Formal Verification

Agent harnesses supply planning guidance, organize execution, and check completion. We study how these components affect success, erroneous acceptance, and cost in two Retail experiments and an Airline pilot in $τ^2$-bench. The primary comparison pairs prewritten task-specific plans (Fixed) with shuffled policy text matched in word count (Sham), isolating the contribution of guidance content. Across 265 matched cells, Fixed improves oracle-verified success by 7.17 percentage points (90% task-clustered bootstrap interval, 1.15--13.36 points), with gains concentrated in higher-complexity tasks. A read-only terminal verifier rejects 61% of Retail oracle-invalid episodes while withholding 17% of correct ones, at less than one cent of additional cost per episode. Which component matters more depends on the loss assigned to erroneous acceptance: at low liability the planning gain dominates; at high liability the verifier's avoided false passes dominate---and a standalone verifier captures nearly all the false-pass benefit of the full planning-plus-verification stack at a fraction of its cost.

Landmark mathematical formalizations have taken specialist teams years to complete. We present FormalFlow, a system that coordinates AI proving agents under human supervision to address statement drift and proof composition in long-horizon formalization. Drawing on software engineering principles and practices, it uses a shared blueprint to guide nested planning, proving and review loops. Agents strengthen verification and review throughout formalization. We completed a machine-checked Lean 4 proof of the quantum soundness of the classical low individual-degree test, a core theorem underlying MIP* = RE. Developing the proof took 63 days; greater parallelism could further reduce this time. The final library contains 126,367 lines of Lean code, all generated by agents. The formalization corrects side conditions and intermediate errors while preserving the published final error bound under corrected assumptions. This work provides a verified foundation for quantum complexity and demonstrates a route to affordable verification of major research proofs by small teams.

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.

LLM coding agents now generate complex programs at a scale that makes thorough human review increasingly difficult, raising the risk of safety and security failures. Common approaches, including fuzz testing, static analysis, and LLM-as-a-Verifier, can detect many failures but struggle to cover all possible edge cases. Formal verification addresses this by providing machine-checkable guarantees over specified properties, but traditionally demands substantial manual specification and proof engineering. We introduce a unified multi-agent framework, MAGS, that generates executable programs with formal safety guarantees, using Dafny as a verification-aware intermediate representation where safety properties can be mechanically checked. MAGS formalizes and freezes human-audited APIs and safety requirements, translates generated code into Dafny, repairs violations using verifier feedback, and compiles verified programs back into executable code. We evaluate MAGS on 100 CUDA kernels, 100 terminal scripts, and 20 robotic-arm tasks. Across all 220 examples, it achieves a 100% success rate in producing programs with non-trivial safety guarantees against frozen specifications. Independent safety and functional evaluations further show strong performance across all three domains, while revealing failures when the auto-formalized semantics do not fully capture the target behavior.

Human values are deep motivational orientations that shape human behaviors. In e-commerce, they reveal the stable drivers behind users' purchase decisions. Compared with short-term interests, consumer values better explain how users evaluate products before purchase. However, consumer values are often implicit in complex and fragmented behavioral trajectories, leaving value measurement from e-commerce behaviors largely underexplored. To this end, we propose the Behavior-to-Value (B2V) task, which aims to identify consumer values from e-commerce behavioral trajectories. Centered on this task, we first construct the E-commerce Consumption Value Taxonomy (ECVT) and introduce B2V-Bench, the first B2V dataset and benchmark, based on anonymized Taobao behavioral logs. B2V-Bench consists of real-world purchase decision episodes, covering 25 types of purchase behaviors, along with corresponding consumer value orientations manifested in each episode. To improve consumer value measurement accuracy, we further present B2V-Verifier, a behavior-to-value measurement model based on Value Verification Tuning, which learns to assess whether behaviors provide sufficient evidence for each value inference. Experiments show that B2V-Verifier outperforms strong LLM baselines, improving multi-label classification by 34%. The dataset and code will be publicly released upon acceptance.

Open-source language models have a reproducibility problem. Despite releasing weights, training data, and recipes, none of them are provably reproducible due to the non-associativity of floating-point arithmetic. Deep learning frameworks often offer a deterministic execution mode, allowing reproducible operations on the same machines. Unfortunately, this determinism does not carry across hardware such that a user can verify that a released checkpoint was actually produced using the declared training recipe. This leaves room for undisclosed data, injected biases, or backdoors that existing techniques such as proof-of-learning or proof-of-training-data cannot rule out. We introduce a new tier of model transparency, fully auditable, in which every operation on every data sample during training is independently reproducible on heterogeneous commodity hardware with bitwise certainty. By imposing a definite order on the sources of training nondeterminism, GPU kernel reductions, data batch ordering across a data-parallel cluster, and inter/intra-node collective communication, we make it possible to replay any individual step of a large, distributed training run on a single piece of commodity hardware and check it against the published trajectory. Because replaying an entire run on one machine is infeasible, we support this with a collective verification scheme in which many independent auditors each certify individual steps, together covering the whole run. We release Open-1B, a model trained under this regime, together with its full pretraining dataset, every intermediate checkpoint, the training codebase, and the audit harness needed to reproduce and verify any step of its training.

Natural language arguments are compelling before they are formally explicit. A premise supports a claim through defeasible warrants, background commitments, and exception conditions that the text leaves implicit. However, formal verification requires the opposite. Making such arguments machine-checkable requires constructing the missing commitments, not only translating given sentences into logic. Construction, however, carries a risk that translation does not: a system free to add premises can make any claim provable, and a formally valid proof may assert the claim outright, prove it without the original premise, or establish more than the claim itself. We address this problem by formulating autoformalization for argumentative material inference as guard completion, in which non-monotonic material support is turned into monotonic formal inference relative to an explicitly constructed guard set. A completion is accepted only when its proof both passes the theorem prover and survives contrastive tests of premise dependence and claim selectivity. We implement this formulation in GUARD, a neuro-symbolic framework in which LLMs construct and formalize candidate guards, Isabelle/HOL verifies the resulting theories and returns step-level feedback for iterative refinement, and the system abstains when no faithful completion can be reached. Our empirical results on Debatepedia and ARCT using different LLMs demonstrate that GUARD yields significant improvements in verified-faithful (+35.3, +32.9 points) and substantial reductions in leakage (-25.9, -21.9 points) over the state-of-the-art LLM-driven theorem proving approach. Moreover, we show that the symbolic soft critique and the explicit assumption layer account for most of these gains, with the soft critique also improving the initial validity of the elicited context and reducing the number of iterations required for successful verification.

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

When a direct proof of a statement $S$ seems hard or even impossible to obtain, there may exist another statement (or set of statements) $S^{*}$, somehow related to $S$, on the basis of which $S$ can be proved. In order to investigate what options can be used to move from $S$ to $S^{*}$, four kinds of semiotic relations inspired by the four master tropes of semiotic research are briefly reviewed. Specifically, our syntagmatic, paradigmatic, antithetic and meronymic relations correspond, respectively, to metonymy, metaphor, irony and synecdoche. It is suggested that these four semiotic relations determine the options to move from $S$ to $S^{*}$, leading to proof by inference, proof by analogy, proof by contradiction, and proof by case analysis. To examine how the four relations are actually used across different kinds of argument, we complement the framework with an empirical study. We turn the four relations into explicit operational definitions and apply them to a cross-genre corpus of mathematical, legal, and everyday argument using a panel of large language models. We find that the relations are used very unevenly across genres: mathematical proofs draw on all four, whereas legal and everyday reasoning rely almost entirely on inference.

