Daily Papers

Reusable Web-agent verification requires a rule to follow changing requirements and support subsequent execution. We introduce AgentProofBench, which connects paired tests of a frozen acceptance rule to execution from identical saved openings. The resource spans 97 tasks, 79 families, and four Web services. Experiments with DeepSeek Flash/Pro establish two linked measurements. Across 48 families, complete-panel and decision-replay tests retain 82/96 Flash and 79/96 Pro source programs; paired reuse-rebuild BA intervals are [-5.47, 1.57] and [-10.16, 0.00] percentage points. Across 22 execution families, deployment-state panel correctness separates program assignments whose two saved openings are both delivered correctly: 32/33 assignments with error-free panels, versus 1/11 with panel errors. All reference-defined program-gate regressions and withheld deliveries occur in the latter group. Neutral continuation attains the highest correct delivery under the tested generic feedback, providing a concrete baseline for measuring the value added by a gate. Released instructions, states, programs, reference rules, and trajectories connect each test failure to its execution consequences. AgentProofBench makes reusable verification assessable at both the requirement and policy levels.

Recent advances in large reasoning models (LRMs) have shown that reinforcement learning with verifiable rewards (RLVR) can substantially improve reasoning in mathematics and code, where outcomes can be checked automatically. Extending this progress to open-ended and agentic tasks remains difficult because reliable rewards are harder to obtain and direct human supervision cannot keep pace with the scale and complexity of model-generated experience. This paper studies how LRMs can continue to improve as human supervision gradually recedes from the learning loop. We examine two connected dimensions of this problem. The reward axis traces the development from per-instance human judgments to reusable verifiers and rewards that operate even without human feedback. The experience axis examines how learning can progress from human-curated tasks and environments toward self-generated curricula, constructed environments, and autonomous co-evolution. We connect these dimensions through a five-level ladder from L0 to L4 that identifies which parts of the learning process remain under continued human control. Our analysis further highlights the risks introduced by increasingly autonomous rewards and experience generation, including reward hacking, feedback drift, curriculum collapse, and environment errors. Consequently, we also provide the evaluation around three complementary objects: policy capability, feedback fidelity, and experience quality. This analysis provides a structured account of current approaches to scaling LRMs beyond human supervision and the open problems involved in developing self-sustaining learning systems toward superintelligence. Furthermore, we maintain a continuously updated https://github.com/visitworld123/Awesome-Scaling-LRM-Beyond-Human-Supervision{GitHub repository} to track the latest advances.

Harness optimization improves long-horizon agents by refining the prompts, tools, memory, and hooks around a frozen model. Offline methods can learn from completed trajectories, but deploy one shared harness that may overfit training tasks and cannot react to evidence revealed during a new run. Online evolution can adapt before, during, or after one run through an evolver, but may have to reason about every intervention from scratch or rely on verifier feedback that is usually unavailable at test time. We introduce Meta^2, which moves offline optimization one level up: rather than optimizing a shared harness, it learns reusable knowledge for harness evolution and applies it within each task online. Offline, Meta^2 learns a textual Meta-Skill M by contrasting training rollouts of the same task agent under three configurations: without an evolver, with an evolver guided by the current version of M, and with an evolver given privileged verifier information available only in training. Contrasts in trajectories and outcomes are aggregated across tasks to refine M into reusable guidance on when and how to evolve, when to leave the harness unchanged, and which interventions to avoid. Online, an evolver combines the frozen M with emerging trajectory evidence to decide whether to KEEP the harness unchanged or EVOLVE it through a task-local edit. Each edit applies to the rest of the same run without resetting its environment or progress. Thus, evolution guidance transfers across tasks while harness edits remain task-local, and held-out verifier feedback is never available to the evolver. On two long-horizon benchmarks, Terminal-Bench 2.1 and DeepSWE 1.1, Meta^2 achieves the highest performance among evaluated methods with GPT-5.6-Terra, reaching 81.00% and 44.44%, respectively. Ablations support the value of contrastive evolution guidance and keeping online harness edits task-local.

Human videos offer a scalable source of demonstrations for dexterous robot manipulation. However, existing human-to-simulation-to-robot (Human2Sim2Robot) pipelines rely on predefined procedures that struggle to accommodate diverse object properties and interactions, particularly those involving articulated and deformable objects. We introduce DexAgent, an agentic Human2Sim2Robot framework that converts a single egocentric human video and a task prompt into physically grounded robot trajectories for policy training. It operates through four stages: semantic understanding of human videos, property-based simulation reconstruction, robot trajectory optimization, and robot data generation. At each stage, DexAgent adapts its approach to the task and object properties by selecting suitable skills from its tool library or developing new ones when needed. Property-specific verifiers assess stage outcomes for physical validity and task-specific requirements and provide feedback for refinement, preventing error propagation through the workflow. This adaptive, verification-guided process allows DexAgent to process diverse objects and long-horizon tasks. In the final stage, DexAgent varies object and robot states in simulation to generate diverse robot trajectories from a single human video, then retextures the rendered observations to facilitate sim-to-real transfer. Newly developed skills and verifiers are retained in its tool library, making it self-evolving to accumulate reusable capabilities. This reduces processing time as DexAgent encounters more human videos. Across eleven real-world tasks, policies trained with DexAgent-generated data achieve a 3.5x higher success rate than competing baselines. Project website: https://dexagent123.github.io/.

LLM agents often lack the operational knowledge to act reliably in new environments, as they must discover specific tool behaviors or environment conventions on their own. Without memory of past attempts, they repeat the same mistakes across tasks, leading to more task failures and longer trajectories. To address this, agentic systems typically rely on human-written guidelines or on procedural memory built from training tasks and an oracle verifier, both of which require prior knowledge of the environment. We present DAEDALUS, a method for bootstrapping reusable agent memory from self-generated practice without existing tasks or oracle verifiers. DAEDALUS pairs two agents: an explorer that interacts with the environment to generate challenging yet solvable tasks, and a solver that attempts them. A heuristic is derived from each solver failure and accepted only after the solver repeatedly succeeds with that heuristic in context. These outcomes also provide feedback for the explorer to refine the difficulty of future tasks. Accepted heuristics are then consolidated into a memory bank for test-time use. Across AppWorld, τ^2-bench, and AutomationBench, DAEDALUS improves mean success rates by up to 15.9 points and pass^5 by up to 2.2x over a no-memory baseline, and is competitive with methods using training tasks, at a lower inference cost than most. We show that performance gains already emerge with a small exploration budget, and that its heuristics also benefit agents from other model families. Our ablations further reveal that solver traces provide the key information needed to derive effective heuristics, while factorizing early discoveries makes exploration more cost-efficient. Beyond memory construction, we find that the tasks generated by DAEDALUS can serve as a proxy for benchmark tasks when ranking models by performance. Code and artifacts: www.github.com/illuin-tech/daedalus.

A central bottleneck for phone-use agents is that controllable, reproducible environments covering real mobile behavior are hard to build at scale. Existing mobile-agent benchmarks have made important progress on evaluation, but they do not by themselves provide a scalable way to construct many new phone-use environments. We present PhoneWorld, a reusable pipeline that converts real GUI trajectories and screenshots into controllable phone-use environments, executable tasks, automatic verifiers, and training rollouts. Rather than hand-building one mobile benchmark at a time, PhoneWorld uses real trajectories to recover which screens matter, how screens connect, which interactions must change environment state, and which user goals admit automatic verification. From these signals, it builds runnable mock Android apps backed by read-only app content and mutable state, then derives executable tasks, rule-based verifiers, and training rollouts from the same environments. In its current instantiation, PhoneWorld covers 34 apps across 16 domains, spanning common consumer mobile behaviors such as search, browsing, shopping, booking, media, and social interaction. Under a fixed training budget, replacing 10K steps from an auxiliary AndroidWorld corpus in an AndroidWorld-based baseline with broad PhoneWorld supervision improves all four evaluation benchmarks at once, raising HYMobileBench by 17.7 points, AndroidControl by 6.0 points, AndroidWorld by 14.7 points, and PhoneWorld by 52.5 points. We then study two additional scaling questions: increasing the amount of PhoneWorld supervision strongly improves PhoneWorld performance, and under a fixed PhoneWorld budget, expanding app coverage yields even larger gains. Overall, PhoneWorld shifts the focus from building one mobile benchmark at a time to scaling the supply of phone-use environments themselves.

