Daily Papers

Decision models support routing, guardrails, and output verification in LLM systems. However, item accuracy alone cannot establish whether models make correct decisions across controlled variations or assign reliable confidence to their predictions. We introduce DecisionPivot, a diagnostic benchmark comprising 48 tasks and 40,033 items across seven decision roles. Its core track contains 7,800 items from 13 generated task families, organized into contrast groups with computed answers verified by independently implemented solvers. The complementary reference track contains 32,233 items from 35 public test sets, preserving their original evaluation metrics. We evaluate 40 decision models and 14 general models using documented, model-specific protocols, assessing item and contrast-group accuracy, probability ordering, calibration, and empirical selective coverage. Our results reveal substantial differences obscured by aggregate scores: two 27B models separated by only 2.6 points on the reference track achieve contrast-group accuracies of 70.1% and 44.2%. Across 2,400 binary contrast pairs, Perplexity Decider correctly ranks the positive member above the negative member in 92.3% of pairs but answers both members correctly in only 74.1%, exposing a gap between probability ordering and decision correctness. Models with similar item accuracy also differ in the reliability of their high-confidence predictions. On a separate 1,296-item subset, GLM-5.3 achieves 93.5\% contrast-group accuracy at a higher reasoning setting, compared with 81.5% at its lowest effort. By linking errors to pivotal details and difficulty levels, DecisionPivot provides fine-grained diagnostics of decision failures that aggregate evaluation alone cannot reveal.

In this paper, we present an innovative process-oriented math process reward model called Math-Shepherd, which assigns a reward score to each step of math problem solutions. The training of Math-Shepherd is achieved using automatically constructed process-wise supervision data, breaking the bottleneck of heavy reliance on manual annotation in existing work. We explore the effectiveness of Math-Shepherd in two scenarios: 1) Verification: Math-Shepherd is utilized for reranking multiple outputs generated by Large Language Models (LLMs); 2) Reinforcement Learning: Math-Shepherd is employed to reinforce LLMs with step-by-step Proximal Policy Optimization (PPO). With Math-Shepherd, a series of open-source LLMs demonstrates exceptional performance. For instance, the step-by-step PPO with Math-Shepherd significantly improves the accuracy of Mistral-7B (77.9\%to84.1\% on GSM8K and 28.6\%to33.0\% on MATH). The accuracy can be further enhanced to 89.1\% and 43.5\% on GSM8K and MATH with the verification of Math-Shepherd, respectively. We believe that automatic process supervision holds significant potential for the future evolution of LLMs.

All 26 neural network merge strategies we tested including weight averaging, SLERP, TIES, DARE, Fisher merging, and evolutionary approaches -- fail the algebraic properties (commutativity, associativity, idempotency) required for conflict-free distributed operation. We prove that this failure is structural: normalisation-based merges cannot simultaneously satisfy all three properties. To resolve this, we present a two-layer architecture -- CRDTMergeState -- that wraps any merge strategy in a CRDT-compliant (Conflict-Free Replicated Data Type) layer. Layer 1 manages contributions via OR-Set CRDT semantics, where the merge operation is set union -- trivially commutative, associative, and idempotent. Layer 2 applies merge strategies as deterministic pure functions over a canonically-ordered contribution set, with randomness seeded from the Merkle root. We prove that this separation guarantees Strong Eventual Consistency: all replicas receiving the same contributions compute identical merged models, regardless of message ordering. Empirical validation spans three tiers: controlled 4x4 tensors (104/104 tests pass), production-scale models up to 7.24B parameters (208 strategy-level tests, 43,368 layer-level property checks at capped tensor resolution), and multi-node convergence under gossip and partition healing (100 nodes, 20 orderings), with CRDT overhead below 0.5 ms. Because the wrapper is transparent, downstream performance is identical by construction, confirmed via byte-identical output verification. The reference implementation is available as crdt-merge v0.9.4.

State-space models (SSMs) maintain a fixed-size recurrent state, but reading and writing it at every decoding step can bottleneck hybrid models. This eager state management causes large state I/O with low arithmetic intensity, leaves speculative decoding no cheap rollback, and feeds state quantization error into subsequent recurrent updates. We introduce ReplaySSM, which unrolls the recurrence to represent the state as a checkpoint and a buffer of recent SSM inputs. This separates output computation from checkpoint updates. By updating the checkpoint periodically, ReplaySSM avoids state writes on most steps and roughly halves the dominant state memory traffic. Keeping recent inputs also makes speculative rollback a buffer-pointer operation and enables output-only verification without materializing intermediate states. The same separation allows a low-precision checkpoint to serve output computation on most steps while a higher-precision checkpoint serves recurrent updates, so rounding error in the low-precision copy never enters later updates. We implement ReplaySSM in vLLM for Mamba-2 and Gated DeltaNet. At serving batch size 256, it accelerates standard decoding by 1.20--1.47times over a tuned vLLM baseline across four hybrid models, and delivers about 1.8times the throughput of vLLM's speculative decoding on the two 120B-class models. Separate state precisions also reduce output KL divergence and downstream accuracy losses compared with a shared low-precision checkpoint.

We present Entropy Adaptive Decoding (EAD), a novel approach for efficient language model inference that dynamically switches between different-sized models based on prediction uncertainty. By monitoring rolling entropy in model logit distributions, our method identifies text regions where a smaller model suffices and switches to a larger model only when prediction uncertainty exceeds a threshold. Unlike speculative decoding approaches that maintain perfect output fidelity through verification, EAD accepts controlled output divergence in exchange for computational efficiency. Our experiments on the MATH benchmark demonstrate remarkable efficiency gains across different model families. Using the LLaMA family, we maintain 96.7\% of the 11B model's performance (50.4\% vs 52.1\%) while using it for only 43\% of tokens, decreasing computational cost by 41.5\%. These gains become more pronounced with larger size differentials in the Qwen family, where we achieve 92.9\% of the 14B model's performance (74.3\% vs 80.0\%) while using it for just 25\% of tokens, decreasing computational cost by 67\%. The consistency of these results across model pairs suggests that language model computation can be significantly optimized by selectively deploying model capacity based on local generation complexity. Our findings indicate that current approaches to model inference may be unnecessarily conservative in their pursuit of perfect output fidelity, and that accepting minor performance trade-offs can enable dramatic reductions in computational costs.

Current document parsing methods compete primarily on model architecture innovation, while systematic engineering of training data remains underexplored. Yet SOTA models of different architectures and parameter scales exhibit highly consistent failure patterns on the same set of hard samples, suggesting that the performance bottleneck stems from shared deficiencies in training data rather than architecture itself. Building on this finding, we present \minerupro, which advances the state of the art solely through data engineering and training strategy optimization while keeping the 1.2B-parameter architecture of \mineru completely fixed. At its core is a Data Engine co-designed around coverage, informativeness, and annotation accuracy: Diversity-and-Difficulty-Aware Sampling expands training data from under 10M to 65.5M samples while correcting distribution shift; Cross-Model Consistency Verification leverages output agreement among heterogeneous models to assess sample difficulty and generate reliable annotations; the Judge-and-Refine pipeline improves annotation quality for hard samples through render-then-verify iterative correction. A three-stage progressive training strategy -- large-scale pre-training, hard sample fine-tuning, and GRPO alignment -- sequentially exploits these data at different quality tiers. On the evaluation front, we fix element-matching biases in OmniDocBench~v1.5 and introduce a Hard subset, establishing the more discriminative OmniDocBench~v1.6 protocol. Without any architectural modification, \minerupro achieves 95.69 on OmniDocBench~v1.6, improving over the same-architecture baseline by 2.71 points and surpassing all existing methods including models with over 200times more parameters.

AI agents are increasingly used to solve complex, multi-step tasks, but existing multi-agent frameworks remain brittle as workflows grow in scale and depth. Small errors at intermediate stages can propagate through agent interactions, while insufficient grounding and weak verification mechanisms further limit reliability. We present Meta-Agent, a two-phase framework that automatically constructs and executes specialized multi-agent systems from natural-language task descriptions. In the construction phase, a task planner decomposes a problem into a directed acyclic graph of agent specifications with explicit input/output contracts and verification criteria. A web search module grounds each specification with external evidence, and a code generation module produces system prompts and tool configurations. A construction-time verification stage then validates generated artifacts and triggers targeted regeneration when failures are detected. In the execution phase, a coordinator dispatches subtasks across the agent graph while execution-time verification gates intermediate outputs. We further introduce a three-level error attribution mechanism that distinguishes local, upstream, and structural failures, enabling targeted recovery strategies ranging from localized retries to partial re-execution and re-decomposition. We evaluate Meta-Agent across coding, contextual learning, and open-ended reasoning tasks. Experiments against strong multi-agent baselines and ablation studies demonstrate consistent improvements in task success rate, error recovery, and workflow stability. The results highlight the importance of tightly integrating planning, grounding, and verification for building reliable multi-agent systems.

We present Cogentic, a multi-agent harness for automated proof discovery on open research problems. While frontier language models can generate strong mathematical ideas in a single shot, single-shot generation is often insufficient for open problems that require exploring multiple competing conjectures, overcoming subtle technical obstructions, and retaining intermediate progress over a long horizon. Cogentic addresses these challenges through an iterative prove-verify loop in which an orchestrator allocates a population of independent provers across distinct proof directions, subjects their output to adversarial verification by several specialized components, and promotes confirmed intermediate results into a persistent verified ledger that later rounds build on. The harness is designed to be able to solve research-level math and theoretical computer science problems. Using either Gemini 3.1 Pro or an early version of Gemini 4 Argon as the base model, Cogentic produced novel results on open problems across online learning, auction theory, and mechanism design. Each result was independently verified by domain experts and is developed in full in companion papers. We list these results, and new ones as they are verified, at https://sites.google.com/view/cogentic .

Extracting patient information from unstructured text is a critical task in health decision-support and clinical research. Large language models (LLMs) have shown the potential to accelerate clinical curation via few-shot in-context learning, in contrast to supervised learning which requires much more costly human annotations. However, despite drastic advances in modern LLMs such as GPT-4, they still struggle with issues regarding accuracy and interpretability, especially in mission-critical domains such as health. Here, we explore a general mitigation framework using self-verification, which leverages the LLM to provide provenance for its own extraction and check its own outputs. This is made possible by the asymmetry between verification and generation, where the latter is often much easier than the former. Experimental results show that our method consistently improves accuracy for various LLMs in standard clinical information extraction tasks. Additionally, self-verification yields interpretations in the form of a short text span corresponding to each output, which makes it very efficient for human experts to audit the results, paving the way towards trustworthy extraction of clinical information in resource-constrained scenarios. To facilitate future research in this direction, we release our code and prompts.

Large language model (LLM) decoding involves generating a sequence of tokens based on a given context, where each token is predicted one at a time using the model's learned probabilities. The typical autoregressive decoding method requires a separate forward pass through the model for each token generated, which is computationally inefficient and poses challenges for deploying LLMs in latency-sensitive scenarios. The main limitations of current decoding methods stem from their inefficiencies and resource demands. Existing approaches either necessitate fine-tuning smaller models, which is resource-intensive, or rely on fixed retrieval schemes to construct drafts for the next tokens, which lack adaptability and fail to generalize across different models and contexts. To address these issues, we introduce a novel methodology called ADED, which accelerates LLM decoding without requiring fine-tuning. Our approach involves an adaptive draft-verification process that evolves over time to improve efficiency. We utilize a tri-gram matrix-based LLM representation to dynamically approximate the output distribution of the LLM, allowing the model to adjust to changing token probabilities during the decoding process. Additionally, we implement a draft construction mechanism that effectively balances exploration and exploitation, ensuring that the drafts generated are both diverse and close to the true output distribution of the LLM. The importance of this design lies in its ability to optimize the draft distribution adaptively, leading to faster and more accurate decoding. Through extensive experiments on various benchmark datasets and LLM architectures, we demonstrate that ADED significantly accelerates the decoding process while maintaining high accuracy, making it suitable for deployment in a wide range of practical applications.

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

Recent speaker verification studies have achieved notable success by leveraging layer-wise output from pre-trained Transformer models. However, few have explored the advancements in aggregating these multi-level features beyond the static weighted average. We present Layer Attentive Pooling (LAP), a novel strategy for aggregating inter-layer representations from pre-trained speech models for speaker verification. LAP assesses the significance of each layer from multiple perspectives time-dynamically, and employs max pooling instead of averaging. Additionally, we propose a lightweight backend speaker model comprising LAP and Attentive Statistical Temporal Pooling (ASTP) to extract speaker embeddings from pre-trained model output. Experiments on the VoxCeleb benchmark reveal that our compact architecture achieves state-of-the-art performance while greatly reducing the training time. We further analyzed LAP design and its dynamic weighting mechanism for capturing speaker characteristics.

