specifically, RLVRR decomposes rewards into two dimensions: content, which preserves deterministic core concepts (e.g., keywords), and style, which evaluates adherence to stylistic properties through LLM-based verification. In this way, RLVRR combines the exploratory strength of RL with the efficiency and reliability of supervised fine-tuning (SFT). Extensive experiments on more than 10 benchmarks with Qwen and Llama models confirm the advantages of our approach. RLVRR (1) substantially outperforms SFT trained with ten times more data and advanced reward models, (2) unifies the training of structured reasoning and open-ended generation, and (3) generalizes more effectively while preserving output diversity. These results establish RLVRR as a principled and efficient path toward verifiable reinforcement learning for general-purpose LLM alignment. We release our code and data at https://github.com/YJiangcm/RLVRR.

Large Language Models (LLMs) have exploded a new heatwave of AI, for their ability to engage end-users in human-level conversations with detailed and articulate answers across many knowledge domains. In response to their fast adoption in many industrial applications, this survey concerns their safety and trustworthiness. First, we review known vulnerabilities of the LLMs, categorising them into inherent issues, intended attacks, and unintended bugs. Then, we consider if and how the Verification and Validation (V&V) techniques, which have been widely developed for traditional software and deep learning models such as convolutional neural networks, can be integrated and further extended throughout the lifecycle of the LLMs to provide rigorous analysis to the safety and trustworthiness of LLMs and their applications. Specifically, we consider four complementary techniques: falsification and evaluation, verification, runtime monitoring, and ethical use. Considering the fast development of LLMs, this survey does not intend to be complete (although it includes 300 references), especially when it comes to the applications of LLMs in various domains, but rather a collection of organised literature reviews and discussions to support the quick understanding of the safety and trustworthiness issues from the perspective of V&V.

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

Recent work on reinforcement learning with verifiable rewards (RLVR) has shown that large language models (LLMs) can be substantially improved using outcome-level verification signals, such as unit tests for code or exact-match checks for mathematics. In parallel, process supervision has long been explored as a way to shape the intermediate reasoning behaviour of LLMs, but existing approaches rely on neural judges to score chain-of-thought steps, leaving them vulnerable to opacity, bias, and reward hacking. To address this gap, we introduce Verifiable Process Reward Models (VPRMs), a reinforcement-learning framework in which intermediate reasoning steps are checked by deterministic, rule-based verifiers. We apply VPRMs to risk-of-bias assessment for medical evidence synthesis, a domain where guideline-defined criteria and rule-based decision paths enable programmatic verification of reasoning traces. Across multiple datasets, we find that VPRMs generate reasoning that adheres closely to domain rules and achieve substantially higher coherence between step-level decisions and final labels. Results show that VPRMs achieve up to 20% higher F1 than state-of-the-art models and 6.5% higher than verifiable outcome rewards, with substantial gains in evidence grounding and logical coherence.

Long chain-of-thought reasoning has made autoregressive decoding the dominant inference cost of modern large language models. Existing methods target either the input side (latent compression) or the output side (speculative decoding and multi-token prediction, MTP), but the two lines of work have been pursued independently. Moreover, output-side methods must incur an expensive verifier pass to validate the unreliable draft tokens predicted by MTP. To address these issues, we propose Pair-In, Pair-Out (PIPO), which unifies both sides by viewing a latent compressor and an MTP head as mirror-image operations: the compressor folds two input tokens into one latent representation, while the MTP head unfolds one hidden state into one additional output token. To remove the verifier cost without sacrificing reliability, PIPO trains a lightweight confidence head that decides whether draft tokens should be accepted. We observe that On-Policy Distillation (OPD) naturally matches the rejection-sampling criterion of speculative decoding, so the confidence head can be trained alongside OPD with negligible extra cost. Experiments on AIME 2025, GPQA-Diamond, LiveCodeBench v6, and LongBench v2 with Qwen3.5-4B and 9B backbones show that PIPO improves pass@4 over regular decoding by up to +7.15 points, while delivering up to 2.64times first-token-latency and 2.07times per-token-latency speedups. Project Page: GitHub.com/RedAI-Infra/PIPO.