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.

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

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.

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}.

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

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

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

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.

Model signing authenticates the full-precision weights W an LLM is released with, yet users run a quantized artifact Q whose producing transformation is not uniquely determined under current disclosure. We separate the non-environment inputs from the execution environment E and measure a quantity that, to our knowledge, has not been measured before: the Independent Verifiability Rate (IVR), the fraction of a popularity-sampled GGUF ecosystem that a third party can re-derive bit-for-bit. Across the 200 most-downloaded Hugging Face GGUF repositories (198 in scope), no artifact or model card records the build environment, so under a recorded-inputs protocol the IVR is 0/198. Yet the artifacts are not irreproducible. On four in-sample repositories that disclose their inputs, the card's information alone reproduces no Q4_K_M file, but two coordinates the card omits - the build's floating-point-contraction setting and, for hybrid models, the per-tensor quantization recipe - re-derive 7/8 target-quant files bit-for-bit on x86 (5/8 on arm64); the fp16 re-derives from the provider's checkpoint, but the calibration imatrix must be shipped and hash-bound, since recomputing it did not match. An older release additionally pins the instruction set and did not re-derive. Reproducing the divergence reported with llama.cpp PR #25353, we show that E is a necessary coordinate and that one compiler setting yields a unique output across the tested platforms at negligible quality cost (+0.06% perplexity). As a security characterization, benign floating-point non-determinism separates from uniformly placed nibble-flip tampering above a detection floor that grows with the environments a verifier must allow, but a targeted embedding edit evades the statistic, so the proposed protocol rests on exact re-derivation; adversarial-fp16 attacks lie outside it. We release the audit data and a re-runnable harness.

Large language models can generate useful code from natural language, but their outputs come without correctness guarantees. Verifiable code generation offers a path beyond testing by requiring models to produce not only executable code, but also formal specifications and machine-checkable proofs. Progress in this direction, however, is difficult to measure: existing benchmarks are often small, focus on only one part of the pipeline, lack ground-truth proofs or rigorous specification validation, or target verification settings far from mainstream software development. We present VeriContest, a benchmark of 946 competitive-programming problems from LeetCode and Codeforces for verifiable code generation in Rust with Verus. Each problem pairs a natural language description with expert-validated formal specifications, judge-accepted Rust code, Verus-checked proofs, and positive and negative test suites. VeriContest is constructed through a three-phase pipeline that scales from manually verified seed problems to semi-automated expansion with human-in-the-loop review. To further strengthen benchmark quality, we use testing as an additional quality-assurance layer for validating postcondition completeness. VeriContest supports isolated and compositional evaluation of specification generation, code generation, proof generation, and end-to-end verified program synthesis. Evaluating ten state-of-the-art models reveals a sharp gap between coding ability and verifiable code generation: the strongest model reaches 92.18% on natural-language-to-code generation, but only 48.31% on specification generation, 13.95% on proof generation, and 5.29% end-to-end. These results identify proof and specification generation as the central bottlenecks for models and establish VeriContest as a rigorous platform for measuring and training future systems that generate code with machine-checkable correctness.

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.

Large language models (LLMs) are increasingly integrated in software development, but ensuring correctness in LLM-generated code remains challenging and often requires costly manual review. Verifiable code generation -- jointly generating code, specifications, and proofs of code-specification alignment -- offers a promising path to address this limitation and further unleash LLMs' benefits in coding. Yet, there exists a significant gap in evaluation: current benchmarks often lack support for end-to-end verifiable code generation. In this paper, we introduce Verina (Verifiable Code Generation Arena), a high-quality benchmark enabling a comprehensive and modular evaluation of code, specification, and proof generation as well as their compositions. Verina consists of 189 manually curated coding tasks in Lean, with detailed problem descriptions, reference implementations, formal specifications, and extensive test suites. Our extensive evaluation of state-of-the-art LLMs reveals significant challenges in verifiable code generation, especially in proof generation, underscoring the need for improving LLM-based theorem provers in verification domains. The best model, OpenAI o4-mini, generates only 61.4% correct code, 51.0% sound and complete specifications, and 3.6% successful proofs, with one trial per task. We hope Verina will catalyze progress in verifiable code generation by providing a rigorous and comprehensive benchmark. We release our dataset on https://huggingface.co/datasets/sunblaze-ucb/verina and our evaluation code on https://github.com/sunblaze-ucb/verina.

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.

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 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

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.

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.

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.

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.

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/

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

Large Language Models (LLMs) 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.

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.

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.

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

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis. In this paper, we present a combination of LLMs and static analysis to synthesize invariants, assertions, and other proof structures for a Rust-based formal verification framework called Verus. In a few-shot setting, LLMs demonstrate impressive logical ability in generating postconditions and loop invariants, especially when analyzing short code snippets. However, LLMs lack the ability to retain and propagate context information, a strength of traditional static analysis. Based on these observations, we developed a prototype based on OpenAI's GPT-4 model. Our prototype decomposes the verification task into multiple smaller ones, iteratively queries GPT-4, and combines its output with lightweight static analysis. We evaluated the prototype with a developer in the automation loop on 20 vector-manipulating programs. The results demonstrate that it significantly reduces human effort in writing entry-level proof code.

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.

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.

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

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.

Verifiable delay functions have found a lot of applications in blockchain technology in recent times. Continuous verifiable delay functions are an improvement over the basic notion of VDFs with recursive capabilities. We are proposing the application of VDF for constructing more space time-efficient provers and simulators required for the iterative non-interactive zero-knowledge systems.

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.

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.

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.

Formal verification is the next frontier for ensuring the correctness of code generated by Large Language Models (LLMs). While methods that co-generate code and formal specifications in formal languages, like Dafny, can, in principle, prove alignment with user intent, progress is bottlenecked by specification quality evaluation. Current benchmarks rely on matching against ground-truth specifications, a manual and expertise-intensive process that has limited existing datasets to a few hundred simple problems and also suffers from a reliability issue. To address this, we introduce VeriEquivBench, a new benchmark with 2,389 complex algorithmic problems that probe the limitations of current models in both code generation and formal reasoning. Our evaluation framework replaces ground-truth matching with a formally grounded metric, the equivalence score, and rigorously verifies the quality of generated specifications and code. Our results show that generating formally verifiable code remains a profound challenge for state-of-the-art LLMs. This underscores both the difficulty of the task and the need for benchmarks like VeriEquivBench to drive progress toward scalable and reliable coding agents.

In LLM inference, the same prompt may yield different outputs across different runs. At the system level, this non-determinism arises from floating-point non-associativity combined with dynamic batching and GPU kernels whose reduction orders vary with batch size. A straightforward way to eliminate non-determinism is to disable dynamic batching during inference, but doing so severely degrades throughput. Another approach is to make kernels batch-invariant; however, this tightly couples determinism to kernel design, requiring new implementations. This coupling also imposes fixed runtime overheads, regardless of how much of the workload actually requires determinism. Inspired by ideas from speculative decoding, we present LLM-42, a scheduling-based approach to enable determinism in LLM inference. Our key observation is that if a sequence is in a consistent state, the next emitted token is likely to be consistent even with dynamic batching. Moreover, most GPU kernels use shape-consistent reductions. Leveraging these insights, LLM-42 decodes tokens using a non-deterministic fast path and enforces determinism via a lightweight verify-rollback loop. The verifier replays candidate tokens under a fixed-shape reduction schedule, commits those that are guaranteed to be consistent across runs, and rolls back those violating determinism. LLM-42 mostly re-uses existing kernels unchanged and incurs overhead only in proportion to the traffic that requires determinism.