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

An autonomous AI ecosystem (SUBSTRATE S3), generating product specifications without explicit instructions about formal methods, independently proposed the use of Z3 SMT solver across six distinct domains of AI safety: verification of LLM-generated code, tool API safety for AI agents, post-distillation reasoning correctness, CLI command validation, hardware assembly verification, and smart contract safety. These convergent discoveries, occurring across 8 products over 13 days with Jaccard similarity below 15% between variants, suggest that formal verification is not merely a useful technique for AI safety but an emergent property of any sufficiently complex system reasoning about its own safety. We propose a unified framework (substrate-guard) that applies Z3-based verification across all six output classes through a common API, and evaluate it on 181 test cases across five implemented domains, achieving 100% classification accuracy with zero false positives and zero false negatives. Our framework detected real bugs that empirical testing would miss, including an INT_MIN overflow in branchless RISC-V assembly and mathematically proved that unconstrained string parameters in tool APIs are formally unverifiable.

Speculative decoding accelerates large language model (LLM) inference without compromising output quality. Recent parallel drafting methods further improve single-request performance by decoupling draft length from drafting latency, enabling longer drafts and higher mean accepted tokens (MAT). However, under high request concurrency, long drafts waste substantial computation on rejected tokens, increasing verification cost and potentially making speculative decoding slower than autoregressive decoding. We present D-Cut, an adaptive pruning method that selects draft tokens jointly across the batch and concentrates the verification budget on tokens most likely to be accepted. D-Cut is motivated by two observations. First, acceptance lengths vary considerably across concurrent requests; D-Cut therefore performs cross-request pruning, allocating the verification budget adaptively according to draft confidence. Second, verification cost depends strongly on the deployment environment, including GPU architecture and parallelism strategy; D-Cut incorporates a runtime cost model to adapt its pruning depth to the target environment. Experiments on dense and mixture-of-experts (MoE) models show that, under high concurrency, D-Cut improves the average speedup from \(1.26\times\) to \(1.65\times\), restores acceleration in dense-model configurations where long-draft baselines are slower than autoregressive decoding, and achieves up to \(3.0\times\) speedup over autoregressive decoding on MoE models.

Complete orthogonal predictive coordinates do not by themselves bind a latent direction to a named intervention. We present a mathematical and synthetic audit motivated by vascular device-vessel suitcordance. Capacity-matched least-squares predictors were exactly equivalent under complete fixed output transforms, whereas an anchor-only observer recovered interpretations only within the span of known perturbation signatures. Six three-dimensional configurations across 64 seeds gave a maximum paired prediction discrepancy of 6.7e-15 but a median untransported edit error of 1.513. Coordinate transport removed that error. Noisy and weak anchors constrained calibration stability, and changing the representation basis required recalibration or verified transport. Across 256 additional fits in dimensions 3-24, prediction equivalence persisted within 4.0e-15. We then evaluated nine deliberate runnable fault classes across 64 seeds. All 576 faulty executions completed, but each violated at least one reconstruction, prediction, delivered-edit or scope contract; all 320 valid control records passed. Repeating a faulty implementation gave exact self-agreement despite error against the separately computed simulator expectation. For one omitted-direction defect, probe coverage followed its analytic law, and rank-aware abstention protected unsupported interpretations. Scalar-noise experiments exposed both missed weak faults and excessive rejection under narrow relative tolerances. These controls provide an executable separation of prediction, semantic support and scientific acceptance. They are synthetic numerical audits, not clinical validation, neural JEPA-Anything replication, agent learning or patient treatment-effect estimation.

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

We address the neural network robustness problem by adding Similarity (i.e., correctly predicted depth-matches into training)-awareness and Distance-to-training-distribution-awareness to the existing output Magnitude (i.e., decision-boundary)-awareness of the softmax function. The resulting SDM activation function provides strong signals of the relative epistemic (reducible) predictive uncertainty. We use this novel behavior to further address the complementary HCI problem of mapping the output to human-interpretable summary statistics over relevant partitions of a held-out calibration set. Estimates of prediction-conditional uncertainty are obtained via a parsimonious learned transform over the class-conditional empirical CDFs of the output of a final-layer SDM activation function. For decision-making and as an intrinsic model check, estimates of class-conditional accuracy are obtained by further partitioning the high-probability regions of this calibrated output into class-conditional, region-specific CDFs. The uncertainty estimates from SDM calibration are remarkably robust to test-time distribution shifts and out-of-distribution inputs; incorporate awareness of the effective sample size; provide estimates of uncertainty from the learning and data splitting processes; and are well-suited for selective classification and conditional branching for additional test-time compute based on the predictive uncertainty, as for selective LLM generation, routing, and composition over multiple models and retrieval. Finally, we construct SDM networks, LLMs with uncertainty-aware verification and interpretability-by-exemplar as intrinsic properties. We provide open-source software implementing these results.

Diffusion Language Models (DLMs) have recently become increasingly competitive with autoregressive (AR) models, and even outperform them on certain tasks. Unlike AR models, DLMs produce output through iterative denoising without a left-to-right order. To further improve the performance of DLMs, we introduce PDC (Prefix-Denoising Consistency), a test-time self-verification method for DLMs. PDC exploits a distinctive test-time signal in DLMs under prefix conditioned regeneration, correct trajectories are more stable and reproducible than incorrect ones. Concretely, given an initially generated sample, PDC splits the sentence at an intermediate position and regenerates the remaining tokens conditioned on the fixed prefix. Across mathematical reasoning and commonsense reasoning benchmarks, PDC consistently improves upon the initial sample, outperforms independent generations under a computational constrained comparison, and is robust to different unmasking strategies and parameter settings. These results highlight prefix-conditioned regeneration as an effective DLM-specific primitive for test-time verification.

Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a chain-of-thought approach, which not only bolsters their reasoning abilities but also provides valuable insights into their problem-solving process. However, there is still significant room for enhancing the reasoning abilities of LLMs. Some studies suggest that the integration of an LLM output verifier can boost reasoning accuracy without necessitating additional model training. In this paper, we follow these studies and introduce a novel graph-based method to further augment the reasoning capabilities of LLMs. We posit that multiple solutions to a reasoning task, generated by an LLM, can be represented as a reasoning graph due to the logical connections between intermediate steps from different reasoning paths. Therefore, we propose the Reasoning Graph Verifier (RGV) to analyze and verify the solutions generated by LLMs. By evaluating these graphs, models can yield more accurate and reliable results.Our experimental results show that our graph-based verification method not only significantly enhances the reasoning abilities of LLMs but also outperforms existing verifier methods in terms of improving these models' reasoning performance.

This research aims to accelerate the inference speed of large language models (LLMs) with billions of parameters. We propose Smart Parallel Auto-Correct dEcoding (SPACE), an innovative approach designed for achieving lossless acceleration of LLMs. By integrating semi-autoregressive inference and speculative decoding capabilities, SPACE uniquely enables autoregressive LLMs to parallelize token generation and verification. This is realized through a specialized semi-autoregressive supervised fine-tuning process that equips existing LLMs with the ability to simultaneously predict multiple tokens. Additionally, an auto-correct decoding algorithm facilitates the simultaneous generation and verification of token sequences within a single model invocation. Through extensive experiments on a range of LLMs, SPACE has demonstrated inference speedup ranging from 2.7x-4.0x on HumanEval-X while maintaining output quality.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity-that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1\% over Beam Search and 3.6\% over Best-of-N, while reducing FLOPs by over 52\%. We will open-source the code to support future research.

Large language model (LLM) agents are increasingly deployed to tackle complex tasks, often necessitating collaboration among multiple specialized agents. However, multi-agent collaboration introduces new challenges in planning, coordination, and verification. Execution failures frequently arise not from flawed reasoning alone, but from subtle misalignments in task interpretation, output format, or inter-agent handoffs. To address these challenges, we present VeriMAP, a framework for multi-agent collaboration with verification-aware planning. The VeriMAP planner decomposes tasks, models subtask dependencies, and encodes planner-defined passing criteria as subtask verification functions (VFs) in Python and natural language. We evaluate VeriMAP on diverse datasets, demonstrating that it outperforms both single- and multi-agent baselines while enhancing system robustness and interpretability. Our analysis highlights how verification-aware planning enables reliable coordination and iterative refinement in multi-agent systems, without relying on external labels or annotations.

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

Large language models (LLMs) increasingly rely on explicit reasoning to solve coding tasks, yet evaluating the quality of this reasoning remains challenging. Existing reasoning evaluators are not designed for coding, and current benchmarks focus primarily on code generation, leaving other coding tasks largely unexplored. We introduce CodeRQ-Bench, the first benchmark for evaluating LLM reasoning quality across three coding task categories: generation, summarization, and classification. Using this benchmark, we analyze 1,069 mismatch cases from existing evaluators, identify five recurring limitations, and derive four design insights for reasoning evaluation in coding tasks. Guided by these insights, we propose VERA, a two-stage evaluator that combines evidence-grounded verification with ambiguity-aware score correction. Experiments on CodeRQ-Bench show that VERA consistently outperforms strong baselines across four datasets, improving AUCROC by up to 0.26 and AUPRC by up to 0.21. We release CodeRQ-Bench at https://github.com/MrLYG/CodeRQ-Bench, supporting future investigations.

Programmable logic controllers (PLCs) run industrial plants, and large language models can already generate independent program organization units (POUs) for them. Whether such logic integrates into an existing PLC project and then runs correctly has been checked only in limited tests. We present SemaPLC, a project-grounded and verification-gated agent harness assembled from conventional tools but governed by a strict completion rule. Rather than stopping when the model judges its own output adequate, SemaPLC declares a task complete only when logged external checks confirm it. Those checks cover the specification, the compilation, and the behavior on a live runtime. On 117 independent-POU tasks matching existing benchmarks, it attains the highest strict verified pass rate on all seven models (72.6\% mean). On a project-context track of 65 tasks whose generated logic must compile and run inside a real project, it attains the highest mean on integrated compilation, static behavior, and dynamic behavior. Of the three layers, dynamic behavior is the most revealing. We measure it by deploying the generated and the reference logic to a live PLC runtime and comparing their executed traces. All methods fall within 10 static points of one another, whereas dynamic scores separate them sharply, from 22.4 to 31.4 for the baselines against 52.2 for SemaPLC. Overall, our verification-gated harness raises the mean at every layer and most sharply at runtime. Execution, not static scoring, is the faithful test of whether generated control logic actually works. SemaPLC is open-sourced at https://github.com/midea-ai/SemaPLC.

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

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

Recent works have revealed the great potential of speculative decoding in accelerating the autoregressive generation process of large language models. The success of these methods relies on the alignment between draft candidates and the sampled outputs of the target model. Existing methods mainly achieve draft-target alignment with training-based methods, e.g., EAGLE, Medusa, involving considerable training costs. In this paper, we present a training-free alignment-augmented speculative decoding algorithm. We propose alignment sampling, which leverages output distribution obtained in the prefilling phase to provide more aligned draft candidates. To further benefit from high-quality but non-aligned draft candidates, we also introduce a simple yet effective flexible verification strategy. Through an adaptive probability threshold, our approach can improve generation accuracy while further improving inference efficiency. Experiments on 8 datasets (including question answering, summarization and code completion tasks) show that our approach increases the average generation score by 3.3 points for the LLaMA3 model. Our method achieves a mean acceptance length up to 2.39 and speed up generation by 2.23.

We present DuPO, a dual learning-based preference optimization framework that generates annotation-free feedback via a generalized duality. DuPO addresses two key limitations: Reinforcement Learning with Verifiable Rewards (RLVR)'s reliance on costly labels and applicability restricted to verifiable tasks, and traditional dual learning's restriction to strictly dual task pairs (e.g., translation and back-translation). Specifically, DuPO decomposes a primal task's input into known and unknown components, then constructs its dual task to reconstruct the unknown part using the primal output and known information (e.g., reversing math solutions to recover hidden variables), broadening applicability to non-invertible tasks. The quality of this reconstruction serves as a self-supervised reward to optimize the primal task, synergizing with LLMs' ability to instantiate both tasks via a single model. Empirically, DuPO achieves substantial gains across diverse tasks: it enhances the average translation quality by 2.13 COMET over 756 directions, boosts the mathematical reasoning accuracy by an average of 6.4 points on three challenge benchmarks, and enhances performance by 9.3 points as an inference-time reranker (trading computation for accuracy). These results position DuPO as a scalable, general, and annotation-free paradigm for LLM optimization.

