Formal Verification

Verification of neural networks against relational specifications, such as global robustness, is crucial for safety-critical applications of cyber-physical systems (CPS), given their increasing adoption of AI components. Compared to simple trace properties (e.g., local robustness), verifying relational specifications requires reasoning about the relationship between multiple network inferences, which brings significant technical challenges. Existing research has explored abstraction techniques based on sound and convex over-approximation of neural network outputs; however, since these approaches are inherently incomplete and may raise false alarms, they further underscore the need of effective abstraction refinement. In this paper, we propose a branch-and-bound (BaB) framework to mitigate the issue, which iteratively splits the problem until all sub-problems are verified. Specifically, our BaB framework features splitting of relational neurons rather than individual neurons as prior works do, and as the core of our technique, we devise a relational neuron selection strategy based on the dual formulation of the verification problem, which allows us to efficiently select the (most likely) optimal relational neuron that maximizes the refinement brought by problem splitting. We evaluate SaBRe on 817 verification problems across ACAS Xu, MNIST-F, MNIST-C, CIFAR and GTSRB. The results show that SaBRe outperforms different baseline approaches, in terms of the number of solved instances and verification efficiency, which demonstrates the effectiveness of our proposed techniques.

Schedulability analysis is essential for certifying real-time systems, but existing tests are often developed through pen-and-paper proofs that are difficult to scale, validate, and maintain. Mechanized verification in PROSA/ROCQ offers a rigorous alternative, yet manually constructing such proofs requires substantial domain expertise and proof-engineering effort. Recent successes of large language models (LLMs) across a wide range of tasks make them promising candidates for generating PROSA/ROCQ scripts for mechanized theorem provers. However, state-of-the-art LLMs often lack the PROSA-specific knowledge required to correctly use its modeling abstractions and proof patterns. This paper introduces PROVE-RT, an LLM-assisted framework for generating PROSA/ROCQ scripts to mechanize schedulability analyses in real-time systems literature. PROVE-RT guides generation through dependency-aware informal sketches, retrieval from processed PROSA documentation, staged skeleton generation, and proof completion. We construct a mechanization-oriented corpus from 1, 191 real-time systems papers, containing 13, 134 informal sketches with dependency information. On a curated evaluation set, direct prompting of state-of-the-art LLMs fails to reliably generate valid PROSA mechanizations, whereas PROVE-RT achieves a success rate of 44.7%. These results show that retrieval-guided and staged LLM assistance can improve automated mechanization of schedulability analysis in PROSA/ROCQ.

Systems that generate GPU kernels with language models report high correctness rates. Those rates come from a single loose test: run the kernel on a few random inputs at one fixed shape and accept it if the output is close to a reference. A kernel can pass that test and still be silently wrong. It can return an ordinary number where the true answer is a NaN or an infinity, differ from run to run, break when the shape changes, or accumulate in fp16 where the reference keeps an fp32 total. We build the instrument that checks correctness properly: a contract-grade verifier of twelve adversarial gates, each a property a correct kernel must satisfy, several of them tolerance-free, so no choice of threshold can explain a failure away. Aimed outward, the verifier audits 2,638 machine-generated kernels that a public system's own harness had already accepted as correct. It finds 39.5% broken beyond any tolerance argument and 62.1% carrying at least one violation. The field's standard test accepts 1,487 kernels the verifier rejects, against only 14 the other way. We defend the finding four independent ways: a 7/7 positive control, a threshold-calibration sweep, 98.5% agreement with the reference benchmark's own correctness code, and a stratified hand-audit. Aimed inward, the verifier judges a kernel of our own: the first native Blackwell tcgen05 training backward for the gated-linear-recurrence (GDN) family, including the reverse-state stage the field still runs on a fallback. We establish its correctness independently, against a double-precision oracle, and train five family members through it. The correctness signal behind reported progress in kernel generation is far weaker than the numbers suggest, and a set of tolerance-free contracts would close most of the gap.

Multi-turn dialogues let users revoke constraints as easily as impose them, but revocation does not reliably take effect: models keep enacting withdrawn requirements (occasionally beneath comments asserting their removal), a failure we call \emph{behavioral relapse}, or revocation inertia. No existing instrument measures this influence per clause, predicts it before delivery, or repairs it under matched budgets. \sysname{} closes the three gaps through the model API alone: a contract ledger pairs every constraint with an executable checker, records revocations as tombstones, and compiles the net constraint state ahead of time into a single specification; a sequential ablation probe measures per-clause adherence and incremental behavioral effect; a repair ladder operates under token- and attempt-matched budgets. On \dataname{} (\NTasks{} HumanEval tasks, \NClauses{} verified checkers), relapse at an 8B operating point climbs from \ScaleDelayedMTwo{} to \ScaleDelayedMEight{} as constraint load grows, while stronger models sit at floor. Under matched checkers, model, and budget, ahead-of-time compilation significantly reduces relapse against a no-ledger verifier-retry baseline (\RestoreDiff{}, 95% CI \RestoreDiffCI{}, $p$ \RestoreDiffP{}); adaptive ladder interventions stacked on top add no detectable gain (95% confidence excludes gains $\geq$ \LadderExcludedGain{}). The probe predicts relapse before delivery (AUROC \AurocPrimary{}); a one-sentence tombstone note recovers about a third of the compilation effect and survives a placebo control. At \CostDeliveryFactor{} delivery overhead and \CostTotalHedged{} of API compute for every result, revocation failure becomes a measurable, predictable, and repairable property of dialogue state rather than an invisible one.

We construct OEIS Open, a benchmark based on 492 open mathematical conjectures from the OEIS, formalized in Lean by Tsoukalas et al. Whereas these conjectures had previously been attempted only with a bespoke agent, our open-source evaluation code runs any generic language model (LM) against them, and is secure against LM cheating attempts. We find that LMs equipped with a minimal set of tools resolve 147 of these conjectures with a budget of $50 per attempt, scoring 30% on OEIS Open. OEIS Open Lite is a random subset of 100 conjectures for cheaper evaluation. When evaluated with a budget of $200 per attempt, the best current LM scores 44% on OEIS Open Lite. Giving LMs access to the mathematics literature via 476,000 papers from arXiv did not increase performance on OEIS Open Lite, and nor did using more sophisticated agent loops. The conjectures covered in this work are of uncertain mathematical significance, and most have likely received little previous attention. Nevertheless, our results show that LMs can resolve open research conjectures autonomously and at modest cost.

Self-correction is particularly useful when a failure constrains the next repair. Coding agents benefit from this property because compilers, tests, and execution traces turn many failures into typed recovery signals, but broad language-agent tasks often expose only a coarse task failure. This creates a tension for generic recovery playbooks: they broaden the agent's context precisely when the system needs a narrower repair interface, mixing incompatible signals for invalid actions, missing procedures, and strict-format errors. Our insight is that development-set failures can recover part of the missing diagnostic substrate by deciding which recovery interventions are admissible before test-time correction. We propose DARC, a diagnosis-guided recovery harness that profiles task-family failure modes, prunes mismatched interventions from a shared recovery library, and freezes a verifier-selected success-cost policy for deployment. This causal order makes correction selective: the harness first determines what kind of failure can be repaired, then decides how much recovery evidence to spend. In ALFWorld, AppWorld, and XBRL Finance, the same protocol yields an action-validity harness, a procedural-recovery fallback, and a format-precision retrieval policy; in each evaluated setting it improves average task performance over base agents and broad playbooks while reducing environment steps or retrieval budget. Our experiments show that failures need not trigger uniformly more context: DARC turns self-correction from prompt expansion into recovery-interface design. DARC provides a practical route toward more reliable agents in domains where compiler-like feedback is absent: making failures actionable before making contexts larger.

Achieving effective self-correction, where models verify and correct their own mistakes, remains a fundamental challenge for large language models (LLMs). In this work, we propose Self-Fix Step-DPO (SFS-DPO), a reinforcement learning based, two-stage framework for step-level self-verification and self-correction. The first stage strengthens step-level reasoning via step-level preference optimization, while the second stage explicitly trains models to self-verify and self-correct. We further introduce a teacher-assisted variant, SFS-DPO-R, which incorporates explanatory rationales for error verification to provide stronger corrective signals. Comprehensive in-domain and out-of-domain evaluations across multiple LLMs demonstrate that SFS-DPO and SFS-DPO-R consistently outperform prior step-level training baselines. Our analysis further reveals improvements in self-correction frequency and effectiveness, highlighting the importance of strengthening step-level reasoning for robust performance.

