Daily Papers

Omni models can describe video content, but can they locate events in time, preserve event order, and judge audio-visual synchronization? We introduce AVTrace (Audio-Visual Temporal Reasoning Assessment and Capability Evaluation), a silver-standard diagnostic suite spanning onset and span grounding, synchronization, next-step prediction, cross-modal localization, chain parsing, and event-conditioned comprehension. It contains 34,114 training examples and category-balanced development and test splits of 3,500 and 7,000 examples. We evaluate five open omni models under their respective input configurations using reference-blind response normalization followed by deterministic scoring. All five off-the-shelf systems score below the test split's majority-label baseline of 0.556 on synchronization verification, and obtain low scores on chain parsing and event-conditioned grounding and comprehension. Development-set perturbations reveal task-dependent sensitivity in Qwen3-Omni-30B to modality removal and changes in visual input processing, without isolating their underlying causes. Parameter-efficient temporal post-training improves Gemma4-E4B-it on several benchmark metrics. On three external image benchmarks, task metrics change modestly, including some degradations, while teacher-forcing perplexity decreases. Together, these findings show that semantic reference-text overlap should not be treated as a proxy for temporal localization, and that AVTrace can identify task-specific weaknesses while providing a testbed for temporal post-training.

Automatic video dubbing (AVD) requires temporally aligned speech, transcripts, and video, yet existing corpora vary in audio quality, transcription reliability, and speaking-face visibility. We introduce VoxDub, a bilingual lip-synchronized audio-visual dataset containing 766K clips and approximately 1.58K hours of in-the-wild Chinese and English recordings, covering varied speakers, scenes, speaking styles, and linguistic content. Its curation pipeline combines speech-centered segmentation with dual-ASR transcription checking, speech quality filtering, face visibility checks, and lip-speech synchronization verification. Text-to-speech (TTS) experiments show that training on VoxDub yields lower word error rates and higher speaker similarity than training on the compared audio-visual corpora, LRS3 and CN-CVS. AVD experiments show broadly comparable speech quality and subjective synchronization. These results support the utility of VoxDub for TTS and AVD training. More details are available on the project website (https://voxdub-dataset.github.io/VoxDub/).

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.

Spatiotemporal neural dynamics and oscillatory synchronization are widely implicated in biological information processing and have been hypothesized to support flexible coordination such as feature binding. By contrast, most deep learning architectures represent and propagate information through activation values, neglecting the joint dynamics of rate and phase. In this work, we introduce Kuramoto oscillatory Phase Encoding (KoPE) as an additional, evolving phase state to Vision Transformers, incorporating a neuro-inspired synchronization mechanism to advance learning efficiency. We show that KoPE can improve training, parameter, and data efficiency of vision models through synchronization-enhanced structure learning. Moreover, KoPE benefits tasks requiring structured understanding, including semantic and panoptic segmentation, representation alignment with language, and few-shot abstract visual reasoning (ARC-AGI). Theoretical analysis and empirical verification further suggest that KoPE can accelerate attention concentration for learning efficiency. These results indicate that synchronization can serve as a scalable, neuro-inspired mechanism for advancing state-of-the-art neural network models.

Existing LLM-driven knowledge graph (KG) construction methods predominantly employ stateless batch processing pipelines, exhibiting structural deficiencies in cross-chunk semantic relation capture, entity disambiguation, and construction process interpretability. These limitations undermine KG quality, retrieval precision, and deployment trust in high-stakes domains. We propose RAGA (Reading And Graph-building Agent), an LLM-based autonomous KG construction and retrieval fusion framework. RAGA provides an atomic toolset supporting full KG lifecycle CRUD operations and embeds a Read-Search-Verify-Construct cognitive constraint into a ReAct tool loop. A KG-vector synchronization mechanism enables hybrid symbolic-vector retrieval, while evidence-anchored verification links every knowledge entry to its source text for auditable provenance. Preliminary experiments on a subset of the QASPER scientific QA dataset indicate that RAGA's fusion retrieval outperforms zero-shot baselines, with KG integration providing measurable gains in both answer and evidence quality. The framework design and experimental baseline serve as a reference for agent-driven autonomous KG construction.

We performed a billion locality sensitive hash comparisons between artificially generated data samples to answer the critical question - can we verify the "correctness" of generative AI output in a non-deterministic, trustless, decentralized network? We generate millions of data samples from a variety of open source diffusion and large language models and describe the procedures and trade-offs between generating more verses less deterministic output in a heterogenous, stochastic network. Further, we analyze the outputs to provide empirical evidence of different parameterizations of tolerance and error bounds for verification. Finally, given that we have the generated an enormous amount of simulated data, we also release a new training dataset called ImageNet-Gen for use in augmenting existing training pipelines. For our results, we show that with a majority vote between three independent verifiers, we can detect image generated perceptual collisions in generated AI with over 99.89% probability and less than 0.0267% chance of intra-class collision. For large language models (LLMs), we are able to gain 100% consensus using greedy methods or n-way beam searches to generate consensus demonstrated on different LLMs. In the context of generative AI training, we pinpoint and minimize the major sources of stochasticity and present gossip and synchronization training techniques for verifiability. Thus, this work provides a practical, solid foundation for AI verification and consensus for the minimization of trust in a decentralized network.

Most existing datasets for speaker identification contain samples obtained under quite constrained conditions, and are usually hand-annotated, hence limited in size. The goal of this paper is to generate a large scale text-independent speaker identification dataset collected 'in the wild'. We make two contributions. First, we propose a fully automated pipeline based on computer vision techniques to create the dataset from open-source media. Our pipeline involves obtaining videos from YouTube; performing active speaker verification using a two-stream synchronization Convolutional Neural Network (CNN), and confirming the identity of the speaker using CNN based facial recognition. We use this pipeline to curate VoxCeleb which contains hundreds of thousands of 'real world' utterances for over 1,000 celebrities. Our second contribution is to apply and compare various state of the art speaker identification techniques on our dataset to establish baseline performance. We show that a CNN based architecture obtains the best performance for both identification and verification.

GPU kernel agents and GPU programming languages have advanced separately, leaving expert kernels difficult to reproduce. Agents usually treat the compiler as a fixed black box and receive only errors, correctness outcomes, and timing, while existing DSLs either hide critical scheduling decisions or expose them through difficult layout abstractions. We present CAKE, a compiler-agent co-design in which agents author CAKE IR, a typed, hardware-explicit schedule representation. CAKE exposes warp roles, memory movement, synchronization, and pipelines while supporting verification, cost modeling, and localized diagnostics. The harness itself evolves: recurring failures become verifier rules, IR primitives, model calibrations, and reusable optimization tactics. In matched implementation-hidden Flash-KMeans clean starts on B200, the best CAKE IR candidate at an 80-million-token budget runs at 1.144x the tuned FlashML baseline, compared with 0.928x for direct CUDA/PTX. Beyond this benchmark, agent-generated Kimi Delta Attention achieves a 2.05x geometric-mean speedup over official FlashKDA and passes end-to-end serving validation. Dispatcher-backed KNN and KMeans improve performance by 1.42x to 2.12x across more than 400 shapes, and four kernel changes are available as upstream PRs. CAKE targets NVIDIA GPUs from Ampere through Blackwell and separates single-shape evolution from library generalization and dispatch.

Traditional frameworks of political communication operate under linear, event-driven assumptions that treat voter persuasion as a static, transactional function. This paper introduces Dynamic Consent Engineering (DCE), a novel interdisciplinary paradigm that synthesizes Edward Bernays' foundational principles of public relations with the S-E-E-D (Snowball, Equilibrium, Elasticity, Dominance) framework of system dynamics. By expanding Bernaysian operational constraints into a four-dimensional resource matrix (incorporating algorithmic media infrastructure alongside manpower, mindpower, and capital), we mathematically formalize how democratic institutions construct, optimize, and sustain political dominance. We map Bernays' classic eight-step engineering workflow directly onto non-linear feedback loops, information time lags, and demographic carrying capacities. Through rigorous modeling of systemic feedback structures, we isolate the dynamic root causes of political elasticity, policy resistance plateaus, and threshold-triggered trust collapses. Finally, we establish a four-step diagnostic pipeline and validate the framework via historical reference mode verification, demonstrating that long-term political stability depends not on ephemeral rhetoric, but on the structural synchronization of policy execution and dynamic feedback calibration.

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

Over the last several years the tools used for model checking have become more efficient and usable. This has enabled users to apply model checking to industrial-scale problems, however the task of validating the implementation of the model is usually much harder. In this paper we present an approach to do end to end verification and validation of a real time system using the SPIN model checker. Taking the example of the cardiac pacemaker system proposed in the SQRL Pacemaker Formal Methods Challenge we demonstrate our framework by building a formal model for the cardiac pacemaker in SPIN, checking for desirable temporal properties of the model (expressed as LTL formulas), generating C code from the model (by refinement of PROMELA) and validating the generated implementation (using SPIN). We argue that a state of the art model checking tool like SPIN can be used to do formal specification as well as validation of the implementation. To evaluate our approach we show that our pacemaker model is expressive enough to derive consistent operating modes and that the refinement rules preserve LTL properties.

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

The rapid advancement of ML models in critical sectors such as healthcare, finance, and security has intensified the need for robust data security, model integrity, and reliable outputs. Large multimodal foundational models, while crucial for complex tasks, present challenges in scalability, reliability, and potential misuse. Decentralized systems offer a solution by distributing workload and mitigating central points of failure, but they introduce risks of unauthorized access to sensitive data across nodes. We address these challenges with a comprehensive framework designed for responsible AI development. Our approach incorporates: 1) Zero-knowledge proofs for secure model verification, enhancing trust without compromising privacy. 2) Consensus-based verification checks to ensure consistent outputs across nodes, mitigating hallucinations and maintaining model integrity. 3) Split Learning techniques that segment models across different nodes, preserving data privacy by preventing full data access at any point. 4) Hardware-based security through trusted execution environments (TEEs) to protect data and computations. This framework aims to enhance security and privacy and improve the reliability and fairness of multimodal AI systems. Promoting efficient resource utilization contributes to more sustainable AI development. Our state-of-the-art proofs and principles demonstrate the framework's effectiveness in responsibly democratizing artificial intelligence, offering a promising approach for building secure and private foundational models.