Assessing the quality of Large Language Model (LLM) outputs presents a critical challenge. Previous methods either rely on text-level information (e.g., reward models, majority voting), which can overfit to superficial cues, or on calibrated confidence from token probabilities, which would fail on less-calibrated models. Yet both of these signals are, in fact, partial projections of a richer source of information: the model's internal hidden states. Early layers, closer to token embeddings, preserve semantic and lexical features that underpin text-based judgments, while later layers increasingly align with output logits, embedding confidence-related information. This paper explores hidden states directly as a unified foundation for verification. We show that the correctness of a solution is encoded as a geometrically separable signature within the trajectory of hidden activations. To validate this, we present Clue (Clustering and Experience-based Verification), a deliberately minimalist, non-parametric verifier. With no trainable parameters, CLUE only summarizes each reasoning trace by an hidden state delta and classifies correctness via nearest-centroid distance to ``success'' and ``failure'' clusters formed from past experience. The simplicity of this method highlights the strength of the underlying signal. Empirically, CLUE consistently outperforms LLM-as-a-judge baselines and matches or exceeds modern confidence-based methods in reranking candidates, improving both top-1 and majority-vote accuracy across AIME 24/25 and GPQA. As a highlight, on AIME 24 with a 1.5B model, CLUE boosts accuracy from 56.7% (majority@64) to 70.0% (top-maj@16).

Parallel diffusion decoding can accelerate diffusion language model inference by unmasking multiple tokens per step, but aggressive parallelism often harms quality. Revocable decoding mitigates this by rechecking earlier tokens, yet we observe that existing verification schemes frequently trigger flip-flop oscillations, where tokens are remasked and later restored unchanged. This behaviour slows inference in two ways: remasking verified positions weakens the conditioning context for parallel drafting, and repeated remask cycles consume the revision budget with little net progress. We propose COVER (Cache Override Verification for Efficient Revision), which performs leave-one-out verification and stable drafting within a single forward pass. COVER constructs two attention views via KV cache override: selected seeds are masked for verification, while their cached key value states are injected for all other queries to preserve contextual information, with a closed form diagonal correction preventing self leakage at the seed positions. COVER further prioritises seeds using a stability aware score that balances uncertainty, downstream influence, and cache drift, and it adapts the number of verified seeds per step. Across benchmarks, COVER markedly reduces unnecessary revisions and yields faster decoding while preserving output quality.

Claim verification with large language models (LLMs) has recently attracted growing attention, due to their strong reasoning capabilities and transparent verification processes compared to traditional answer-only judgments. However, existing approaches to online claim verification, which requires iterative evidence retrieval and reasoning, still mainly rely on prompt engineering or pre-designed reasoning workflows, without unified training to improve necessary skills. Therefore, we introduce Veri-R1, an online reinforcement learning (RL) framework that enables an LLM to interact with a search engine and to receive reward signals that explicitly shape its planning, retrieval, and reasoning behaviors. This dynamic interaction of LLM with retrieval systems more accurately reflects real-world verification scenarios and fosters comprehensive verification skills. Empirical results show that Veri-R1 improves joint accuracy by up to 30% and doubles the evidence score, often surpassing its larger-scale model counterparts. Ablation studies further reveal the impact of reward components, and the link between output logits and label accuracy. Our results highlight the effectiveness of online RL for precise and faithful claim verification, providing an important foundation for future research. We release our code to support community progress in LLM empowered claim verification.

The goal of L-step speculative decoding is to accelerate autoregressive decoding of a target model by using a cheaper draft model to generate a candidate path of L tokens. Based on a verification algorithm involving target and draft model probabilities, a prefix of the candidate sequence is accepted, and an additional correction token is sampled from a residual distribution to ensure that the final output adheres to the target distribution. While standard speculative decoding uses a verification algorithm which is independent at each token on the path, a recent extension called block verification uses a joint condition involving all sampled on-path probabilities. Block verification (BV) was shown to be optimal over all verification algorithms which use only on-path probabilities, improving on standard speculative decoding. In this work, we first show that block verification is optimal even over verification algorithms that use off-path probabilities, by constructing an information-agnostic linear program (LP). Further, we can extend our LP to the setting where the draft model samples multiple candidate paths, and use it to construct a natural class of multi-path block verification generalizations. While computing the optimal algorithm in this class is not tractable, by considering a stricter class of greedy algorithms, we can formulate an efficient method called greedy multi-path block verification (GBV). Empirically, GBV can improve block efficiency by over 30% and reduce decoding walltimes by over 15% relative to BV. On Llama-3 70B, GBV can improve the end-to-end decoding throughput over SOTA multi-path verification methods by more than 15%.

As large language models become increasingly widespread, third-party providers that deploy open-weight models have become an important part of the ecosystem. Auditing the quality of their inference APIs is therefore an open problem. We formalize hosted model routing as a stochastic process and propose \textbf{Ventor-QTest}, a composite black-box audit that requires no probability information from the target API. Its repeated-request component sends each frozen constrained context to the target multiple times, reconstructs a categorical output distribution from the returned text counts, and reports average fidelity loss (AFL) as a null-bias-corrected, within-window mean coarsened-KL statistic. Its long-sequence component uses independent runs to report extreme fidelity loss (EFL) through the empirical upper tail of a run-level reference-centered-surprisal statistic. Across three logprob-capable route conditions, AFL shows strong linear descriptive agreement with a logprob-derived coarsened-KL comparator. Across seven route snapshots, 20-run sequence probes reveal route-specific EFL variation. AFL and EFL have little detectable route-level association with GPQA-Diamond accuracy. In contrast, pronounced EFL coincides with a decline in Terminal-Bench pass rate as task exposure increases. This pattern may arise because correctness in long-horizon tasks is more sensitive to extreme fidelity loss. These results motivate reporting AFL and EFL jointly, particularly when auditing long-horizon agentic tasks. The open-source implementation is available at https://github.com/Tencent/AI-Infra-Guard/tree/main/services/api_checker/ventor_qtest.

Verifying claims about AI workloads is a prerequisite for credible AI governance of covert adversaries (who comply with monitoring only when detection likelihood is high), yet the apparent non-determinism of GPU floating-point arithmetic forces auditors to accept approximate output matches. Covert adversaries can exploit unverifiable degrees of freedom in monitored computation. Attack vectors include steganography, unreported modification of inference software, and covert computation via unreported batch elements. Empirically, we analyze how modern inference engines (vLLM, HF transformers) produce deterministic but non-invariant outputs, without needing to set performance-compromising determinism flags, if the right information is available for re-computation and no atomic functions are called in the backend. We demonstrate that such bitwise-precise re-computation does not require access to identical hardware, via a software-only emulation of LLM inference across multiple NVIDIA GPU variants. Thus, accumulated rounding errors can be an auditable signature of the software and hardware setup used for inference, instead of a constraint on verifiability.

We study the XAI (explainable AI) on the face recognition task, particularly the face verification here. Face verification is a crucial task in recent days and it has been deployed to plenty of applications, such as access control, surveillance, and automatic personal log-on for mobile devices. With the increasing amount of data, deep convolutional neural networks can achieve very high accuracy for the face verification task. Beyond exceptional performances, deep face verification models need more interpretability so that we can trust the results they generate. In this paper, we propose a novel similarity metric, called explainable cosine (xCos), that comes with a learnable module that can be plugged into most of the verification models to provide meaningful explanations. With the help of xCos, we can see which parts of the two input faces are similar, where the model pays its attention to, and how the local similarities are weighted to form the output xCos score. We demonstrate the effectiveness of our proposed method on LFW and various competitive benchmarks, resulting in not only providing novel and desiring model interpretability for face verification but also ensuring the accuracy as plugging into existing face recognition models.

Large language models (LLMs) have shown impressive capabilities in adapting to various tasks when provided with task-specific instructions. However, LLMs using standard decoding strategies often struggle with deviations from the inputs. Intuitively, compliant LLM outputs should reflect the information present in the input, which can be measured by point-wise mutual information (PMI) scores. Therefore, we propose Diver, a novel approach that enhances LLM Decoding through span-level PMI verification. During inference, Diver first identifies divergence steps that may lead to multiple candidate spans. Subsequently, it calculates the PMI scores by assessing the log-likelihood gains of the input if the candidate spans are generated. Finally, the optimal span is selected based on the PMI re-ranked output distributions. We evaluate our method across various downstream tasks, and empirical results demonstrate that Diver significantly outperforms existing decoding methods in both performance and versatility.

We introduce Self-Verified Reasoner (SVR-R1), a multi-turn RL framework that turns a model's own verification into a learning signal for multimodal reasoning. For each query, the model proposes an answer using the same weights, and issues a binary self-verdict (Yes/No). A 'No' triggers a second-chance rethink; a 'Yes,' or a turn cap, finalizes the output for computing the outcome-based reward. SVR-R1 is implemented with GRPO and an asynchronous multi-turn rollout framework and needs no external supervision or auxiliary critics. We evaluate SVR-R1 on vision-language reasoning benchmarks and show that it improves accuracy by a large margin over strong standard GRPO baselines. Training dynamics show decreasing reliance on verification-fewer verification turns, yet higher test accuracy-indicating that the gap between verification and generation narrows as the policy internalizes self-correction and chooses the most confident answer via our framework. SVR-R1 bridges the less explored intersection of inference-time self-refinement and RL training for VLMs, offering a simple yet effective recipe for bootstrapping multimodal reasoning. We will open-source SVR-R1 to facilitate future research in VLMs.

The proliferation of AI-generated text has intensified the need for reliable authorship verification, yet current output-based methods are increasingly unreliable. We observe that the ordinary typing interface captures rich cognitive signatures, measurable patterns in keystroke timing that reflect the planning, translating, and revising stages of genuine composition. Drawing on large-scale keystroke datasets comprising over 136 million events, we define the Cognitive Load Correlation (CLC) and show it distinguishes genuine composition from mechanical transcription. We present a non-intrusive verification framework that operates within existing writing interfaces, collecting only timing metadata to preserve privacy. Our analytical evaluation estimates 85 to 95 percent discrimination accuracy under stated assumptions, while limiting biometric leakage via evidence quantization. We analyze the adversarial robustness of cognitive signatures, showing they resist timing-forgery attacks that defeat motor-level authentication because the cognitive channel is entangled with semantic content. We conclude that reframing authorship verification as a human-computer interaction problem provides a privacy-preserving alternative to invasive surveillance.

This paper explores three novel approaches to improve the performance of speaker verification (SV) systems based on deep neural networks (DNN) using Multi-head Self-Attention (MSA) mechanisms and memory layers. Firstly, we propose the use of a learnable vector called Class token to replace the average global pooling mechanism to extract the embeddings. Unlike global average pooling, our proposal takes into account the temporal structure of the input what is relevant for the text-dependent SV task. The class token is concatenated to the input before the first MSA layer, and its state at the output is used to predict the classes. To gain additional robustness, we introduce two approaches. First, we have developed a Bayesian estimation of the class token. Second, we have added a distilled representation token for training a teacher-student pair of networks using the Knowledge Distillation (KD) philosophy, which is combined with the class token. This distillation token is trained to mimic the predictions from the teacher network, while the class token replicates the true label. All the strategies have been tested on the RSR2015-Part II and DeepMine-Part 1 databases for text-dependent SV, providing competitive results compared to the same architecture using the average pooling mechanism to extract average embeddings.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce the linear constraint-driven clipping framework, a class of scalable and efficient methods designed to enhance the efficacy of NN verifiers. Under this framework, we develop two novel algorithms that efficiently utilize linear constraints to 1) reduce portions of the input space that are either verified or irrelevant to a subproblem in the context of branch-and-bound, and 2) directly improve intermediate bounds throughout the network. The process novelly leverages linear constraints that often arise from bound propagation methods and is general enough to also incorporate constraints from other sources. It efficiently handles linear constraints using a specialized GPU procedure that can scale to large neural networks without the use of expensive external solvers. Our verification procedure, Clip-and-Verify, consistently tightens bounds across multiple benchmarks and can significantly reduce the number of subproblems handled during BaB. We show that our clipping algorithms can be integrated with BaB-based verifiers such as α,β-CROWN, utilizing either the split constraints in activation-space BaB or the output constraints that denote the unverified input space. We demonstrate the effectiveness of our procedure on a broad range of benchmarks where, in some instances, we witness a 96% reduction in the number of subproblems during branch-and-bound, and also achieve state-of-the-art verified accuracy across multiple benchmarks. Clip-and-Verify is part of the α,β-CROWN verifier (http://abcrown.org), the VNN-COMP 2025 winner. Code available at https://github.com/Verified-Intelligence/Clip_and_Verify.