First-stage recommenders in multi-stage systems produce a ranked candidate list from which a limited prefix is forwarded to downstream rankers. Because each forwarded item must be processed by more expensive ranking stages, this shortlist cannot be arbitrarily large. The first-stage objective is therefore high coverage of relevant items within the forwarded prefix, commonly measured by Recall@$k$. A relevant item may be available deeper in the retrieved list but absent from the shorter prefix that is actually consumed. This paper studies post-hoc verification for promoting such candidates into the consumed shortlist without retraining or replacing the retriever. We introduce a lightweight generative verifier for retrieval models. Given a retriever state and a candidate item, the verifier scores the item through the likelihood of its identifier tokens. It is trained post hoc with next-token cross entropy, requires no sampled negatives or candidate pool during training, and scores only the retriever's top-$K$ candidates at inference. The interface is minimal: the retriever supplies a query state and candidate items, and the item representation can use any fixed tokenization. Across Amazon product recommendation and YaMBDa music recommendation, the same verifier training recipe improves Recall@10 for SASRec, GRU4Rec, NextItNet, and MiniOneRec. Ablations show that the improvements are not explained solely by injecting item-content features into the retriever, supporting verification as a post-hoc output-side adaptation mechanism.

Vision-language and language models increasingly interpret materials data, yet benchmarks report that they hallucinate invalid properties and violate physical law. Evaluation matches final answers to scarce human labels, while discovery agents verify final proposals or density functional theory (DFT) execution. Neither measures the physical consistency of a model's reasoning chain. Materials data carries its own physics, making a large class of materials reasoning verifiable without annotation. We introduce MatPCR, a label-free benchmark whose programmatic oracles check diffraction geometry through Bragg's law, scale bars, spectral peaks, and Materials Project-grounded checks of near-hull stability, computed band-gap class, and net magnetization. We define the Physical-Consistency Rate over image and structure inputs; introduce Constraint-Grounded Self-Verification, an agentic loop whose gain survives self-refinement and equal-compute re-prompting controls; release an open verifier useful in distribution but near chance on all six held-out constraint types; and derive an exact identity for how oracle error displaces the reported rate.

An LLM agent acts on the world by emitting actions: shell commands to run, edits to apply. A wrong action does not always fail loudly; it can fail silently, producing a plausible but incorrect effect that raises no error. We argue that a cheap deterministic check, run before an action takes effect, is an effective and underused form of agent oversight, and we study it across two action modalities in one framework. The idea is to fix an action's correct effect by construction, before any executor runs, so that silent failure is measured directly and the verifier may abstain rather than guess. For shell commands, a static verifier over 9930 commands and 482 tools catches 95.8% of invalid commands at a 10.0% false-positive rate. Its syntax and binary checks are oracle-exact, giving zero false positives while catching half of all errors; the flag check is bounded only by help-text coverage and accounts for every false positive. For code edits, a benchmark of 640 edits over 224 files isolating the apply step exposes a sharp split. Content-anchored formats such as search/replace and diff fail cleanly, whereas location-anchored formats fail silently: line numbers corrupt 99.1% of files under a one-line shift, and function-name edits hit the wrong function 12.7% of the time. In both settings a refuse-when-unsure policy turns silent failures into recoverable ones at a tunable cost in applicability: selective grounding reaches 0.958 recall at 7.0% false positives, and an anchor-and-verify applier records one silent misapplication in 8320 trials (0.01%). We release both benchmarks, the verifiers, and the guards.

Post-training with reinforcement learning (RL) is a critical phase in the development of code-generating large language models (LLMs), as it ensures adherence to instructions and the production of functionally correct code. This process typically requires computationally intensive code sample generation from Transformer-based LLMs and substantial GPU-CPU communication for sequence verification. To address these computational challenges, this work examines whether RL-based post-training can be performed entirely offline by leveraging existing datasets rather than generating new samples. The findings indicate that, with only a few hours of training, zero-shot code generation performance of LLMs can be substantially improved without online sampling. Additionally, offline RL produces performance gains across models ranging from 0.5B to 7B parameters, although the extent of improvement varies among model families.

Software development follows an implementation-verification loop in which developers or agents iteratively revise an implementation until an evaluator, such as a test suite, accepts it. The evaluator checks the implementation against a set of requirements under a model of the deployment environment. Yet even a formal proof that the implementation satisfies the requirements under the model cannot guarantee acceptable behavior after deployment. Requirements only approximate stakeholder intent, and the model only approximates the real deployment environment. We call these together - requirement gap and model gap - the two-gap framework, which unifies the main failure modes of agentic software engineer-ing: reward hacking exploits omissions in the requirements or model, while hallucination widens the gaps by fabricating requirements or environment assumptions. Because neither gap can generally be certified closed in an open, changing world, the goal shifts from closing them to continuously narrowing them. We therefore propose an assurance-revision loop that uses deployment evidence to revise the requirements, model, or evaluator when stakeholders reject the resulting behavior. We then cast assured agentic development as a resource-allocation problem over human judgment, agent capability, and compute. The two principal bottlenecks mirror the two gaps: human judgment for the requirement gap and faithful, costly evaluation for the model gap. Reality remains the final verifier: acceptable behavior under actual deployment conditions is the ultimate test, while predeployment evaluations remain proxies for it.

We prove a full Adam theorem for spectral heavy-tail onset in a closed Gaussian Stein-Hermite teacher-student state-evolution model. The theorem begins with the actual full-batch Adam recurrences, derives the population gradient by Stein-Hermite calculus, proves finite-width covariance concentration, converts multi-step Adam momentum into an exact non-centered Gaussian sign kernel, controls the diagonal Adam denominator by a basis-homogenization theorem, derives a regularly varying projected update response from a Hermite edge-transfer theorem, pushes the response through the exact Gram update, and proves approximate-target KL contraction with matching upper and lower hitting bounds. The final law is (\tau_\varepsilon=\Theta(\Delta_1^{-\gamma}d^\rho\log(\Psi_0/\varepsilon))), where (\Delta_1) is the first spike-bulk spectral gap. The result is full in the following precise sense: every step from Adam's momentum and denominator to the spectral hitting law is formalized inside the closed state-evolution model. We also prove that a stronger arbitrary-gradient Adam theorem is impossible, and that exact two-step linear-network loss dynamics do not identify factor spectra or heavy-tail hitting times.

We consider the problems of formal verification and synthesis in parametric Markov decision processes (MDPs) with general measurable state and action spaces. The heart of our approach is a parameter flattening transformation, which allows us to transform parametric MDPs into semantically equivalent non-parametric MDPs. Building on this transformation, we introduce the novel notion of parametric supermartingale certificates, which generalize the traditional supermartingale certificates---used for non-parametric MDPs---to the parametric setting. We use our parametric supermartingale certificates to design algorithms for verification and approximate synthesis in polynomial arithmetic parametric MDPs. This leads to the first verification and synthesis algorithms for parametric MDPs with general state and action spaces. We implement our algorithms and experimentally evaluate them on several continuous parametric random walk benchmarks.