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.

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.

Recent advancements in large language models (LLMs) suggest great promises in code and proof generations. However, scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are crucial challenges overlooked by existing LLM-based methods with a special focus on targeting isolated, function-level verification tasks. To systematically explore and address the significant challenges of verifying entire software repositories, we introduce RVBench, the first verification benchmark explicitly designed for repository-level evaluation, constructed from four diverse and complex open-source Verus projects. We further introduce RagVerus, an extensible framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories. RagVerus triples proof pass rates on existing benchmarks under constrained model inference budgets, and achieves a 27% relative improvement on the more challenging RVBench benchmark, demonstrating a scalable and sample-efficient verification solution.

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.

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.

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

Machine learning models are increasingly used in societal applications, yet legal and privacy concerns demand that they very often be kept confidential. Consequently, there is a growing distrust about the fairness properties of these models in the minds of consumers, who are often at the receiving end of model predictions. To this end, we propose \name -- a system that uses Zero-Knowledge Proofs (a cryptographic primitive) to publicly verify the fairness of a model, while maintaining confidentiality. We also propose a fairness certification algorithm for fully-connected neural networks which is befitting to ZKPs and is used in this system. We implement \name in Gnark and demonstrate empirically that our system is practically feasible. Code is available at https://github.com/infinite-pursuits/FairProof.

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 model (LLM) coding agents increasingly operate with shell access, allowing them to write scripts, move files, alter permissions, and modify system configurations. However, an agent may achieve a user's goal while causing unintended harm, such as deleting unrelated files, weakening access controls, or corrupting data, in response to benign inputs without explicit jailbreaking. This failure mode is particularly important because apparent task success may reassure users that an agent behaved correctly, causing harmful side effects to go unnoticed. We call this harmful success: the agent successfully completes the intended benign task while simultaneously causing unintended harm. Despite its importance, harmful success is difficult to measure because conventional task-success metrics overlook harmful behaviors, while existing safety evaluations are often designed solely to assess harmful outcomes. We introduce VeriHarm, an automatic framework for constructing programmatically verifiable benchmarks that directly measure harmful success. VeriHarm minimally perturbs coding tasks to elicit unintended harmful behavior while maintaining the benignity of the task and preserving the original task objective. It then synthesizes executable harm tests that, together with the original task-correctness tests, evaluate both task accuracy and harmful outcomes. Frontier agents, including GPT-5.6-Sol and Claude-Opus-5, achieve an average task accuracy of 95% on our curated VeriHarm-Bench, yet still struggle to complete tasks safely: their safe success rate, the fraction of tasks completed successfully without triggering the designated harm, averages only 37%. These results suggest that successful task completion can frequently coexist with unintended harm, and that task-success metrics alone may substantially understate the potential safety risks of coding agents.

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.

AI coding agents produce code faster than humans can review it. In our approach, the prover is the judge of whether the code is correct. Under a verifier-driven loop, AI agents wrote and verified bare-metal security software in Ada/SPARK spanning classical and post-quantum cryptography, TLS 1.3, IKEv2, X.509, and a Matrix client. GNATprove discharged 49,280 proof obligations, established functional correctness for selected primitives, and proved the absence of run-time errors for the rest, at roughly 20-40 times lower supervision cost than comparable hand verification. GNATprove alone was insufficient: some defects could not be detected and were resolved using known-answer tests, interoperability, or human review of specifications. Given weak checks, the agent tried to bypass them and reported success. We report where each layer caught faults and draw the central lesson: what an agent can be trusted to establish is bounded by the strength of its feedback.

Recent work has demonstrated that coding agents can formalize entire advanced mathematics textbooks in Lean 4, yet existing efforts concentrate on branches of mathematics already well-represented in mathlib and measure success solely through kernel acceptance. We address both limitations by applying a coding agent to formalize Numerical Methods for Ordinary Differential Equations, a textbook in numerical analysis that is largely absent from mathlib, stressing the agent's capacity to develop new theory from scratch. We further introduce a systematic, reproducible three-dimensional framework for evaluating the quality of agent-produced formalizations beyond compilation: semantic correctness, Mathlib reuse, and cross-file reuse via LLM-as-judge methods. Applying this framework to our own formalization and to the released outputs of RepoProver and M2F, we uncover recurring unfaithful formalization patterns, including incomplete multi-part statements, added weakening hypotheses, and parameter restrictions, that kernel acceptance entirely obscures. Our results suggest that compilation-based metrics substantially overstate formalization quality, and we provide a reproducible audit methodology to support more rigorous evaluation of future autoformalization systems.

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

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.

Multi-domain thinking verifiers trained via Reinforcement Learning with Verifiable Rewards (RLVR) are a cornerstone of modern post-training. However, their adoption in code generation has lagged behind that of execution feedback due to the prohibitive costs of the full RLVR pipeline. In this work, we ablate three primary choices along the performance-cost trade-off in RLVR: intermediate thinking traces, learning from negative samples, and on-policy training. We introduce Aletheia, a controlled, execution-grounded testbed to facilitate a contamination-free analysis of code verifier training recipes across disparate model sizes and covariate shifts across two common verifier application scenarios. Our analysis reveals that the optimal training recipe is scale-dependent: on-policy learning is the primary performance driver for small verifiers, whereas the thinking budget becomes the most vital factor at larger scales. While leveraging negative samples has a consistent impact on top-1 selection accuracy across sizes, their contribution to ranking reconstruction increases monotonically with scale and plays a key role in stabilizing training at large sizes. Our Pareto optimality analysis demonstrates that eliminating on-policy training at larger model scales yields a verifier that performs comparably to the full RLVR recipe. Furthermore, we find that eschewing thinking traces serves as a compute-efficient strategy at lower budgets, offering a strong trade-off between training cost and verifier accuracy. Ultimately, our work provides the empirical foundation necessary to efficiently deploy robust code verifiers, thereby enabling their wider adoption in post-training pipelines for large code generation models.

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.

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.

Terminal agents are increasingly deployed beyond software engineering in science and other specialized domains. Constructing training environments requires executable reference behavior and a domain-specific verifier that distinguishes semantic correctness from superficially plausible artifacts. Authoring these components for each task requires repeated engineering and limits reuse. We introduce software-in-the-loop reconstruction, a self-supervised framework that obtains reference outputs and verification targets from existing software workflows, executable programs mapping structured inputs to outputs. For each workflow, we execute multiple input configurations and partition cases into public observations and hidden evaluations. Given the instruction, input schema, and public input--output observations, an agent constructs an editable program without access to the source workflow. The candidate is evaluated on hidden configurations against workflow outputs. A hierarchical verifier combines domain-specific semantic comparison, structural validity, and anti-shortcut checks, while public feedback supports iterative revision. The construction admits additional workflows and configurations without authoring a reference solution for each task. We instantiate SWR with 500 workflows and 46 software families across six domains. Across three attempts per task, Qwen3.8-Max solves 838 tasks and produces 1,422 verified trajectories, which we oversample to 3,000 reconstruction-only training examples. Supervised fine-tuning of Qwen3.8-27B improves mean Terminal-Bench 2 performance from 47.94% to 53.56% across three seeds and achieves the highest mean among four matched-token corpus controls on all four reported evaluations. These results indicate that existing scientific software can provide scalable, behaviorally verified supervision for terminal agents.

Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated great potential in enhancing the reasoning capabilities of large language models (LLMs), achieving remarkable progress in domains such as mathematics and programming where standard answers are available. However, for open-ended tasks lacking ground-truth solutions (e.g., creative writing and instruction following), existing studies typically regard them as non-reasoning scenarios, thereby overlooking the latent value of reasoning capabilities. This raises a key question: Can strengthening reasoning improve performance in open-ended tasks? To address this, we explore the transfer of the RLVR paradigm to the open domain. Yet, since RLVR fundamentally relies on verifiers that presuppose the existence of standard answers, it cannot be directly applied to open-ended tasks. To overcome this challenge, we introduce Verifiable Multiple-Choice Reformulation (VMR), a novel training strategy that restructures open-ended data into verifiable multiple-choice formats, enabling effective training even in the absence of explicit ground truth. Experimental results on multiple benchmarks validate the effectiveness of our method in improving LLM performance on open-ended tasks. Notably, across eight open-ended benchmarks, our VMR-based training delivers an average gain of 5.99 points over the baseline. Code will be released upon acceptance to facilitate reproducibility.

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.

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification.

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.

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.

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.

Agentic AI systems orchestrate multiple LLM-based agents through workflow architectures that coordinate decisions, tools, and external actions. While current platforms emphasize runtime safeguards, little support exists for verifying workflows during system design. From a Modeling \& Simulation perspective, this gap is analogous to composing conceptual models without verifying whether their building blocks interact coherently. We propose a design-time verification approach that models agentic workflows as compositions of reusable building blocks and checks their compatibility through twelve structural rules. We implemented these rules in a software prototype and evaluated them using two openly released datasets: 48 workflows with known design flaws and 168 variants that preserve workflow logic but alter graph structure. Results show that our verifier reliably detects violations even when flawed designs are obscured through structural transformations such as splitting tasks between agents. Future works could combine our verification with community repositories of building blocks to compose safe agentic workflows.

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.

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.

Offline retrieval-augmented generation (RAG) on edge devices is updated through signed knowledge packs that carry text and precomputed embedding vectors. A signature proves who published a pack, not that its vectors encode its text. We study this text-vector integrity gap. A verifier that recomputes vectors and accepts them within a cosine tolerance concedes a predictable share of queries to an attacker who controls the vectors: the hijack rate equals the distribution of angular retrieval margins at the tolerance (the margin law). Margins are small in five corpora and two embedding models, so an idealised tolerance at the level of floating-point noise leaves up to 5.5% of queries exposed (at most 1.2% in any corpus once exact duplicate documents are excluded), and a threshold calibrated from our CPU INT8-FP32 comparison of a small embedding model (at the empirical 0.1% quantile of honest cosines) leaves 98-100% exposed; on a Raspberry Pi 5 running a local language model, such an attack lowers correct answers from 0.75 to 0.39. Integrity audits of compressed vector stores fare no better: on a FAISS product-quantisation index over 57,638 documents, tampered vectors that all pass the audit put the attacker's document first for 25% of targets. Verifying quantisation codes instead, with ambiguity decided by the verifier, a calibrated guard band and canonicalisation, accepted every honest vector in our samples on three platforms and left the publisher no choice. We also show that common floating-point and dynamic-INT8 inference pipelines are not bit-reproducible across batch sizes or architectures, and report pre-registered negative results on abstention, context pruning and semantic screening. We release code and data.

Machine learning programs, such as those performing inference, fine-tuning, and training of LLMs, are commonly delegated to untrusted compute providers. To provide correctness guarantees for the client, we propose adapting the cryptographic notion of refereed delegation to the machine learning setting. This approach enables a computationally limited client to delegate a program to multiple untrusted compute providers, with a guarantee of obtaining the correct result if at least one of them is honest. Refereed delegation of ML programs poses two technical hurdles: (1) an arbitration protocol to resolve disputes when compute providers disagree on the output, and (2) the ability to bitwise reproduce ML programs across different hardware setups, For (1), we design Verde, a dispute arbitration protocol that efficiently handles the large scale and graph-based computational model of modern ML programs. For (2), we build RepOps (Reproducible Operators), a library that eliminates hardware "non-determinism" by controlling the order of floating point operations performed on all hardware. Our implementation shows that refereed delegation achieves both strong guarantees for clients and practical overheads for compute providers.

We often interact with untrusted parties. Prioritization of privacy can limit the effectiveness of these interactions, as achieving certain goals necessitates sharing private data. Traditionally, addressing this challenge has involved either seeking trusted intermediaries or constructing cryptographic protocols that restrict how much data is revealed, such as multi-party computations or zero-knowledge proofs. While significant advances have been made in scaling cryptographic approaches, they remain limited in terms of the size and complexity of applications they can be used for. In this paper, we argue that capable machine learning models can fulfill the role of a trusted third party, thus enabling secure computations for applications that were previously infeasible. In particular, we describe Trusted Capable Model Environments (TCMEs) as an alternative approach for scaling secure computation, where capable machine learning model(s) interact under input/output constraints, with explicit information flow control and explicit statelessness. This approach aims to achieve a balance between privacy and computational efficiency, enabling private inference where classical cryptographic solutions are currently infeasible. We describe a number of use cases that are enabled by TCME, and show that even some simple classic cryptographic problems can already be solved with TCME. Finally, we outline current limitations and discuss the path forward in implementing them.

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).

AI agents are increasingly used for programming, but do not provide any guarantee on the correctness of generated code. Verified code generation, in which an agent produces both an implementation and a machine-checked proof of its specification, offers a stronger path toward trustworthy AI-generated software. Existing benchmarks in this direction either focus on individual functions or only evaluate proof generation with provided implementations. It is still an open question whether agents can make coherent implementation and proof choices across real multi-module codebases. To bridge this gap, we introduce Vero, the first benchmark to evaluate joint implementation and proof synthesis at the repository level. Vero contains 43 multi-module instances sourced from real-world repositories spanning Python, Dafny, Verus, and Coq, and covering diverse domains from cryptographic protocols to distributed systems. Each instance consists of a multi-module Lean 4 repository with predetermined API interfaces, manually curated formal specifications, and reference implementations, supporting both proof-only and code-and-proof evaluation modes. To improve benchmark reliability, Vero also includes an audit mechanism where agents are allowed to formally prove unsatisfiability of provided specification or incorrectness of reference code, which surfaces and corrects latent code and specification errors during curation. We evaluate frontier coding-agent configurations with Lean toolchain access. The strongest agent fully solves only 27 of 43 instances and closes no specifications on the hardest repositories. Vero provides a concrete testbed for measuring progress toward repository-scale verified software synthesis, where current agents still fall short. We release the benchmark, curation pipeline, and evaluation harness at https://github.com/sunblaze-ucb/vero.

LLM agents often retry after external validation rejects a candidate, but the interface between validation and the next model call remains underspecified. We introduce VeriHarness, a code-controlled agent loop in which models generate candidates while external validators control acceptance, budgets, and traces. We use it to compare raw diagnostics with feedback that identifies the failure location, observed value, and admissible alternatives. Across 50 paired TextWorld games under a four-call cap, feedback containing all three fields raises terminal success from 14/50 to 36/50 for Qwen2.5-Coder-14B (+44 percentage points) and from 8/50 to 29/50 for Llama-3.1-8B (+42 points). Ablations locate most of the gain in the admissible alternatives: feedback containing only the location and observed value remains near the raw diagnostic baseline. Presenting the complete repair information in prose instead of a keyed JSON record yields nearly the same success, providing no evidence that JSON syntax itself improves repair. The ordering persists across the tested call budgets and one sampled-decoding setting.