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.

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%.

Safety verification in Computer Numerical Control (CNC) machining has traditionally relied on simulation-based methods that require repetitive tests when requirements change. This paper introduces a formal verification framework that conceptualizes the physical CNC workspace as a Spatial Heap, treating physical occupancy as a managed logical resource. Central to our approach is a Parser-Prover Handshake that decouples machine kinematics from formal logic. By mapping tool trajectories and safety buffers into a discrete spatial model prior to evaluation, the framework enables the use of Separation Logic (SL) to verify safety via formal triples. Within this model, physical collisions are redefined as logical Spatial Data Races, detected through the failure of the separating conjunction to establish disjointness. Furthermore, we extend the methodology to collaborative environments using Concurrent Separation Logic (CSL), where physical hand-offs are verified as formal ownership transfers. Additionally, the framework scales to multi-axis kinematics (e.g., 5-axis Table-Table configurations) by treating the workpiece as a dynamically mutable spatial resource. By serving as a complement to traditional geometric simulation, this approach reduces the number of required iterative test cycles, offering a foundation for autonomous, less-collision manufacturing.

Retrieval-augmented language models (RALMs) have shown strong performance and wide applicability in knowledge-intensive tasks. However, there are significant trustworthiness concerns as RALMs are prone to generating unfaithful outputs, including baseless information or contradictions with the retrieved context. This paper proposes SynCheck, a lightweight monitor that leverages fine-grained decoding dynamics including sequence likelihood, uncertainty quantification, context influence, and semantic alignment to synchronously detect unfaithful sentences. By integrating efficiently measurable and complementary signals, SynCheck enables accurate and immediate feedback and intervention, achieving 0.85 AUROC in detecting faithfulness errors across six long-form retrieval-augmented generation tasks, improving prior best method by 4%. Leveraging SynCheck, we further introduce FOD, a faithfulness-oriented decoding algorithm guided by beam search for long-form retrieval-augmented generation. Empirical results demonstrate that FOD outperforms traditional strategies such as abstention, reranking, or contrastive decoding significantly in terms of faithfulness, achieving over 10% improvement across six datasets.

Large language models (LLMs) are increasingly being explored for automating SystemVerilog Assertion (SVA) generation, yet most evaluations report correctness on a single syntactic representation of an input. Such point accuracy does not reveal whether a model's correct output is stable when the same RTL behavior is written differently. This paper presents a controlled metamorphic evaluation of LLM-based SVA generation under semantics-preserving RTL transformations. Starting from the VERT dataset, we construct a quality-filtered conditional-control pool and a stratified 40-program evaluation set containing 295 assignment behaviors. We evaluate two open code models, Qwen2.5-Coder-7B and DeepSeek-Coder-V2-Lite, with an identical evaluation prompt and greedy decoding. Three transformations are studied: operand reordering, deterministic identifier renaming, and redundant parenthesization. Beyond baseline and transformed accuracy, we measure conditional robustness, invariance failure, and any-flip rate, with 10,000-sample clustered bootstrap intervals at the RTL-program level. Across all six model-transformation conditions, 9.7%-27.0% of behaviors that were correct on the original RTL become incorrect after a semantics-preserving transformation. Aggregate accuracy can therefore hide substantial instability: under identifier renaming, DeepSeek-Coder-V2-Lite improves from 53.9% to 63.7% accuracy while 19.5% of its originally correct behaviors fail. Manual review of 30 sampled correct-to-wrong transitions identifies dropped path predicates, branch-polarity errors, Boolean-structure corruption, and output-contract violations. The results show that point accuracy alone is insufficient for characterizing LLM reliability in assertion generation and motivate robustness-aware evaluation for AI-assisted hardware verification.

The performance of autonomous Web GUI agents heavily relies on the quality and quantity of their training data. However, a fundamental bottleneck persists: collecting interaction trajectories from real-world websites is expensive and difficult to verify. The underlying state transitions are hidden, leading to reliance on inconsistent and costly external verifiers to evaluate step-level correctness. To address this, we propose AutoWebWorld, a novel framework for synthesizing controllable and verifiable web environments by modeling them as Finite State Machines (FSMs) and use coding agents to translate FSMs into interactive websites. Unlike real websites, where state transitions are implicit, AutoWebWorld explicitly defines all states, actions, and transition rules. This enables programmatic verification: action correctness is checked against predefined rules, and task success is confirmed by reaching a goal state in the FSM graph. AutoWebWorld enables a fully automated search-and-verify pipeline, generating over 11,663 verified trajectories from 29 diverse web environments at only $0.04 per trajectory. Training on this synthetic data significantly boosts real-world performance. Our 7B Web GUI agent outperforms all baselines within 15 steps on WebVoyager. Furthermore, we observe a clear scaling law: as the synthetic data volume increases, performance on WebVoyager and Online-Mind2Web consistently improves.

Given the increasing adoption of modern AI-enabled control systems, ensuring their safety and reliability has become a critical task in software testing. One prevalent approach to testing control systems is falsification, which aims to find an input signal that causes the control system to violate a formal safety specification using optimization algorithms. However, applying falsification to AI-enabled control systems poses two significant challenges: (1)~it requires the system to execute numerous candidate test inputs, which can be time-consuming, particularly for systems with AI models that have many parameters, and (2)~multiple safety requirements are typically defined as a conjunctive specification, which is difficult for existing falsification approaches to comprehensively cover. This paper introduces Synthify, a falsification framework tailored for AI-enabled control systems. Our approach performs falsification in a two-phase process. At the start, Synthify synthesizes a program that implements one or a few linear controllers to serve as a proxy for the AI controller. This proxy program mimics the AI controller's functionality but is computationally more efficient. Then, Synthify employs the ε-greedy strategy to sample a promising sub-specification from the conjunctive safety specification. It then uses a Simulated Annealing-based falsification algorithm to find violations of the sampled sub-specification for the control system. To evaluate Synthify, we compare it to PSY-TaLiRo, a state-of-the-art and industrial-strength falsification tool, on 8 publicly available control systems. On average, Synthify achieves a 83.5% higher success rate in falsification compared to PSY-TaLiRo with the same budget of falsification trials. The safety violations found by Synthify are also more diverse than those found by PSY-TaLiRo, covering 137.7% more sub-specifications.

The pursuit of autonomous driving has produced one of the richest sensor data collections in all of robotics. However, its scale and diversity remain largely untapped. Each dataset adopts different 2D and 3D modalities, such as cameras, lidar, ego states, annotations, traffic lights, and HD maps, with different rates and synchronization schemes. They come in fragmented formats requiring complex dependencies that cannot natively coexist in the same development environment. Further, major inconsistencies in annotation conventions prevent training or measuring generalization across multiple datasets. We present 123D, an open-source framework that unifies such multi-modal driving data through a single API. To handle synchronization, we store each modality as an independent timestamped event stream with no prescribed rate, enabling synchronous or asynchronous access across arbitrary datasets. Using 123D, we consolidate eight real-world driving datasets spanning 3,300 hours and 90,000 kilometers, together with a synthetic dataset with configurable collection scripts, and provide tools for data analysis and visualization. We conduct a systematic study comparing annotation statistics and assessing each dataset's pose and calibration accuracy. Further, we showcase two applications 123D enables: cross-dataset 3D object detection transfer and reinforcement learning for planning, and offer recommendations for future directions. Code and documentation are available at https://github.com/kesai-labs/py123d.

Agent harnesses enable large language models to act through tools, observe the results, and iteratively work toward a task goal. Verification checks and revises agents' work to improve output quality. Yet there is limited guidance on how harnesses should organize this effort. We study verification as an axis of test-time scaling by examining when to intervene, who checks the work, and how checking leads to revision. Our framework spans four layers of the agent lifecycle: initial instructions, mid-turn reminders, completion gates, and independent review. We compare 17 designs across seven frontier coding models on Terminal-Bench (TB) and SWE-bench Verified (SWE), and introduce VisualBench for expert evaluation of visual and interactive artifacts. Initial instructions and execution-time reminders yield modest, model-dependent average gains on the coding benchmarks, without substantially increasing average output token use. Completion gates can yield larger gains but may substantially increase cost. Independent review by a critic offers a more favorable accuracy-cost tradeoff, improving average accuracy by 5.9-9.5 percentage points on TB and 3.9-6.6 on SWE at 1.13-1.25 and 1.00-1.04 times baseline cost, respectively. On VisualBench, independent review achieves net preferences of 13.2-23.8 points over the baseline across its four designs, exceeding the evaluated L0-L2 designs. Additional review rounds or independent critics further improve average TB accuracy by up to 3.5 percentage points. Together, these results provide empirical guidance for verification design in agent harnesses and support independent review as a practical axis of test-time scaling.