A compact controller can coordinate stronger experts by selecting whom to consult, formulating requests, and integrating their responses. We study whether learning from both the controller's decisions and the experts' reasoning and code improves its generation after expert removal. We introduce \textsc{Rivet} for \emph{collaboration internalization}: expert-augmented reinforcement learning applies a shared outcome signal to controller decisions and returned expert spans, and verified trajectory internalization consolidates complete successful interactions through format-aware supervised training. The deployed controller generates reasoning, code, and interaction structure with local Python execution and no external LLM. Across seven competition-mathematics benchmarks, RIVET-1.7B and RIVET-4B achieve average accuracies of $28.25\%$ and $44.16\%$; Stage~II improves RIVET-4B's accuracy after expert removal by $6.49$ points, and GPQA-Diamond results provide evidence of generalization to scientific reasoning. Ablations show gains from ordinary trajectory supervision and additional format weighting, supporting the effectiveness of training on the content and structure of verified collaborations.

The integration of Large Language Models (LLMs) into automated code optimization introduces a critical reliability risk we term the Efficiency Hallucination: an LLM's tendency to issue non-functional mutations with unsubstantiated performance claims on already-optimized code. This is driven by the Evaluation Trap, wherein binary benchmarks incentivize unnecessary modifications over safely abstaining. We present a validation framework using classification penalty methods, evaluated across 180 optimization runs on nine models (GPT, Claude, Gemini) using EffiBench. Under standard prompts, models exhibit a 100% over-edit rate on optimal code. Our guardrail raises correct abstention from 0% to to 44.4%, preserving a 100% edit rate on sub-optimal code with zero false abstentions. Calibration is uneven: GPT-5.4 Mini approaches near-perfect abstention, and simple code is recognized more reliably than complex code. Our framework offers a training-free mechanism to mitigate LLM overconfidence before deployment in production.

We present a machine-checked Lean~4 formalization of Dong and Yang's classification of optimal finite-length $(n,4)$ binary block codes for binary symmetric channels. The formalization was developed mainly by feeding the paper's proofs to an AI tool. To establish correctness, the authors verified the main theorem statements in Lean and the accepted axioms. This note discusses the corrections and simplifications made to the AI-generated formalization, and records discrepancies found in the paper during the formalization. The Lean code is available at https://github.com/shhyang/n4code_lean.

Most of mathematical knowledge has been communicated through so-called informal use of mathematics and natural language. With large language models (LLMs) being highly adept in using natural language, they achieve strong performance, yet not perfect, in informal mathematical reasoning. Restraining LLMs to informal reasoning misses out on the opportunity to use the discrete verification abilities that machines offer through machine-checkable proofs. In this paper, we bridge the gap between informal and formal reasoning by integrating Lean signals into the informal reasoning process. We introduce Magenta, a training-free agentic pipeline that, given only a natural-language problem, produces an answer, expresses it as a Lean 4 statement, and constructs a machine-checked proof. A statement judge verifies whether the formalisation preserves the original problem, while an error-attribution judge routes failed attempts either to mathematical re-derivation or local Lean repair. Magenta achieves 100% accuracy across all evaluated olympiad benchmarks, including AIME 2025, AIME 2026, and HMMT February 2026. When paired with the open-weight K2-Horizon-7B reasoner, it solves all six IMO 2026 problems. Our analysis shows that statement adjudication is essential for preventing false certificates and that feedback-guided correction outperforms independent resampling on difficult problems.

We study how model post-training and test-time inference design affect natural-language proof generation for hard olympiad mathematics. Starting from Nemotron 3 Ultra, we train two specialist checkpoints using supervised fine-tuning and reinforcement learning, and evaluate checkpoint choice, verification, and refinement. Based on these findings, we present an open-model test-time-compute pipeline. The system operates entirely in natural language, with no formal prover, external tools, or internet access. Three Nemotron 3 Ultra checkpoints - the general-availability model and two post-trained specialists - power an iterative search that generates, verifies, and refines candidate proofs; a separate high-compute stage then selects each final submission. The system scored 30 out of 42 points at IMO 2026, reaching the gold-medal threshold. We release the two post-trained checkpoints as well as the training data, the training and inference code, the submitted solutions, and Nemotron-IMO-Bench, a new benchmark of 200 novel olympiad-level problems.

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.

AI-based automated vehicle testing is challenging because a model that passes every test condition can still fail in the real world. Formal verification offers a way to directly address this gap. On a simulated highway and an arterial road we trained two small end-to-end steering networks each in CARLA, one on clear conditions alone and one on clear, fog, night and low sun. All four models were driven against a 2.19 ft lane-departure budget. Without driving again, we used bound propagation, a formal method that reads the trained weights, to compute how far steering can drift at every disturbance strength between two captured images. One calculation covers more than a campaign could drive: on the arterial it spans 133 poses, where ten intensities each would be 10^133 combinations, in minutes on one GPU. Not only did formal verification find conditions that broke the clear-trained policy without simulation testing, it provided some preliminary evidence for potential failures between the test cases. Our overall conclusion is that formal verification is a viable complement to simulation, and could be adopted as a part of verification and validation for automated driving.

The development of generative artificial intelligence resources enables opportunities of speeding up systems and engineering design work. This contribution introduces a framework of formal operations for assembling context in LLM-based engineering design. This framework involves the assembly of modular context units, including policy prompts, reference units with persistence, and user questions with prompt vectoring. This approach enables the systematic structuring of interactions with generative models. A formal method for evaluating modelling-as-code LLM outputs is also presented, which enables the evaluation of compliance to intent from LLM answers and thereby asses the support from LLMs for systems architecture modelling.

Frontier gains in language-model reasoning come from reinforcement learning on reasoning traces and are concentrated in domains with a cheap, sound verifier. We argue the field's binding constraint is the verification gap: no scalable, incorruptible reward for reasoning outside formal domains. We make four contributions. (1) Theory: in a joint-Gaussian model of best-of-N selection, verifier-gold correlation rho is the exact exchange rate between test-time compute and capability, and an unsound verifier pays a polynomial penalty N^(1/rho^2); a margin-free copula form predicts realized soundness of real LLM judges to 4% median error. (2) Demonstration: in program-synthesis testbeds with executable ground truth, including a pre-registered scaled replication, unsound verifiers lose Soundness-under-Pressure as optimization grows (0.94 to 0.32 at N=4096) while a sound verifier improves monotonically; reality-anchored settlement beats a frozen verifier under i.i.d. and adversarial pressure, driving the hacking gap from ~0.27 to ~0; soundness scales log-linearly with settled labels, with on-policy settlement ~10x more label-efficient than random labeling. With real LLM judges and unit-test execution as gold, a weak judge loses soundness under best-of-N (p<0.001), a stronger judge is more robust, and selection alone manufactures +0.53 hacking gaps from honest samples. Under real GRPO training, a frozen reward model traces the full overoptimization curve (executed reward collapses 90%) while the same model refit on a 10% settlement stream preserves 6x the executed reward. (3) Paradigm: proof-carrying cognition, where reasoning steps are typed probabilistic claims priced by a self-built world model trained only on held-out reality and settled by proper scoring rules. (4) Benchmark: we specify Soundness-under-Pressure as the headline metric for a reality-settled reasoning benchmark.