We consider the problem of how a trusted, but computationally bounded agent (a 'verifier') can learn to interact with one or more powerful but untrusted agents ('provers') in order to solve a given task. More specifically, we study the case in which agents are represented using neural networks and refer to solutions of this problem as neural interactive proofs. First we introduce a unifying framework based on prover-verifier games, which generalises previously proposed interaction protocols. We then describe several new protocols for generating neural interactive proofs, and provide a theoretical comparison of both new and existing approaches. Finally, we support this theory with experiments in two domains: a toy graph isomorphism problem that illustrates the key ideas, and a code validation task using large language models. In so doing, we aim to create a foundation for future work on neural interactive proofs and their application in building safer AI systems.

Scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are challenges overlooked by existing function-centric methods. We introduce RagVerus, a framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories, achieving a 27% relative improvement on our novel RepoVBench benchmark -- the first repository-level dataset for Verus with 383 proof completion tasks. RagVerus triples proof pass rates on existing benchmarks under constrained language model budgets, demonstrating a scalable and sample-efficient verification.

In the rapidly evolving domain of distributed ledger technology, scalability and interoperability have become paramount challenges for both academic and industry sectors. In this paper, we introduce a comprehensive formal model to address atomic composability across multiple rollups on Ethereum. The proposed model incorporates mechanisms like buffering, dependency management, concurrency control, and the groundbreaking zero-knowledge proofs. Moreover, we evaluate its practical repercussions, strengths, and weaknesses, ensuring resilience against manipulative or erroneous actions. The application of the proposed model to shared sequencers and other existing solutions accentuates its versatility and universality.

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.

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.

Large language model safeguards decide whether to answer before seeing how an answer will be used. This creates a basic problem for dual-use tasks: the same answer can help an authorized professional or an attacker, while an attacker can imitate a benign request and interaction history. We separate the capability released by the model from the evidence available about downstream use. When that evidence is copyable, we derive the exact worst-case floor on attacker assistance while preserving useful answers. The result yields a safety trilemma: Useful Capability, Reliable Safety, and Open Access cannot coexist. We then show how a trusted credential can complement existing safeguards by adding hard-to-copy information that predicts actual downstream use, and identify the stronger condition needed to eliminate the floor. Evidence from dual-use evaluations, adaptive attacks, and deployed trusted-access programs supports the practical relevance of these conditions.

We describe a verification pipeline that takes production Rust cryptographic code and produces machine-checked correctness proofs in Lean 4. The pipeline combines three components: symbolic extraction tools (Charon and Aeneas, or Hax) that lift Rust into Lean 4; formal cryptographic specification libraries (ArkLib and CompPoly, from the Verified zkEVM project) that provide the mathematical targets; and AI provers (Aristotle from Harmonic AI and Aleph from Logical Intelligence) that close the resulting proof obligations. Every proof is checked by the Lean kernel, so AI output cannot compromise soundness. Within the scope of the Ethereum Foundation's zkEVM Verification Project, we applied the pipeline to cryptographic primitives in Plonky3 (FRI folding, Mersenne31 and KoalaBear field arithmetic, Horner polynomial evaluation) and RISC Zero (Merkle inclusion verification). In addition, Aleph authored proofs of two bounds-style theorems in Plonky3's compute_log_arity_for_round that previously stood as sorry. The paper describes the architecture, walks through a running example based on Aleph's two proofs, reports which classes of proof obligations AI closed and which required manual work, and discusses the engineering gaps we encountered: Lean 4 toolchain drift across tools and specific Aeneas/Hax extraction limits. We also document concrete missing lemmas, tactic gaps, and code-generation friction points discovered during proof development. We hope this contribution lowers the barrier to adoption of formal verification and facilitates more effective use of AI in this pipeline. The result is a working pipeline for formal verification of Rust, with kernel-checked proofs and reproducible artefacts.

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.

Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this work, we address this scalability bottleneck by exploiting an informative structure in formal verification: the observation that compilers map a vast space of diverse proof attempts to a compact set of structured failure modes. We introduce a learning-to-refine framework that leverages this compression to perform efficient learning and proof exploration. We perform tree search that corrects errors locally conditioned on explicit verifier feedback, thereby circumventing the costs associated with accumulating a long history of proof attempts. Extensive evaluations show that our method consistently amplifies the reasoning capabilities of base provers across varying scales. Notably, our approach achieves state-of-the-art performance on PutnamBench among publicly reported sim8B and sim32B parameter models under comparable test-time budgets, offering a scalable paradigm for next-generation verifier-guided reasoning.

Code verification has recently found great success as a critical component in training large scale reasoning models for coding. Synthetic techniques such as self-generated test cases and reward models provide a way to enhance code capabilities beyond predefined tests. Building on these advancements, we propose new benchmarks designed to systematically evaluate the impact of synthetic verification methods on assessing solution correctness. We introduce HE-R, HE-R+, MBPP-R, and MBPP-R+, which transform existing coding benchmarks into scoring and ranking datasets to evaluate the effectiveness of synthetic verifiers. Using these benchmarks, we analyze synthetic verification methods in standard, reasoning-based, and reward-based LLMs. Our results show that recent reasoning models significantly improve test case generation and that scaling test cases enhances verification accuracy.

Multi-agent LLM systems share state through memory stores, vector indices, and tool registries. We model such sharing as long-running read-generate-write operations under deterministic-generation semantics -- the regime durable-execution engines enforce by deterministic replay -- and formalize four concurrency anomalies in TLA+: stale-generation, phantom-tool, causal-cascade, and tool-effect reordering, structural analogues of classical isolation anomalies, each with a TLC counter-example. The exclusion lattice over these anomalies is trivial; the contribution is the mechanically verified realizability and strict separation of one maximal chain within it, L_0 subsetneq cdots subsetneq L_4, to our knowledge the first machine-checked consistency hierarchy for such runtimes. A development of 274 Verus obligations (zero assume, zero admit; trust base: two structural axioms and a mutex correspondence) proves the detectors sound and complete against the specifications and each runtime its avoidance set. Three deployed Rust runtimes realize L0-L1 (pessimistic locking, serializable snapshot isolation, default-SI), each verified against stale-generation and refined to its state machine; L2-L4 are exec-mode-verified with dependency-free prevention twins (A3, A6, A2: 0/1000 versus 1000/1000), and L2 is run live across three model families (A3 prevented in all 120 retracted sessions). We reproduce a silent lost update in ByteDance's deer-flow, formalizing its fix as a verified L_0 to L_1 refinement, and exhibit tool-effect reordering in LangGraph's ToolNode on unmodified output, removed by an L3 commit-order sequencer. The verified detector, refinements, and realizability artifacts are the contribution; the phenomena and lattice are classical.

EigenAI is a verifiable AI platform built on top of the EigenLayer restaking ecosystem. At a high level, it combines a deterministic large-language model (LLM) inference engine with a cryptoeconomically secured optimistic re-execution protocol so that every inference result can be publicly audited, reproduced, and, if necessary, economically enforced. An untrusted operator runs inference on a fixed GPU architecture, signs and encrypts the request and response, and publishes the encrypted log to EigenDA. During a challenge window, any watcher may request re-execution through EigenVerify; the result is then deterministically recomputed inside a trusted execution environment (TEE) with a threshold-released decryption key, allowing a public challenge with private data. Because inference itself is bit-exact, verification reduces to a byte-equality check, and a single honest replica suffices to detect fraud. We show how this architecture yields sovereign agents -- prediction-market judges, trading bots, and scientific assistants -- that enjoy state-of-the-art performance while inheriting security from Ethereum's validator base.