In autonomous driving, multi-modal perception tasks like 3D object detection typically rely on well-synchronized sensors, both at training and inference. However, despite the use of hardware- or software-based synchronization algorithms, perfect synchrony is rarely guaranteed: Sensors may operate at different frequencies, and real-world factors such as network latency, hardware failures, or processing bottlenecks often introduce time offsets between sensors. Such asynchrony degrades perception performance, especially for dynamic objects. To address this challenge, we propose AsyncBEV, a trainable lightweight and generic module to improve the robustness of 3D Birds' Eye View (BEV) object detection models against sensor asynchrony. Inspired by scene flow estimation, AsyncBEV first estimates the 2D flow from the BEV features of two different sensor modalities, taking into account the known time offset between these sensor measurements. The predicted feature flow is then used to warp and spatially align the feature maps, which we show can easily be integrated into different current BEV detector architectures (e.g., BEV grid-based and token-based). Extensive experiments demonstrate AsyncBEV improves robustness against both small and large asynchrony between LiDAR or camera sensors in both the token-based CMT and grid-based UniBEV, especially for dynamic objects. We significantly outperform the ego motion compensated CMT and UniBEV baselines, notably by 16.6 % and 11.9 % NDS on dynamic objects in the worst-case scenario of a 0.5 s time offset. Code will be released upon acceptance.

Verifying the reliability of complex, multi-step reasoning in Large Language Models (LLMs) remains a fundamental challenge, as existing methods often lack both faithfulness and precision. To address this issue, we propose the Graph of Verification (GoV) framework. GoV offers three key contributions: First, it explicitly models the underlying deductive process as a directed acyclic graph (DAG), whether this structure is implicit or explicitly constructed. Second, it enforces a topological order over the DAG to guide stepwise verification. Third, GoV introduces the notion of customizable node blocks, which flexibly define the verification granularity, from atomic propositions to full paragraphs, while ensuring that all requisite premises derived from the graph are provided as contextual input for each verification unit. We evaluate GoV on the Number Triangle Summation task and the ProcessBench benchmark with varying levels of reasoning complexity. Experimental results show that GoV substantially improves verification accuracy, faithfulness, and error localization when compared to conventional end-to-end verification approaches. Our code and data are available at https://github.com/Frevor/Graph-of-Verification.

LLMs are widely used in complex AI applications. These applications underscore the need for LLM outputs to adhere to a specific format, for their integration with other components in the systems. Typically the format rules e.g., for data serialization formats such as JSON, YAML, or Code in Programming Language are expressed as context-free grammar (CFG). Due to the hallucinations and unreliability of LLMs, instructing LLMs to adhere to specified syntax becomes an increasingly important challenge. We present SynCode, a novel framework for efficient and general syntactical decoding with LLMs, to address this challenge. SynCode leverages the CFG of a formal language, utilizing an offline-constructed efficient lookup table called DFA mask store based on the discrete finite automaton (DFA) of the language grammar terminals. We demonstrate SynCode's soundness and completeness given the CFG of the formal language, presenting its ability to retain syntactically valid tokens while rejecting invalid ones. SynCode seamlessly integrates with any language defined by CFG, as evidenced by experiments focusing on generating JSON, Python, and Go outputs. Our experiments evaluating the effectiveness of SynCode for JSON generation demonstrate that SynCode eliminates all syntax errors and significantly outperforms state-of-the-art baselines. Furthermore, our results underscore how SynCode significantly reduces 96.07% of syntax errors in generated Python and Go code, showcasing its substantial impact on enhancing syntactical precision in LLM generation. Our code is available at https://github.com/uiuc-focal-lab/syncode

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

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.

Machine learning-based intrusion detection systems (IDS) are critical for securing Industrial Internet of Things (IIoT) environments. Most adversarial research against them perturbs the feature vector or the traffic that produces it, and depends on gradient access, repeated model queries, or a learned model of benign traffic. A smaller line of work reshapes packet timing without querying the detector, but makes malicious traffic mimic a learned model of benign timing. Across these approaches, one assumption of industrial monitoring pipelines has received little attention: temporal synchronization. An IDS reconstructs operational state by aggregating telemetry into sliding or tumbling windows, so its view depends not only on what is observed but on when each observation falls relative to a window boundary. We introduce the Phantom State Attack (PSA), which exploits that dependence under a passive, zero-query threat model. Rather than modifying packets, perturbing features, querying the classifier, or fitting any model of benign traffic, PSA injects bounded timing drift calibrated to the attack flow's own inter-arrival variability, moving observations across the nearest window boundary by the minimal shift needed. The IDS then reconstructs a phantom state that diverges from the true process state. We evaluate PSA on ToN-IoT and CIC IIoT 2025 (DataSense), against Random Forest, MLP and XGBoost, measuring detection degradation, synchronization distortion, stealth, and attacker cost. PSA degrades detection on flows carrying enough packets for window-boundary redistribution, and leaves others almost unchanged, so its effect is conditional. A query-based baseline reaches higher raw success but needs many queries per window, while PSA needs none. The results identify temporal aggregation as an attack surface reachable under weaker assumptions than prior evasion techniques.

Multi-step enterprise agent tasks fail in a characteristic way: single-pass inference has no checkpoint between deciding an answer and committing to it. We study one production system (Leni) whose architecture installs such checkpoints: verification loops (execute, observe, compare, correct) staffed by lightweight task-specialized post-trained models. We evaluate the unmodified production configuration on three public benchmarks stressing distinct failure modes: SpreadsheetBench Verified (silent computation error), BullshitBench v2 (premise confabulation), and the GAIA validation split (cascade error over long tool chains). The full system improves over its frontier base model by +11.0 percentage points on SpreadsheetBench (91.25% vs 80.25%, n=400, p<0.001), +7 to +10 percentage points on BullshitBench (98% vs 91%, n=100), and roughly +15 points on GAIA validation (75.2% pass@1, n=165; 83.0% best-of-k). Our central contribution is a decomposition of that uplift: most of it comes from scaffolding, routing, and specialist models rather than from the verification step itself, whose isolated contribution is small (+1.5 points) but concentrated at the top of the score distribution, where it converts otherwise-failing tasks. We instrument the loop end-to-end, yielding an empirical verifier confusion matrix (catch rate about 0.20, fix rate 0.75, no false-alarm regressions) that grounds a compounding-reliability model. Specialist-swap ablations suggest that the loop's value depends on who observes it: replacing the small trained verifier with the generating frontier model eliminates most rescues. A valid-premise control shows zero over-rejections in 100 expert-level questions.

Lyapunov functions and barrier certificates give state-space guarantees of stability and safety, but synthesizing and verifying them---especially for nonlinear, high-dimensional systems---remains an open challenge. Existing pipelines verify candidates with numerical solvers (sum-of-squares programs), interval methods, or satisfiability-modulo-theories (SMT) solvers, which often require relaxations, are conservative, or scale poorly with model dimension and nonlinearity. These limitations have also shaped benchmark design: standard test suites are dominated by low-dimensional polynomial systems chosen to suit what solvers can handle rather than what engineering applications require. We address both sides of this challenge. First, we introduce DynaCertBench, a benchmark of 105 instances: 80 non-redundant systems curated from the literature, extended with high-dimensional and control-constrained variants and new nonlinearly coupled systems, comprehensively spanning stability, region-of-attraction, forward-invariance, and safety tasks. Second, we present LLM2Cert, an LLM-driven framework that synthesizes candidate certificates and verifies them against their proof obligations: each obligation is routed to an SMT solver or directly to the Lean Proof-Repair agent. On DynaCertBench, LLM2Cert verifies 81 of 105 instances (77.1%), a 17.1 percentage point improvement over one-shot proposal without feedback. On the 81 fixed certificates, LLM2Cert verifies 22 that All-SMT leaves unresolved. Code and data are available at https://github.com/FormalCert-AI/llm2cert.

Safety heads are lightweight classifiers attached to pretrained language models for flagging harmful inputs before generation. Their empirical detection performance has been studied, but their formal robustness properties remain largely unexplored. We ask when a State Space Model (SSM)-based safety head can be certified to produce the same prediction for all inputs within a bounded embedding-space perturbation. We prove that the answer turns on a single condition: the l_infty norm of the state transition matrix must satisfy A_infty<1 (the contraction condition), which enables exact interval bound propagation (IBP) certification for linear time-invariant classifiers. When the contraction condition holds, the reachable output interval has bounded steady-state width and examples can be certified as robustly classified. When it fails, the interval grows exponentially with sequence length and certification is impossible at any practical perturbation radius. We enforce contraction with a hinge penalty and show on toxic comment data that certified fraction improves from 41\% to 59\%, with a sharp empirical phase transition at A_infty=1 matching the theory. Applying a contraction-regularized S4 head to jailbreak detection on JailbreakBench, we achieve a zero-shot transfer to AdvBench (DR=0.994) and HarmBench (DR=0.988). A logistic regression on mean-pooled Mamba-130M embeddings matches or exceeds the S4 head on every detection metric, confirming that harmful intent is already linearly separable in the embedding space. The S4 safety head's contribution is not superior discrimination but the formal certification that no probe-based approach provides.

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.