Full justified representation (FJR) is among the strongest known satisfiable proportionality axioms for approval-based committee elections. Recent work has shown that an FJR committee can be found in polynomial time, but verifying whether a given committee satisfies FJR remains coNP-complete. We introduce FJR+, a strict strengthening of FJR and EJR+ that can be verified and satisfied in polynomial time. We then analyze the Residual-Budget Greedy (RBG) algorithm and prove that it selects a partial committee such that every size-$k$ completion satisfies FJR+. This freedom allows us to use sequential Phragmén to obtain a priceable completion. The resulting rule always satisfies FJR+ and the sub-core, and it is priceable whenever at least $k$ candidates receive an approval. We also obtain a Droop-quota version of FJR+. Finally, we extend FJR+ to approval-based participatory budgeting with arbitrary project costs. A project-specific version of RBG computes this property in polynomial time and can be continued to a priceable outcome satisfying a cost-based version of the sub-core.

Symbolic network verifiers can reason about correctness across vast spaces of routing inputs and failures, but only for the protocols and features an expert has encoded by hand. Creating and maintaining a faithful model of the control plane is both difficult and never-ending, since no written source specifies perfectly what a network does: vendor implementations deviate from the RFCs, and behaviour shifts with releases. The burden of constant upkeep ultimately keeps verification out of many networks that need it. We argue that the model should instead evolve automatically to faithfully capture the actual network behaviour. To achieve that, we leverage the only source that specifies it unambiguously: the router software itself. In a counterexample-guided loop, a coding agent proposes extensions to the verifier's symbolic encoding, while a trusted oracle (e.g., emulated routers) supplies the ground-truth routing state. The agent iteratively refines the network model using each disagreement with the oracle. As early evidence, a prototype of this system taught a 3,000-line SMT-based verifier three features it did not support: OSPF areas, BGP route reflection, and L3VPN over EVPN, converging autonomously on models that match the oracle, even noticing vendor-specific behaviour. Automating model growth shifts the hard problem from writing verification systems to systematically testing them; we propose a research agenda for trusting and harnessing automatically evolved verifiers.

Autoformalisation (AF) systems map natural language reasoning steps into formal statements in a proof assistant such as Lean. We consider how to assess the faithfulness of these systems. Existing approaches require expensive human-annotated ground truth, or rely on LLM judges or embedding models, which come with limited guarantees of accuracy. In addition, these methods typically only consider inputs that are known to be correct, and therefore do not assess whether the AF translates incorrect inputs faithfully. To address these limitations, we propose a new benchmark for AF faithfulness that is cheap to apply, sound under weak assumptions, and assesses both positive and negative examples. Our method is based on automatically generating perturbed reasoning steps that are designed to be invalid, and then measuring validity preservation on unperturbed steps and invalidity preservation on perturbed steps. We apply our method to eight AF systems across four mathematical datasets, and observe pervasive sycophancy: many AFs "silently correct" invalid inputs into provable statements. The most validity-preserving fine-tuned AFs are also the most sycophantic, suggesting a tension between validity and invalidity preservation in current AF systems.

First-order concept synthesis asks a system to infer one formula that classifies labeled objects consistently across several finite relational structures. Every candidate can be evaluated exactly, but quantified first-order formulas form a vast search space, and LLM outputs are often semantically promising without being fully correct. We introduce Hypothesis Frontier, a verifier-guided neurosymbolic framework that evaluates each LLM formula on every training object, retains the strongest verified hypothesis across rounds, and uses its remaining errors to guide subsequent generation. Symbolic processing repairs invalid formulas while remaining anchored to the LLM-generated hypothesis, and simplifies train-valid formulas without changing any training prediction. Under matched models, problem sets, and LLM-round budgets, Hypothesis Frontier solves substantially more problems than repeated original-prompt generation. After the final formulas are selected, exact simplification shortens many train-valid formulas while preserving every training prediction. Exact symbolic reasoning therefore helps both to solve more induction problems and to compress many of the resulting formulas.

Counterfactual video understanding evaluates whether models grasp physical and commonsense regularities. However, existing multiple-choice question (MCQ) benchmarks inadvertently leak target events through their questions and candidate options. This reduces the core challenge from active discovery to text-guided verification. In this paper, we present FADE, an effective training framework for counterfactual discovery and explanation. Our method is built on an evidence-first, two-stage training paradigm. First, evidence-internalized supervised fine-tuning grounds the model's predictions in decisive visual anomalies. Second, we apply a fading-anchor reinforcement learning strategy that progressively removes textual guidance, compelling the model to independently discover and explain evidence. To rigorously evaluate this capability, we also introduce an effective pipeline that converts existing MCQ datasets into aligned MCQ, open-ended question answering (OQA), and captioning tasks without requiring additional data curation. Our simple approach yields strong results. Using Qwen3-VL-8B as the baseline, FADE achieves state-of-the-art strict paired scores across all three tasks on DualityVidQA-test and IPV-Bench, outperforming GPT-5.6. In specific, when transitioning from constrained MCQs to unconstrained OQA and captioning, our model demonstrates remarkable robustness. Its performance retention is 90.4% and 67.4% on DualityVidQA-test-substantially higher than the 48.1% and 30.7% retained by GPT-5.6. We hope this simple framework can serve as a solid baseline for future research in unconstrained counterfactual video understanding.

Advances in advanced artificial intelligence tools have sparked research in robot autonomy, but the development of such systems has largely focused on execution rather than verifying the feasibility actions planning models propose. Like general-purpose LLMs, robotics planning models carry risks: biased toward user-specified goals, they may suggest actions misaligned with scientific ethics, they may be unsafe due to an inability to "remember" prior safety risks, or they may be vulnerable to adversarial attacks on the autonomy ecosystem. We propose a LLM-driven verification layer between planning and execution to evaluate action permissibility. Our LLM-as-a-Judge ensemble combines chain-of-thought reasoning across models and synthesizes those expert judge outputs, mirroring a combination of a mixture of experts and self-consistency approach. This layer serves as middleware, gating plans from the server's planning module before they reach the MCP server and therefore the robot's low-level controls: plans are approved, rejected for reformulation, or escalated for human review. With this system, we achieve near 85% precision across accept/escalate/reject categories 97% containment of adversarial attacks, with negligible errors between accepting and rejecting tasks, and errors mostly manifesting at the escalate boundary.

Large language models can write parametric CAD programs from a natural-language description (text-to-CAD generation), but a single sample is often wrong. Increasing test-time compute by sampling multiple candidates only helps if a good candidate can be identified, yet no ground-truth model is available at generation time. Existing systems often require a separate verifier, such as a vision-language judge, to select among candidates. We investigate whether the candidate pool itself provides enough signal for effective selection and a verifier-free alternative. We introduce 3D CAD consensus selection, hereafter consensus selection: sample $N$ parametric CAD programs, compile them to 3D models, and return the candidate that agrees most with the rest of the pool. The method is training-free and compatible with existing CAD agents. We investigate geometric and topological notions of agreement, each of which improves its corresponding evaluation metric. On the exact candidate pools of a state-of-the-art CAD generation method, geometric consensus improves all three geometric metrics over the method's verifier, while topological consensus matches it on topology. Across every tested LLM and prompt variant, geometric consensus also improves geometric accuracy over random selection from the same pool, reducing Chamfer distance by $1-10\%$.

GK is a query-directed first-order prover that extends ordinary resolution-based proof search with explicit positive and negative claims, numerical confidence values, and prioritized default rules with exceptions. It works directly with non-ground clauses, including equality and function terms. Candidate proofs are found by bounded first-order proof search; exception conditions of defaults are checked by further bounded searches, recursively when exceptions themselves depend on defaults. This avoids requiring a finite global grounding, while allowing incomplete searches to be reported as such. This paper adds structure-preserving quantitative reporting to that framework. Retained proof histories are used in two calculations. The first reconstructs the uncertain ground premises used by each proof and computes the probability that at least one retained proof is available, without counting shared premises independently. The second resolves positive and negative support at intermediate atoms before that support is propagated through later rules; the same calculation evaluates uncertain exception conditions for individual rule applications. Reports separate positive support, negative support, conflict, and ignorance and identify detected incomplete calculations or fallbacks. The implementation performs bounded reconstruction and dependency traversal after proof search and still requires no global grounding. Analytic examples and independent simulators reproduce the reference calculations on their stated fragments. Comparisons with probabilistic logic, probabilistic ASP, default logic, and goal-directed ASP identify cases of agreement, semantic difference, unsupported translation, and incomplete computation.