Leading benchmarks for formal theorem proving with large language models are small collections drawn from competition math, such as the IMO and Putnam, that poorly represent field-specific applications. We introduce StochBench, a Lean 4 benchmark of 450 graduate stochastic-processes problems at varying abstraction levels, each paired with its natural-language source. Addressing a field underrepresented in Mathlib, it covers finite and countable Markov chains, renewal processes, random walks, martingales, stopping times, queues, Brownian motion, stochastic calculus, weak convergence, and Poisson and continuous-time Markov processes. Our Opus 4.8-based agent achieves a 34.9% proof rate (157/450) under a 15-minute per-problem limit. StochBench better represents domain-specific applied mathematics while remaining challenging for advanced provers.

Hallucination detection is crucial for large language models (LLMs), as hallucinated content creates significant barriers in applications requiring factual accuracy. Current detection methods mainly depend on internal signals like uncertainty and self-consistency checks, using the model's pre-trained knowledge to identify unreliable outputs. However, pre-trained knowledge may become outdated and has coverage limitations, especially for specialized or recent information. To address these limitations, retrieval-augmented generation (RAG) has emerged as a promising solution by retrieving relevant evidence at inference time, grounding outputs beyond the model's parametric knowledge. In this paper, we target a critical and practical learning problem RAG-based hallucination detection (RHD), where RAG is employed to enhance hallucination detection by addressing information updating challenges. To address RHD, we propose a novel method Evidence-Aligned Entity Verification (EAEV), which detects entity-level hallucinations by leveraging RAG to align generated entities with retrieved evidence contexts. Specifically, EAEV evaluates entity-evidence alignment through three complementary dimensions and introduces counterfactual stability analysis to ensure robust alignments under evidence perturbations. Experiments across multiple RAG benchmarks demonstrate that EAEV achieves consistent improvements over existing methods with strong generalization capabilities.

Reasoning agents increasingly rely on external tools such as web search to answer complex queries. Reinforcement learning (RL) finetuning algorithms such as GRPO have improved long-form reasoning in text-only language models, particularly for coding and mathematics. Reliable tool use in multimodal agents, however, remains challenging because models must interpret text and images while integrating noisy retrieved evidence, often under sparse outcome-level supervision without explicit verification signals. We present Self-Verification via Reinforcement Learning (SVRL), an RL-only finetuning framework that trains multimodal agents to verify and filter retrieved evidence within their own reasoning traces, reducing reliance on external verifiers at inference time. SVRL also introduces a search-aware penalty that discourages unnecessary tool calls and a query-diversity reward that encourages diverse, well-formed search queries, providing fine-grained feedback on when and what to search. Finetuning Qwen-2.5-VL-7B with SVRL on only 5{,}000 visual question answering examples yields consistent gains in multi-hop VQA generalization and tool efficiency across benchmarks. Overall, SVRL narrows the gap between compact agents and much larger proprietary models while requiring substantially lower training and inference cost.

Multi-agent federations need governance that answers three questions under adversarial conditions: who participated (identity), did they conform (enforcement), and who decides (authority). A separate question is whether the verification machinery that polices a federation's outputs can also steer a generate-and-test loop toward better answers. Part I. PRIMA introduced prime-power agent identity and a consensus token whose factorization indexes participation, but assumed honest agents. We present PRIMUS, which couples prime-power identity with BLS aggregate signatures (PIAC), derives a safe-kill threshold that reduces false-positive agent termination from 80% to 0.00% under 10% channel noise, gives the closed-form economic boundary where singleton governance outperforms Byzantine quorum ($γ^* \approx 9f$, verified flat across n = 50 to 10,000), and specifies VRF succession with lease and fencing that makes safety unconditional under partial synchrony. Five problems are identified as provably unfixable within the model and stated as scope boundaries. Part II. A verifier is not a solver. We ask whether PRIMA's binary artifact-fidelity verdict can be converted into a graded fitness signal, and measure the conversion on binary covering codes. Calibration against injected fault burden is strong ($ρ$ = 0.676 deterministic, 0.819 full); against real LLM-generated candidates the same scores fall to 0.158 and 0.406, roughly a quarter of the calibration value (the same-designer confound, measured). As a pre-filter it beats a random-score control convincingly and a binary gate narrowly. Under 400 iterations of explicit optimization it was not gamed, but only because the objective saturated after one honest answer. A cross-family judge preserves the burden-ordering signal while destroying individual judgments. No covering-code record resulted. Measured program cost: USD 164.78.

For every coherent and sufficiently expressive finite syntactic system S, we prove the existence of at least one theorem that S cannot produce autonomously. The result is a metatheorem: it proves the existence of a theorem, and applies to every finite syntactic system - security mechanisms, AI systems, formal verifiers, legal systems, economic models, and the formal system in which it is itself proved.

We report on our ongoing project to develop a computational pipeline, AutoGraphForge, for an automated graph-theoretic conjecturing-refuting-formalizing-proving system. Conjecture generation is counterexample-guided and runs in rounds: a Graffiti3 generator proposes conjectures over a small, evolving snapshot table $T$ (initially a few hundred graphs with their computed invariants) that grows only by counterexamples to its own conjectures. A novelty filter of $559$ classical and folklore relations, closed under transitive composition and linear identity substitution, decides via a linear program whether a candidate is already implied by known results. Surviving candidates are tested against a dataset of about $348,000$ graphs, unioning the complete House of Graphs invariant export, the exhaustive census of all connected graphs on at most nine vertices, several extremal families (strongly regular, minimal Ramsey, Cayley, cages, barbells, lollipops, spiders), and random models. Counterexample-search algorithms then attack the remainder. Run for several rounds on an HPC cluster, the loop yields $6,522$ conjectures that survived the refutation dataset, the novelty filter and every active-search run -- among them nontrivial relations between the annihilation number and the edge-cover number for bipartite and regular graphs, which we prove by hand. A subsequent formalization and proving stage deterministically translates each surviving conjecture into a Lean 4 statement skeleton; every candidate proof is kernel-verified against a pinned mathlib4 and our custom invariant preamble. This stage integrates two neural provers -- DeepSeek-Prover-V2-671B (served with vLLM) and the Lean-specialised OProver-32B -- behind the independent kernel check. It is implemented end-to-end and passes initial sanity checks, with the full pipeline currently running on the cluster.

An agent that inherits six one-line memories may pull at most one archived source record before acting; a directive written into the store can steer that choice: a pointer to the record, a criterion that identifies it, or both. Across twelve registered studies on one instrument lineage (14,760 attempts) we measured where the request goes under each form. On six direct-provider models a length-matched criterion exceeded a bare id by +35.0 points [+31.2, +38.8] (Study D); the contrast failed its registered superiority rule on a nine-model OpenRouter-served panel (Study E). Appending the id cancelled the criterion on three Claude models (Opus 5: 40/40 to 0/40; Study F-x); six byte-matched edits gave each exact string its own effect (Study G), and a re-run at eighty runs per cell left fifteen of thirty replication contrasts within the margin, fifteen unresolved and none beyond (Study G'). A ratification line (+96.0 points on Opus 5) and a budget of two credits restored the target on all three (Study J); across five criterion strings the suffix's cancellation held for four of the five wordings on Opus 5 and all five wordings on Fable 5.1 (Study H2); in a second store every model followed the criterion (Study H1). Continued into a decision, the criterion moved the choice toward the current record (+100.0 points, Opus 5) and away from it on Fable 5.1 (Study I). A one-character plan pointer's effect (+78.0 points; Study B, after a correction of its first repository report) returned the same verdict under a prospectively registered re-run (+81.7 points; Study B'). All results are descriptive effects of exact edits on fixed panels with registered intervals and no mechanism claim.