Large language models (LLMs) can translate natural language into optimization code, but silent failures pose a critical risk: code that executes and returns solver-feasible solutions may encode semantically incorrect formulations, creating a feasibility-correctness gap of up to 90 percentage points on compositional problems. We introduce ReLoop, addressing silent failures from two complementary directions. Structured generation decomposes code production into a four-stage reasoning chain (understand, formalize, synthesize, verify) that mirrors expert modeling practice, with explicit variable-type reasoning and self-verification to prevent formulation errors at their source. Behavioral verification detects errors that survive generation by testing whether the formulation responds correctly to solver-based parameter perturbation, without requiring ground truth -- an external semantic signal that bypasses the self-consistency problem inherent in LLM-based code review. The two mechanisms are complementary: structured generation dominates on complex compositional problems, while behavioral verification becomes the largest single contributor on problems with localized formulation defects. Together with execution recovery via IIS-enhanced diagnostics, ReLoop raises correctness from 22.6% to 31.1% and execution from 72.1% to 100.0% on the strongest model, with consistent gains across five models spanning three paradigms (foundation, SFT, RL) and three benchmarks. We additionally release RetailOpt-190, 190 compositional retail optimization scenarios targeting the multi-constraint interactions where LLMs most frequently fail.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Terminal agents rely on self-verification to assess and correct their solutions as they solve tasks through interaction with command-line environments. Yet how trustworthy such self-verification is remains poorly understood. To investigate this question systematically, we introduce a diagnostic framework that identifies the first complete solution in each trajectory, determines whether it is objectively correct, and uses this ground truth to quantify the agent's subsequent verification and recovery behavior. Applying it to ten terminal agents on TerminalBench2.1, we find that verification is nearly universal after a complete candidate is formed, yet only 61.43\% of incorrect candidates are detected and only 49.36\% of detected errors are successfully repaired. These results show that the main weakness in self-verification lies not in initiating verification, but in detecting and repairing errors. Motivated by these findings, we propose Student-Conditioned Verification Distillation (SCVD), which lets the student first produce a candidate solution and distills a stronger teacher's subsequent verification and recovery from the same interaction context. Across three Qwen3.5 backbones, SCVD improves Pass@1 on TerminalBench2.1 by 9.74--16.85 percentage points over the corresponding base models and by 4.49--8.61 points over the standard full-trajectory distillation, while avoiding the pronounced out-of-distribution degradation of full-trajectory distillation on SWE-bench Verified.

Digital signatures prove key possession, not authorship. An author who generates text with AI, constructs intermediate document states post-hoc, and signs each hash produces a signature chain indistinguishable from genuine composition. We address this gap between cryptographic integrity and process provenance. We introduce proof-of-process, a primitive category for evidence that a physical process, not merely a signing key, produced a digital artifact. Our construction, the jitter seal, injects imperceptible microsecond delays derived via HMAC from a session secret, keystroke ordinal, and cumulative document hash. Valid evidence requires that real keystrokes produced the document through those intermediate states. We propose the Adversarial Collapse Principle as an evaluation criterion: evidence systems should be judged by whether disputing them requires a conjunction of specific, testable allegations against components with independent trust assumptions. We present Witnessd, an architecture combining jitter seals with Verifiable Delay Functions, external timestamp anchors, dual-source keystroke validation, and optional hardware attestation. Each layer forces allegations at different capability levels; disputing authentic evidence requires coordinated claims across independent trust boundaries. The system does not prevent forgery: a kernel-level adversary can defeat it, and typing AI-generated content produces valid evidence. The contribution is converting vague doubt into falsifiable allegations. We evaluate across 31,000 verification trials with deterministic rejection of invalid proofs.

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

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

A login screen that appears after a tap on Sign in is expected; the same screen after a tap on View order is an attack. For GUI agents, safety is therefore a property of the transition rather than of the screen, and a monitor that inspects only screens can be defeated by reusing a legitimate one. Judging a transition requires an expectation of what should have followed the action. Existing GUI world models provide one, but they output it as text, code, or images, so checking it against the observed screen requires a second model to judge the two. We argue that a world model meant for verification should instead predict in the space in which observations are encoded, and present LGWM, a decoder-free, action-conditioned world model that predicts the representation of the next screen directly, trained without semantic annotation on 1.85M real GUI transitions. Verification reduces to a vector comparison, and the same signal reveals whether a mismatch is harmful. We evaluate on RSWT-BENCH, a diagnostic where each credential screen appears under both a legitimate and a hijacked transition, so detectors that see only the screen are at chance by construction. The training-free score reaches 0.987 AUC at 17 ms per decision, on par with the strongest closed-source VLMs and about ten AUC points above generative GUI world models at over three orders of magnitude lower latency. The residual direction reaches 0.953 AUC at separating harmful from benign violations, where prompted VLMs are near chance. Further analyses show that the prediction is a usable future state rather than an anomaly score. World models have mostly served as simulators or planners; our results point to a third role, verification, for which predicting in representation space is the natural design.

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.

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.

This paper reports a single, fully instrumented case study of a large-scale architectural refactoring by an AI coding agent under a specification-first protocol, with no human review of the generated code and no pre-existing oracle to validate the target behaviour. The task, dismantling a central invariant across a large interdependent codebase, was assessed by the author as effectively infeasible through incremental refactoring, the kind of change that conventionally calls for a rewrite instead. Under the protocol described here, the agent completed it successfully. The system is a 717,725-line production TypeScript application across 3,648 files. The task required dismantling a core lifetime invariant: the guarantee that a UI panel remains open for the duration of an AI request. The target behaviour was that a streaming generation survives the closing of its panel and can be reattached, on reopening, to the same live stream with no loss or duplication. The protocol: formal specification by the agent, 14 refinement cycles auditing that specification against the source code, atomic implementation, a compile/test feedback loop, then 17 verification cycles auditing the code against the frozen specification. Across 31 audit passes, 201 defects were corrected before any human executed the program. The convergence criterion was empirical: two consecutive verification passes returning zero findings. The change touched 189 files (31 new); with the extraction phase, the two commits total 288 files, 34,770 insertions, 16,422 deletions. Across the first and roughly thirty later sessions, the software behaved as specified, no bug observed. Elapsed: three days; cost: USD 2,430. The full specification and raw session logs, 1,500+ pages in French, are published as evidence, allowing inspection of the process and submission to a language model for consistency checking.

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

The automated generation of design RTL based on large language model (LLM) and natural language instructions has demonstrated great potential in agile circuit design. However, the lack of datasets and benchmarks in the public domain prevents the development and fair evaluation of LLM solutions. This paper highlights our latest advances in open datasets and benchmarks from three perspectives: (1) RTLLM 2.0, an updated benchmark assessing LLM's capability in design RTL generation. The benchmark is augmented to 50 hand-crafted designs. Each design provides the design description, test cases, and a correct RTL code. (2) AssertEval, an open-source benchmark assessing the LLM's assertion generation capabilities for RTL verification. The benchmark includes 18 designs, each providing specification, signal definition, and correct RTL code. (3) RTLCoder-Data, an extended open-source dataset with 80K instruction-code data samples. Moreover, we propose a new verification-based method to verify the functionality correctness of training data samples. Based on this technique, we further release a dataset with 7K verified high-quality samples. These three studies are integrated into one framework, providing off-the-shelf support for the development and evaluation of LLMs for RTL code generation and verification. Finally, extensive experiments indicate that LLM performance can be boosted by enlarging the training dataset, improving data quality, and improving the training scheme.

We introduce Leap+Verify, a framework that applies speculative execution -- predicting future model weights and validating predictions before acceptance -- to accelerate neural network training. Inspired by speculative decoding in language model inference and by the Automatically Scalable Computation (ASC) architecture for program execution, Leap+Verify decomposes training into three dynamically detected regimes (chaotic, transition, stable) using activation-space cosine similarity as a real-time Lyapunov proxy signal. Within each regime, analytic weight predictors (momentum, linear, quadratic extrapolation) attempt to forecast model parameters K training steps ahead; predictions are accepted only when validated against a held-out loss criterion. We evaluate Leap+Verify on GPT-2 124M and Qwen 2.5-1.5B trained on WikiText-103 across five random seeds, sweeping prediction depth K in {5, 10, 25, 50, 75, 100}. Momentum-based prediction (Adam moment extrapolation) fails catastrophically at both scales, with predicted losses exceeding actuals by 100-10,000x -- a universal norm explosion in optimizer-state extrapolation. Finite-difference predictors (linear, quadratic) succeed where momentum fails: at 124M, they achieve 24% strict acceptance at K=5 in stable regimes; at 1.5B, they achieve 37% strict acceptance in transition regimes. The scale-dependent finding is in regime distribution: GPT-2 124M spends 34% of training in stable regime, while Qwen 1.5B spends 64% in chaotic regime and reaches stable in only 0-2 of 40 checkpoints. Larger models are more predictable when predictable, but less often predictable -- the practical bottleneck shifts from predictor accuracy to regime availability. Cross-seed results are highly consistent (less than 1% validation loss variance), and the three-regime framework produces identical phase boundaries (plus or minus 50 steps) across seeds.

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).

Software testing and verification are critical for ensuring the reliability and security of modern software systems. Traditionally, formal verification techniques, such as model checking and theorem proving, have provided rigorous frameworks for detecting bugs and vulnerabilities. However, these methods often face scalability challenges when applied to complex, real-world programs. Recently, the advent of Large Language Models (LLMs) has introduced a new paradigm for software analysis, leveraging their ability to understand insecure coding practices. Although LLMs demonstrate promising capabilities in tasks such as bug prediction and invariant generation, they lack the formal guarantees of classical methods. This paper presents a comprehensive study of state-of-the-art software testing and verification, focusing on three key approaches: classical formal methods, LLM-based analysis, and emerging hybrid techniques, which combine their strengths. We explore each approach's strengths, limitations, and practical applications, highlighting the potential of hybrid systems to address the weaknesses of standalone methods. We analyze whether integrating formal rigor with LLM-driven insights can enhance the effectiveness and scalability of software verification, exploring their viability as a pathway toward more robust and adaptive testing frameworks.

This paper presents a program logic for reasoning about multithreaded Java-like programs with dynamic thread creation, thread joining and reentrant object monitors. The logic is based on concurrent separation logic. It is the first detailed adaptation of concurrent separation logic to a multithreaded Java-like language. The program logic associates a unique static access permission with each heap location, ensuring exclusive write accesses and ruling out data races. Concurrent reads are supported through fractional permissions. Permissions can be transferred between threads upon thread starting, thread joining, initial monitor entrancies and final monitor exits. In order to distinguish between initial monitor entrancies and monitor reentrancies, auxiliary variables keep track of multisets of currently held monitors. Data abstraction and behavioral subtyping are facilitated through abstract predicates, which are also used to represent monitor invariants, preconditions for thread starting and postconditions for thread joining. Value-parametrized types allow to conveniently capture common strong global invariants, like static object ownership relations. The program logic is presented for a model language with Java-like classes and interfaces, the soundness of the program logic is proven, and a number of illustrative examples are presented.