This work focuses on the impact and detection of clear contact lenses in the context of iris recognition. While the detection of cosmetic or patterned contact lenses has been extensively studied under the presentation attack detection (PAD) paradigm, clear prescription contact lenses, that are typically transparent, have received comparatively less attention despite their widespread use. Unlike patterned lenses, clear lenses introduce no salient texture artifact, making them difficult to detect and are often assumed to have no impact on iris recognition. We first examine this assumption using the commercial VeriEye matcher on four benchmark datasets and show that clear lenses marginally degrade genuine match scores and increase verification error. We then propose a two-stage contact-lens detection framework. Stage1 uses an existing PAD model to identify patterned lenses, while Stage2 focuses on the more challenging clear-lens versus no-lens distinction using a ConvNeXt-Base model equipped with Mask-Guided Spatial Attention (MGSA). The proposed MGSA module incorporates a Hough-derived anatomical ROI mask together with learned spatial attention and Squeeze-and-Excitation channel recalibration, allowing the network to focus on subtle limbal cues associated with clear lens wear. Across four datasets, the full pipeline consisting of both patterned and clear contact lens detection achieves between 90.0%--98.8% accuracy. Finally, we introduce a z-score calibration method that adjusts VeriEye match scores when a clear lens is detected in the input images. This calibration reduces EER by 4.1%--28.3% across datasets, demonstrating that reliable clear contact lens detection can directly improve iris verification performance.

Recommendation systems thrive on personalization, where ''correctness'' is rarely a binary truth but a matter of subjective human preference. As Large Language Models (LLMs) are deployed as autonomous verifiers of safety and quality guidelines, they face a distinctive challenge: context-aware preference alignment. Recent gains in Reinforcement Learning with Verifiable Rewards (RLVR) are indexed mostly on objective, mathematical tasks. Through a large-scale study spanning both proprietary and open-source models on four real-world verification tasks from a production recommender platform, we ask whether explicit reasoning generalizes to subjective, human-centric industry rubrics. We expose a fundamental vulnerability: rigid, math-centric reasoning traces actively degrade verification, and applying standard RLVR triggers a phenomenon we term reasoning collapse, in which the policy abandons deliberation in favor of rapid heuristic guessing. We introduce a conditional length-penalized post-training algorithm that intertwines verification accuracy with bounded reasoning length, halting collapse and recovering performance. Finally, we show that a reasoning trace's efficacy is tightly coupled with its socio-linguistic framing: across 1500 synthesized personas, verification accuracy swings by nearly 0.38 macro-F1 depending solely on the adopted reasoning persona---evidence that much subjective-verification error is really reasoning-style mismatch. This observation motivates a mid-training architecture that routes reasoning through contextually aligned personas. This work offers both a scalable algorithmic patch and a long-term architectural blueprint for aligning reasoning models with real-world subjective constraints.

AI tools that help people judge online claims are usually evaluated while the tool is present. This paper asks a different question: after using such a tool, what can the user still do on their own? I call this epistemic transfer. It refers to the effect of prior AI-assisted verification on later unassisted performance on new claims. In this paper, I make three contributions. First, I distinguish epistemic transfer from nearby outcomes such as correction effects, trust, reliance, and human--AI team performance. Second, I introduce two simple quantities for studying it: the Epistemic Transfer Effect (ETE), which compares delayed unassisted performance across conditions, and Tool-Removal Cost (TRC), which measures the immediate drop in performance when the tool is taken away. Third, I turn these ideas into a practical evaluation protocol that can be used in online experiments or field studies. The protocol combines answer-first and evidence-first AI conditions with active-practice and no-practice controls, delayed tests on held-out claims, behavioral measures, and participant- and item-level analyses. Putting ETE and TRC together yields a diagnostic space that separates capability building, capability plus tool advantage, epistemic inertness or de-skilling, and verification on loan. The point is not that every AI tool must teach. The point is that when independent judgment matters, we should test not only whether a tool helps now, but also what it leaves behind.

The reliability of AI generative models is typically measured by output correctness, yet in practice it depends on the effort required to verify those outputs. We argue that current evaluation metrics overlook a critical failure mode: Verification-Cost Errors (VCEs), defined as incorrect input-output pairs that a declared fraction of the verifier population fails to identify within the verification budget available in a given deployment context. Unlike standard notions of "hallucination", VCEs are defined operationally, by the failure of correct identification within budget rather than by any property of the output itself. Plausibility and authoritative presentation are hypothesised contributors to that failure, not defining conditions. To capture this asymmetry, we introduce the notion of verification cost relative to a deployment budget as an operational dimension that current evaluation does not routinely capture. The quantity is presented as a conceptual instrument rather than a finalized metric. Evidence from code generation and multi-modal document understanding shows that high benchmark accuracy can mask significant verification effort in practice. We therefore take the position that correctness alone is insufficient as a measure of reliability. AI evaluation should explicitly account for verification cost, reflecting whether errors can be detected under realistic resource constraints.

Large language models (LLMs) are high-value assets that can be derived through redeployment, fine-tuning, quantization, or further alignment. Because deployed LLMs are commonly exposed only through query APIs, ownership verification must often rely on black-box text responses. This setting is difficult: generations are open-ended and can vary across repeated queries, while existing black-box fingerprints rely on signals that are fragile under a final-response interface, including full-text matching, soft behavioral features, or model-specific prompts designed not to transfer. We propose TCF (Targeted Counterfactual Fingerprinting), a black-box LLM fingerprinting framework that converts open-ended generation comparison into constrained-answer targeted counterfactual transfer. TCF restricts each verification query to a finite answer space, reducing the surface-form ambiguity that enters the verification score, and optimizes a prompt perturbation toward a counterfactual target different from the protected model's clean answer on the original prompt. Verification reduces to checking whether the suspect model's parsed final answer matches the recorded target. We introduce the source-model counterfactual margin (SCM), a protected-model-only quantity that certifies the target is unlikely before the perturbation and likely after it; SCM controls target selection, perturbation stopping, and fingerprint filtering. Under explicit derived-preservation and independent-transfer budgets motivated by local behavioral closeness, we derive a target-accuracy gap between derived and independent models. Across four LLM families, TCF achieves an average AUC of 0.9861, improving over TRAP, ProFLingo, and ZeroPrint by 0.07 to 0.19.

Test-time scaling is often implemented by spending more compute along one axis: sampling more solutions, extending a chain of thought, or applying a stronger evaluator. Under a fixed inference budget, these choices compete. This paper formulates test-time reasoning as a compute-allocation problem in which a system must decide whether the next unit of compute should be spent on generation, verification, or stopping. We introduce CoBa, a compute-balanced routing policy that first obtains a small set of candidates, applies cheap verification broadly, and routes uncertain or high-value candidates to stronger verification. On 3,129 example-generator evaluations spanning MATH-500, AIME 2024/2025, AMC 2023, and procedural symbolic reasoning, CoBa-Routed-Strong reaches 85.13% macro accuracy, statistically matching a self-evaluation weighted-voting proxy at 85.20% while using 49.1% fewer parameter-weighted tokens. It also matches best-of-16 majority voting within 0.01 macro-accuracy points while using 58.9% fewer parameter-weighted tokens; paired tests retain a small best-of-16 edge at substantially higher cost. Paired bootstrap tests show significant gains over single-sample decoding, while the remaining gap to the pool oracle exposes headroom for sharper routing. For local reasoning systems, test-time scaling becomes a question of where the next computation is most valuable.

Content provenance standards, such as C2PA, are increasingly used to attach signed records of origin, editing history, and rights to digital images. However, provenance transparency can conflict with privacy -- assertions that strengthen trust in an image may also reveal sensitive information about the creator or capture context. We propose soft redaction for image provenance: a mechanism that replaces sensitive provenance assertions with zero-knowledge proofs (ZKPs) of selected properties over hidden data. Our work focuses on distance proofs. We first show how location assertions can support proofs of proximity to a public reference point, using Chebyshev polynomial approximations within the ZKP proof circuit. We then extend the approach to L2 distance proofs over biometric embeddings, enabling privacy-preserving claims related to likeness to help enforce personality rights with images. Finally, we apply the same distance-proof construction to perceptual hashes (visual fingerprints), supporting an anti-spoofing use case in watermark-based recovery of stripped provenance metadata. Our results demonstrate that ZKPs over image provenance can provide practical soft-redaction capabilities, compatible with C2PA, that may be constructed in seconds and verified in milliseconds.