A reasoning model can improve from its own on-policy experience, but this inner loop is fragile: terminal verifiers provide reliable yet sparse supervision, while dense same-model guidance can reinforce false confidence or overconcentrate learning on a narrow solution mode. We introduce FlowBalance, a verifier-grounded self-improvement method that learns a normalized distribution over complete responses. For each on-policy trajectory, a frozen training-time view of the same policy uses privileged context to produce token-level log-probability gains, which are aggregated into a trajectory-level self-guidance score. FlowBalance calibrates this score with the verifier-derived group advantage: guidance is retained on positive-advantage trajectories, reversed on negative-advantage trajectories, and disabled when the rollout group provides no outcome preference. The resulting energy exponentially reweights a reference policy, and profiled trajectory balance fits the normalized target with one log-partition estimate per rollout group. This realizes outcome-calibrated self-guidance via trajectory balance, without a separate token-level imitation loss. Our analysis establishes within-group contrast preservation, a minimum-change reverse-KL characterization, monotonic verifier control of target reward, and an exact correction against false-positive self-guidance on rejected responses. On mathematical reasoning, FlowBalance improves average performance over FlowRL on both Qwen3-4B and Qwen3-8B, while also improving training speed and stability, avoiding direct OPSD's response-length collapse, and exhibiting higher correct-strategy diversity in a controlled AIME24 diagnostic.

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

Scientific benchmarks are commonly built by domain experts who write tasks and cross-check one another's work, or who adapt existing material from textbooks, published papers, and online resources. These routes can produce strong evaluations, but they require substantial per-item labor. Language models can reduce this repeated work by proposing candidates quickly. The remaining problem is acceptance. We target scientific questions whose answers require computations with specialist software rather than unaided reasoning alone. A candidate is invalid if its script fails or returns a different answer, or trivial if a model answers it without the software. We present ToolGate, which treats every generated item as a proposal and keeps it only if three gates pass. First, an executable solution script must reproduce the proposed answer when run with the scientific software. Second, randomized no-tool screening rejects candidates that models can already solve from the prompt alone. Third, a tool-using agent must solve each survivor within a fixed time limit. We instantiate ToolGate in FEniCSx with 500 generation attempts. The local-verification gate retains 478 candidates. For final reporting, we rescreen this pool after generation: two randomized no-tool screens exclude 222 from the reported pool, and direct GPT-5.5 API calls at medium reasoning (the API default) exclude another 121. Of the remaining 135, a GPT-5.5 Codex CLI agent with access to FEniCSx solves 130; exact deduplication leaves 128 unique protocol survivors. ToolGate turns repeated answer checking and difficulty screening into an auditable process while leaving domain design and final review to experts.

Despite recent advances in large vision-language models (LVLMs), object hallucination remains a major barrier to their reliable deployment. Existing detection methods often characterize visual grounding using attention from individual layers, leaving its evolution across layers underexplored. We propose CADMP, a lightweight object hallucination detection framework that combines adjacent-layer cross-modal attention drift with prediction sensitivity to targeted visual masking. During decoding, CADMP quantifies distributional changes between consecutive cross-modal attention maps to capture abrupt transitions in visual grounding. It then selects the transition with the largest drift, locates the corresponding visually relevant regions, and measures the change in prediction probability after masking these regions. These two signals provide complementary evidence: attention drift characterizes the stability of internal visual grounding, while probability variation verifies whether a prediction truly depends on the identified visual evidence. A lightweight detector integrates both signals to identify hallucinated predictions. Experiments on multiple benchmarks and representative open-source LVLMs demonstrate that CADMP achieves consistently competitive detection performance. Ablation studies further confirm the complementary contributions of adjacent-layer drift modeling and mask-based grounding verification.

Agent evaluations face two distinct evidentiary questions: whether a reported claim is recomputable from retained evidence (sufficiency), and whether the retained records cover the committed experiment set (coverage). Generic logs and hash-linked transcripts answer neither reliably. We introduce ClaimReceipt, a claim-relative receipt specification and selective verifier that binds typed transaction evidence to a signed experiment manifest and returns PASS, INVALID, or INCONCLUSIVE per claim. We freeze the specification before implementation (SHA-256 18d109...b81). On 1,392 historical buyer--seller records, a CR-2 verifier reproduces all five manually labeled audit verdicts, exactly replays 600 deterministic and 792 post-generation records, makes every one of 13 declared field groups non-redundant under tested ablations, and returns the expected result on 11/11 semantic faults with 0/8 false positives. We then run a separate prospective CR-3 epoch: 30 assignments are committed before inference, terminal receipts are signed and chained, and private evidence is encrypted for an auditor. Complete evidence yields coverage and accounting PASS; withholding one terminal receipt returns INCONCLUSIVE_COVERAGE, while withholding all private openings preserves coverage and protocol verification but makes economic claims inconclusive, exactly matching a preregistered prediction. Receipt instrumentation adds 0.021% of model-inference time and 9.9 KB per transaction. A specification-legibility probe indicates that our own frozen specification is not yet unambiguous to an independent reader. Claim verification therefore requires both claim-sufficient evidence and a committed universe against which omissions become visible.

Multi-agent systems have shown strong performance in domains with reliable verifiers such as coding, where multi-parallel candidate generation selected by a verifier is effective. However, such pipelines would not generalize to open-ended, long-horizon research tasks without a verifier. While majority voting or self-consistency is often used to reach consensus as a proxy verifier, parallel agents repeatedly explore the same evidence, while access to peers' partial findings cause search to converge on an early candidate before alternatives are tested. We present ArcticSwarm, a multi-agent research architecture that separates evidence gathering from evidence integration. Subagents publish findings to a shared bulletin board, while gated isolation lets selected search tasks maintain their own prior, preventing early consensus. Structured review at three commitment boundaries enforce only confident candidates to be propagated. As a result, ArcticSwarm reaches 82.6% on the full BrowseComp-Plus set with the open-weight Qwen 3.5-27B model, compared with 78.8% without gated isolation and 74.5% additionally with structured review disabled, outperforming aligned baseline MiroFlow runs (70.6%). Extending to live-web BrowseComp, ArcticSwarm reaches 73.6% with GPT-5, which is well above the reported provider system (54.9%) and MiroFlow (63.4%). Overall, the results show that restricting peer reads during evidence gathering and strengthening commitment boundaries before a hypothesis is shared can broaden search and improve long-horizon multi-agent deep research.