In the rapidly evolving field of Electronic Design Automation (EDA), the deployment of Large Language Models (LLMs) for Register-Transfer Level (RTL) code generation has emerged as a promising direction. However, because RTL code describes concurrent hardware behavior with strict cycle-level timing and thus differs fundamentally from software code, LLM-based RTL code generation remains bottlenecked by (i) sparse feedback and limited test coverage of simulation-centric evaluation, (ii) regressions and repair hallucinations introduced by whole-file regeneration during debugging, and (iii) semantic drift as intent is reinterpreted across repair iterations and agent handoffs. In this work, we propose Veri-Sure, a multi-agent framework that establishes a design contract to align agents' intent and uses a patching mechanism guided by static dependency slicing to perform precise, localized repairs. By integrating a multi-branch verification pipeline that combines trace-driven temporal analysis with formal verification, Veri-Sure yields more robust and reliable RTL code generation. We also introduce VerilogEval-v2-EXT, extending the original benchmark with 53 more industrial-grade design tasks and stratified difficulty levels, and show that Veri-Sure achieves state-of-the-art verified-correct RTL code generation performance, surpassing standalone LLMs and prior agentic systems. Code and dataset are available at https://github.com/xyjoey/Veri-Sure.

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

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.

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.

Scaling pre-training, post-training, and test-time compute have become the central paradigms for improving the capabilities of LLMs. In this work, we identify verification, the ability to determine the correctness of a solution, as a new scaling axis. To unlock this and demonstrate its effectiveness, we introduce LLM-as-a-Verifier, a general-purpose verification framework that provides fine-grained feedback for agentic tasks without requiring additional training. Unlike standard LM judges that prompt LLMs to produce discrete scores for candidate solutions, LLM-as-a-Verifier computes the expectation over the distribution of scoring token logits to generate continuous scores. This probabilistic formulation enables verification to scale along multiple dimensions: (1) score granularity, (2) repeated evaluation, and (3) criteria decomposition. In particular, we show that scaling the scoring granularity leads to better separation between positive and negative solutions, resulting in more calibrated comparisons. Moreover, scaling repeated evaluation and criteria decomposition consistently lead to additional gains in verification accuracy through variance and complexity reduction. We further introduce a cost-efficient ranking algorithm for selecting the best solution among candidates using the verifier's continuous scores. LLM-as-a-Verifier achieves state-of-the-art performance on Terminal-Bench V2 (86.5%), SWE-Bench Verified (78.2%), RoboRewardBench (87.4%), and MedAgentBench (73.3%). Beyond verification, the fine-grained signals from LLM-as-a-Verifier can also serve as a proxy for estimating task progress. We build an extension for Claude Code, enabling developers to monitor and improve their own agentic systems. Finally, we show that LLM-as-a-Verifier can provide dense feedback for RL, improving the sample efficiency of SAC and GRPO on robotics and mathematical reasoning benchmarks.

Reference-free faithfulness metrics verify each atomic claim a model makes against ground truth, and are increasingly used to evaluate grounded generation. We show they share a blind spot: they measure only precision -- are the stated claims supported? -- and therefore reward abstention, since a model can score near-perfect faithfulness by saying almost nothing. We make this measurable using Formula 1 telemetry, a domain where strategic ground truth is derived deterministically and, crucially, completely: for each decision we know the full set of facts that mattered. This completeness -- absent in open-domain faithfulness benchmarks -- lets us measure recall (coverage of the relevant facts) exactly, alongside precision. On a multilingual (EN/ES/PT) benchmark of 7,253 decision instances spanning 150 races, the most precise frontier model covers under half of the relevant facts and ranks last by F1, so requiring coverage reorders the systems; the same effect reappears in a second complete-oracle domain (NOAA weather forecasts). A prompt ablation shows the low coverage is not an under-prompting artifact: explicitly asking models to be thorough does not close the gap. We pair faithfulness with coverage into a single score, validate the metric (controlled perturbation; agreement across a model-free regex extractor and a cross-family LLM extractor, system-level Spearman 1.0), and give a verifier-guided generation method that improves precision and recall without references. We release the benchmark, structured annotations, metric, baselines, and an interactive demo.

Outer-learning algorithms use infinitesimal sensitivities to propose finite changes to initialization or training parameters. For hard-ReLU training, the derivative of the finite program and the derivative of its flow limit do not by themselves specify the response at a chosen radius. We characterize the intervening regime in which the perturbation radius is proportional to the GD step. Integer event rounding then survives at leading order: smooth Euler bias shifts each discrete phase, and upstream rounding moves downstream branch boundaries. We derive the crossing indices and a uniform endpoint expansion for finitely many separated transverse events in piecewise-C^2 dynamics, away from recursive phase boundaries. In contractive affine regions, an explicit remainder and complete branch verification certify finite candidate comparisons. Scalar phase frequencies and a coupled feedback ablation test the mechanism; frozen nonlinear-network experiments show radius-dependent prediction accuracy, including incomplete branch matches and failed-word tails. Together with local AD and uniform flow consistency, the result identifies sufficient response regimes: differentiating training is a choice of perturbation resolution as well as a choice of derivative.

Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by faithfulness: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended. We introduce Bidirectional Provability Fingerprinting (), a framework that certifies faithfulness by characterizing each candidate through its forward and backward consequence neighborhoods in the ambient theory and matching these against probes derived from the natural-language statement. We further introduce four novel components: (i) Counterfactual Probe Generation (), a contrastive procedure that synthesizes probes targeting specific drift directions; (ii) the Equivalence Spectrum, a continuous faithfulness score that replaces brittle binary verdicts; (iii) Adaptive Probe Budget Allocation (), an information-theoretic budget router; and (iv) Faithfulness-Guided Decoding (), which uses signals as a reward during autoformalization. We prove a drift detection theorem and a PAC-faithfulness result establishing that the equivalence class of a natural language statement is learnable from O(log(1/δ)/varepsilon) probes under mild assumptions. We release , a benchmark of 2{,}183 NL/Lean~4 pairs with controlled drift labels across six subfields of mathlib4. \,+\, detects 89.6% of drifted formalizations at a 3.0% false-positive rate-against 41.2% for typecheck and 63.3% for LLM-judge baselines, and reduces the rate at which a state-of-the-art autoformalizer emits drifted statements by 47%. https://pmlrbd.github.io/BPF/

Falsification searches for counterexamples to formal specifications in cyber-physical systems (CPS). With specifications written in Signal Temporal Logic (STL), falsification can be formulated as a robustness optimization problem, traditionally tackled with black-box search algorithms. In parallel, large language models (LLMs) have recently emerged as surprisingly effective optimizers when coupled with iterative prompting. In this work, we connect these ideas and introduce LLM-Falsifier, an LLM-based approach that falsifies specifications by minimizing the STL robustness degree. Beyond generic prompt-based optimization, our key idea is to expose the LLM to semantic information that is natural for language models but absent from standard numerical optimizers, including natural-language input and output names, output trajectories, and critical-time witnesses for the minimum robustness value. These additions enable smarter and more sample-efficient robustness search. On the ARCH-COMP falsification benchmarks, LLM-Falsifier is shown to outperform existing falsification tools based on a range of optimization paradigms, from surrogate-based and Bayesian optimization to search-based testing, on 14 of 21 specifications when measured by the average number of simulations required to find a counterexample.

Vericoding refers to the generation of formally verified code from rigorous specifications. Recent AI models show promise in vericoding, but a unified methodology for cross-paradigm evaluation is lacking. Existing benchmarks test only individual languages/tools (e.g., Dafny, Verus, and Lean) and each covers very different tasks, so the performance numbers are not directly comparable. We address this gap with AlgoVeri, a benchmark that evaluates vericoding of 77 classical algorithms in Dafny, Verus, and Lean. By enforcing identical functional contracts, AlgoVeri reveals critical capability gaps in verification systems. While frontier models achieve tractable success in Dafny (40.3% for Gemini-3 Flash), where high-level abstractions and SMT automation simplify the workflow, performance collapses under the systems-level memory constraints of Verus (24.7%) and the explicit proof construction required by Lean (7.8%). Beyond aggregate metrics, we uncover a sharp divergence in test-time compute dynamics: Gemini-3 effectively utilizes iterative repair to boost performance (e.g., tripling pass rates in Dafny), whereas GPT-OSS saturates early. Finally, our error analysis shows that language design affects the refinement trajectory: while Dafny allows models to focus on logical correctness, Verus and Lean trap models in persistent syntactic and semantic barriers. All data and evaluation code can be found at https://github.com/haoyuzhao123/algoveri.

Verifying the success of computer use agent (CUA) trajectories is a critical challenge: without reliable verification, neither evaluation nor training signal can be trusted. In this paper, we present lessons learned from building a best-in-class verifier for web tasks we call the Universal Verifier. We design the Universal Verifier around four key principles: 1) constructing rubrics with meaningful, non-overlapping criteria to reduce noise; 2) separating process and outcome rewards that yield complementary signals, capturing cases where an agent follows the right steps but gets blocked or succeeds through an unexpected path; 3) distinguishing between controllable and uncontrollable failures scored via a cascading-error-free strategy for finer-grained failure understanding; and 4) a divide-and-conquer context management scheme that attends to all screenshots in a trajectory, improving reliability on longer task horizons. We validate these findings on CUAVerifierBench, a new set of CUA trajectories with both process and outcome human labels, showing that our Universal Verifier agrees with humans as often as humans agree with each other. We report a reduction in false positive rates to near zero compared to baselines like WebVoyager (geq 45\%) and WebJudge (geq 22\%). We emphasize that these gains stem from the cumulative effect of the design choices above. We also find that an auto-research agent achieves 70\% of expert quality in 5\% of the time, but fails to discover all strategies required to replicate the Universal Verifier. We open-source our Universal Verifier system along with CUAVerifierBench; available at https://github.com/microsoft/fara.