The synthesis of inductive loop invariants remains a critical bottleneck in automated program verification. While Large Language Models (LLMs) show promise in mitigating this issue, they often fail on complex programs, producing invariants that are invalid or computationally ineffective. Although fine-tuning is a natural strategy to address these limitations, obtaining high-quality training data remains an open challenge. We first formalize the properties required for a high-quality training invariant, and then present Wonda, a rigorous data curation pipeline that extracts such invariants from raw verifier output via AST-based normalization followed by LLM-driven semantic rewriting and augmentation with provable quality guarantees. Fine-tuning Small Language Models (SLMs) on Wonda-curated data yields consistent gains across the Qwen3, Llama-3.1, and Mistral families: the 4B and 8B Qwen3 models nearly double invariant correctness and double speedup rates, while Llama-3.1-8B triples both. On the challenging InvBench suite, the same 4B model outperforms an off-the-shelf model 20x its size and matches the end-to-end verification time of GPT-OSS-120B, while a 14B Qwen3 model matches that of the frontier model GPT-5.2, all without test-time compute overhead. Our code is publicly available on GitHub.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

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

The proliferation of Large Language Models (LLMs) accessed via black-box APIs introduces a significant trust challenge: users pay for services based on advertised model capabilities (e.g., size, performance), but providers may covertly substitute the specified model with a cheaper, lower-quality alternative to reduce operational costs. This lack of transparency undermines fairness, erodes trust, and complicates reliable benchmarking. Detecting such substitutions is difficult due to the black-box nature, typically limiting interaction to input-output queries. This paper formalizes the problem of model substitution detection in LLM APIs. We systematically evaluate existing verification techniques, including output-based statistical tests, benchmark evaluations, and log probability analysis, under various realistic attack scenarios like model quantization, randomized substitution, and benchmark evasion. Our findings reveal the limitations of methods relying solely on text outputs, especially against subtle or adaptive attacks. While log probability analysis offers stronger guarantees when available, its accessibility is often limited. We conclude by discussing the potential of hardware-based solutions like Trusted Execution Environments (TEEs) as a pathway towards provable model integrity, highlighting the trade-offs between security, performance, and provider adoption. Code is available at https://github.com/sunblaze-ucb/llm-api-audit

Vision-Language Models (VLMs) have demonstrated remarkable progress in multimodal tasks, but remain susceptible to hallucinations, where generated text deviates from the underlying visual content. Existing hallucination detection methods primarily rely on output logits or external verification tools, often overlooking their internal mechanisms. In this work, we investigate the outputs of internal attention heads, postulating that specific heads carry the primary signals for truthful generation.However, directly probing these high-dimensional states is challenging due to the entanglement of visual-linguistic syntax and noise. To address this, we propose VIB-Probe, a novel hallucination detection and mitigation framework leveraging the Variational Information Bottleneck (VIB) theory. Our method extracts discriminative patterns across layers and heads while filtering out semantic nuisances through the information bottleneck principle. Furthermore, by leveraging the gradients of our VIB probe, we identify attention heads with strong causal influence on hallucinations and introduce an inference-time intervention strategy for hallucination mitigation. Extensive experiments across diverse benchmarks demonstrate that VIB-Probe significantly outperforms existing baselines in both settings. Our code will be made publicly available.

With the widespread adoption of large language models (LLMs), hallucinations, which are non-factual fabrications in model outputs, have become serious concerns. Reasoning capabilities have received attention as a self-verification process to improve output reliability. However, the effect of reasoning within a closed system where LLMs cannot rely on external tools or knowledge has yet to be clarified. We therefore conduct experiments under strict constraints (recommending peer-reviewed journal articles in computer science) to examine the effect of reasoning across multiple models (GPT-5.2 and Gemini 3 Flash). Our results reveal a problematic trade-off between constraint compliance and factual accuracy. Non-reasoning models exhibit high constraint violation rates (66-75%) but maintain factual accuracy, while reasoning models reduce violations (13-26%) but systematically distort known facts to satisfy constraints and increase complete fabrication. This trade-off pattern is consistent across both models despite different architectures, indicating a fundamental limitation of reasoning. Furthermore, reasoning does not uniformly improve output authenticity: effects diverge by model, reflecting different allocations of the compliance-truthfulness trade-off. These findings challenge the assumption that reasoning universally improves reliability: reasoning models trade honest constraint violations for detection-resistant distortions.

Fault attacks are active, physical attacks that an adversary can leverage to alter the control-flow of embedded devices to gain access to sensitive information or bypass protection mechanisms. Due to the severity of these attacks, manufacturers deploy hardware-based fault defenses into security-critical systems, such as secure elements. The development of these countermeasures is a challenging task due to the complex interplay of circuit components and because contemporary design automation tools tend to optimize inserted structures away, thereby defeating their purpose. Hence, it is critical that such countermeasures are rigorously verified post-synthesis. As classical functional verification techniques fall short of assessing the effectiveness of countermeasures, developers have to resort to methods capable of injecting faults in a simulation testbench or into a physical chip. However, developing test sequences to inject faults in simulation is an error-prone task and performing fault attacks on a chip requires specialized equipment and is incredibly time-consuming. To that end, this paper introduces SYNFI, a formal pre-silicon fault verification framework that operates on synthesized netlists. SYNFI can be used to analyze the general effect of faults on the input-output relationship in a circuit and its fault countermeasures, and thus enables hardware designers to assess and verify the effectiveness of embedded countermeasures in a systematic and semi-automatic way. To demonstrate that SYNFI is capable of handling unmodified, industry-grade netlists synthesized with commercial and open tools, we analyze OpenTitan, the first open-source secure element. In our analysis, we identified critical security weaknesses in the unprotected AES block, developed targeted countermeasures, reassessed their security, and contributed these countermeasures back to the OpenTitan repository.

Multiple-choice question answering (MCQA) has been a popular format for evaluating and reinforcement fine-tuning (RFT) of modern multimodal language models. Its constrained output format allows for simplified, deterministic automatic verification. However, we find that the options may leak exploitable signals, which makes the accuracy metrics unreliable for indicating real capabilities and encourages explicit or implicit answer guessing behaviors during RFT. We propose ReVeL (Rewrite and Verify by LLM), a framework that rewrites multiple-choice questions into open-form questions while keeping answers verifiable whenever possible. The framework categorizes questions according to different answer types, apply different rewriting and verification schemes, respectively. When applied for RFT, we converted 20k MCQA examples and use GRPO to finetune Qwen2.5-VL models. Models trained on ReVeL-OpenQA match MCQA accuracy on multiple-choice benchmarks and improve OpenQA accuracy by about six percentage points, indicating better data efficiency and more robust reward signals than MCQA-based training. When used for evaluation, ReVeL also reveals up to 20 percentage points of score inflation in MCQA benchmarks (relative to OpenQA), improves judging accuracy, and reduces both cost and latency. We will release code and data publicly.

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

Recent advancements in reinforcement learning with verifiable rewards have pushed the boundaries of the visual reasoning capabilities in large vision-language models (LVLMs). However, training LVLMs with reinforcement fine-tuning (RFT) is computationally expensive, posing a significant challenge to scaling model size. In this work, we propose ProxyThinker, an inference-time technique that enables large models to inherit the visual reasoning capabilities from small, slow-thinking visual reasoners without any training. By subtracting the output distributions of base models from those of RFT reasoners, ProxyThinker modifies the decoding dynamics and successfully elicits the slow-thinking reasoning demonstrated by the emerged sophisticated behaviors such as self-verification and self-correction. ProxyThinker consistently boosts performance on challenging visual benchmarks on spatial, mathematical, and multi-disciplinary reasoning, enabling untuned base models to compete with the performance of their full-scale RFT counterparts. Furthermore, our implementation efficiently coordinates multiple language models with parallelism techniques and achieves up to 38 times faster inference compared to previous decoding-time methods, paving the way for the practical deployment of ProxyThinker. Code is available at https://github.com/MrZilinXiao/ProxyThinker.

Prompt attacks, including jailbreaks and prompt injections, pose a critical security risk to Large Language Model (LLM) systems. In production, guardrails must mitigate these attacks under strict low-latency constraints, resulting in a deployment gap in which lightweight classifiers and rule-based systems struggle to generalize under distribution shift, while high-capacity LLM-based judges remain too slow or costly for live enforcement. In this work, we examine whether lightweight, general-purpose LLMs can reliably serve as security judges under real-world production constraints. Through careful prompt and output design, lightweight LLMs are guided through a structured reasoning process involving explicit intent decomposition, safety-signal verification, harm assessment, and self-reflection. We evaluate our method on a curated dataset combining benign queries from real-world chatbots with adversarial prompts generated via automated red teaming (ART), covering diverse and evolving patterns. Our results show that general-purpose LLMs, such as gemini-2.0-flash-lite-001, can serve as effective low-latency judges for live guardrails. This configuration is currently deployed in production as a centralized guardrail service for public service chatbots in Singapore. We additionally evaluate a Mixture-of-Models (MoM) setting to assess whether aggregating multiple LLM judges improves prompt-attack detection performance relative to single-model judges, with only modest gains observed.

Speculative decoding (SD) has become a popular technique to accelerate Large Language Model (LLM) inference, yet its real-world effectiveness remains unclear as prior evaluations rely on research prototypes and unrealistically small batch sizes. We present, to our knowledge, the first systematic study of SD on a production-grade and widely deployed inference engine (vLLM), covering multiple SD variants (n-gram, EAGLE/EAGLE-3, Draft-Model, Multi-Token Prediction) across diverse workloads, model scales, and batch sizes. We analyze key factors governing SD performance, and quantify a theoretical upper bound on SD speedup. Our results show that verification by the target model dominates the execution, while acceptance length varies markedly across output token positions, requests, and datasets. Comparing measured performance with theoretical bounds reveals substantial gaps between observed and theoretical upper bounds, and we leverage this observation to highlight new research opportunities that our study opens up in improving SD.

The synergy between symbolic knowledge, often represented by Knowledge Graphs (KGs), and the generative capabilities of neural networks is central to advancing neurosymbolic AI. A primary bottleneck in realizing this potential is the difficulty of automating KG construction, which faces challenges related to output reliability, consistency, and verifiability. These issues can manifest as structural inconsistencies within the generated graphs, such as the formation of disconnected isolated islands of data or the inaccurate conflation of abstract classes with specific instances. To address these challenges, we propose HyDRA, a Hybrid-Driven Reasoning Architecture designed for verifiable KG automation. Given a domain or an initial set of documents, HyDRA first constructs an ontology via a panel of collaborative neurosymbolic agents. These agents collaboratively agree on a set of competency questions (CQs) that define the scope and requirements the ontology must be able to answer. Given these CQs, we build an ontology graph that subsequently guides the automated extraction of triplets for KG generation from arbitrary documents. Inspired by design-by-contracts (DbC) principles, our method leverages verifiable contracts as the primary control mechanism to steer the generative process of Large Language Models (LLMs). To verify the output of our approach, we extend beyond standard benchmarks and propose an evaluation framework that assesses the functional correctness of the resulting KG by leveraging symbolic verifications as described by the neurosymbolic AI framework, SymbolicAI. This work contributes a hybrid-driven architecture for improving the reliability of automated KG construction and the exploration of evaluation methods for measuring the functional integrity of its output. The code is publicly available.