As increasingly capable open-weight large language models (LLMs) are deployed, improving their tamper resistance against unsafe modifications, whether accidental or intentional, becomes critical to minimize risks. However, there is no standard approach to evaluate tamper resistance. Varied data sets, metrics, and tampering configurations make it difficult to compare safety, utility, and robustness across different models and defenses. To this end, we introduce TamperBench, the first unified framework to systematically evaluate the tamper resistance of LLMs. TamperBench (i) curates a repository of state-of-the-art weight-space fine-tuning attacks and latent-space representation attacks; (ii) enables realistic adversarial evaluation through systematic hyperparameter sweeps per attack-model pair; and (iii) provides both safety and utility evaluations. TamperBench requires minimal additional code to specify any fine-tuning configuration, alignment-stage defense method, and metric suite while ensuring end-to-end reproducibility. We use TamperBench to evaluate 21 open-weight LLMs, including defense-augmented variants, across nine tampering threats using standardized safety and capability metrics with hyperparameter sweeps per model-attack pair. This yields novel insights, including effects of post-training on tamper resistance, that jailbreak-tuning is typically the most severe attack, and that Triplet emerges as a leading alignment-stage defense. Code is available at: https://github.com/criticalml-uw/TamperBench

Modern AI systems rely on vector embeddings stored and searched using floating-point arithmetic. While effective for approximate similarity search, this design introduces fundamental non-determinism: identical models, inputs, and code can produce different memory states and retrieval results across hardware architectures (e.g., x86 vs. ARM). This prevents replayability and safe deployment, leading to silent data divergence that prevents post-hoc verification and compromises audit trails in regulated sectors. We present Valori, a deterministic AI memory substrate that replaces floating-point memory operations with fixed-point arithmetic (Q16.16) and models memory as a replayable state machine. Valori guarantees bit-identical memory states, snapshots, and search results across platforms. We demonstrate that non-determinism arises before indexing or retrieval and show how Valori enforces determinism at the memory boundary. Our results suggest that deterministic memory is a necessary primitive for trustworthy AI systems. The reference implementation is open-source and available at https://github.com/varshith-Git/Valori-Kernel (archived at https://zenodo.org/records/18022660).

We study inference-time pattern-memory gating in a production-scale clinical natural language processing (NLP) pipeline. The pipeline pairs a generator (Llama-3.3 70B) proposing extractions with a verifier (MMed-Llama-3.1 70B) accepting or rejecting them, over 167,034 PMC-Patients narratives, and adds a lightweight memory that learns at deployment which extractions to filter, so the verifier need not re-examine candidates already seen to fail. We report four findings. First, learning filtering rules directly from the verifier's rejections failed at full scale: the relation-extraction filter stayed empty despite 785,797 logged rejections, because they were spread too thinly across too many distinct forms to accumulate. Second, a simpler rule using a fixed clinical ontology produced the same filtering without the verifier, capturing 49,734 ontology-violating relations on a held-out 5,000-patient set. Third, of five versions of the question-answering filter, four failed for distinct, instructive reasons; the fifth succeeded by checking whether a patient's extracted entities support the question asked, and where it applies was 1.84 times likelier to flag an answer the verifier would reject than one it would accept. Fourth, one pattern held across all five: a filter is selective only when it tests the same evidence the verifier weighs, not when it imitates the verifier's output. Together these give a transferable result for any generator-verifier pipeline: the most natural memory design can fail silently at scale, and whether a pre-generation gate is selective is decided before any engineering effort, by whether its signal probes the question the verifier itself answers. Throughout, the system flags suspect extractions rather than deleting them, so every decision stays visible for clinical review. All code and test artefacts are released openly.

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.

Large language models (LLMs), exemplified by ChatGPT, have gained considerable attention for their excellent natural language processing capabilities. Nonetheless, these LLMs present many challenges, particularly in the realm of trustworthiness. Therefore, ensuring the trustworthiness of LLMs emerges as an important topic. This paper introduces TrustLLM, a comprehensive study of trustworthiness in LLMs, including principles for different dimensions of trustworthiness, established benchmark, evaluation, and analysis of trustworthiness for mainstream LLMs, and discussion of open challenges and future directions. Specifically, we first propose a set of principles for trustworthy LLMs that span eight different dimensions. Based on these principles, we further establish a benchmark across six dimensions including truthfulness, safety, fairness, robustness, privacy, and machine ethics. We then present a study evaluating 16 mainstream LLMs in TrustLLM, consisting of over 30 datasets. Our findings firstly show that in general trustworthiness and utility (i.e., functional effectiveness) are positively related. Secondly, our observations reveal that proprietary LLMs generally outperform most open-source counterparts in terms of trustworthiness, raising concerns about the potential risks of widely accessible open-source LLMs. However, a few open-source LLMs come very close to proprietary ones. Thirdly, it is important to note that some LLMs may be overly calibrated towards exhibiting trustworthiness, to the extent that they compromise their utility by mistakenly treating benign prompts as harmful and consequently not responding. Finally, we emphasize the importance of ensuring transparency not only in the models themselves but also in the technologies that underpin trustworthiness. Knowing the specific trustworthy technologies that have been employed is crucial for analyzing their effectiveness.