Large language models (LLMs) can generate text that resembles a mathematical proof, but resemblance does not establish correctness. A formal proof checker verifies whether each proof step follows established logical rules. Coq bases its rules on the Calculus of Inductive Constructions, a logical framework that defines which proof steps the system may accept. This pilot study evaluated six open-weight LLMs on the same 100 theorems from CoqStoq, a benchmark derived from real Coq projects. Each LLM received one attempt per theorem with the temperature set to 0, and Coq checked every proposed proof in the theorem's original project environment. We counted a proof as successful only if the Coq kernel accepted it. Gemma 4 verified 12 of 100 theorems, Llama 3.3 verified 8, and DeepSeek Coder V2 Lite verified 1. Qwen 3.5, Mistral Small 3.1, and GPT-OSS verified none. The 21 successful model-theorem results covered 15 distinct theorems, 11 of which were not solved by a baseline of standard Coq tactics. All verified theorems had short or medium human-written reference proofs; no model verified a theorem with a long reference proof. Because the proof-length analysis was exploratory, this pattern does not establish that proof length caused the difference. For the three models with at least one success, the total generation cost per verified proof ranged from 741 to 36,193 output tokens, 14.9 to 178.0 seconds, and 0.0167 to 0.2000 aggregate GPU hours. We could not calculate these ratios for models with no verified proofs. Across 600 attempts, the models produced 21 kernel-verified proofs, giving an overall success rate of 3.5%. The study reports descriptive differences among the models but does not statistically test whether one model outperforms another. Therefore, the results do not establish a universal ranking of the six models.

Building reliable applications that leverage large language models (LLMs) remains a significant challenge. While LLMs offer impressive capabilities across diverse tasks, their outputs often lack accuracy and provide no clear measure of confidence. This uncertainty compounds in flows of multiple calls to LLMs and other tools, making it difficult for developers and end-users to trust the results. This paper introduces a probabilistic language for programming LLM-based flows. It enables developers to quantify and propagate uncertainty throughout the application's flow, and experiment with different inference scaling techniques without adding a single line of code beyond the flow's logic. We present an experimental study to demonstrate this capability, and a case study building a theorem proving agent for the Rocq theorem prover.

The integration of Large Language Models (LLMs) into software engineering has shifted the focus from function-level generation to repository-scale assistance. However, existing benchmarks largely rely on bug reports from GitHub Issues, which often allow models to bypass genuine understanding via pattern matching on error logs. This misalignment under-measures Edit Bias, which refers to premature generation, where models prematurely propose code modifications instead of understanding the existing repository architecture. Furthermore, current LLM-as-a-Judge scalar scoring suffers from high variance and low interpretability. This work introduces RepoProbe, a novel benchmark for evaluating repository-level code understanding through open-ended Q&A using GitHub Discussions, which focuses on open-ended architectural inquiries rather than defect reporting. To ensure rigorous evaluation, we propose a Checklist-Based Verification Protocol that decomposes answers into atomic, verifiable facts, thereby replacing subjective ratings with objective verification. Our evaluation of state-of-the-art (SOTA) LLMs reveals a persistent gap between high clarity and evidencegrounded technical correctness. It also quantitatively confirms the prevalence of edit bias, in which models prioritize code generation instead of architectural analysis. Finally, we demonstrate that our verification protocol significantly improves evaluation reliability compared to traditional evaluations with scalar scoring.

Although Multimodal Large Language Models (MLLMs) have made substantial progress, their spatial reasoning may still produce intermediate judgments inconsistent with the input image, allowing errors to propagate through the reasoning chain and affect the final answer. Existing methods mainly improve spatial reasoning through training or additional spatial information, without considering whether the reasoning process itself is faithful to the model input. Our study shows that unfaithful reasoning chains significantly reduce final-answer accuracy. To address this issue, we propose a modular and training-free framework for spatial reasoning verification and correction. The framework constructs a Spatial Evidence Graph (SEG), which associates atomic spatial evidence extracted from Chain-of-Thought reasoning with visual entities, spatial relations, source steps, and visual evidence. Spatial Evidence Reliability Assessment (SERA) evaluates the reliability of visual evidence based on object existence, localization, and geometric measurements. The framework then identifies the earliest spatial evidence unit contradicted by reliable visual evidence and guides the original MLLM to revise the subsequent reasoning and final answer. Across 15 model-dataset settings, our method achieves an average accuracy of 68.94%, outperforming the compared baselines by 8.55 percentage points on average. Our code will be open-sourced.

Large Language Models (LLMs) have transformed computational linguistics and achieved remarkable performance across numerous natural language processing tasks, yet significant gaps persist in understanding how these systems process culturally embedded linguistic expressions. This paper introduces ProverbIT, a novel Italian benchmark comprising 100 multiple-choice questions designed to evaluate LLMs' ability to complete Italian proverbs. We assess 13 frontier models, including Large Reasoning Models (LRMs) and traditional LLMs, across three tasks: proverb completion, multiple-choice selection with correct answers, and multiple-choice selection without correct answers. Our evaluation reveals surprising results: while nearly all models demonstrate knowledge of the proverbs through successful completion tasks, performance drops dramatically when transitioning to multiple-choice formats without correct answers, with even state-of-the-art reasoning models showing substantial degradation. Through detailed Chain-of-Thought analysis of two LRMs, we uncover that models exhibit a strong bias toward selecting literal synonyms and frequently mention correct proverb endings during reasoning without successfully identifying their absence from the given options. These findings suggest that current LLMs rely heavily on memorized patterns rather than deeper semantic understanding of culturally grounded expressions, highlighting important limitations in their reasoning capabilities for figurative language comprehension.

With the growing adoption of artificial intelligence in high-stakes decision-making, identifying the causes of outcomes--particularly failures--and determining who is responsible has become a critical concern. In this work, we examine how well formal definitions of \textit{responsibility attribution}, grounded in the framework of \textit{actual causality}, align with human judgments of responsibility. To this end, we conduct a large-scale survey to elicit human judgments of responsibility in multi-agent sequential decision-making scenarios, using a modified version of the card game Goofspiel. We evaluate multiple responsibility attribution methods, assess their alignment with human judgments about responsibility, and identify factors that significantly shape responsibility judgments. While no single responsibility attribution method consistently aligns with human responses, our findings highlight key factors that influence human responsibility judgments, including agent-specific biases and amount of information available to agents during decision-making.

Coding agents increasingly work across sessions, but prose notes can preserve a conclusion without the program state that supported it. After an upstream change, a repository may still build even though earlier verification claims are no longer valid. EA-Graph is an artifact-anchored memory for verification claims. It represents artifacts at sub-path granularity, resolves aliases to leaf definitions, anchors each claim to the content used to establish it, and keeps evidence strength separate from freshness. When replacement content is unavailable, the claim becomes unprovable rather than guessed. EA-Graph is evaluated on generated repositories whose behavior-to-artifact ground truth is known by construction. The task is to classify prior claims as unaffected, affected, or unprovable after value drift, logic drift, and deliberately withheld upstream content. The analysis covers 42 sessions across seven clean worlds, 14 model-world instances, three memory conditions, and two model tiers. In the Haiku round, artifact-anchored memory outscored prose notes and no persistent memory in all seven worlds; each exact paired Wilcoxon comparison yielded p = 0.0156. In the Sonnet round, the anchored condition was perfect, but frequent control ceilings left the preregistered contrasts non-significant. No session fabricated withheld content. These results support a bounded claim: artifact-anchored memory improved the smaller model's provability judgments in this testbed. An exploratory comparison further suggests that structured claim memory may narrow a capability gap by externalizing in-session re-derivation, but it does not establish cross- model equivalence. The study makes no claim about efficiency or repair quality.