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

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.

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

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.

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.

Safety claims on self-improving agent runtimes are almost always self-graded: a policy file, a guardrail, or a README commitment. We describe falsifiable release gates, and a methodology to build and validate such systems, such that every new capability must pass a pre-specified, machine-verifiable acceptance suite before it ships, and a fixed set of standing invariants is preserved at each gate. I think we applied the method in the Antahkarana, an open runtime, via seven gates from basic observability into a self governing loop that suggests changes to its own policy. no action goes to an effector without a safety-critical property capability token minted by a control ring is exhaustively machine-checked over the one million recorded reachable state space of a bounded model and re-checked against execution traces. A purposely broken model gives the shortest counterexample, so the checker has teeth, is apparent. The self-enhancement loop is positively Constrained: the entire write surface is policy rules, tightening changes. may auto-apply loosening changes always require a human merge and a proposal autoclosed is one that mispredicts its own effect; We publish the acceptance measured results for all the seven gates, define precisely the scope of each claim (a bounded of the coordination skeleton (not the learned components) and free the runtime, either command line tools and the gate suite, so the results reproduce, and gates can run against other agent frameworks. Reviewers may repeat the single command central non-bypass in seconds.

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited interpretability. To address these, we propose an end-to-end framework using transformers to construct analytical Lyapunov functions (local), which simplifies formal verification, enhances interpretability, and provides valuable insights for control engineers. Our framework consists of a transformer-based trainer that generates candidate Lyapunov functions and a falsifier that verifies candidate expressions and refines the model via risk-seeking policy gradient. Unlike Alfarano et al. (2024), which utilizes pre-training and seeks global Lyapunov functions for low-dimensional systems, our model is trained from scratch via reinforcement learning (RL) and succeeds in finding local Lyapunov functions for high-dimensional and non-polynomial systems. Given the analytical nature of the candidates, we employ efficient optimization methods for falsification during training and formal verification tools for the final verification. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature.

The growing demand for efficient long-sequence modeling on edge devices has propelled widespread adoption of State Space Models (SSMs) like Mamba, due to their superior computational efficiency and scalability. As its autoregressive generation process remains memory-bound, speculative decoding has been proposed that incorporates draft model generation and target model verification. However, directly applying speculative decoding to SSMs faces three key challenges: (1) hidden state backtracking difficulties, (2) tree-based parallel verification incompatibility, and (3) hardware workload mismatch. To address these challenges, we propose SpecMamba, the first FPGA-based accelerator for Mamba with speculative decoding, which features system, algorithm, and hardware co-design. At the system level, we present a memory-aware hybrid backtracking strategy to coordinate both models. At the algorithm level, we propose first-in-first-out (FIFO)-based tree verification with tiling to minimize memory access. At the hardware level, we customize a dataflow that computes linear layers in parallel and SSM layers in series to enable maximal overlapping. Implemented on AMD FPGA platforms (VHK158 and VCK190), SpecMamba achieves a 2.27x speedup over GPU baselines and a 2.85x improvement compared to prior FPGA solutions, while demonstrating 5.41x and 1.26x higher energy efficiency, respectively.

How do multi-turn reasoning systems fail? The expected answer is logical contradiction, in which the system's maintained state becomes unsatisfiable. We show that the dominant mode is instead satisfiable drift, where the internal state stays consistent while the returned answer silently violates prior commitments. We build DRIFT-Bench (Decomposing Reasoning Into Failure Types), a solver-instrumented benchmark of 816 test problems across three constraint domains, and evaluate four methods on it across four open-weight models (8B-120B parameters). MUS-Repair, which feeds minimal unsatisfiable subsets back to the generator, is strongest in every setting (+1.8 to +15.0 pp over the best non-MUS baseline). But the central finding is what repair leaves behind. After structured feedback, models rarely contradict themselves. They forget. Residual errors are 98-100% satisfiable drift across all settings, while contradiction drops to near zero. Reliable multi-turn systems must separately validate that the returned answer respects the maintained state. Code is available at https://github.com/kaons-research/drift-bench.

Natural-language software requirements are often ambiguous, inconsistent, and underspecified; in safety-critical domains, these defects propagate into formal models that verify the wrong specification and into implementations that ship unsafe behavior. We show that large language models, equipped with an SMT solver, can audit such requirements: translating them into formal logic, detecting ambiguity through stochastic variation in the generated formalization, and exposing inconsistency, vacuousness, and safety violations through solver queries on the resulting specification. We present VERIMED, a neurosymbolic pipeline that operationalizes this idea for medical-device software requirements, and report two findings. First, stochastic variation across independent formalizations is a signal of ambiguity: requirements that admit multiple plausible interpretations produce SMT-inequivalent formalizations, and bidirectional SMT equivalence checking turns this disagreement into a solver-checkable test. Second, the usefulness of symbolic feedback depends on its granularity: in counterexample-guided repair on a hemodialysis question-answering benchmark, concrete SMT counterexamples raise verified accuracy from 55.4% to 98.5%. Over an extensive experimental evaluation on open-source hemodialysis safety requirements, we show that the LLM-based approach in VERIMED successfully reduces ambiguity-sensitive requirements and enables rigorous auditing of software requirements through SMT-based queries.

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

On-policy distillation (OPD) reduces train-test state mismatch by training a student on its own generated trajectories, but weak students may visit teacher-misaligned prefixes where supervision is less representative. We introduce SAKI (Supervision Allocation with KL-constrained Interpolation), which combines a KL-constrained teacher-guided rollout with maximal coupling and reuses realized accept/correction events to route token-level supervision. Accepted positions retain sampled-token reverse-KL supervision, while correction positions receive direct supervision on the teacher's highest-probability token. Under maximal coupling, the correction probability is exactly TV(p_t, q_t), so the same trust-region radius controls rollout deviation and upper-bounds intervention and specialized-supervision frequency. We further implement an engine-resident speculative verifier that preserves the exact-q trajectory distribution and coupling semantics while improving matched-workload rollout throughput by 4.22x. Across seven mathematical reasoning benchmarks, SAKI improves the matched teacher-guided baseline in Mean@8 and Pass@8 for both 1.7B and 0.6B students. Placement controls and fixed-prefix analysis further support correction-triggered routing as a conflict-adaptive supervision signal.

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

This paper introduces VeriThoughts, a novel dataset designed for reasoning-based Verilog code generation. We establish a new benchmark framework grounded in formal verification methods to evaluate the quality and correctness of generated hardware descriptions. Additionally, we present a suite of specialized small-scale models optimized specifically for Verilog generation. Our work addresses the growing need for automated hardware design tools that can produce verifiably correct implementations from high-level specifications, potentially accelerating the hardware development process while maintaining rigorous correctness guarantees. Our code and data are available at https://github.com/wilyub/VeriThoughts{this URL}.

Autonomous coding agents increasingly execute multi-step software work, but lifecycle states such as reviewed, tested, DONE, and ready-to-merge remain claims unless supported by current evidence. We present Proof-or-Stop Lifecycle Control, a method that permits lifecycle transitions only when fresh, tracked-source-state-bound, mechanically verifiable evidence satisfies the relevant gate. The method treats agent outputs as claims rather than lifecycle state, and uses proof operationally to mean gate-admissible evidence under a stated trust model, not semantic program correctness. We evaluate an open-source implementation through mechanism tests, a powered control-policy ablation, and operated self-application evidence. The unattended-loop engine passed 10 of 10 scenarios with zero false-DONE, and local-key receipt bundles rejected 18 tamper classes with zero false accepts. In a 9,240-cell ablation, the pre-registered A4 versus A2-prime comparison reduced visible-pass/hidden-fail amplification from 31 of 1,800 injected cells under a compute-budgeted naive loop to 2 of 1,800 under the gated loop, a 1.6 percentage-point improvement in not-amplified rate with a 95 percent confidence interval of [0.8, 2.5]. A near-compute A3 versus A4 comparison, 14 of 1,800 versus 2 of 1,800, indicates that the gain is associated with enforcing review as a lifecycle gate rather than merely adding a reviewer. The self-application corpus contains 565 stories and 1,007 review findings, with 94.8 percent resolved, plus a 68-row high/critical cross-vendor exhibit. These results support Proof-or-Stop as a model-agnostic, host-neutral control layer for deciding which autonomous-agent claims a lifecycle may act on. The evaluation is limited to one model family, 24 ablation tasks, and a self-hosted corpus.

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.

Large language models (LLMs) have shown strong performance in Verilog generation from natural language description. However, ensuring the functional correctness of the generated code remains a significant challenge. This paper introduces a method that integrates verification insights from testbench into the training of Verilog generation LLMs, aligning the training with the fundamental goal of hardware design: functional correctness. The main obstacle in using LLMs for Verilog code generation is the lack of sufficient functional verification data, particularly testbenches paired with design specifications and code. To address this problem, we introduce an automatic testbench generation pipeline that decomposes the process and uses feedback from the Verilog compiler simulator (VCS) to reduce hallucination and ensure correctness. We then use the testbench to evaluate the generated codes and collect them for further training, where verification insights are introduced. Our method applies reinforcement learning (RL), specifically direct preference optimization (DPO), to align Verilog code generation with functional correctness by training preference pairs based on testbench outcomes. In evaluations on VerilogEval-Machine, VerilogEval-Human, RTLLM v1.1, RTLLM v2, and VerilogEval v2, our approach consistently outperforms state-of-the-art baselines in generating functionally correct Verilog code. We open source all training code, data, and models at https://anonymous.4open.science/r/VeriPrefer-E88B.

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.