Redacting Personally Identifiable Information (PII) from unstructured text is critical for ensuring data privacy in regulated domains. While earlier approaches have relied on rule-based systems and domain-specific Named Entity Recognition (NER) models, these methods fail to generalize across formats and contexts. Recent advances in Large Language Models (LLMs) offer a promising alternative, yet the effect of architectural and training choices on redaction performance remains underexplored. LLMs have demonstrated strong performance in tasks that require contextual language understanding, including the redaction of PII in free-form text. Prior work suggests that with appropriate adaptation, LLMs can become effective contextual privacy learners. However, the consequences of architectural and training choices for PII Redaction remain underexplored. In this work, we present a comprehensive analysis of LLMs as privacy-preserving PII Redaction systems. We evaluate a range of LLM architectures and training strategies for their effectiveness in PII Redaction. Our analysis measures redaction performance, semantic preservation, and PII leakage, and compares these outcomes against latency and computational cost. The results provide practical guidance for configuring LLM-based redactors that are accurate, efficient, and privacy-aware. To support reproducibility and real-world deployment, we release PRvL, an open-source suite of fine-tuned models, and evaluation tools for general-purpose PII Redaction. PRvL is built entirely on open-source LLMs and supports multiple inference settings for flexibility and compliance. It is designed to be easily customized for different domains and fully operable within secure, self-managed environments. This enables data owners to perform redactions without relying on third-party services or exposing sensitive content beyond their own infrastructure.

We introduce Generative Universal Verifier, a novel concept and plugin designed for next-generation multimodal reasoning in vision-language models and unified multimodal models, providing the fundamental capability of reflection and refinement on visual outcomes during the reasoning and generation process. This work makes three main contributions: (1) We build ViVerBench, a comprehensive benchmark spanning 16 categories of critical tasks for evaluating visual outcomes in multimodal reasoning. Results show that existing VLMs consistently underperform across these tasks, underscoring a substantial gap from human-level capability in reliable visual verification. (2) We design two automated pipelines to construct large-scale visual verification data and train OmniVerifier-7B, the first omni-capable generative verifier trained for universal visual verification and achieves notable gains on ViVerBench(+8.3). Through training, we identify three atomic capabilities in visual verification and demonstrate how they generalize and interact synergistically. (3) We propose OmniVerifier-TTS, a sequential test-time scaling paradigm that leverages the universal verifier to bridge image generation and editing within unified models, enhancing the upper bound of generative ability through iterative fine-grained optimization. Beyond generation, we extend universal verifier to broader world-modeling interleaved reasoning scenarios. Empirically, OmniVerifier-TTS achieves improvements on T2I-ReasonBench(+3.7), and GenEval++(+4.3), outperforming existing parallel test-time scaling methods, such as Best-of-N. By endowing multimodal reasoning with reliable visual verification, OmniVerifier advances both reliable reflection during generation and scalable test-time refinement, marking a step toward more trustworthy and controllable next-generation reasoning systems.

Agent environments are essential for large language model (LLM) development. They use programmatic verifiers to turn complex outcomes into rewards. Verifiers can be attacked into awarding full credit to cheating agents without completing the intended task, causing inaccurate evaluation and misalignment in training. As agent environments scale in numbers and difficulty, so must the repairing of exploitable verifiers. To this end, we ask whether today's model with scaled compute can automatically harden agent environments to prevent potentially stronger future models from reward hacking. We introduce a scalable, fully automatic approach to weak-to-strong verifier hardening. It first sets up an isolated verifier sandbox that agents cannot directly modify, then uses a hacker-fixer loop to find and repair remaining verifier vulnerabilities. We apply this loop to Terminal Bench, KernelBench, and SETA, substantially reducing attack success across these agent environments. The iterative design scales with the hardening budget, producing progressively stronger defenses as the number of loop iterations increases and outperforming the static, non-iterative baseline. An earlier version of our hacker-fixer loop has been adopted by the official Terminal Bench repository as a way to audit exploits in its environments. Project page: https://verifier-hardening.github.io/.

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.

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

Speculative decoding accelerates autoregressive (AR) language models by letting a small model draft tokens serially and a large model verify them in parallel. We reverse these roles. Starting from a standard AR checkpoint, we fine-tune the large model into a proposer that predicts a block of future tokens in a single forward pass, then use one additional forward pass to verify the proposed block. This gives ProVe, Proposer-Verifier decoding. The verifier can be a smaller AR model or the proposer itself; the latter gives ProVe-lossless, which reproduces the proposer's greedy AR decoding. Block proposals already provide substantial room for acceleration: with a block size of 16, the proposed block has an average AR-matching prefix of 6.6 tokens on GSM8K. Across six benchmarks with a 32B proposer, ProVe-lossless reaches 2.5x average AR throughput without training a separate draft head. With a small 3B verifier, ProVe reaches 2.7x average throughput at 2.6 accuracy points below AR on the six-task average, providing a controllable tradeoff between speed and accuracy.

Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-based proof automation are drawn from mathematics in the Mathlib ecosystem, whereas proofs in software verification are developed inside definition-rich codebases with substantial project-specific libraries. We introduce VeriSoftBench, a benchmark of 500 Lean 4 proof obligations drawn from open-source formal-methods developments and packaged to preserve realistic repository context and cross-file dependencies. Our evaluation of frontier LLMs and specialized provers yields three observations. First, provers tuned for Mathlib-style mathematics transfer poorly to this repository-centric setting. Second, success is strongly correlated with transitive repository dependence: tasks whose proofs draw on large, multi-hop dependency closures are less likely to be solved. Third, providing curated context restricted to a proof's dependency closure improves performance relative to exposing the full repository, but nevertheless leaves substantial room for improvement. Our benchmark and evaluation suite are released at https://github.com/utopia-group/VeriSoftBench.

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

QDNA-ID is a trust-chain framework that links physical quantum behavior to digitally verified records. The system first executes standard quantum circuits with random shot patterns across different devices to generate entropy profiles and measurement data that reveal device-specific behavior. A Bell or CHSH test is then used to confirm that correlations originate from genuine non classical processes rather than classical simulation. The verified outcomes are converted into statistical fingerprints using entropy, divergence, and bias features to characterize each device. These features and metadata for device, session, and random seed parameters are digitally signed and time stamped to ensure integrity and traceability. Authenticated artifacts are stored in a hierarchical index for reproducible retrieval and long term auditing. A visualization and analytics interface monitors drift, policy enforcement, and device behavior logs. A machine learning engine tracks entropy drift, detects anomalies, and classifies devices based on evolving patterns. An external verification API supports independent recomputation of hashes, signatures, and CHSH evidence. QDNA-ID operates as a continuous feedback loop that maintains a persistent chain of trust for quantum computing environments.

The popularity of the Rust language continues to explode; yet, many critical codebases remain authored in C, and cannot be realistically rewritten by hand. Automatically translating C to Rust is thus an appealing course of action. Several works have gone down this path, handling an ever-increasing subset of C through a variety of Rust features, such as unsafe. While the prospect of automation is appealing, producing code that relies on unsafe negates the memory safety guarantees offered by Rust, and therefore the main advantages of porting existing codebases to memory-safe languages. We instead explore a different path, and explore what it would take to translate C to safe Rust; that is, to produce code that is trivially memory safe, because it abides by Rust's type system without caveats. Our work sports several original contributions: a type-directed translation from (a subset of) C to safe Rust; a novel static analysis based on "split trees" that allows expressing C's pointer arithmetic using Rust's slices and splitting operations; an analysis that infers exactly which borrows need to be mutable; and a compilation strategy for C's struct types that is compatible with Rust's distinction between non-owned and owned allocations. We apply our methodology to existing formally verified C codebases: the HACL* cryptographic library, and binary parsers and serializers from EverParse, and show that the subset of C we support is sufficient to translate both applications to safe Rust. Our evaluation shows that for the few places that do violate Rust's aliasing discipline, automated, surgical rewrites suffice; and that the few strategic copies we insert have a negligible performance impact. Of particular note, the application of our approach to HACL* results in a 80,000 line verified cryptographic library, written in pure Rust, that implements all modern algorithms - the first of its kind.