Agentic AI systems routinely transport conclusions across biological, clinical and financial contexts, and the emerging safeguard is local verification: checking at each step that the entity is representable in the chosen tool, that parameters are compatible, and that outputs cohere with the plan. We prove this class of safeguard is structurally incomplete. Modelling a covering of context space by its nerve and evidence by a real-valued 1-cochain, an agent chaining evidence performs path integration: its conclusion is path-independent if and only if the cochain is exact, and disagreement between valid reasoning paths is exactly the holonomy of a first Cech cohomology class. Hodge decomposition partitions evidence conflict into a gradient part (calibration), a curl part (local inconsistency, visible at triple overlaps) and a harmonic part. Our central result is that no family of simplex-supported consistency checks can distinguish omega from omega+h for harmonic h, which nonetheless generates non-zero disagreement between valid paths; detection requires a statistic on a cycle basis. The resulting procedure, Ksetra, estimates by coboundary projection and gates abstention on the harmonic component, which we give a mechanism: it arises from effect modification combined with overlap-specific population composition, and vanishes to machine precision when effect modification is absent. The degrees of freedom of an evidence network partition into calibration, coherence and transport, yielding an exact F-test for the existence of a global claim; we quantify its distortion under unequal precision and supply the precision-whitened form that restores exactness. Foreign exchange, where the arbitrage-free null makes the cochain exactly a coboundary, serves as a calibration bench: the test is correctly sized, fires on loop arbitrage, and ignores triangular arbitrage.

Training-free speculative decoding drafts by matching an exact suffix of the context against a pool of earlier context. That lookup misses correct drafts already in the pool, most visibly on tool-calling traffic, where a request repeats almost everything but the few values minted for it, and where one rejected token discards the correct continuation behind it. We diagnose the failure position by position across ten benchmarks and find it to be a problem of addressing rather than of coverage: on our densest tool-calling benchmark, about half of what the strongest exact-match drafter misses is present in the pool yet unreachable by exact matching. We therefore propose a second, semantic draft source: the same pool, re-keyed by the hidden state the verifier has already computed at each committed token, together with a merge that lets it ride inside an existing lexical drafter's tree. In three published drafters, at matched pool and budget, it lifts accepted length by 24-29%. Oilbird reaches 4.4x autoregressive decoding speed on API-Bank, against 3.9x for the strongest training-free baseline in our harness and 2.0x for EAGLE-3.

How do you verify a long-horizon agent when its own state and self-reports are exactly what you cannot trust? We present an agent instrument built so that verification is structural rather than post-hoc. A deterministic Executive owns all belief; a language model may only file typed proposals, and a claim is admitted only when a prediction pre-registered before acting is matched against observation by code. Two properties make the instrument a verifier of its own science, not just of the agent: every run invalidates itself when per-organ write-error, render-size, or salted-canary-echo floors are breached (four of the first eight architecture runs were invalidated, each localizing a real defect); and a render-invisible shadow reference compiles the plan the full system would have committed in every ablation cell, so drift metrics are defined even where the mechanism under test has been removed. Using this instrument we report a clean, single-variable result on a failure every long-horizon agent suffers: ablating the commitment mechanism flips goal-abandonment from 0.00 to 1.00 while binding error stays flat at 0.00 (three seeds per cell, up to 394 reference beats per run, every run gated valid). The binding channel, by contrast, does not reappear as per-beat drift when its repair is ablated -- because binding is code-owned, the failure class is structurally absorbed, its only residue appearing one layer upstream as a collapse in hypothesis formation. We report these under full disclosure that task efficacy is null (zero level completions across 52 gated runs on ARC-AGI-3), pre-registered as a structural defeater. The contribution is a verification methodology for agent development and the drift decomposition it makes measurable.

Agentic systems driven by large language models (LLMs) are increasingly deployed in real-world workflows where they act on persistent operational data. Before deployment, these systems need to be verified against business requirements that govern workflow execution and data evolution. However, existing approaches do not provide such system-level guarantees, as they mainly constrain or analyse behaviour at the agent's interface level. We study here the verification of agentic systems comprising a single LLM and a tool orchestration harness over relational operational data. We formalise them as Stateful Tool-Enabled Agentic Deployments (STEADs), give their semantics, define the problem of verifying them against First-Order Computation Tree Logic (FO-CTL) specifications, and show that it is undecidable. We identify sufficient conditions for exact preservation of FO-CTL specifications under a finite-domain restriction, over which verification is PSPACE-complete. The key requirement is that renaming opaque identifiers in the data must correspondingly rename the selected tool calls. We show that LLM-driven agents can violate this condition and introduce a canonical deployment wrapper that guarantees it for arbitrary base agents while preserving already-equivariant behaviour. We prove that computing canonical representations required by this construction is graph-isomorphism-hard. Finally, we illustrate our framework on an LLM agent orchestrating a case-management workflow.

Combining Bayesian learning and quantitative verification is a powerful toolset for analysing key quantitative properties of software systems, like reliability and response time. However, the accuracy and robustness of verification results strongly depend on the prior knowledge (PK) underlying Bayesian inference. This knowledge reflects original beliefs about the probability of events and typically depends on domain expertise. Using inaccurate or uninformative PK can negatively affect quantitative analysis, yielding incorrect verification results. Our EPIK approach tackles this important challenge by eliciting and embedding PK in quantitative verification equipped with Bayesian estimators. Unlike existing approaches that require PK on formal model transition parameters, EPIK leverages system-level properties that are directly observable and are linked to real-world semantics. EPIK formulates a twofold optimisation problem to derive the distributions of unknown transition parameters and then embeds these distributions to verify new or difficult-to-measure (elusive) properties. The detailed experimental evaluation using multiple variants of real-world case studies and diverse EPIK instantiations shows its effectiveness, flexibility and generality.

Long-term memory is essential for LLM-based agents to sustain interactions and reliably leverage distant history. However, existing memory systems typically process heterogeneous dialogue content through a uniform summarization and retrieval pipeline, leading to either excessive token consumption or irreversible loss of fine-grained evidence. We argue that historical dialogue content should be handled differently according to its compressibility, temporal dynamics, and fidelity requirements. Based on this insight, we propose LeanMem, a lightweight long-term memory framework. LeanMem first filters out low-value content, then stores informative segments as compact profile memory, temporally structured event memory, or source-grounded record memory, depending on the nature of the information. During maintenance, only dynamically evolving event memories are selectively updated, avoiding redundant consolidation of stable profiles and immutable records. During inference, LeanMem dynamically selects memory types and allocates retrieval budgets according to query-specific evidence demands, assembling relevant evidence on demand. On LoCoMo and LongMemEval-S with GPT-4.1-mini and Qwen3-8B, LeanMem improves accuracy over the strongest memory-based baseline in every setting, by up to 15.1 points, at the lowest or near-lowest construction cost, inference tokens, and latency. The code and datasets are included in the supplementary materials.

Large language model (LLM) agents must retain reusable information, control a bounded active context, and recover earlier evidence during long-horizon interaction. Existing methods commonly optimize long-term memory (LTM) and short-term memory (STM) separately, while unified policies are often trained primarily with trajectory-level feedback, which provides weak credit for individual memory decisions. We present Verifiable Memory (VerMem), a framework that represents LTM, active context, and episodic history as distinct states and controls them with one memory operation policy. Seven atomic operations let the policy add, revise, or soft-delete LTM entries; retrieve LTM into the active context; filter or summarize the active context; and restore selected episodic fragments. VerMem is initialized by supervised fine-tuning and trained with a three-stage reinforcement-learning curriculum. The local verifier scores executable memory transitions, and a global verifier assesses evidence coherence and terminal-memory consistency after task completion. These scores are combined with programmatically computed task, evidence-recall, efficiency, and constraint signals through hierarchical credit assignment. The verifiers are used only during training. Across five benchmarks and two LLM backbones, VerMem achieves the best result on the vast majority of reported metrics and consistently outperforms strong memory baselines. Under controlled online-token budgets on three interactive benchmarks, it also achieves the strongest efficiency--performance frontier among the compared methods. Code is available at https://github.com/Sun-SYSU-24/VerMem.

Speculative decoding verifies a tree of draft tokens in one target-model forward pass. For a mixture-of-experts (MoE) target, however, parallel verification can activate the union of the experts selected by all tree nodes, even though only a small subset of those nodes reaches the accepted output. Token count, activated-expert union size, and expert-weight traffic are therefore distinct cost measures: reducing the token workload need not shrink the expert union proportionally, and under offloading, transfer traffic also depends on cache residency. We introduce AcceptMoE, a verifier-side expert selector that combines target-router scores with offline-estimated commitment probabilities and automatically adjusts the number of eligible experts for each verification block, eliminating the need for a user-specified expert budget. Under offloading, AcceptMoE conditions expert eligibility on cache residency instead of predicting natural routes and prefetching the corresponding expert weights. Although constraining target-expert eligibility changes the model distribution, across 12 model-task pairs spanning three MoE targets and four benchmarks, AcceptMoE's mean accuracy is 0.27 percentage points lower than that of EAGLE-3 speculative decoding with natural routing. Served with SGLang at batch size one, it reaches 1.290 times the throughput of this baseline with all expert weights in GPU memory, and 2.06 times under physical expert offloading, while reducing host-to-device traffic by 73.6 percent to 77.1 percent.