Multimodal Large Language Models (MLLMs) exhibit impressive performance across various visual tasks. Subsequent investigations into enhancing their visual reasoning abilities have significantly expanded their performance envelope. However, a critical bottleneck in the advancement of MLLMs toward deep visual reasoning is their heavy reliance on curated image-text supervision. To solve this problem, we introduce a novel framework, ``Reasoning-Rendering-Visual-Feedback'' (RRVF), that enables MLLMs to learn complex visual reasoning from only raw images. This framework builds on the ``Asymmetry of Verification'' principle, i.e., verifying the rendered output against the source image is substantially easier than performing deep visual reasoning to generate a faithful, structured representation such as code. We demonstrate that this relative ease provides an ideal reward signal for optimization via Reinforcement Learning (RL), thereby reducing reliance on image-text supervision. RRVF implements a closed-loop iterative process encompassing reasoning, rendering, and visual feedback components, enabling the model to perform complex reasoning, including self-correction through multi-turn interactions. This process is optimized end-to-end using the GRPO algorithm. Extensive evaluations are conducted on image-to-code generation across two diverse domains: data charts and web interfaces. The RRVF-trained model not only outperforms existing similarly sized open-source MLLMs and supervised fine-tuning baselines but also exhibits superior generalization. Notably, the model outperforms the more advanced MLLM used to generate visual feedback during training. Code is available at https://github.com/L-O-I/RRVF.

Large language models for mathematical reasoning are typically trained with outcome-based rewards, which credit only the final answer. In our experiments, we observe that this paradigm is highly susceptible to reward hacking, leading to a substantial overestimation of a model's reasoning ability. This is evidenced by a high incidence of false positives - solutions that reach the correct final answer through an unsound reasoning process. Through a systematic analysis with human verification, we establish a taxonomy of these failure modes, identifying patterns like Miracle Steps - abrupt jumps to a correct output without a valid preceding derivation. Probing experiments suggest a strong association between these Miracle Steps and memorization, where the model appears to recall the answer directly rather than deriving it. To mitigate this systemic issue, we introduce the Rubric Reward Model (RRM), a process-oriented reward function that evaluates the entire reasoning trajectory against problem-specific rubrics. The generative RRM provides fine-grained, calibrated rewards (0-1) that explicitly penalize logical flaws and encourage rigorous deduction. When integrated into a reinforcement learning pipeline, RRM-based training consistently outperforms outcome-only supervision across four math benchmarks. Notably, it boosts Verified Pass@1024 on AIME2024 from 26.7% to 62.6% and reduces the incidence of Miracle Steps by 71%. Our work demonstrates that rewarding the solution process is crucial for building models that are not only more accurate but also more reliable.

AI agents that execute tasks via tool calls frequently hallucinate results - fabricating tool executions, misstating output counts, or presenting inferences as facts. Recent approaches to verifiable AI inference rely on zero-knowledge proofs, which provide cryptographic guarantees but impose minutes of proving time per query, making them impractical for interactive agents. We propose NabaOS, a lightweight verification framework inspired by Indian epistemology (Nyaya Shastra), which classifies every claim in an LLM response by its epistemic source (pramana): direct tool output (pratyaksha), inference (anumana), external testimony (shabda), absence (abhava), or ungrounded opinion. Our runtime generates HMAC-signed tool execution receipts that the LLM cannot forge, then cross-references claims against these receipts to detect hallucinations in real time. We evaluate on NyayaVerifyBench, a new benchmark of 1,800 agent response scenarios across four languages with injected hallucinations of six types. NabaOS detects 94.2% of fabricated tool references, 87.6% of count misstatements, and 91.3% of false absence claims, with <15ms verification overhead per response. For deep delegation (agents performing multi-step web tasks), our cross-checking protocol catches 78.4% of URL fabrications via independent re-fetching. We compare against five approaches: zkLLM (cryptographic proofs, 180s/query), TOPLOC (locality-sensitive hashing), SPEX (sampling-based proof of execution), tensor commitments, and self-consistency checking. NabaOS achieves the best cost-latency-coverage trade-off for interactive agents: 94.2% coverage at <15ms versus zkLLM's near-perfect coverage at 180,000ms. For interactive agents, practical receipt-based verification provides better cost-benefit than cryptographic proofs, and epistemic classification gives users actionable trust signals rather than binary judgments.

We present PDE-Agents, a multi-agent ecosystem that automates the full lifecycle of partial differential equation (PDE) / finite element method (FEM) simulations through natural-language interaction. Three specialist large language model (LLM) agents (Simulation, Analytics, Database) are orchestrated via a LangGraph supervisor, with a local open-source LLM stack (Qwen3-Coder-Next, Llama 4 Scout) on dual NVIDIA RTX PRO 6000 GPUs. The architecture is model-agnostic, validated across two LLM generations. A GraphRAG knowledge base (Neo4j, 768-d vector embeddings) encodes curated material properties, known failure patterns, and prior run lineage. We report seven contributions: (i) a verification and validation (V&V) study confirming second-order spatial convergence (O(h^2)) on the heat-equation solver; (ii) a three-way ablation over 50 tasks with a frozen KG (KG On, KG Off, KG Smart), where KG Smart reaches 100% success and the highest output quality (physics 0.933 vs. 0.853 for KG Off; MPF 0.926 vs. 0.796); (iii) a novel-material experiment with three fictional materials known only to the KG, where KG Smart attains near-perfect material property fidelity (MPF = 1.00) versus 0.34 for the KG-free baseline; (iv) a failure analysis tracing KG On's three failures to budget exhaustion and timeout, establishing warm-start injection as the dominant reliability factor; (v) an adaptive framework selecting the optimal retrieval mode per task; (vi) production metrics from 1,369 runs (97.8% success, 57.6% first-try); and (vii) a 100-task KG growth experiment showing a difficulty-dependent gain, with hard-task MPF improving 8.8% while easy/novel tasks stay at ceiling. All code, models, and evaluation artifacts are released openly. Our findings show that integration pattern, not knowledge content, determines whether GraphRAG augmentation helps or hinders LLM agents.

Agentic coding harnesses - such as Agent-Skills, Superpowers, and Agent-Rigor - are increasingly deployed to augment underlying LLMs for real-world software engineering tasks. Existing benchmarks evaluate these agents almost exclusively on outcome correctness: whether generated code passes tests or resolves issues. We argue that this outcome-only lens is insufficient: an agent that arrives at a correct solution through reckless trial-and-error, without planning, verification, or graceful recovery, is fundamentally less reliable than one that follows sound engineering discipline. We introduce RigorBench, the first benchmark designed to measure process discipline in AI coding agents. RigorBench evaluates these harnesses across five pillars: Planning Fidelity, Verification Coverage, Recovery Efficiency, Abstention Quality, and Atomic Transition Integrity. A composite RigorScore aggregates these dimensions into a single metric via a weighted sum. We curate a suite of 30 tasks spanning five categories - Plan-Then-Build, Verify-Or-Die, Doom Loop Gauntlet, Know When to Fold, and Don't Break the Build-and evaluate leading harnesses in a controlled with/without experimental design against baseline coding assistants. Our results show that structured process discipline not only improves process quality scores by an average of 41% but also raises downstream outcome correctness by 17%, providing the first quantitative evidence that how agents code matters as much as what they produce. We release the full benchmark, scoring rubrics, and trajectory analysis tools as open-source artifacts.

Computer-use agents are usually improved by strengthening perception: better models for reading a screenshot and choosing where to click. Yet a screenshot is only a lossy rendering of the underlying program state, e.g., the files, application backends, and DOM that hold the task data. Different states can produce the same pixels, while code can inspect and modify that state directly. StateAct is a code-first, multi-agent harness built around this distinction. Its main agent works directly with program state by using code, while a dedicated GUI subagent handles screenshot-and-click interaction on the few subgoals that need it, just 28 of 108 tasks and 1.1% of main-agent steps. The same direct access to program state also supports verification: an independent finish gate double-checks the saved result for structural failures, e.g., output that is missing, unsaved, or written to the wrong path. To stay on track over hundreds of steps, the main agent hands subgoals to fresh subagents, keeping its own context focused. On OSWorld 2.0, StateAct lifts Claude Opus 4.8 from 20.6% to 26.9% on binary success, and from 54.8% to 61.6% on partial success, at ~ 9x lower cost per task than the same model driven by screenshots alone; a code-only variant with no GUI subagent reaches only 45.9% partial, below that screenshot-based baseline's 54.8%. In general, grounding action, verification, and memory in state, what we call state-grounding, shifts the main bottleneck from perception toward reasoning: failures depend more on what the agent thinks than on what it sees.

Any-to-any models predict any modality from any combination of others within a single network, a formulation used in multimodal vision and vision-language models, and increasingly in scientific domains such as ecology and astronomy. Existing any-to-any models are typically trained from scratch using encoder-decoder or diffusion architectures, impacting their performance and preventing them from using strong pre-trained decoder-only models as a prior. In this work, we investigate decoder-only any-to-any multimodal modeling, which treats all modalities symmetrically and supports arbitrary modalities as inputs and outputs without modality-specific heads, losses, or task pipelines. Because every modality is both an input and an output of the same model, the resulting model, named Modus, can support a range of applications, such as chained generation through intermediate modalities or cross-modal self-verification by scoring the model's own outputs with another generated modality. Modus demonstrates strong out-of-the-box performance and is competitive with specialist and multitask baselines using a single model across various benchmarks. All materials are open-sourced at https://modus-multimodal.epfl.ch/.

Linear relaxation based perturbation analysis (LiRPA) for neural networks, which computes provable linear bounds of output neurons given a certain amount of input perturbation, has become a core component in robustness verification and certified defense. The majority of LiRPA-based methods focus on simple feed-forward networks and need particular manual derivations and implementations when extended to other architectures. In this paper, we develop an automatic framework to enable perturbation analysis on any neural network structures, by generalizing existing LiRPA algorithms such as CROWN to operate on general computational graphs. The flexibility, differentiability and ease of use of our framework allow us to obtain state-of-the-art results on LiRPA based certified defense on fairly complicated networks like DenseNet, ResNeXt and Transformer that are not supported by prior works. Our framework also enables loss fusion, a technique that significantly reduces the computational complexity of LiRPA for certified defense. For the first time, we demonstrate LiRPA based certified defense on Tiny ImageNet and Downscaled ImageNet where previous approaches cannot scale to due to the relatively large number of classes. Our work also yields an open-source library for the community to apply LiRPA to areas beyond certified defense without much LiRPA expertise, e.g., we create a neural network with a probably flat optimization landscape by applying LiRPA to network parameters. Our opensource library is available at https://github.com/KaidiXu/auto_LiRPA.

We introduce a novel, general-purpose audio generation framework specifically designed for anomaly detection and localization. Unlike existing datasets that predominantly focus on industrial and machine-related sounds, our framework focuses a broader range of environments, particularly useful in real-world scenarios where only audio data are available, such as in video-derived or telephonic audio. To generate such data, we propose a new method inspired by the LLM-Modulo framework, which leverages large language models(LLMs) as world models to simulate such real-world scenarios. This tool is modular allowing a plug-and-play approach. It operates by first using LLMs to predict plausible real-world scenarios. An LLM further extracts the constituent sounds, the order and the way in which these should be merged to create coherent wholes. Much like the LLM-Modulo framework, we include rigorous verification of each output stage, ensuring the reliability of the generated data. The data produced using the framework serves as a benchmark for anomaly detection applications, potentially enhancing the performance of models trained on audio data, particularly in handling out-of-distribution cases. Our contributions thus fill a critical void in audio anomaly detection resources and provide a scalable tool for generating diverse, realistic audio data.

Over the past decade, there has been a steady advancement in enhancing face recognition algorithms leveraging advanced machine learning methods. The role of the loss function is pivotal in addressing face verification problems and playing a game-changing role. These loss functions have mainly explored variations among intra-class or inter-class separation. This research examines the natural phenomenon of facial symmetry in the face verification problem. The symmetry between the left and right hemi faces has been widely used in many research areas in recent decades. This paper adopts this simple approach judiciously by splitting the face image vertically into two halves. With the assumption that the natural phenomena of facial symmetry can enhance face verification methodology, we hypothesize that the two output embedding vectors of split faces must project close to each other in the output embedding space. Inspired by this concept, we penalize the network based on the disparity of embedding of the symmetrical pair of split faces. Symmetrical loss has the potential to minimize minor asymmetric features due to facial expression and lightning conditions, hence significantly increasing the inter-class variance among the classes and leading to more reliable face embedding. This loss function propels any network to outperform its baseline performance across all existing network architectures and configurations, enabling us to achieve SoTA results.