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.

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.

As demand for LLM inference grows, it is becoming increasingly important that providers and their customers can verify that inference processes are performed correctly, without errors or tampering. However, re-running the same inference process twice often leads to different results due to benign numerical noise, making it difficult to distinguish legitimate variation from actual problems. To address this problem, we introduce Token-DiFR (Token-Divergence-From-Reference), a method for verifying inference outputs by comparing generated tokens against predictions made by a trusted reference implementation conditioned on the same random seed. Sampling seed synchronization tightly constrains valid outputs, leaving providers minimal room to deviate from correct inference, which allows output tokens themselves to serve as auditable evidence of correctness at zero additional cost to the provider. Token-DiFR reliably identifies sampling errors, simulated bugs, and model quantization, detecting 4-bit quantization with AUC > 0.999 within 300 output tokens. For applications requiring sample-efficient forward-pass verification, we additionally introduce Activation-DiFR, a scheme that uses random orthogonal projections to compress activations into compact fingerprints for subsequent verification. Activation-DiFR detects 4-bit quantization with AUC > 0.999 using just 2 output tokens, while reducing communication overhead by 25-75% relative to existing methods. We release an open-source integration with vLLM to accelerate practical deployment of verifiable inference.

Large language models for code generation increasingly rely on synthetic data, where both problem solutions and verification tests are generated by models. While this enables scalable data creation, it introduces a previously unexplored bottleneck: the verification ceiling, in which the quality and diversity of training data are fundamentally constrained by the capabilities of synthetic verifiers. In this work, we systematically study how verification design and strategies influence model performance. We investigate (i) what we verify by analyzing the impact of test complexity and quantity: richer test suites improve code generation capabilities (on average +3 pass@1), while quantity alone yields diminishing returns, (ii) how we verify by exploring relaxed pass thresholds: rigid 100% pass criteria can be overly restrictive. By allowing for relaxed thresholds or incorporating LLM-based soft verification, we can recover valuable training data, leading to a 2-4 point improvement in pass@1 performance. However, this benefit is contingent upon the strength and diversity of the test cases used, and (iii) why verification remains necessary through controlled comparisons of formally correct versus incorrect solutions and human evaluation: retaining diverse correct solutions per problem yields consistent generalization gains. Our results show that Verification as currently practiced is too rigid, filtering out valuable diversity. But it cannot be discarded, only recalibrated. By combining calibrated verification with diverse, challenging problem-solution pairs, we outline a path to break the verification ceiling and unlock stronger code generation models.

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

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.

The widespread lack of broad source code verification on blockchain explorers such as Etherscan, where despite 78,047,845 smart contracts deployed on Ethereum (as of May 26, 2025), a mere 767,520 (< 1%) are open source, presents a severe impediment to blockchain security. This opacity necessitates the automated semantic analysis of on-chain smart contract bytecode, a fundamental research challenge with direct implications for identifying vulnerabilities and understanding malicious behavior. Prevailing decompilers struggle to reverse bytecode in a readable manner, often yielding convoluted code that critically hampers vulnerability analysis and thwarts efforts to dissect contract functionalities for security auditing. This paper addresses this challenge by introducing a pioneering decompilation pipeline that, for the first time, successfully leverages Large Language Models (LLMs) to transform Ethereum Virtual Machine (EVM) bytecode into human-readable and semantically faithful Solidity code. Our novel methodology first employs rigorous static program analysis to convert bytecode into a structured three-address code (TAC) representation. This intermediate representation then guides a Llama-3.2-3B model, specifically fine-tuned on a comprehensive dataset of 238,446 TAC-to-Solidity function pairs, to generate high-quality Solidity. This approach uniquely recovers meaningful variable names, intricate control flow, and precise function signatures. Our extensive empirical evaluation demonstrates a significant leap beyond traditional decompilers, achieving an average semantic similarity of 0.82 with original source and markedly superior readability. The practical viability and effectiveness of our research are demonstrated through its implementation in a publicly accessible system, available at https://evmdecompiler.com.

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

Large language models (LLMs) are increasingly used to generate Verus contracts for Rust programs together with the proofs that establish them. Yet verifier acceptance, the common measure of success, shows only that the implementation satisfies the generated contract, so it leaves open whether the contract captures the intended behavior. Assessing specification generation therefore requires an evaluation methodology, not a single metric. We present VerusEval, a framework that evaluates generated contracts along six dimensions, including Verus-native checks for semantic triviality, validated input-output (I/O) suites, and contract equivalence, and that relates them so that the strength and blind spots of each become measurable. Evaluating 13,716 artifacts from four workflows, five LLMs, and two prompting settings on 762 tasks, we find that acceptance overstates quality: only 42.3\% of the accepted artifacts complete all three semantic checks without a flag, and across workflows and models, higher acceptance does not consistently come with more correct contracts. I/O evaluation rejects 23.6\% of the accepted artifacts, yet only 63.2\% of those that pass it are proved equivalent. Of the accepted artifacts flagged by contract comparison, 84.1\% have a rejected completeness obligation, and the direction of a failure prioritizes inspection of the generated contract or the reference; it does not by itself establish which artifact is defective. Screening and review further identify 36 candidate defects among 61 selected reference contracts, and repairing one of them makes 10 of its 11 failing artifacts equivalent. Based on these findings, we derive four actionable lessons for evaluation, generation, and benchmark maintenance.

Reinforcement learning with verifiable rewards (RLVR) has become a key technique for enhancing large language models (LLMs), with verification engineering playing a central role. However, best practices for RL in instruction following remain underexplored. In this work, we explore the verification challenge in RL for instruction following and propose VerIF, a verification method that combines rule-based code verification with LLM-based verification from a large reasoning model (e.g., QwQ-32B). To support this approach, we construct a high-quality instruction-following dataset, VerInstruct, containing approximately 22,000 instances with associated verification signals. We apply RL training with VerIF to two models, achieving significant improvements across several representative instruction-following benchmarks. The trained models reach state-of-the-art performance among models of comparable size and generalize well to unseen constraints. We further observe that their general capabilities remain unaffected, suggesting that RL with VerIF can be integrated into existing RL recipes to enhance overall model performance. We have released our datasets, codes, and models to facilitate future research at https://github.com/THU-KEG/VerIF.

Large language models are increasingly used to generate code from natural language, but ensuring correctness remains challenging. Formal verification offers a principled way to obtain such guarantees by proving that a program satisfies a formal specification. However, specifications are frequently missing in real-world codebases, and writing high-quality specifications remains expensive and expertise-intensive. We present VeriSpecGen, a traceable refinement framework that synthesizes intent-aligned specifications in Lean through requirement-level attribution and localized repair. VeriSpecGen decomposes natural language into atomic requirements and generates requirement-targeted tests with explicit traceability maps to validate generated specifications. When validation fails, traceability maps attribute failures to specific requirements, enabling targeted clause-level repairs. VeriSpecGen achieve 86.6% on VERINA SpecGen task using Claude Opus 4.5, improving over baselines by up to 31.8 points across different model families and scales. Beyond inference-time gains, we generate 343K training examples from VeriSpecGen refinement trajectories and demonstrate that training on these trajectories substantially improves specification synthesis by 62-106% relative and transfers gains to general reasoning abilities.