Reinforcement learning with verifiable rewards (RLVR) and standard benchmark evaluation both rely on an automatic verifier that turns a free text answer into a binary reward. Prior work reports that one evaluation harness accepts only about 94% of its own ground truth answers, blaming LaTeX parsing. That is an aggregate: it does not say which answer forms consume the error budget. We supply the decomposition. We apply metamorphic testing to the verifier rather than the model, generating certified equivalent answer variants, that is, rewrites that preserve mathematical meaning by construction, so that any rejection is a provable false negative needing no human adjudication. We then measure rejection per answer category across four widely used verifiers over 307,420 verdicts. We find three things. (1) Self validation ranges from 53.8% to 95.2% on identical inputs, a spread of 41.3 points. The published figure describes one implementation, not the task; two configurations of the same library disagree on 49.9% of pairs. (2) The residual is not spread across parsing categories but concentrated in whitespace and punctuation, which account for 93.0% of in contract failures for the default LaTeX configuration. A trailing period or newline dominates the budget. (3) Separating rejection from execution failure shows that verifiers with similar aggregate error fail for opposite reasons, and that a reference numeric cascade accepts off by one wrong answers as a step function of magnitude, from 0% below 10^4 to 100% at or above, because its relative tolerance is scale invariant.

Inference cascades cut cost by answering most queries with a cheap model and escalating a hard tail to a frontier model that acts as verifier. A natural extension closes the loop: fine-tune the cheap student on the verifier's rejections so the escalation rate, and cost, fall each round. We measure this loop on real LLMs and report four findings. First, the verifier's blind spot, the fraction of the student's wrong answers it accepts, is large and moves adversarially: it grows with student capability ($β$ from 0.12 to 0.55 as the student scales 0.5B to 32B) and shrinks with verifier capability, so it is worst in the cheap-student, cheap-verifier regime cascades exist to create. Second, buying it away returns the saving: a frontier verifier drives $β$ to about 0.05 but then escalates on 46% of hard-MATH queries against a 39% true error rate, paying the frontier price on nearly half of all traffic. Third, naive corrective fine-tuning on the verifier-rejected tail does not improve the small student but degrades and ultimately collapses it, across every teacher we tried (cross-family and same-family), so at this scale the self-improving loop is self-defeating. Fourth, through all of this the cascade's own dashboard, every metric computed through the verifier, reads a flat 3% error while true delivered error swings up to 32%: the system is blind to its own degradation by construction. We then give the theory that explains the blindness, a two-population conservation law, $ε_\infty \lesssim q_0 β_0$, under which every in-loop metric improves while true quality does not, and a synthetic study that validates the mechanism. The practical conclusion: the reliability of a self-improving cascade cannot be read from any metric computed through its own verifier.

MutMem V1 introduced retention-preserving, cryptographically authorized mutation for persistent agent memory but did not provide a complete portable verification contract or clean-install reproduction path. MutMem V2 closes that publication gap without introducing a second memory engine. It specifies exact canonical bytes, domain-separated object and bundle commitments, mandatory recall-evidence membership and ordering, external trust anchors, identity epochs, revocation, authorization, request receipts, ordered disclosure, and three mutation terminal types. The released protocol contains 18 versioned object schemas, 39 recall vectors, 15 mutation vectors, and 37 closed recall failure reasons. Independent Node and Python implementations agree on verdict and primary reason for all 72 structural and cryptographic terminals; a production-conformance corpus agrees on 42/42 cases across 28 required classes. A clean Node v26.8.1 installation reaches first-boot, restart, and scheduler readiness with no experimental memories. A separately scoped 120-unit Canary experiment supports only explicit-marker traversal. Every public table regenerates from a self-hashed aggregate, and an independent verifier reconstructs the statistics and claim boundaries. Historical V1 empirical results remain historical. MutMem V2 supports claims about portable integrity, authorization, traceability, conformance, and reproducibility under stated assumptions; it does not establish semantic truth, universal robustness, or independent replication.

Flagship language models appear saturated on benchmarks like MMLU (Hendrycks et al., 2021), scoring above 90% - yet benchmarks test only what the experimenter thought to ask, the availability bias of fixed question sets. LLMPEDIA makes this bias measurable and browsable. We recursively materialized ~1.3M articles from three model families' parametric memory (GPT-5-mini, DeepSeek-V3.2, Llama-3.3-70B) without retrieval, then audited a stratified sample of atomic claims against Wikipedia and a curated web stack, coloring every claim supported, refuted, or insufficient (Saeed and Razniewski, 2026). On a uniform random sample the true rate is 68.4% - more than 21 pp below MMLU - with 30.5% of claims insufficient: assertions no benchmark probes and the world's largest encyclopedia cannot adjudicate - long-tail knowledge or plausible hallucination, the evidence cannot tell - extending to free text the coverage gap GPTKB established for triples (Hu et al., 2025). The resulting live, open encyclopedia lets visitors inspect this frontier one claim at a time through five one-click views - link-traversal exploration, claim-level factuality, cross-model and political-persona comparison, and a guided topic drill-down - each page, claim, and verdict at a stable URL. LLMPEDIA is live at https://llmpedia.net

The SAIR Mathematics Distillation Challenge on Equational Theories asks a solver to classify whether one magma identity implies another and, for either verdict, to return a certificate accepted by a deterministic Lean judge. We present a single-file solver organized as a cheapest-first cascade. Its false branch combines coefficient tests over structured algebra families, bounded finite-model search, an explicit central-groupoid witness, and several infinite-carrier witnesses. Its true branch is a proof-producing ordered unit superposition procedure with Knuth-Bendix ordering, bidirectional demodulation, indexing, memoised substitution, and anytime size deepening. Search results remain outside the trusted base: successful derivations are replayed as small Lean terms, and countermodels are rechecked by the competition judge. The frozen solver is a 189,504-byte Python file with SHA-256 f2392533c9f4c03b.... In local runs through official judge revision 2848228, it produced accepted certificates for all 1,889 rows of the six public sets with no language-model calls. Separate measurements recorded full agreement on the 800 published Stage 1 evaluation-distribution problems, 100 accepted rows in the canonical Marathon manifest without tokens, and 200 accepted rows in the hosted playground. These are regression and playground measurements, not a leaderboard result and not evidence about a hidden set. All quantitative claims are tied to immutable result ledgers; the paper makes no completeness or comparative-superiority claim.

Social media fact-checking has long been challenged by evidence-level and aggregation-level conflicts, where erroneous evidence mimics authoritative news sources. To capture this challenge and support conflict verification tasks, we present ContraNote, a large-scale real-world dataset curated from X's Community Notes system. It includes 33,686 posts for evaluating evidence-level conflict resolution, and 54,474 instances for evaluating aggregation-level prioritization. Additionally, we propose CoVer, a factual adjudication framework with three-stage pipelines: evidence schema normalization, factual consensus and support verification. This prioritizes evidence over noise to prevent it from compromising the final verdict. Technical evaluations show that CoVer achieves strong performance compared with state-of-the-art baselines across ContraNote (86.0% Acc., 68.0% mac. F1, 64.5 bal. Acc. on Conflict; and 88.5% Acc., 88.5 mac. F1 and 89.2 bal. Acc. on Prioritization), CONFACT-HumC (88.4% Acc.) and CONFACT-ModC (89.4% Acc.).