AI verification crosses a trust boundary: a verifier must learn enough to establish an authorized claim, yet the same evidence can reveal sensitive details about the model, workload, or hardware. We introduce minimal information disclosure (MID), which designs and quantifies the information content of verifier-facing evidence itself. MID measures collateral leakage with conditional mutual information: what the release reveals about the protected property after the authorized result is known. MID is general by design: it can accommodate different verification goals, protected properties, evidence sources, and deployment constraints. To demonstrate MID's practicality, we evaluate it on four physical measurements and six verification tasks spanning execution type, hardware identity, compute scale, and model identity. These experiments use three mechanism-design variables--the evidence channel, collection policy, and release transformation--but MID is not limited to these choices and can accommodate other deployable mechanisms. Across these tasks, MID produces three releases with perfect held-out verification and zero measured collateral leakage, while the remaining tasks yield explicit privacy--utility frontiers. MID also supports ZKP-certified releases: we demonstrate our proposed linear-projection mechanism using a Groth16 zk-SNARK.

We assess 18 chapter-specific reviews of the ten mathematical results announced by OpenAI on 1 August 2026, alongside review standards, Lean formalizations, subsequent research, and mathematical references. The article audits this review record without claiming a complete reconstruction of all ten proofs. No confirmed substantive mathematical error in a principal result remains in the examined assessments, although review depth varies and some dependencies remain partly checked. Chapter 8 presents the strongest reservation: a specialist review requests major revision of compressed analytic arguments. In Chapter 6, an apparent polarity error was withdrawn after an overbar lost during PDF extraction was recovered from the typeset source. Subsequent research independently reuses the Chapter 3 proof mechanism and confirms that Connes's rigidity conjecture is false, without independently reproducing Chapter 4's stronger infinite-family result. Among the cited follow-ups, Chapter 7 receives the strongest direct theorem-level corroboration through a stronger hardness theorem. Related equality results in Chapter 8 do not verify the analytic inequality proof. Some follow-ups disclose material AI assistance. We argue that confidence should combine formal checking, human reconstruction, independent mathematical use, and a public record supporting correction of both proofs and reviews.

We present MechGeo, a Mathlib native agentic framework that jointly addresses faithful autoformalization and certified proof construction for Euclidean geometry. In this framework, GeoFormalizer represents informal problems in GeoIR, deterministically translates them into Lean 4, and iteratively repairs candidate statements using structural diagnostics and semantic evaluation. GeoProver constructs geometric proof plans, derives intermediate lemmas, and selectively algebraizes suitable subgoals through a library verified in Lean. Singular or SymPy may generate algebraic certificates, but all resulting proofs and counterexamples are checked by Lean's kernel. Experiments across seven LLM backbones show substantial improvements in autoformalization, particularly for models with weaker direct translation performance. On 43 historical IMO geometry problems, GeoFormalizer generates formal statements that GeoProver proves in 29 cases; for the remaining 14, it constructs counterexamples verified in Lean and proves all repaired statements after expert correction. Together with IMO 2026 Problem 2, this yields, to the best of our knowledge, the largest reported collection of automated, kernel-checked Lean proofs for IMO geometry problems. On the 14 geometry statements in LEAP's Lean-IMO-Bench, MechGeo proves 12 for the first time, formally refutes the remaining two, and proves both repaired statements. These results establish counterexample guided diagnosis, geometric reasoning, and certified symbolic computation as a practical foundation for trustworthy formal geometry.

Deep research benchmarks require expert-level tasks and reliable evaluation grounded in task-specific knowledge. Existing benchmarks rely heavily on expert authoring or pre-existing human-authored materials, while fully automatic construction struggles to ensure consistent and traceable verification. To address this gap, we introduce a verifiable benchmark of 500 deep research tasks spanning 31 topics and 10 major categories, with three query forms designed to probe complementary capabilities required for deep research. The benchmark is constructed automatically using an iterative Explorer-Formalizer-Challenger pipeline that progressively transforms simple questions into deep research tasks. Each task is represented as a directed acyclic graph (DAG) of atomic steps and associated checkpoints, enabling the query, DAG, and rubrics to evolve together in a controlled manner. Experiments demonstrate that the benchmark clearly discriminates among models and query types, while its fact-grounded pointwise rubrics enable fine-grained, human-aligned, and stable evaluation. Our data, implementation, and results are publicly available.

Existing indoor layout generators produce globally plausible layouts yet may retain local violations such as collisions, out-of-bounds placements, obstructed openings, and blocked circulation. Most prior work focuses on full-scene synthesis or scene-level optimization, with limited support for identifying responsible objects and locally repairing affected regions. We present Roomer, a reflective repair framework that casts these violations as sparse, object-grounded repair problems. Roomer encodes layouts as RoState'' and uses RoReview'' to bind measured violations to implicated objects. A geometry-conditioned vision-language model planner proposes a structured local edit, while a deterministic solver validates it and generates a finite set of candidate edits when needed. Each candidate is committed only if full-scene verification confirms that it resolves the target violation without new hard violations or broken protected constraints. We train the planner on Roomer-CC, a controlled-corruption dataset that pairs faulty layouts with object-grounded violation evidence and known-feasible inverse StatePatches. Since existing benchmarks rarely assess whether physically valid layouts are usable, we introduce Roomer-Eval to assess distributional quality, physical validity, and practical usability. Experiments show that Roomer repairs residual violations while preserving valid regions, improves physical validity and usability, and transfers across external generators.

Large language models are increasingly used to reason about software vulnerabilities, but their outputs can silently violate domain knowledge, limiting their reliability in safety-critical settings such as medical devices. Prior work either treats that output as a prediction to be scored or constrains it to walks within a single knowledge graph; neither checks whether reasoning over a binary is consistent with an independent body of domain knowledge. We present EntailLLM, which validates each LLM-proposed analyst path by entailment: the path is a traversal of the binary's function call graph, the domain knowledge is represented in a separate graph, and verification aligns the two under temporal annotated logic. Across three CWE classes, four LLMs, three prompting strategies, and seven binaries varying in size from 405 to 12,696 function call-graph nodes, domain knowledge raises pooled entailment from 78% to 98%, with entailment decreasing in only 3% of the experiments. EntailLLM is deployed end-to-end on real medical-device binaries, reaching 98% pooled entailment without per-device tuning. Our system inherits the formal guarantees of generalized annotated logic, providing logical verification of LLM output that is both explainable and grounded in well-defined semantics.

As digital drawings are increasingly shared online, reliable authorship verification has become important for protecting artists and resolving disputes. Yet when authorship is questioned, verification may have to rely only on the disputed drawing and reference drawings known to be created by the claimed artist. This setting is challenging for two reasons. First, artist-specific drawing behavior, such as pen pressure and movement speed, is informative but is not available from a completed drawing. Second, similarities in the depicted object or scene can obscure similarities arising from the artist. We propose IDraw, a framework that learns from drawings paired with tablet-pen sensor signals collected from separate training artists. This allows IDraw to infer drawing behavior from completed images during a later authorship dispute, without requiring sensor data from the artist being verified. IDraw also reduces the influence of drawing content by identifying information shared by drawings of the same object across different artists and suppressing it before comparing drawings. To support this approach, we construct the first multimodal dataset for digital drawing authorship verification, containing 1,110 drawings from 37 artists and 14 types of tablet-pen sensor signals. Evaluated on previously unseen artists across nine image-encoder backbones, IDraw consistently outperforms standard image-based verification and reduces verification error by up to 40%. These results demonstrate that inferring drawing behavior from completed images and suppressing drawing content improve digital drawing authorship verification.