Large language models (LLMs) cannot retain post-deployment experience without parameter updates. We introduce DIVE, a diversity-driven framework that enables frozen LLMs to improve by evolving persistent natural-language skills from task experience and verifier feedback. These skills encode reusable reasoning procedures, verification strategies, common failure modes, and output constraints and are both executed and revised by the same underlying model without access to a teacher model. Since natural-language skill evolution is a stochastic, non-convex search process, optimizing a single skill trajectory can overfit to sampled experience or converge to a suboptimal solution. DIVE mitigates this optimization variance by independently evolving multiple skill populations from bootstrapped experience, adaptively refining them through diverse transformations, and jointly selecting a complementary set of skills. Across six mathematical and logical reasoning tasks and multiple model families, DIVE consistently outperforms existing reasoning methods, prompt-optimization approaches, skill-development frameworks, and memory-based baselines. It achieves rapid self-improvement from accumulated experience, obtaining substantially larger performance gains with fewer rollouts than parameter-based methods such as SFT and GRPO, and prompt optimization with GEPA. Further, the resulting skills transfer across model scales and families, enabling smaller models such as GPT-5-nano to match or outperform larger counterparts, i.e., GPT-5, under conventional prompting. These results establish diversity-driven skill evolution as an effective, interpretable, and parameter-free approach to LLM self-improvement.

Agentic LLM coding tools compress long session histories into compaction summaries that subsequent sessions inherit as ground truth. This paper documents a failure mode in Claude Code where partial standard output from timed-out commands (exit code 143) is recorded in compaction summaries as confirmed results, propagating false positives across sessions and model versions without re-verification. The underlying mechanism is a conflation of observation and persistence, where information that appeared in the terminal is treated as equivalent to information written to durable storage. This finding extends the analysis of LLM self-evaluation failures reported in prior work on non-determinism in LLM-as-judge grading by showing that agentic tools exhibit analogous reliability deficits when reporting on their own operational outcomes. The failure has direct implications for any workflow that relies on agentic session continuity for data processing, scientific computation, or multi-step automation.

We propose self-speculative decoding for speech-aware LLMs by using the CTC encoder as a draft model to accelerate auto-regressive (AR) inference and improve ASR accuracy. Our three-step procedure works as follows: (1) if the frame entropies of the CTC output distributions are below a threshold, the greedy CTC hypothesis is accepted as final; (2) otherwise, the CTC hypothesis is verified in a single LLM forward pass using a relaxed acceptance criterion based on token likelihoods; (3) if verification fails, AR decoding resumes from the accepted CTC prefix. Experiments on nine corpora and five languages show that this approach can simultaneously accelerate decoding and reduce WER. On the HuggingFace Open ASR benchmark with a 1B parameter LLM and 440M parameter CTC encoder, we achieve a record 5.58% WER and improve the inverse real time factor by a factor of 4.4 with only a 12% relative WER increase over AR search. Code and model weights are publicly available under a permissive license.

Visual outcomes are increasingly central to multimodal large language models, making reliable and fine-grained verification essential for scaling generalist foundation models. In this work, we investigate multimodal meta-verification, which leverages verifier-generated rationales rather than decision-only signals, and explore how to effectively incorporate meta-verification feedback into multimodal verifier training. We identify two key findings. First, symbolic verifier outputs (e.g., bounding boxes) outperform textual explanations as meta-verification rationales, enabling efficient rule-based reinforcement learning rewards while avoiding reliance on model-based rewards from auxiliary judge models. Second, decoupling reinforcement learning objectives for binary judgment and meta-verification substantially outperforms joint reward optimization, due to intrinsic differences in output structure and learning dynamics. Based on these insights, we train OmniVerifier-M1, a generalist visual verifier leveraging symbolic meta-verification and decoupled reinforcement learning. OmniVerifier-M1 provides robust verification and fine-grained error localization, and further enables M1-TTS, a verifier-driven agentic generation system achieving dynamic region-level self-correction. This approach paves the way for more reliable, interpretable, and fine-grained multimodal verification, supporting safer and more controllable foundation model deployment.

Inference-Time Scaling (ITS) has largely succeeded in verifiable domains like math and coding, where cheap verification enables scalable output selection. However, extending ITS to tasks prone to systematic failure - driven by faulty initial assumptions or unmet multidimensional constraints - typically relies on costly external solvers or brittle, model-based verifiers. Our key insight is that the intrinsic statistics of parallel sample sets, specifically length-adjusted tail entropy, provide a robust discriminative signal for solution quality without access to ground truth. Crucially, these statistics serve as a difficulty gate for adaptive compute allocation, dynamically routing problems across scaling regimes. First, Intrinsic Selection (iS) ranks candidates post-hoc, matching consensus-based algorithms across three domains and improving engineering design selection by 20% over pass@1 baselines. Second, Intrinsic Particle Filtering (iPF) generalizes this to step-level resampling, guiding generation toward high-confidence reasoning trajectories to improve pass@1 by 6.1 points on average on hard math problems. Finally, Particle Distillation (dPF) injects privileged guidance via early logit blending and KL-guided resampling, steering generation past systematic reasoning errors to satisfy expert rubrics, yielding up to 26.5% gains on complex clinical responses. Our pipeline applies seamlessly across broad-purpose, domain-specialized, and multimodal architectures, successfully extending ITS to open-ended domains without requiring trained reward models or exact ground-truth verification.

On-policy self-distillation (OPSD) trains a large language model using supervision from a teacher instantiated from the same model as the student. The teacher is conditioned on privileged information (PI), such as verified solutions. The student, which does not observe PI, learns from the teacher's next-token distributions along its own sampled responses. However, PI can bias supervision toward shortcut reasoning with limited verification or reconsideration, accompanied by a sharp drop in the entropy of the output distribution. To address this challenge, we introduce self-distillation with verbal regularization (VRSD), which uses system prompts to regulate how the teacher uses PI, thereby encouraging rethinking and exploration to counteract premature commitment. Theoretically, we model prompting as attenuating the influence of PI on the teacher distribution and derive conditions for entropy preservation. Across three models and four tasks, VRSD improves Pass@1 over OPSD in 11 of 12 model-task settings, by 3.9 percentage points on average, while generally maintaining higher token entropy.

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning steps. In this work, we introduce Prove, a simple yet effective framework that leverages translated programs derived from natural language solutions as a verification mechanism to filter out potentially incorrect reasoning paths before aggregating final answers. Unlike vanilla majority voting, our approach filters out solutions whose corresponding program output is inconsistent with the generated solution, aggregating only those that pass verification. We conducted extensive experiments using 13 open-source LLMs from various model families and sizes, ranging from 0.5B to 13B parameters, across eight mathematical benchmarks. Our results show that Prove consistently outperforms vanilla majority voting as a heuristic for solving mathematical reasoning tasks across all model sizes and datasets, achieving improvements of up to 18% on GSM8K and 8% on MATH-500. Our codes are available at https://github.com/declare-lab/prove.

We present a novel inference scheme, self-speculative decoding, for accelerating Large Language Models (LLMs) without the need for an auxiliary model. This approach is characterized by a two-stage process: drafting and verification. The drafting stage generates draft tokens at a slightly lower quality but more quickly, which is achieved by selectively skipping certain intermediate layers during drafting Subsequently, the verification stage employs the original LLM to validate those draft output tokens in one forward pass. This process ensures the final output remains identical to that produced by the unaltered LLM, thereby maintaining output quality. The proposed method requires no additional neural network training and no extra memory footprint, making it a plug-and-play and cost-effective solution for inference acceleration. Benchmarks with LLaMA-2 and its fine-tuned models demonstrated a speedup up to 1.73times.

Text-to-video generation models have shown significant progress in the recent years. However, they still struggle with generating complex dynamic scenes based on compositional text prompts, such as attribute binding for multiple objects, temporal dynamics associated with different objects, and interactions between objects. Our key motivation is that complex tasks can be decomposed into simpler ones, each handled by a role-specialized MLLM agent. Multiple agents can collaborate together to achieve collective intelligence for complex goals. We propose GenMAC, an iterative, multi-agent framework that enables compositional text-to-video generation. The collaborative workflow includes three stages: Design, Generation, and Redesign, with an iterative loop between the Generation and Redesign stages to progressively verify and refine the generated videos. The Redesign stage is the most challenging stage that aims to verify the generated videos, suggest corrections, and redesign the text prompts, frame-wise layouts, and guidance scales for the next iteration of generation. To avoid hallucination of a single MLLM agent, we decompose this stage to four sequentially-executed MLLM-based agents: verification agent, suggestion agent, correction agent, and output structuring agent. Furthermore, to tackle diverse scenarios of compositional text-to-video generation, we design a self-routing mechanism to adaptively select the proper correction agent from a collection of correction agents each specialized for one scenario. Extensive experiments demonstrate the effectiveness of GenMAC, achieving state-of-the art performance in compositional text-to-video generation.

Advancing code reasoning in large language models (LLMs) is fundamentally limited by the scarcity of high-difficulty datasets, especially those with verifiable input-output test cases necessary for rigorous solution validation at scale. We introduce rStar-Coder, which significantly improves LLM code reasoning capabilities by constructing a large-scale, verified dataset of 418K competition-level code problems, 580K long-reasoning solutions along with rich test cases of varying difficulty. This is achieved through three core contributions: (1) we curate competitive programming code problems and oracle solutions to synthesize new, solvable problems; (2) we introduce a reliable input-output test case synthesis pipeline that decouples the generation into a three-step input generation method and a mutual verification mechanism for effective output labeling; (3) we augment problems with high-quality, test-case-verified long-reasoning solutions. Extensive experiments on Qwen models (1.5B-14B) across various code reasoning benchmarks demonstrate the superiority of rStar-Coder dataset, achieving leading performance comparable to frontier reasoning LLMs with much smaller model sizes. On LiveCodeBench, rStar-Coder improves Qwen2.5-7B from 17.4% to an impressive 57.3%, and Qwen2.5-14B from 23.3% to 62.5%, surpassing o3-mini (low) by3.1%. On the more challenging USA Computing Olympiad, our 7B model achieves an average pass@1 accuracy of 16.15%, outperforming the frontier-level QWQ-32B. Code and the dataset will be released at https://github.com/microsoft/rStar.

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

Assessing ways in which Language Models can reduce their hallucinations and improve the outputs' quality is crucial to ensure their large-scale use. However, methods such as fine-tuning on domain-specific data or the training of a separate ad hoc verifier require demanding computational resources (not feasible for many user applications) and constrain the models to specific fields of knowledge. In this thesis, we propose a dialectic pipeline that preserves LLMs' generalization abilities while improving the quality of its answer via self-dialogue, enabling it to reflect upon and correct tentative wrong answers. We experimented with different pipeline settings, testing our proposed method on different datasets and on different families of models. All the pipeline stages are enriched with the relevant context (in an oracle-RAG setting) and a study on the impact of its summarization or its filtering is conducted. We find that our proposed dialectic pipeline is able to outperform by significative margins the standard model answers and that it consistently achieves higher performances than Chain-of-Thought only prompting.

We present SPL (Structured Prompt Language), a declarative language that composes deterministic and probabilistic computation modes in a single specification. While existing frameworks separate these -- orchestration systems (AutoGen, CrewAI, LangGraph) for LLM calls, symbolic tools (SymPy, SageMath, Lean) for computation -- SPL unifies them. It provides GENERATE/EVALUATE for probabilistic computation and SOLVE/ASSERT for deterministic computation, sharing syntax, variable bindings, and runtime routing. A .spl specification runs unchanged across local nodes (Ollama), cloud APIs (OpenRouter, Anthropic), and distributed grids (Momagrid), with model and verifier selection deferred to invocation time. We validate SPL through an extensive 78-recipe cookbook and a controlled 1,200-run experiment (10 models x 20 problems x 2 arms x 3 repetitions; the 20 problems span 6 difficulty tiers). The solver arm achieves 82-93% machine-verified correctness (sonnet-4-6: 85%, gemma4:e2b: 93%) while the LLM-only arm measures output production without mathematical verification, making the comparison one of verified correctness against unverified fluency. A backend difficulty gradient emerges (SymPy 78%, Sage 54%), and the dominant failure mode is solver_error (kernel-rejected expressions), not format non-compliance.