AI compute verification is one of the first tangible and tractable points for international policy aimed at AI governance. Determining whether frontier labs, or any operator, comply with agreements requires the regulating authority to discern how their compute is used. The elementary building block of AI compute is the GPU, and any activity it executes leaves a physical trace. Here, we show that an external observer can identify the class of the workload running on an NVIDIA H200 from its power draw. Unlike on-chip NVML telemetry, which can be spoofed or replayed, such a physical channel can in principle be observed independently of operator cooperation. We recorded $930$ five-second traces at $\sim 10$ MHz, covering seventeen open LLM families and twenty-five non-AI workloads. Over this corpus we separate training from inference and from non-AI computation with an accuracy of $97\%$ and a macro-averaged F1 score of $0.955$, evaluated on model families unseen during training. AI workload spectral content predominantly lies below $\sim 20$kHz and training is particularly recognizable through the memory-bound optimizer update. The GPU operator is then treated as adversarial and able to reshape the physical computation itself. Four evasion strategies are tested to disguise training as inference, producing an additional 680 adversarial traces. A detector hardened against evasion strategies, with the tested strategy held out, catches training $\geq 99\%$ of the time for three of the four strategies. The fourth, diluted low-rank adaptation (LoRA), is detected $48$--$88\%$ of the time with a hardened classifier, rising to $\geq 98\%$ with an additional rescue rule. While these attacks are not a comprehensive evaluation against adversarial behaviour, they offer initial insights beyond genuine activities and a dataset for developing and testing stronger evasion mechanisms.

The advent of foundation models have enabled a new era in zero-shot classification. Yet, key challenges persist. Despite their impressive generalization power that leverages the immense pre-training knowledge, both foundation models for image and text as well as vision-text hybrids lack the representational power needed for fine-grained, minutiae-based class separation that some real-world tasks require. To address the current gaps in the literature, we propose VeriCam, a pipeline designed to learn highly specialized features that enable classification of unknown classes in unseen data. VeriCam works by leveraging the representation power of image models trained for the verification task, where the model develops an intricate feature space that incorporates fine-grained details. By training a model to discriminate between pairs of images from the same and different classes, a relational graph is constructed, representing the class relationships between data points. We then present two approaches for graph clustering: a naive algorithm and a specific setup for the Leiden graph clustering algorithm. The pipeline is validated on the LPLCv2 dataset, which comprises real-world traffic surveillance images. We show that the dataset carries an inherent capture device bias that is posed as a generalization challenge for downstream License Plate recognition tasks such as OCR. As such, we dynamically identify capture devices with a label-agnostic approach, enabling the construction of a fair and unbiased benchmark. In the cross-device scenario, our pipeline reaches an F1-Score of 93.45 in the verification baseline and a V-Measure score of 80.13 in the clustering step. All code is publicly available at https://github.com/lmlwojcik/VeriCam

Masked diffusion language models predict tokens from a partially observed response canvas, enabling bidirectional conditioning and parallel token refinement. Yet standard masked-diffusion decoders use a rigid inference interface: the number of masked positions allocated to the answer is fixed before generation begins. Choosing this length is difficult. A short canvas can truncate reasoning or code, while a long canvas wastes computation and can perturb denoising. We introduce CARVE (Counterfactual-Aware Reveal with Verified Expansion), a training-free variable-length algorithm for masked diffusion LMs. Starting from a shorter canvas, CARVE can grow the response during decoding by inserting additional [MASK] positions. Rather than keeping every insertion, CARVE tests a candidate expanded canvas and asks a counterfactual question: would the model make similar predictions for the unresolved positions in the original canvas if the extra masked space were present? The inserted masks are kept only when they induce low Jensen-Shannon (JS) divergence on aligned unresolved positions. This makes length growth a verified stability decision rather than a pure confidence heuristic. CARVE applies without retraining to both full-canvas and blockwise diffusion decoders. Across code generation and mathematical reasoning benchmarks, CARVE consistently improves average performance over fixed-length baselines across all evaluated model families. Crucially, CARVE achieves these accuracy gains while reducing inference cost, reaching half the FLOPs of fixed-length decoding in some settings.

Large language models can often generate plausible mathematical reasoning traces, but reliably identifying the correct solution among multiple candidates remains a key challenge. Existing test-time reasoning pipelines typically rely on text-based verifiers that re-read each generated solution, making verification an expensive component of inference. Prior work has shown, however, that LLMs often encode correctness-related signals in their internal representations, including awareness of when their own answers are likely to be wrong. Building on this observation, we introduce HSRM, a lightweight hidden-state reward model that verifies candidate solutions by directly reading the generator's internal representations rather than re-processing its text. HSRM extracts hidden states from a frozen generator at reasoning-step boundaries and uses a small Transformer encoder to rank candidates. It is trained from self-generated trajectories with outcome labels, requiring neither human-written process supervision nor a large pretrained verifier. Across four mathematical reasoning benchmarks, HSRM matches or outperforms a 55M-parameter text-only energy verifier in 15 of 16 generator--dataset settings while using only about 2M parameters, providing an efficient alternative to text-only verification by reusing representations already computed during generation.

Long-paragraph detailed audio captioning, which requires dense and transcript-faithful descriptions of fine-grained audio content, remains unsolved for current audio-visual multimodal language models. We attribute this failure to two structural problems. The first is data poverty, as no public corpus jointly provides long clips, paragraph captions, and verbatim-transcript fidelity. The second is generation-mode failure, evidenced by a 44.8 to 46.4 percentage-point gap between right-audio and shuffled-audio multiple-choice question (MCQ) accuracy. We address both within Self-Check Captioning (SCC), a unified framework that instantiates audio-grounded question answering as the verification primitive at every lifecycle stage. SCC yields three artifacts. Long-paragraph Audio Caption 50k (LACap-50k) is a 50,222-clip audio-visual corpus with 491.5-word captions and a post-hoc automatic speech recognition (ASR) audit. Layer-Curvature Supervised Fine-Tuning (LC-SFT) is the first on-policy supervised fine-tuning method to weight tokens by intermediate-layer evidence, motivated by our identification of Late-Layer Semantic-Entropy Collapse (SEC). SCC-Verifier arbitrates among caption rollouts via audio-grounded self-answering at inference. Across multiple benchmarks, our system attains state-of-the-art among open-source captioners and is competitive with proprietary baselines. We release LACap-50k to fill the resource gap for long-paragraph detailed audio captioning research.

Speculative decoding speeds up generation with an efficient draft model (drafter) that proposes tokens for a target model to verify in one pass, preserving the target's output distribution. High-acceptance block-diffusion drafters such as DFlash and DFlare fill an entire block in one parallel pass. In many cycles, the target accepts the whole block, so the drafter exhausts its trained block horizon before verification fails. We call this unrealized acceptance stranded speed-up. A mean committed length, per prompt or per cycle, hides it, whereas the acceptance histogram exposes it as a spike in the ceiling bin, the fraction of cycles that accept the entire block. We recommend the histogram as a preflight check before spending training compute. Naively widening the block at inference does not recover the speed-up, because once the block outgrows its training size, the drafter's bidirectional attention shifts its distribution even at early positions and erodes front-of-block verification. Instead, we post-train the drafter on a longer block with a short curriculum that emphasizes the newly exposed positions, a method we call DBloom. Expanding the pretrained DFlash and DFlare drafters from block size 16 to 24 across Qwen3-8B and Qwen3-4B targets raises the per-prompt committed length on the high-ceiling benchmarks by a median of +0.8 tokens (up to +1.1). Once continuation fine-tuning precedes expansion, the increase reaches 1.37 tokens. The same expansion also lifts committed length on all seven benchmarks for Gemma-4-12B-IT, a different model family, by a median of +0.41 tokens (Arm A), and the full continuation-then-expand pipeline (Arm B) adds +0.29 to +0.98 tokens over the same B16 drafter. In a prompt-matched comparison against JetSpec, a contemporary tree-based drafter not used in our design, DBloom commits more tokens on every benchmark at tree budgets up to 64 nodes.