Online-judge verdicts and the datasets and benchmarks built on them are treated as ground truth for evaluating and training large language models for code. Yet prior audits have sounded a warning: official suites accept buggy submissions. These audits, however, stop at the warning and offer no practical remedy. Our remedy has two parts: an off-the-shelf coding agent, serving as a test-suite auditor, both builds adversarial test suites to expose what official suites miss and supplies these suites where no official suite exists; a certification chain determines whether each agent-flagged submission is genuinely buggy without relying on the official judge: multiple independently written accepted solutions agree on the expected output for every test, brute-force solutions settle disagreements, and a per-problem validator certifies each failing input legal. One such agent identifies 589 verified accepted-but-buggy submissions among AtCoder's 20,375 audited accepted submissions; extending the same certification to all five agents yields a union floor of 906 such submissions. Five agents, scored separately, each stay within 1.7pp of official-suite coverage on logic bugs those suites catch. On post-cutoff Codeforces problems with no available official suites, the same test-building method leads all five reproduced baselines at every tested input budget. Where an official suite exists, the agent audits suite adequacy instead of assuming it; where none exists, agent suites catch the most buggy submissions among methods we reproduced and tested.

Two prompts can request the same code change and produce the same correct patch, yet cause a coding agent to perform radically different kinds and amounts of work. We study this effect in a preregistered benchmark spanning 4,644 valid runs, 24 deterministic coding tasks, seven reasoning models, and two real agent harnesses. The central finding is that prompt wording does not merely scale total effort; it changes where that effort is spent. Multiple approaches and deep thinking primarily inflate reasoning. Multiple approaches increases reasoning by 2.4x to 7.4x across all six open models and creates about three elaborated but discarded solution branches, while still yielding only one implemented solution and no success gain. Maximum certainty activates a different pathway: repeated verification propagates into extra test runs, tool calls, turns, latency, and context growth. Runs with high redundant verification cost 18x the clean-run median, execute 2.5x more tool calls, and take 3x longer, again without a success gradient. These mechanisms therefore have distinct cost carriers: some prompts are reasoning-heavy and token-borne, while others are tool-heavy and system-borne. Harness design amplifies both effects and changes cost per successful task by 5x to 30x in our setting. The findings survive a frozen holdout, paraphrase tests, a Kimi-K3 replication, and a first-party Claude Sonnet 5 study. In contrast, bounded-efficiency wording preserves diagnosis and final validation while avoiding the measured waste mechanisms. Prompt engineering for coding agents is therefore work design: it determines what the agent thinks through, what it executes, and when it stops.

When a self-improving AI-for-science system claims a new capability, the evidence is usually a benchmark delta, a description-length gate, or a p-value. None separates a real gain from extra search, from a changed verifier, or from adaptation to a fallible oracle. We build a two-sided audit whose negative side is a formal fact: a pseudoknot-free oracle provably cannot represent a crossing base pair, so the prior verifier's range is bounded exactly, offline, before any run. "New" is relative to the agent's prior self, never to the base model. First, how far a single fallible oracle can inflate a capability claim. An invented, solver-free operator solves 43/60 crossing RNA targets under the predictor it optimizes, above a context-free floor of 0/60; under three predictors, 1/60 survives. Paired on the same 43 targets, a predictor the operator never saw confirms 2 of its designs against 26 for a minimum-free-energy solver (p = 8e-7). No statistic computed from the system and its own oracle sees that gap. Second, agent-written procedures can beat a human-written one under a judge no objective can flatter, at a fraction of the compute. Of six frontier models, the two whose operators ran without timeouts carry over at 0.293 against our 0.095 (n = 951 paired units, target-clustered [+0.108, +0.297], p = 5e-5) while spending 4.6-10x fewer oracle calls. Three rungs: difference under an outside adjudicator (reached), not bought with compute (reached, both directions), mechanism identified and transferable (not reached; seven candidates tested, none moves the statistic). The ceiling is the panel itself: its three predictors share nearest-neighbour thermodynamic parameters, two agreeing at kappa = 0.673. The audit is as unsparing about our own system: matched undirected search is an exact zero, and a search-free probe puts 84% of our headline effect on targets a random sequence already solves.

Cryptographic code is critical infrastructure that must be correct, yet formally verifying production libraries remains difficult. Existing language-model proof systems solve isolated obligations with specifications and premises already given, leaving production-library verification unresolved. We present CryptoProver, an AI-based system that synthesizes internal specifications and Verus-checked proofs from high-level API contracts. Without changing executable code, CryptoProver constructs a new independent proof of curve25519-dalek and verifies RustCrypto's previously unverified chacha20 implementation against an RFC 8439 specification. These cryptographic lineages underpin deployed systems including Signal and Shadowsocks; Signal has an estimated 218M global downloads. The independent, human-led curve25519-dalek verification was developed publicly over eight months by five main contributors. Given the API contracts and a fixed trusted library of field specifications, arithmetic facts, axioms, and vstd, CryptoProver synthesizes the internal specifications and proofs in 11.4 hours with USD 466.99 in recorded API cost. CryptoProver follows a trust-first design principle: mechanical gates reject specification weakening, invented axioms, and cross-module breakage, while isolation blocks reference proof retrieval, including from git history.

Tool calling allows large language models (LLMs) to invoke external computation during problem solving, a useful capability in various fields including AI for mathematics. We study this setting through weighted sum-of-squares (SOS) decomposition, a machine-checkable route to proving polynomial nonnegativity and hence polynomial inequalities. A candidate decomposition can be checked exactly, but finding one requires choosing among non-unique regroupings and coordinating multiple symbolic transformations. We develop an agent that combines algebraic task training, symbolic tools, and verifier-grounded optimization for this task. Rather than training only on the composite SOS task, we construct 1.35 million synthetic examples covering eight supporting polynomial tasks together with weighted-SOS decomposition. We first apply supervised fine-tuning (SFT) to direct algebra problems and simulated symbolic traces, and then use Group Relative Policy Optimization (GRPO) with task-specific symbolic rewards. The SFT corpus contains no native tool-calling messages; at evaluation, the agent uses native SymPy calls for expansion, collection, reordering, and factorization. Every final SOS answer is checked by exact expansion and coefficient comparison. On held-out, same-generator synthetic problems, the full SFT+GRPO+tools system is the strongest of four evaluated configurations, reaching 78.96% verified success on weighted SOS, compared with 44.73% for the base model with the same tools, and 91.75% macro accuracy across nine polynomial tasks. Within this controlled setting, our work provides a case study of combining domain-specific skill training, executable tools, and verifier feedback, and may inform the design of tool-calling agents in other domains with exactly checkable outputs.

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

Large Language Model (LLM) agents rely on external tools to perform multistage tasks. Existing agent frameworks typically assume that tool calls are atomic and return binary success or failure signals. However, real-world systems exhibit non-atomic behaviors such as timeouts after dispatch, delayed visibility, and partial state updates. These mismatches lead to reliability issues including duplicate actions, task success, and unnecessary tool executions. A lightweight, verification-aware tool wrapper is introduced that augments tool calls with postcondition verification, verify-before-retry logic, and idempotency keys. The approach is evaluated in a controlled simulated environment with injected non-atomic failures across multiple task templates. The results demonstrate that the proposed method significantly reduces duplicate actions, while maintaining comparable task success rates. Overall, the findings suggest that strengthening tool interaction semantics is a promising direction for improving LLM agent reliability without requiring modifications to the underlying language model.

Text-to-molecule generation is typically formulated as a one-shot sequence generation problem, where a model directly maps target descriptions to molecular representations. However, molecular descriptions often contain informative structural constraints, and violating such constraints can change the molecular identity. This makes chemical verification and error correction important but underexplored. To fill this gap, we propose MolGVR, a chemistry-grounded Generator--Verifier--Refiner framework. The Generator infers structural evidence and generates candidate molecules. The Verifier addresses the lack of chemical validation by converting descriptions into chemical constraints and checking candidates against them. The Refiner addresses generation failures by revising candidates rejected by the Verifier. Experiments on ChEBI-20 and PCDes show that MolGVR improves exact-match performance. These results suggest that coupling generation with executable verification and feedback-guided refinement is an effective way to improve text-to-molecule generation.

Fortran has been the cornerstone of high-performance computing for decades and remains unmatched in many domains. Yet the language faces an expertise gap: a new generation of scientists is barely familiar with it, while many experienced Fortran developers are only now transitioning to modern ecosystems such as JAX. This gap often results in "Fython" - Python code written with a Fortran mindset - that fails to leverage modern frameworks. We present FGPT, a transpiler framework designed to bridge this gap. It provides a systematic pipeline that transpiles Fortran into GPU-adapted Fortran, auto-differentiable Fortran via Tapenade, or NumPy and JAX scripts. Its architecture comprises three stages: (i) a frontend that parses Fortran and extracts target procedures along with all their dependencies; (ii) a middle-end that lowers the code into an intermediate representation, then into GPU-adapted or auto-differentiable Fortran, or a NumPy class; and (iii) a backend that transforms NumPy scripts into JAX modules optimized for GPU acceleration and automatic differentiation. Large language models fail when applied to the scale of community scientific codes-often spanning hundreds of thousands of lines-where consistent transformations, strict numerical fidelity, and validation against production tests are non-negotiable. FGPT addresses these challenges by preserving program semantics throughout the entire translation. We verified the framework on representative climate modeling kernels and demonstrated that it produces correct, differentiable Python implementations without requiring manual intervention. By combining rigorous compiler techniques with modern accelerator support, FGPT offers a scalable, trustworthy path for modernizing legacy Fortran code.