Experimental studies of generative AI in education mostly report average effects, yet field evidence shows that AI can narrow attainment gaps or widen them. We argue that the direction depends on the judgement burden, the expertise a learner must supply to screen AI output before learning from it, and that expert verification before release moves this burden from students to an accountable tutor. We test the argument in a two-cohort difference-in-differences design in which one half of a compulsory firstyear university economics course received AI-generated podcasts, FAQs and quiz-based study guides, produced with a source-grounded model and checked by a named graduate teaching assistant (170 students; 340 examination marks). Access was associated with a 2.34-mark advantage on a 50-mark component. The share of marks below the upper-second classification boundary fell by 24.7 percentage points relative to the counterfactual, effects were significant at every threshold from 23 to 31 marks and at none above, and roughly three-quarters of the average originated in the bottom quintile. The threshold estimate is robust to removing the lowest-scoring students from the pre-intervention cohort; the average effect is not. Interviews and feedback from 36 students indicate that the verification label gave students a reason to engage with AI-generated material without ending their scrutiny of it. Evaluations of AI learning resources that report only mean effects cannot detect whether the students the resources are meant to help are the ones who gain.

Open-ended generation tasks require outputs to satisfy diverse and often implicit task-specific evaluation rubrics. The sheer number of relevant rubrics leads to prohibitively high verification costs and incomplete assessments of a response, making reinforcement learning (RL) post-training with rubric-based rewards difficult to scale. This problem is exacerbated by the fact that often the best way to combine these rubrics into one single reward is also highly prompt-specific. We propose Reinforcement Learning with Adversarial Critic (RLAC), a post-training approach that addresses these challenges via dynamic rubric verification. Our approach employs a large language model (LLM) as a critic that dynamically identifies only the most likely failure modes (e.g., a factual error or unhandled edge case), which are then verified by an external validator to optimize both generator and critic jointly. By training both the generator and the critic, this game enhances the critic's error detection and the generator's output quality while reducing required verifications. Our experiments demonstrate that RLAC improves factual accuracy in text generation and correctness in code generation, while also outperforming exhaustive verification and reward model methods. We show that dynamic critics are more effective than fixed critics, showcasing the potential of RLAC for scaling RL post-training to free-form generation tasks.

Reinforcement learning (RL) has become a representative post-training paradigm for LLMs, enabling strong reasoning and agentic capabilities. However, rollout generation remains a dominant latency bottleneck because autoregressive sampling decodes responses sequentially and a small number of long-tailed generations often determine completion time. Speculative decoding (SD) offers a natural way to address this bottleneck, as it is a well-established technique for serving fixed LLMs that reduces latency by rapidly drafting tokens and accepting them through parallel verification while preserving the target-model distribution. However, its practical speedups do not directly carry over to RL rollouts: (i) the evolving target policy makes any fixed drafter increasingly mismatched with the policy's output distribution; and (ii) active batch sizes shrink throughout rollout decoding, shifting decoding from compute-bound to memory-bound regimes where parallel verification can exploit underutilized compute. Therefore, accelerating RL rollouts requires both a drafter that remains effective under long, high-temperature generations from an evolving policy and system-aware use of SD that avoids compute-bound regimes. We present EfficientRollout, a system-aware self-SD framework designed to address this gap for RL rollouts. EfficientRollout induces a quantized drafter from the target model (i.e. self-speculative decoding), keeping it coupled to the evolving policy without separate drafter pretraining or online adaptation. It further coordinates a system-aware SD toggle policy with acceptance-aware draft-length adaptation, enabling speculation only in beneficial regimes while matching the drafting budget to evolving drafter quality. EfficientRollout reduces rollout and end-to-end latency by up to 19.6% and 12.7%, respectively, over an accelerated AR rollout baseline, while preserving final model quality.

We introduce {rm C{small LEVER}}, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, {rm C{small LEVER}} avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use {rm C{small LEVER}} to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).

Having reliable specifications is an unavoidable challenge in achieving verifiable correctness, robustness, and interpretability of AI systems. Existing specifications for neural networks are in the paradigm of data as specification. That is, the local neighborhood centering around a reference input is considered to be correct (or robust). While existing specifications contribute to verifying adversarial robustness, a significant problem in many research domains, our empirical study shows that those verified regions are somewhat tight, and thus fail to allow verification of test set inputs, making them impractical for some real-world applications. To this end, we propose a new family of specifications called neural representation as specification, which uses the intrinsic information of neural networks - neural activation patterns (NAPs), rather than input data to specify the correctness and/or robustness of neural network predictions. We present a simple statistical approach to mining neural activation patterns. To show the effectiveness of discovered NAPs, we formally verify several important properties, such as various types of misclassifications will never happen for a given NAP, and there is no ambiguity between different NAPs. We show that by using NAP, we can verify a significant region of the input space, while still recalling 84% of the data on MNIST. Moreover, we can push the verifiable bound to 10 times larger on the CIFAR10 benchmark. Thus, we argue that NAPs can potentially be used as a more reliable and extensible specification for neural network verification.

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

Deployed language models must produce outputs that are both correct and format-compliant. We study this structured-output reliability gap using two mathematical benchmarks -- GSM8K and MATH -- as a controlled testbed: ground truth is unambiguous and the output contract is strict (JSON with required fields). We evaluate three 7-9B models under five prompting strategies and report output accuracy -- the joint event of mathematical correctness and valid JSON structure -- as the primary metric. A systematic format failure emerges: NAIVE prompting (no system prompt) achieves up to 85% task accuracy on GSM8K but 0% output accuracy across all models and datasets. REFERENCE prompting (a minimal hand-written JSON format prompt) fares little better, yielding 0% output accuracy for two of four models tested. Constrained decoding enforces syntactic validity but incurs 3.6x-8.2x latency overhead and in several settings degrades task performance substantially. To overcome this limitation, we developed AloLab, an iterative system-prompt optimizer (meta-agent: Claude Sonnet 4.5) requiring only black-box API access to the target model; it reaches 84-87% output accuracy on GSM8K and 34-40% on MATH across five independent runs per model, with 29/30 paired McNemar comparisons against the best static prompt significant at p < 0.05, at near-NAIVE inference latency and without model fine-tuning. The same format failure extends to GPT-4o (OpenAI, 2024), a proprietary closed-source model: REFERENCE achieves 0% output accuracy due to systematic markdown-fence wrapping, while AloLab reaches 95.2% [94.8, 95.6]. An ablation replacing the Sonnet 4.5 meta-agent with Claude 3 Haiku reduces mean output accuracy to 61.0% and increases run-to-run standard deviation from <1 pp to 21.8 pp, confirming that meta-agent capability is a primary driver of optimization quality.

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

Factual hallucination remains a central challenge for large language models (LLMs). Existing mitigation approaches primarily rely on either external post-hoc verification or mapping uncertainty directly to abstention during fine-tuning, often resulting in overly conservative behavior. We propose VeriFY, a training-time framework that teaches LLMs to reason about factual uncertainty through consistency-based self-verification. VeriFY augments training with structured verification traces that guide the model to produce an initial answer, generate and answer a probing verification query, issue a consistency judgment, and then decide whether to answer or abstain. To address the risk of reinforcing hallucinated content when training on augmented traces, we introduce a stage-level loss masking approach that excludes hallucinated answer stages from the training objective while preserving supervision over verification behavior. Across multiple model families and scales, VeriFY reduces factual hallucination rates by 9.7 to 53.3 percent, with only modest reductions in recall (0.4 to 5.7 percent), and generalizes across datasets when trained on a single source. The source code, training data, and trained model checkpoints will be released upon acceptance.

Without accurate transcription of numerical data in scientific documents, a scientist cannot draw accurate conclusions. Unfortunately, the process of copying numerical data from one paper to another is prone to human error. In this paper, we propose to meet this challenge through the novel task of automatic table verification (AutoTV), in which the objective is to verify the accuracy of numerical data in tables by cross-referencing cited sources. To support this task, we propose a new benchmark, arXiVeri, which comprises tabular data drawn from open-access academic papers on arXiv. We introduce metrics to evaluate the performance of a table verifier in two key areas: (i) table matching, which aims to identify the source table in a cited document that corresponds to a target table, and (ii) cell matching, which aims to locate shared cells between a target and source table and identify their row and column indices accurately. By leveraging the flexible capabilities of modern large language models (LLMs), we propose simple baselines for table verification. Our findings highlight the complexity of this task, even for state-of-the-art LLMs like OpenAI's GPT-4. The code and benchmark will be made publicly available.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's uses of shortcuts and wrong reasoning while the later poses challenges in accommodating alternative solutions. In this work, we seek to use symbolic programs as a means for automated evaluation if a model can consistently produce correct final answers across various inputs to the program. We begin by extracting programs for popular math datasets (GSM8K and MATH) using GPT4-o. For those executable programs verified using the original input-output pairs, they are found to encapsulate the proper reasoning required to solve the original text questions. We then prompt GPT4-o to generate new questions using alternative input-output pairs based the extracted program. We apply the resulting datasets to evaluate a collection of LLMs. In our experiments, we observe significant accuracy drops using our proposed evaluation compared with original static examples, suggesting the fragility of math reasoning in state-of-the-art LLMs.

Text-to-image models increasingly generate readable Chinese text that still contains local rendering defects, such as a character with an extra or missing stroke or a malformed component. Such errors are invisible to OCR and vision-language models, which are trained for recognition and are therefore invariant to the very structural deviations that define a rendering error. We formalize text rendering verification as a target-conditioned problem: given a target character and an image crop, decide whether the crop is a correct rendering of that character. Our verifier TEXTVERIFIER feeds the text tower a character's Ideographic Description Sequence (IDS) rather than a single-character symbol, and is trained on 12.7M crop-IDS pairs plus label-free "same-character, different-quality" hard pairs sampled from the training trajectory of a text-region inpainting model. To evaluate this ability we build TEXTRENDERBENCH-ZH, the first per-character benchmark for generated Chinese text, annotating position, identity, and correctness for 7,358 characters. TEXTVERIFIER reaches an F1 of 0.844, far above OCR confidence (0.526), a general VLM (0.329), and TextPecker (0.590). Used as a per-character reward for Flow-GRPO post-training, it further reduces rendering errors, showing that its score can both detect and correct errors.

Recently, given the docstring for the target problem and the target function signature, large language models (LLMs) have been used not only to generate source code, but also to generate test cases, consisting of test inputs and assertions (e.g., in the form of checking an actual output against the expected output). However, as shown by our empirical study on assertions generated by four LLMs for the HumanEval benchmark, over 62% of the generated assertions are incorrect (i.e., failed on the ground-truth problem solution). To detect incorrect assertions (given the docstring and the target function signature along with a sample of example inputs and outputs), in this paper, we propose a new approach named DeCon to effectively detect incorrect assertions via LLM-generated postconditions for the target problem (a postcondition is a predicate that must always be true just after the execution of the ground-truth problem solution). Our approach requires a small set of I/O examples (i.e., a sample of example inputs and outputs) for the target problem (e.g., the I/O examples included in the docstring for a target problem in HumanEval). We use the given I/O examples to filter out those LLM-generated postconditions that are violated by at least one given I/O example. We then use the remaining postconditions to detect incorrect assertions as those assertions that violate at least one remaining postcondition. Experimental results show that DeCon can detect averagely more than 64% (63% and 65.5% detected by GPT-3.5 and GPT-4, respectively) incorrect assertions generated by four state-of-the-art LLMs, and DeCon can also improve the effectiveness of these LLMs in code generation by 4% in terms of Pass@1. In addition, although DeCon might filter out correct assertions, the fault-finding ability of the remaining correct assertions decreases only slightly.

Recent advances have shown that scaling test-time computation enables large language models (LLMs) to solve increasingly complex problems across diverse domains. One effective paradigm for test-time scaling (TTS) involves LLM generators producing multiple solution candidates, with LLM verifiers assessing the correctness of these candidates without reference answers. In this paper, we study generative verifiers, which perform verification by generating chain-of-thought (CoT) reasoning followed by a binary verdict. We systematically analyze verification dynamics across three dimensions - problem difficulty, generator capability, and verifier generation capability - with empirical studies on 12 benchmarks across mathematical reasoning, knowledge, and natural language reasoning tasks using 14 open-source models (2B to 72B parameter range) and GPT-4o. Our experiments reveal three key findings about verification effectiveness: (1) Easy problems allow verifiers to more reliably certify correct responses; (2) Weak generators produce errors that are easier to detect than strong generators; (3) Verification ability is generally correlated with the verifier's own problem-solving capability, but this relationship varies with problem difficulty. These findings reveal opportunities to optimize basic verification strategies in TTS applications. First, given the same verifier, some weak generators can nearly match stronger ones in post-verification TTS performance (e.g., the Gemma2-9B to Gemma2-27B performance gap shrinks by 75.5%). Second, we identify cases where strong verifiers offer limited advantage over weak ones, as both fail to provide meaningful verification gains, suggesting that verifier scaling alone cannot overcome fundamental verification challenges.