Modern agent frameworks compose planners, tool agents, remote services, and shared specialists into runtime delegation graphs, but their revocation APIs still resemble token or subtree invalidation. When one delegation is withdrawn, the runtime must know which agents lose authority while independently authorized agents keep working. We study this authority consistency problem and introduce VERA (Verifiable Edge Revocation for Agents), a verifier-checkable revocation contract and API emitted by agent-runtime adapters as signed evidence. Under disjunctive authority, revoking edge e invalidates exactly T_intent(e,G) = reach(G) \ reach(G \ {e}), the agents whose every authorizing root path used e. Used as a contract, this target exposes two runtime failures: tree cascades over-revoke shared agents, while deployer-scoped cascades under-revoke cross-domain descendants. In a LangGraph framework-replt cells repeated 20 times yield 500compiled-framework traces and 2,000 valid signed delegation decisions; 13/25 cells contain runtime multi-parsharing and 8/25 contain cross-deployer shies 500/500 target proofs, preserves all320 alternate-parent shared-agent cases that tree cascade revokes, and rejects unauthorized signers and omission attacks. Baseline replay over 1,9that holder/node and tree-style targetscannot express this behavior. We further validate schema portability on A2A, AutoGen, and CrewAI artifacts: nine traces, including five executable Cregned delegation events that pass schema and signature checks.

Generating formally verified programs from natural language remains challenging: existing approaches either produce code in a single pass without recourse when verification fails, or rely on open-ended agentic reasoning that is non-deterministic and opaque. We introduce SKILLFORGE, a framework that decomposes formal code synthesis into a library of atomic, reusable skills, each targeting a specific subtask such as specification inference, body synthesis, invariant generation, error diagnosis, or targeted repair, and defined by a prompt template, tool binding, and decidable success criterion. A verification-driven harness orchestrates these skills: it submits candidates to the Dafny verifier, diagnoses failures into structured categories, deterministically routes to the appropriate repair skill, and iterates until formal correctness is proved or a budget is exhausted. On a curated benchmark of natural language to Dafny specification pairs, SKILLFORGE substantially outperforms both state-of-the-art agentic approaches (including ReAct-style agents, MCTS-based repair, and RL-guided verification) and traditional iterative baselines, while requiring fewer tokens and lower latency. Ablation studies confirm that every skill contributes measurably, and the harness converges rapidly with the majority of programs verified on the first attempt.

Proof assistants such as Lean 4 promise the paradigm of formally verified mathematics, but large-scale formalization projects have faced major barriers to entry, including the need for expertise in formal verification (as well as the underlying mathematics) and the significant time required for writing formal proofs. AI coding agents have dramatically reduced these barriers; human users can now use natural language to prompt agents to write complex proofs in Lean. This opens up the intriguing possibility of internet-scale mathematical collaboration involving both humans and AI agents, where correctness is machine-checked. To realize this possibility, we introduce Prove2Me (https://prove2.me), an open collaborative platform for formalizing mathematics. Users launch formalization "missions", to which AI agents contribute formal proofs toward completion. We designed mechanisms and a specialized harness in Prove2Me that enable large-scale collaboration so that agents can build on one another's work and freely reuse existing results. In doing so, Prove2Me aims to turn math formalization into a scalable, crowd-sourced effort open to anyone with an agent.

Developments in high-performance computing (HPC) technology continue to drastically increase quantities of available processing power. In the context of digital evolution, this explosive growth offers opportunities to advance both hypothesis-driven explorations of multi-scale biological phenomena and application-driven evolutionary optimization targeting hard problem domains. A particular opportunity arises from emerging next-generation AI/ML hardware accelerator platforms, such as the 880,000-processor Cerebras Wafer-Scale Engine (WSE). Such hardware, however, constrains on-device data storage and movement --- a challenge compounded by vulnerability to failures arising over numerous device components. Best-effort relaxations that depart from a traditional deterministic computing paradigm can help accommodate such constraints, but complicate reproducibility and risk introducing artifactual biases. We explore these concerns, developing a framework to measure runtime behavior of best-effort code and examining case studies of best-effort computing in digital evolution projects. The first case study applies best-effort CPU-cluster multiprocessing to a multicellularity evolution model, which provides 92% scaling efficiency at 64 processes ($2.1\times$ speedup) and exhibits robust median quality of service, even under hardware anomalies. The second case study examines WSE-based simulations, demonstrating best-effort strategies to track spatiotemporal population history --- through sparse, asynchronous device-to-host sampling that tolerates hardware faults. In sum, across potential forms and scopes of best-effort relaxation, we argue that digital evolution is uniquely positioned to contribute in developing post-deterministic HPC paradigms.

Large language models (LLMs) have shown growing potential for automated theoretical computer science (TCS) research, yet existing benchmarks remain far from realistic research settings. We introduce \ourbenchmark, an expert-validated benchmark for evaluating LLMs on frontier, end-to-end TCS research. \ourbenchmark contains $143$ instances drawn from papers accepted to STOC, FOCS, SODA, and COLT in 2025-2026, preserving paper-specific definitions, assumptions, and proof dependencies, with expert-verified Lean formalizations and proofs. Evaluations of leading LLMs reveal that current models remain far from reliably completing the full research pipeline. In particular, autoformalization is the sharpest bottleneck: the best model achieves only $11.5$ on translating natural-language claims into formal theorem statements, compared with $28.6$ Pass@8 when proving human-provided formal statements. Building on \ourbenchmark, we further develop an automated TCS research framework that generates, formalizes, filters, and proves new claims. Of $64$ generated claims, only $6$ ultimately pass expert evaluation and proof verification, indicating that beyond formalization, limited research taste remains another major barrier to autonomous TCS research.

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.

We address the use of large language models (LLMs) to help discover Isabelle proofs. An Isabelle build establishes that the submitted theory is accepted, but not that an LLM changed only what the developer authorised. We present CAPRI, a contract-aware repair workflow in which Isabelle checks the proof and an independent checker enforces a machine-readable edit contract. Prompts, proposals, candidate repositories, diagnostics, verdicts, and hashes are retained for audit. We evaluate five workflows on twelve failed proofs from four developments, with three replicates per task and condition, giving 180 runs and 138 valid repairs. Of 144 terminal candidates accepted by Isabelle, six had modified protected text; all arose in iterative workflows that could edit a complete theory. A proof-body-only interface produced 29/36 valid repairs and no contract violations, compared with 31/36 for the corresponding full-theory workflow. One-shot repair produced 22/36, while a later prospectively frozen iterative workflow produced 32/36; these figures compare complete workflows rather than individual mechanisms. A separate post hoc OpenRouter campaign found no improvement in the designated Luna comparisons. A Sol configuration with matched demonstrations produced 33/36 repairs, compared with 29/36 in the frozen OpenAI Responses condition, but the difference was not statistically significant in a one-sided exact McNemar test ($p=0.0625$).

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.