Retrieval-augmented generation improves the factuality of large language models by grounding responses in retrieved evidence, yet existing evaluation frameworks struggle to provide consistent, fine-grained diagnostics across the diverse spectrum of user queries, ranging from close-ended fact-seeking to open-ended explanatory requests. We propose Q-CARE, a query-agnostic and fully reference-free framework that enables fine-grained assessment by decomposing queries into sub-queries and answers into atomic claims. Q-CARE establishes a unified evaluation principle based on query coverage and claim verifiability, yielding coverage-aware retriever metrics (C-Prec@k, C-nDCG@k) and claim-level generator metrics (Completeness, Conciseness, and Verifiableness). On a human-annotated benchmark spanning eight datasets, Q-CARE achieves higher correlation with human judgments than four existing RAG evaluation metrics, including RAGEval and RAGChecker, proving its effectiveness as a reliable, automated evaluation framework. Code and data are publicly available at https://github.com/DISL-Lab/Q-CaRE-COLM-26.

Branch and Bound (BaB) aims to achieve complete verification of neural networks by adaptively partitioning the problem and applying off-the-shelf verifiers to subproblems. Its problem-splitting history can be represented as a tree, where each subproblem corresponds to a child node. A key problem of BaB lies in searching for the verdict boundaries across all the paths that divide the verified and unverified subproblems. We observe that the existing BaB approach tackles this problem by solving each expensive subproblem sequentially along the tree path as its depth increases, requiring costly bounds propagation at every visited BaB tree node (i.e., subproblem), which is inefficient. To address this issue, we propose effective search approaches that leverage the monotonicity of each path to efficiently and precisely locate the verdict boundary by simultaneously splitting multiple activation functions (e.g., ReLU), rather than processing them one at a time as in the classical approach. Our approach performs an effective exponential search along each path, allowing us to skip many boundary-unrelated subproblems when identifying the verdict boundary. The enhanced version further improves this process by estimating the boundary's position using quantitative information obtained from subproblem solving. We perform experimental evaluation on commonly-used benchmarks to assess our proposed techniques, and compare them with recent BaB-based approaches.

Verification consumes the majority of modern chip design effort, yet the formal verification tools that provide mathematical guarantees of correctness remain expensive and restrictively licensed. While large language models (LLMs) have shown promise for hardware design, existing approaches to RTL repair validate their results through simulation - which exercises only a subset of inputs - or rely on commercial tools, and few combine formal proof with an entirely open-source toolchain. In this paper, we present a multi-agent pipeline that couples an LLM with an open-source formal backend (Yosys, SymbiYosys, and Z3) to repair RTL through counterexample-guided iteration: the framework generates formal properties, verifies the design, and feeds counterexamples back to the LLM until the design is proved correct by k-induction or an iteration budget is exhausted. Through an ALU case study, we show that the pipeline can detect and repair a real functional bug with a formal proof of correctness. Across a six-benchmark suite, one design is repaired reliably, and we characterize four distinct failure modes: bounded-cover vacuity, specification ambiguity, temporal-logic bugs, and multi-property pressure. We frame this work as a feasibility study with a detailed failure analysis, and additionally report a practical limitation of the Yosys bind directive relevant to the open-source formal verification community.

SWE-bench-like benchmarks are widely used for evaluating LLM's issue resolution capability. They typically follow a common construction pipeline: each PR (Pull Request) is paired with its linked issue by extracting issue references from the PR description; the issue description is used as the problem statement, and the PR patch serves as the test oracle. However, due to the inherent complexity of developing and maintaining large repositories, such PR-Issue pairings are often misaligned in practice. In this work, we systematically study SWE-bench Verified instances, finding that 13.6% exhibit misalignment across five patterns in eleven fine-grained scenarios. To enable reliable and scalable construction of those benchmarks in the future, we propose PAIChecker, a multi-agent system for checking PR-Issue misalignment in SWE-bench-like benchmarks. Specifically, PAIChecker adopts a three-phase design that combines specific pattern identification, cross-agent label synthesis, and code-level validation, thereby enabling more accurate, generalizable, and progressively verified detection. Experiments on SWE-Gym and SWE-bench Multilingual show that PAIchecker achieves the best performance across all four LLM backbones, reaching up to 92.12% and 91.67% binary accuracy, respectively.

An agent playing a Nash-equilibrium strategy in a two-player zero-sum imperfect-information game secures the game value but forfeits the additional value offered by a flawed opponent. Diffuse deviations pose a particular challenge: binary release rules may gather too little evidence to act, while a full best response to an incomplete opponent model can be highly exploitable. We introduce \emph{budget-constrained confidence-scheduled restricted responses} (CS-RNR), the first opponent-exploitation method whose safety guarantee is a certificate the agent computes on the strategy it actually deploys, so that every exploit it commits to is one it has audited itself. The method tracks pooled action frequencies with anytime-valid confidence sequences and treats a frequency as exploitable only once its interval separates from an equilibrium reference. The confirmed deviations define a conservative opponent model, which a restricted-response solve turns into candidate counter-strategies over a grid of pin levels. Before deployment, each complete candidate is evaluated by a full-tree best response. The resulting certificate is compared with a user-specified budget and committed atomically with the strategy. Because this check is performed on the played strategy, model quality determines the exploitation achieved while the certificate controls reference-relative expected loss. In Leduc hold'em, CS-RNR obtains $6.2\times$ the steady-state gain of a money-verified binary gate while keeping every deployed strategy within budget. A trajectory mixture using the same estimator reaches $13.6\times$ the budget. Across Leduc, Liar's Dice, and 5-rank Leduc, all $36{,}000$ audited hands satisfy the reported certificate tolerance.

Constraint programming is a core technology for solving complex combinatorial problems in scheduling, planning, configuration, and verification. Trusting its results therefore demands guarantees at two levels: that reformulations applied beforehand are semantics-preserving, and that solvers produce correct answers. In this work, we introduce a framework that addresses both verification levels in the Lean theorem prover: it can be used to prove formulation-level properties, such as equivalence, equisatisfiability, and the correctness of symmetry-breaking constraints, parametrically for entire problem families; and to check solver-produced certificates for individual instances via translation backends to external formats such as MiniZinc, SMT-LIB, and OPB. Combining both levels yields an end-to-end workflow that establishes the satisfiability or unsatisfiability of a constraint problem without trusting the external solver. Experimental results show that our framework's verified symmetry breaking also pays off in practice: a single parametric proof per problem family, reused across all instance sizes, reduces solver search effort by a factor of up to 2x10^7, while the entire in-Lean certification stays affordable, taking at most a few minutes for our largest instances.

Scaling test-time computation can improve language-model reasoning, but uniform budgets waste computation on easy inputs, while verifier-guided refinement relies on external feedback. We introduce Self-Verifying Refinement (SVR), an oracle-free multi-turn reinforcement learning framework that learns to use self-verification as a compute-control policy. At each turn, the model produces a solution together with a discrete correctness verdict and a confidence score; it retains the current answer only when the verdict is Correct and confidence exceeds a threshold, and otherwise continues refinement using its own self-verification. Ground-truth correctness is used only to construct training rewards and is never exposed to the policy through refinement prompts or required at inference. SVR is trained with GRPO on fixed-horizon trajectories using rewards that promote solution correctness, calibration-aware self-verification, and stop-ready correct states; adaptive stopping is activated only at inference. On seven mathematical reasoning benchmarks with Qwen3.5-2B, SVR achieves a macro-average accuracy of 0.563 with only 2.99 inference turns on average. In the evaluated complete-system comparison, it exceeds standard GRPO, strong multi-turn baselines, and a fixed-budget oracle-guided score-feedback reference while requiring substantially fewer turns than fixed ten-turn inference. These results demonstrate that learned self-verification can serve as an effective internal control signal for answer retention and adaptive test-time compute allocation.