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

Retrieval-augmented generation (RAG) grounds answers in retrieved passages, yet relevance does not guarantee sufficiency: a topical passage may still fail to justify the answer. We study evidence sufficiency verification for selective RAG answering, in which a verifier receives a question, a candidate answer, and retrieved evidence and decides whether the evidence supports, refutes, or is insufficient for the answer, answering only when support is established. We present SURE-RAG, an aggregation protocol that treats evidence sufficiency as a set-level property: missing hops and unresolved conflicts cannot be detected by scoring passages independently. A shared claim-evidence verifier produces a local relation distribution for each (claim, passage) pair, which SURE-RAG aggregates into four interpretable answer-level feature blocks (coverage, relation strength, uncertainty, and retrieval), producing a three-way decision and an auditable selective score. We evaluate on HotpotQA-RAG v3, a controlled multi-hop benchmark, under an artifact-aware protocol (shortcut baselines, counterfactual swaps, no-oracle checks, and GPT-4o audits). Calibrated SURE-RAG attains 0.9075 Macro-F1 (raw 0.8951 +/- 0.0069), well above DeBERTa mean-pooling (0.6516) and a GPT-4o judge (0.7284), and on par with a strong concat cross-encoder (0.8888 +/- 0.0109) while remaining fully auditable. At 30% coverage, risk falls from 0.2588 to 0.1642, a 37% relative reduction. As a boundary-mapping experiment, we contrast SURE-RAG with GPT-4o on HaluBench unsafe detection: the ranking reverses (0.3343 vs. 0.7389 unsafe-F1), indicating that controlled sufficiency verification and natural hallucination detection are distinct problems.

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

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

Language models (LMs) are widely used by an increasing number of users, underscoring the challenge of maintaining factuality across a broad range of topics. We first present VERIFY (Verification and Evidence RetrIeval for FactualitY evaluation), a pipeline to evaluate LMs' factuality in real-world user interactions. VERIFY considers the verifiability of LM-generated content and categorizes content units as supported, unsupported, or undecidable based on the retrieved evidence from the Web. Importantly, factuality judgment by VERIFY correlates better with human evaluations than existing methods. Using VERIFY, we identify "hallucination prompts" across diverse topics, i.e., those eliciting the highest rates of incorrect and inconclusive LM responses. These prompts form FactBench, a dataset of 1K prompts across 150 fine-grained topics. Our dataset captures emerging factuality challenges in real-world LM interactions and can be regularly updated with new prompts. We benchmark widely-used LMs from GPT, Gemini, and Llama3.1 family on FactBench, yielding the following key findings: (i) Proprietary models exhibit better factuality, with performance declining from Easy to Hard hallucination prompts. (ii) Llama3.1-405B-Instruct shows comparable or lower factual accuracy than Llama3.1-70B-Instruct across all evaluation methods due to its higher subjectivity that leads to more content labeled as undecidable. (iii) Gemini1.5-Pro shows a significantly higher refusal rate, with over-refusal in 25% of cases. Our code and data are publicly available at https://huggingface.co/spaces/launch/factbench.

We consider the problem of language model inversion: given outputs of a language model, we seek to extract the prompt that generated these outputs. We develop a new black-box method, output2prompt, that learns to extract prompts without access to the model's logits and without adversarial or jailbreaking queries. In contrast to previous work, output2prompt only needs outputs of normal user queries. To improve memory efficiency, output2prompt employs a new sparse encoding techique. We measure the efficacy of output2prompt on a variety of user and system prompts and demonstrate zero-shot transferability across different LLMs.

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

Verification for retrieval-augmented generation usually scores each retrieved chunk and drops the ones that fail. We show this cannot work for multi-hop questions, and show what does. Per-chunk scoring assumes one chunk is a sufficient premise for the answer. Multi-hop questions are built so that none is, and the paragraph carrying the answer is the one the question does not name. Entailment scoring reaches 0.643, 0.523 and 0.560 AUC on HotpotQA, 2WikiMultihopQA and MuSiQue, against 0.951 on single-hop SQuAD. Seven controls rule out model capacity, premise length, hypothesis template, decision threshold, retriever, answer-matching criterion and prompt. End to end across three datasets, three generator sizes and two prompts, per-chunk gating is significantly worse than not filtering at all in every cell, and its penalty grows with generator capability. The repair is to condition verification on the decomposed sub-question rather than the original query. Using MuSiQue's gold decomposition, entailment on a later hop rises from 0.546, which is chance, to 0.840, a paired lift of +0.355 with a bootstrap interval of [0.331, 0.382]. An off-the-shelf Qwen2.5-7B decomposer, given the question and the top retrieved paragraph, reaches 0.637 and captures 31% of that ceiling; decomposing without retrieval reaches 0.533, below the original question. Iterative retrieval systems already produce such decompositions and discard them before verifying.

Using large language models (LLMs) to generate source code from natural language prompts is a popular and promising idea with a wide range of applications. One of its limitations is that the generated code can be faulty at times, often in a subtle way, despite being presented to the user as correct. In this paper, we explore ways in which formal methods can assist with increasing the quality of code generated by an LLM. Instead of emitting code in a target language directly, we propose that the user guides the LLM to first generate an opaque intermediate representation, in the verification-aware language Dafny, that can be automatically validated for correctness against agreed on specifications. The correct Dafny program is then compiled to the target language and returned to the user. All user-system interactions throughout the procedure occur via natural language; Dafny code is never exposed. We describe our current prototype and report on its performance on the HumanEval Python code generation benchmarks.

Integer overflow accounts for one of the major source of bugs in software. Verification systems typically assume a well defined underlying semantics for various integer operations and do not explicitly check for integer overflow in programs. In this paper we present a specification mechanism for expressing integer overflow. We develop an automated procedure for integer overflow checking during program verification. We have implemented a prototype integer overflow checker and tested it on a benchmark consisting of already verified programs (over 14k LOC). We have found 43 bugs in these programs due to integer overflow.

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

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

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

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

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

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

Large language models are trained on vast amounts of internet data, prompting concerns and speculation that they have memorized public benchmarks. Going from speculation to proof of contamination is challenging, as the pretraining data used by proprietary models are often not publicly accessible. We show that it is possible to provide provable guarantees of test set contamination in language models without access to pretraining data or model weights. Our approach leverages the fact that when there is no data contamination, all orderings of an exchangeable benchmark should be equally likely. In contrast, the tendency for language models to memorize example order means that a contaminated language model will find certain canonical orderings to be much more likely than others. Our test flags potential contamination whenever the likelihood of a canonically ordered benchmark dataset is significantly higher than the likelihood after shuffling the examples. We demonstrate that our procedure is sensitive enough to reliably prove test set contamination in challenging situations, including models as small as 1.4 billion parameters, on small test sets of only 1000 examples, and datasets that appear only a few times in the pretraining corpus. Using our test, we audit five popular publicly accessible language models for test set contamination and find little evidence for pervasive contamination.

It is important that consumers and regulators can verify the provenance of large neural models to evaluate their capabilities and risks. We introduce the concept of a "Proof-of-Training-Data": any protocol that allows a model trainer to convince a Verifier of the training data that produced a set of model weights. Such protocols could verify the amount and kind of data and compute used to train the model, including whether it was trained on specific harmful or beneficial data sources. We explore efficient verification strategies for Proof-of-Training-Data that are compatible with most current large-model training procedures. These include a method for the model-trainer to verifiably pre-commit to a random seed used in training, and a method that exploits models' tendency to temporarily overfit to training data in order to detect whether a given data-point was included in training. We show experimentally that our verification procedures can catch a wide variety of attacks, including all known attacks from the Proof-of-Learning literature.

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.

Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most proofs, particularly those written by AI systems, have neither property, and translating them into formal languages remains challenging in many frontier math settings. We propose Pseudo-Formalization (PF), a proof format that captures the modularity and precision of formal proofs while retaining the flexibility of natural language. A Pseudo-Formal proof is decomposed into self-contained modules, each stating its premises, conclusion, and proof in natural language. To verify the correctness of a regular natural language proof, an LLM translates it to Pseudo-Formal and then verifies each module independently, an algorithm we call Block Verification (BV). We evaluate PF+BV on two benchmarks spanning olympiad and research-level mathematics, where it pareto-dominates LLM-as-judge baselines on error-finding precision and recall. To support future work, we release our research-level proof verification benchmark ArxivMathGradingBench.

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

Multi-path speculative decoding accelerates lossless sampling from a target model by using a cheaper draft model to generate a draft tree of tokens, and then applies a verification algorithm that accepts a subset of these. While prior work has proposed various verification algorithms for i.i.d rollouts, their relative performance under matched settings remains unclear. In this work, we firstly present a systematic evaluation of verification strategies across model families, tasks, and sampling regimes, and find that Traversal Verification dominates consistently, with OT-based methods lagging far behind. Our analysis uncovers that this occurs because OT-based methods achieve high multi-token acceptance near the root of the draft tree, while multi-token gains are most impactful deeper in the draft tree, where draft and target distributions diverge. Based on this insight, we propose delayed tree expansion, which drafts a partial single path, delaying the i.i.d. branching point. We show that delayed tree expansion preserves the target distribution and improves on root-node i.i.d rollouts. Further, we develop a dynamic neural selector that estimates the expected block efficiency of optimal-transport-based verification methods from draft and target features, enabling context-dependent expansion decisions. Our neural selector allows OT-based methods like SpecInfer to outperform Traversal Verification for the first time, achieving 5% higher average throughput across a wide range of models, datasets, and sampling settings.

Verified proof edits offer a natural source of supervision for improving language-model-generated Lean proofs. Yet verification establishes that an edit is correct, not that its training signal is free of search artifacts. We introduce LeanPolish, a symbolic Lean 4 pipeline that releases 33,402 accepted local edits and 65,596 same-state failed attempts, and use it to study what models learn from this supervision. First-success search admits a goal-independent rule with perfect ranking accuracy; teacher-selected evaluation sites also reward trivial deletions. Continuing menu evaluation beyond the first success removes the ordering shortcut: a trained ranker selects the best candidate on 70.1% of evaluated held-out states, versus 36.9% for the strongest frozen baseline. For compression, iterating the symbolic pass raises miniF2F savings from 19.7% to 27.5%, exceeding the neural hybrids we test there. Verified neural editing helps on other proof sources, but matched frozen-model controls show that its gains need not come from training. The supervision does improve whole-proof rewriting: fine-tuning raises verified token reduction from 2.8% to 5.5% on 19 PutnamBench proofs. Together, the released edits, complete candidate pools, and controlled evaluations separate learning to imitate a search policy from improving on that search. They provide a reproducible basis for studying proof improvement while keeping correctness, compression, and edit policy distinct.

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

Large language models (LLMs) transfer well to new tasks out-of-the-box simply given a natural language prompt that demonstrates how to perform the task and no additional training. Prompting is a brittle process wherein small modifications to the prompt can cause large variations in the model predictions, and therefore significant effort is dedicated towards designing a painstakingly "perfect prompt" for a task. To mitigate the high degree of effort involved in prompt-design, we instead ask whether producing multiple effective, yet imperfect, prompts and aggregating them can lead to a high quality prompting strategy. Our observations motivate our proposed prompting method, ASK ME ANYTHING (AMA). We first develop an understanding of the effective prompt formats, finding that question-answering (QA) prompts, which encourage open-ended generation ("Who went to the park?") tend to outperform those that restrict the model outputs ("John went to the park. Output True or False."). Our approach recursively uses the LLM itself to transform task inputs to the effective QA format. We apply the collected prompts to obtain several noisy votes for the input's true label. We find that the prompts can have very different accuracies and complex dependencies and thus propose to use weak supervision, a procedure for combining the noisy predictions, to produce the final predictions for the inputs. We evaluate AMA across open-source model families (e.g., EleutherAI, BLOOM, OPT, and T0) and model sizes (125M-175B parameters), demonstrating an average performance lift of 10.2% over the few-shot baseline. This simple strategy enables the open-source GPT-J-6B model to match and exceed the performance of few-shot GPT3-175B on 15 of 20 popular benchmarks. Averaged across these tasks, the GPT-J-6B model outperforms few-shot GPT3-175B. We release our code here: https://github.com/HazyResearch/ama_prompting