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

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

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

Computer-use agents provide a promising path toward general software automation because they can interact directly with arbitrary graphical user interfaces instead of relying on brittle, application-specific integrations. Despite recent advances in benchmark performance, strong computer-use agents remain expensive and slow in practice, since most systems invoke large multimodal models at nearly every interaction step. We argue that this uniform allocation of compute is fundamentally inefficient for long-horizon GUI tasks. Such trajectories are highly heterogeneous: many steps are routine and can be handled reliably by smaller, cheaper policies, while errors tend to concentrate at a relatively small number of high-risk moments. Across computer-use benchmarks, these failures repeatedly take two forms: progress stalls, where the agent loops, repeats ineffective actions, or fails to make meaningful progress, and silent semantic drift, where the agent continues taking locally plausible actions after already deviating from the user's true goal. To address this inefficiency, we propose an event-driven, step-level cascade for computer-use agents that runs a small policy by default and escalates to a stronger model only when lightweight learned monitors detect elevated risk. Our framework combines two complementary signals: a Stuck Monitor that detects degraded progress from recent reasoning-action history and triggers recovery, and a Milestone Monitor that identifies semantically meaningful checkpoints where sparse verification is most informative for catching drift. This design turns always-on frontier-model inference into adaptive, on-demand compute allocation over the course of an evolving interaction. The framework is modular and deployment-oriented: it can be layered on top of existing computer-use agents without changing the underlying agent architecture or retraining the large model.

A framework that persists execution state so a run can be interrupted, survive a crash, and continue must decide what a resume means for effects that already happened. Five widely deployed agent workflow frameworks answer differently, none exposes a machine-checkable contract, and measured behavior violates even the fragments they state. The RESUME CONTRACT states six properties over the persistence API (prefix continuation, effect exactly-once, fork determinism, checkpoint validity, consume-once, recovery determinism), plus fork-intent and liveness obligations. A TLA+ model checks a reference semantics exhaustively, unchanged at scaled bounds (7.4 million states), and the reference conjunction is additionally TLAPS-proved unbounded (196 obligations); a 39-cell fault matrix and two companion modules yield the separating models independence requires. A deterministic, LLM-free harness measures them at pinned releases. LangGraph 1.2.9 durably records a second resume value and never consults it, persists schema-invalid state silently, and re-executes durably recorded work after a real SIGKILL: exactly-once across interrupts, at-least-once across crashes, on one API. CrewAI 1.15.2 re-executes completed effect-bearing methods against its written claim; pydantic-graph 1.x cannot resume after a mid-node crash; no two probed frameworks share a conformance profile. Consume-once holds sequentially and fails under concurrent delivery: k processes resuming one parked interrupt fire the gated effect k times, saturation 1.0 in 36 of 40 cells, and the failure crosses hosts. REMIT, a reference sequencer whose Verus-verified recovery core is line-identical to the shipped executable, repairs the fork and validity cells. The cross-process cell is repaired at the read path: an opt-in gate claims consumption in the shared store, serving one racer and refusing the rest before any node executes.

In recent years, unified vision-language models (VLMs) have rapidly advanced, effectively tackling both visual understanding and generation tasks within a single design. While many unified VLMs have explored various design choices, the recent hypothesis from OpenAI's GPT-4o suggests a promising generation pipeline: Understanding VLM->Visual Feature->Projector->Diffusion Model->Image. The understanding VLM is frozen, and only the generation-related modules are trained. This pipeline maintains the strong capability of understanding VLM while enabling the image generation ability of the unified VLM. Although this pipeline has shown very promising potential for the future development of unified VLM, how to easily enable image editing capability is still unexplored. In this paper, we introduce a novel training-free framework named UniEdit-I to enable the unified VLM with image editing capability via three iterative steps: understanding, editing, and verifying. 1. The understanding step analyzes the source image to create a source prompt through structured semantic analysis and makes minimal word replacements to form the target prompt based on the editing instruction. 2. The editing step introduces a time-adaptive offset, allowing for coherent editing from coarse to fine throughout the denoising process. 3. The verification step checks the alignment between the target prompt and the intermediate edited image, provides automatic consistency scores and corrective feedback, and determines whether to stop early or continue the editing loop. This understanding, editing, and verifying loop iterates until convergence, delivering high-fidelity editing in a training-free manner. We implemented our method based on the latest BLIP3-o and achieved state-of-the-art (SOTA) performance on the GEdit-Bench benchmark.

Optimizing Register Transfer Level (RTL) code is crucial for improving the power, performance, and area (PPA) of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts. This paper presents SymRTLO, a novel neuron-symbolic RTL optimization framework that seamlessly integrates LLM-based code rewriting with symbolic reasoning techniques. Our method incorporates a retrieval-augmented generation (RAG) system of optimization rules and Abstract Syntax Tree (AST)-based templates, enabling LLM-based rewriting that maintains syntactic correctness while minimizing undesired circuit behaviors. A symbolic module is proposed for analyzing and optimizing finite state machine (FSM) logic, allowing fine-grained state merging and partial specification handling beyond the scope of pattern-based compilers. Furthermore, a fast verification pipeline, combining formal equivalence checks with test-driven validation, further reduces the complexity of verification. Experiments on the RTL-Rewriter benchmark with Synopsys Design Compiler and Yosys show that SymRTLO improves power, performance, and area (PPA) by up to 43.9%, 62.5%, and 51.1%, respectively, compared to the state-of-the-art methods.

Following multiple instructions is a crucial ability for large language models (LLMs). Evaluating this ability comes with significant challenges: (i) limited coherence between multiple instructions, (ii) positional bias where the order of instructions affects model performance, and (iii) a lack of objectively verifiable tasks. To address these issues, we introduce a benchmark designed to evaluate models' abilities to follow multiple instructions through sequential instruction following (SIFo) tasks. In SIFo, the successful completion of multiple instructions is verifiable by examining only the final instruction. Our benchmark evaluates instruction following using four tasks (text modification, question answering, mathematics, and security rule following), each assessing different aspects of sequential instruction following. Our evaluation of popular LLMs, both closed-source and open-source, shows that more recent and larger models significantly outperform their older and smaller counterparts on the SIFo tasks, validating the benchmark's effectiveness. All models struggle with following sequences of instructions, hinting at an important lack of robustness of today's language models.

The decompose-then-verify strategy for verification of Large Language Model (LLM) generations decomposes claims that are then independently verified. Decontextualization augments text (claims) to ensure it can be verified outside of the original context, enabling reliable verification. While decomposition and decontextualization have been explored independently, their interactions in a complete system have not been investigated. Their conflicting purposes can create tensions: decomposition isolates atomic facts while decontextualization inserts relevant information. Furthermore, a decontextualized subclaim presents a challenge to the verification step: what part of the augmented text should be verified as it now contains multiple atomic facts? We conduct an evaluation of different decomposition, decontextualization, and verification strategies and find that the choice of strategy matters in the resulting factuality scores. Additionally, we introduce DnDScore, a decontextualization aware verification method which validates subclaims in the context of contextual information.

Speculative Decoding (SD) accelerates large language model inference by allowing a lightweight draft model to propose tokens that are subsequently verified in parallel by a larger target model. Recent approaches introduce lossy verification schemes to further improve efficiency by relaxing strict distributional matching. Yet such relaxation silently rewrites the decoding distribution, and the resulting acceleration can come at the cost of unstable, sometimes severely degraded generation quality. In this work, we present a principled analysis of the distributions induced by lossy verification methods. We show that many seemingly distinct approaches differ only superficially and can be classified into two categories: truncation-based verification and collaborative verification. We further construct a diagnostic evaluation framework across curated benchmarks. For truncation-based methods, we identify a fundamental pitfall: performance can degrade significantly compared to the true truncation sampling baseline due to distributional distortion. For collaborative verification, we uncover a key principles: controlling the overshoot of draft probabilities relative to target probabilities is essential to prevent low-quality outputs. Our code is available at https://github.com/ZhouYuxuanYX/Fast-HSD.

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

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

Contemporary neural inference architectures rely on dense floating-point weight matrices stored in high-bandwidth memory (VRAM), incurring severe memory-wall bottlenecks and preventing native execution inside deterministic virtual machines like the Ethereum Virtual Machine (EVM). Verifying termination and arithmetic invariants for recursive dynamical systems over continuous domains is generally undecidable in the Blum-Shub-Smale model. Here, we present the formal verification and bare-metal empirical validation of WERR (Waves & Errors) and Phase III Orbital Error Dynamics (OED), a non-tensor decision paradigm that procedurally synthesizes non-linear decision boundaries on demand from a 24-byte coordinate seed Θ= (c_x, c_y, zoom) along the boundary of the Mandelbrot set (partialM). By projecting the recurrence z_{n+1} = z_n^2 + c onto the modular residue ring Z/9Z and the fixed-point domain Q_{16.16}, we establish ten machine-verified theorems in Lean 4 (v4.34.1) with Mathlib4 and zero unproven conjectures (sorry): proving I_3 = {0,3,6} subset Z/9Z ideal closure, universal fuel-bounded halting (le 9 and le 12 steps), absence of Q_{16.16} square overflow below 2^{63}-1, non-constant boundary escape sensitivity, and a parametric EVM gas bound (le 22,557 le 24,000 gas). Evaluated on a 40-core Dual Intel Xeon server, the vectorized 36-iteration CPU kernel processes 100,000 decisions in 6.49 s (15,397 decisions/s, 0 Bytes VRAM, 15.15x speedup), while a sigmoidal outlier gate suppresses 100.00% of adversarial spikes while preserving 89.60% of clean baseline signals.