Large language models (LLMs) have proven to be very capable, but access to the best models currently rely on inference providers which introduces trust challenges -- how can we be sure that the provider is using the model configuration they claim? We propose TOPLOC, a novel method for verifiable inference that addresses this problem. TOPLOC leverages a compact locality sensitive hashing mechanism for intermediate activations which can detect unauthorized modifications to models, prompts, or precision with 100% accuracy, achieving no false positives or negatives in our empirical evaluations. Our approach is robust across diverse hardware configurations, GPU types, and algebraic reorderings, which allows for validation speeds significantly faster than the original inference. By introducing a polynomial encoding scheme, TOPLOC minimizes memory overhead of the generated commits by 1000times, requiring only 258 bytes of storage per 32 new tokens compared to the 262KB requirement of storing the token embeddings directly for Llama-3.1-8B-Instruct. Our method empowers users to verify LLM inference computations efficiently, fostering greater trust and transparency in open ecosystems and lays a foundation for decentralized and verifiable AI services.

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

Speculative decoding has emerged as a pivotal technique to accelerate LLM inference by employing a lightweight draft model to generate candidate tokens that are subsequently verified by the target model in parallel. However, while this paradigm successfully increases the arithmetic intensity of memory-bound inference, it causes significant compute inefficiency: the majority of draft tokens fail verification and are discarded, resulting in waste of computation. Motivated by the goal of recollecting this wasted computation, we propose a novel system that transforms discarded drafts into reusable tokens. Our key insight is to perform auto-regressive prediction at the hidden states level and postpone the integrating token information after the hidden states generation, so the draft hidden states are not contaminated by incorrect tokens, enabling hidden state reuse. To implement such a system, first we introduce a draft model architecture based on auto-regressive hidden states, which preserves richer semantics than token-based drafters to facilitate draft repurposing. Second, we design an efficient token information injection mechanism that leverages our specialized draft model to construct high-quality draft token trees and enables resampling tokens from verification failures. Third, we eliminate the overhead hidden in our design to further maximize hardware utilization. We conducted extensive evaluations against various baselines, demonstrating up to a 3.3x speedup against standard speculative decoding.

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

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

We present Sable, an argument system and single-GPU prover for the statement that a committed, integer-quantized transformer produced a given token sequence from a given prompt, bit for bit. Sable fixes an integer function F_O with no floating-point step, in which every rounding, normalization, softmax and sampling decision is determined by its inputs, and proves it with a constraint system whose relations provably never wrap modulo the 31-bit KoalaBear prime. The proof batches zerochecks and LogUp-GKR lookups into one sumcheck per domain, and commits to every witness tensor and weight in one multilinear commitment built from Reed-Solomon codes, BLAKE3 Merkle trees and a mixed-length BaseFold opening. The prover streams the model layer by layer on one GPU. On one NVIDIA RTX PRO 6000 Blackwell GPU, Sable proves all 64 layers of Qwen2.5-32B in 92.5 s for 4,096 tokens and 398 s for 16,384 tokens, and covers Qwen3-32B and the mixture-of-experts Qwen3-30B-A3B (4,096 tokens in 121.8 and 84.7 s). A proof costs 41 to 50 times the serving time, or 6.4 cents per 4,096-token request at public GPU prices, and 40 to 64 times less time per parameter and token than zkLLM. On WikiText-2, F_O's greedy token matches the BF16 model's at 86.3% of positions; on Qwen3, F_O is within 1.6 points of BF16 on MMLU and 1.7 points on GSM8K. A verifier with a compiled core checks a proof on one CPU core in 19 to 56 s. In the random-oracle model, the interactive proof has round-by-round soundness error 2^-103. The proof is not zero-knowledge, so the system targets open-weight models. Code: https://github.com/moonmath-ai/Sable

Recent advances in large language models (LLMs) have improved their performance on coding benchmarks. However, improvement is plateauing due to the exhaustion of readily available high-quality data. Prior work has shown the potential of synthetic self-instruct data, but naively training on a model's own outputs can cause error accumulation, especially in coding tasks, where generalization may collapse due to overly simple or erroneous training data, highlighting the need for rigorous quality checks on synthetic data. In this work, we explore an effective approach whereby the model itself verifies the correctness of its own data. We thus propose Sol-Ver, a self-play solver-verifier framework that jointly improves a single model's code and test generation capacity. By iteratively refining code (LLM-as-a-solver) and tests (LLM-as-a-verifier) together, we boost both capabilities without relying on human annotations or larger teacher models. Experiments with the Llama 3.1 8B model demonstrate substantial performance enhancements, achieving average relative improvements of 19.63% in code generation and 17.49% in test generation on MBPP and LiveCodeBench.

In recent years, generative artificial intelligence (GenAI) has demonstrated remarkable capabilities in high-stakes domains such as molecular science. However, challenges related to the verifiability and structural privacy of its outputs remain largely unresolved. This paper focuses on the task of molecular toxicity repair. It proposes a structure-private verification framework - ToxiEval-ZKP - which, for the first time, introduces zero-knowledge proof (ZKP) mechanisms into the evaluation process of this task. The system enables model developers to demonstrate to external verifiers that the generated molecules meet multidimensional toxicity repair criteria, without revealing the molecular structures themselves. To this end, we design a general-purpose circuit compatible with both classification and regression tasks, incorporating evaluation logic, Poseidon-based commitment hashing, and a nullifier-based replay prevention mechanism to build a complete end-to-end ZK verification system. Experimental results demonstrate that ToxiEval-ZKP facilitates adequate validation under complete structural invisibility, offering strong circuit efficiency, security, and adaptability, thereby opening up a novel paradigm for trustworthy evaluation in generative scientific tasks.

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.

Coding agents are increasingly deployed for end-to-end software engineering tasks, where a readily available oracle evaluator that defines the success criteria is often absent. This motivates verifications for coding agents that can reliably judge and explain their behavior. However, verification is non-trivial as coding agents are increasingly capable of solving long-horizon software engineering tasks. Their execution trajectories can be extremely long, containing hundreds of iterative interactions with code repositories and external tools. Existing verifiers either rely on general-purpose LLMs without specialized training or train dedicated critics that predominantly focus on producing scalar rewards, highlighting the relatively limited exploration of training-based generalist verification. We introduce SWE-Critix, a post-training pipeline for training generalist verifiers of coding-agent trajectories. Given a task and its execution trajectory, the learned verifier predicts the completion label and generates a natural-language analysis that explains its judgment. Our pipeline combines supervised fine-tuning (SFT) with reinforcement learning (RL) and trains a series of 30B models on trajectories from CodeForge-Preview. On a held-out test set, SWE-Critix improves classification accuracy from 57% for the base Qwen3-30B-A3B reasoning model to 66% after SFT and 78% after RL. We release our models, datasets, and training code to facilitate further research.

Tool-using automation systems, from scripts and CI bots to agentic assistants, fail in recurring patterns. Common failures include unsafe side effects, invalid arguments, uncontrolled retries, and leakage of sensitive outputs. Many mitigations are model-centric and prompt-dependent, so they are brittle and do not generalize to non-LLM callers. We present Policy-First Tooling, a model-agnostic permission layer that mediates tool invocation through explicit constraints, risk-aware gating, recovery controls, and auditable explanations. The paper contributes a compact policy DSL, a runtime enforcement architecture with actionable rationale and fix hints, and a reproducible benchmark based on trace replay with controlled fault and misuse injection. In 225 controlled runs across five policy packs and three fault profiles, stricter packs improve violation prevention from 0.000 in P0 to 0.681 in P4, while task success drops from 0.356 to 0.067. Retry amplification decreases from 3.774 in P0 to 1.378 in P4, and leakage recall reaches 0.875 under injected secret outputs. These results make safety to utility trade-offs explicit and measurable.