Serial verification gates are a core reliability primitive in LLM harnesses: a candidate answer is returned only if k verifier calls all accept it. Under conditionally independent gates, the recent Odds Law (arXiv:2606.15712) shows that posterior log-odds grow linearly in k, so failure decays exponentially, and states that "a tight theory of partially correlated verifier cascades remains open." This note gives a minimal such theory. Modeling the per-instance false-accept rate on the generator's own errors as a latent variable αsim G (de Finetti), the exact cascade posterior is ell_k = ell_0 - ln m_k, with m_k the k-th moment of G. Then: (i) ell_k is concave in k for every non-degenerate G -- the Odds Law is its tangent at the first gate and an upper bound; (ii) for Beta(a,b) latents, failure decays polynomially, 1-r_k asymp k^{-b}, with correlation parameter ρ_v = 1/(a+b+1); (iii) a blind-spot atom of mass 1-π at α=1 caps the evidence extractable from any number of gates at -ln(1-π) nats, so reliability saturates below 1; (iv) letting the true-accept rate also vary (βsim H) yields a trichotomy -- gates eventually always help, plateau, or actively harm -- decided by the upper-tail exponents of G and H, with closed-form crossover k^dagger. The mechanism is survivorship: errors surviving gates are the high-α ones. The theory is measurable: R repeated verdicts per instance identify the first R moments of G, so two verdicts identify ρ_v; beta-binomial likelihood and NPMLE recover the reliability curve and the ill-posed ceiling. In synthetic tests, independence-based extrapolation underestimates failure by 20x at k=5 and ~3000x at k=10; the correlated fit at R=8 tracks held-out depths. The practical lever is decorrelation -- changing model family, modality, or evidence source -- not adding gates.

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

Multi-agent large language model (LLM) systems often rely on verifier and critic agents to suppress hallucinations, but verification is delayed. During this delay, false claims can propagate through the agent network. We model this process as delayed consensus on a graph with grounded corrector nodes. Spectral decomposition by the grounded Laplacian yields a closed-form stability threshold for the verification dose: correction that is too strong or too delayed can turn consensus into oscillation. The most unstable regime occurs when the communication and verification delays coincide; for delay two, the threshold is the inverse golden ratio. The same framework gives a supermodular placement objective and a greedy (1-1/e)-approximation rule for assigning a limited corrector budget to influential nodes. Experiments across five open models confirm the predicted dose-delay oscillations. By contrast, grounded factual answering makes truth an absorbing boundary and eliminates the effect, suggesting that the instability is specific to signed-belief tasks while grounded verification remains stabilizing

The standard paradigm for solving coding tasks via large language models (LLMs) is to generate-then-rank programs, where the latter step uses a verifier in the ranking process. The growing consensus is that a comprehensive verifier (e.g., a full test suite) should be prioritized over an outcome reward model (ORM) whenever possible, with little consideration given to the trade-offs involved. We aim to challenge this assumption by systematically exploring the tradeoff between speed and accuracy. We find that ORMs play a crucial role in scaling verification through trading accuracy for speed, even when a comprehensive verifier is available. Their value becomes especially apparent when used in a generate-prune-then-rank approach, where a faster but less accurate verifier removes incorrect solutions prior to ranking -- leading to a system that is 11.65x faster while only being 8.33% less accurate than the full test suite. We analyze the generate-prune-then-rank approach and show that it works by filtering out incorrect but highly ranked solutions. These findings enable the design of scalable and accurate program ranking systems.

Modern LLM RL systems separate rollout generation from policy optimization. These two stages are expected to produce token probabilities that match exactly. However, implementation differences can make them assign different values to the same sequence under the same model weights, inducing Training-Inference Mismatch (TIM). TIM is difficult to inspect because it is entangled with off-policy drift and common stabilization mechanisms. In this work, we isolate TIM in a zero-mismatch diagnostic setting (VeXact), and show that small token-level numerical disagreements can independently cause training collapse. We further show that TIM changes the effective optimization problem, and identify a set of remedies that could mitigate TIM. Our results suggest that TIM is not benign numerical noise, but a systems-level perturbation that should be treated as a first-order factor in analyzing LLM RL stability.

Large Language Models (LLMs) present a critical trade-off between inference quality and computational cost: larger models offer superior capabilities but incur significant latency, while smaller models are faster but less powerful. Existing serving strategies often employ fixed model scales or static two-stage speculative decoding, failing to dynamically adapt to the varying complexities of user requests or fluctuations in system performance. This paper introduces , a novel framework that reimagines LLM inference as an adaptive routing problem solved through multi-level speculative decoding. dynamically constructs and optimizes inference "paths" (chains of models) based on real-time feedback, addressing the limitations of static approaches. Our contributions are threefold: (1) An adaptive model chain scheduling mechanism that leverages performance profiling (execution times) and predictive similarity metrics (derived from token distribution divergence) to continuously select the optimal sequence of draft and verifier models, minimizing predicted latency per generated token. (2) A multi-level collaborative verification framework where intermediate models within the selected chain can validate speculative tokens, reducing the verification burden on the final, most powerful target model. (3) A synchronized state management system providing efficient, consistent KV cache handling across heterogeneous models in the chain, including precise, low-overhead rollbacks tailored for asynchronous batch processing inherent in multi-level speculation. Preliminary experiments demonstrate the validity of our method.

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.

Recently, the rapid development of large language models (LLMs) has reshaped software engineering by enabling autonomous code agents that plan, execute, and utilize external tools iteratively to tackle complex tasks. Beyond achieving functional correctness, these agents must faithfully follow process instructions and constraints throughout the development lifecycle. However, existing benchmarks typically focus on final functional correctness or confine instruction-following evaluation to single-turn, general chat or simple code generation scenarios, leaving instruction-following in multi-turn agentic coding underexplored. To bridge this gap, we propose MTAC-IFBench, a comprehensive benchmark for this critical capability. It features multi-turn progressive software development instructions with diverse constraints spanning 6 primary and 18 secondary categories. With an average of 7.04 turns and 91.33 constraints per instance, it poses a rigorous challenge to current LLMs. To make the evaluation reliable, we construct a checklist for each constraint and functional requirement, and integrate verification scripts and judge agents to verify each checklist item. MTAC-IFBench identifies significant deficiencies in existing code agents in multi-turn instruction-following, with their performance degrading rapidly as the interaction session grows longer.

We address the problem of runtime trajectory anomaly detection, a critical capability for enabling trustworthy LLM agents. Current safety measures predominantly focus on static input/output filtering. However, we argue that ensuring LLM agents reliability requires auditing the intermediate execution process. In this work, we formulate the task of Trajectory Anomaly Detection. The goal is not merely detection, but precise error localization. This capability is essential for enabling efficient rollback-and-retry. To achieve this, we construct TrajBench, a dataset synthesized via a perturb-and-complete strategy to cover diverse procedural anomalies. Using this benchmark, we investigate the capability of models in process supervision. We observe that general-purpose LLMs, even with zero-shot prompting, struggle to identify and localize these anomalies. This reveals that generalized capabilities do not automatically translate to process reliability. To address this, we propose TrajAD, a specialized verifier trained with fine-grained process supervision. Our approach outperforms baselines, demonstrating that specialized supervision is essential for building trustworthy agents.

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

We propose claim-level falsification as a principle for test-time scaling and instantiate it through Claim-Level Reliability Assessment (CLR), a training-free framework that reallocates test-time compute from additional solution sampling to targeted verification. Since whole-trace evaluation often obscures decisive errors due to signal dilution from routine tokens, CLR condenses each reasoning trace into a compact set of decision-critical claims, thereby isolating its logical anchors. Furthermore, recognizing the inherent difficulty of generating entirely correct solutions under fixed model capabilities, CLR shifts the focus to semantic falsification. This approach exploits a fundamental asymmetry between solution construction and claim refutation. Constructing a valid solution requires a flawless reasoning path, whereas refuting an incorrect claim requires identifying only a single decisive flaw. This targeted search for negative evidence systematically compresses the survival space of high-confidence incorrect traces, effectively suppressing erroneous consensus via nonlinear reliability scoring. Across four LLMs and four reasoning benchmarks under matched budgets, CLR generally improves upon pass@1 and self-consistency. On GPT-OSS-20B/CMIMC25, for instance, CLR exceeds pass@1 by 27.15 percentage-points and raises self-consistency accuracy from 77.50\% to 82.19\% with 37.0\% fewer tokens.

Online Surgical Phase Recognition (SPR) models can reach high frame-wise accuracy, yet their predictions often lack temporal stability, fragmenting workflow understanding and reducing the reliability of downstream assistance. We show that this instability is not random noise but arises from two mechanisms: early misclassifications corrupt temporal feature states and propagate forward to form error cascades, and phase transitions follow evidence-accumulation dynamics whereas most online SPR systems rely on memoryless frame-wise decisions, making them sensitive to transient confidence fluctuations. We propose a unified Train-Inference-Evaluation framework that explicitly stabilizes temporal inference dynamics using model-agnostic, plug-and-play components. For training, the Temporal Error-Cascade (TEC) loss suppresses error onset and mitigates forward error propagation by stabilizing temporal feature evolution. For inference, the Evidence-Gated Transition Predictor (EGTP) enforces evidence-driven state transitions, allowing phase changes only when accumulated evidence exceeds a confidence boundary. For evaluation, we introduce the Temporal Fragmentation Index (TFI), a reliability-aware metric that quantifies instability-induced temporal disagreement beyond conventional frame-wise and token-based measures. Experiments on Cholec80 and AutoLaparo across three representative backbones show that the proposed framework substantially improves temporal stability and reduces prediction fragmentation, while maintaining or modestly improving frame-wise performance.

Large language model (LLM)-based reasoning systems have recently achieved gold medal-level performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also sufficiently supported. To train LLM-based reasoners in such challenging, open-ended settings, strong verifiers capable of catching step-level mistakes are necessary prerequisites. We introduce Hard2Verify, a human-annotated, step-level verification benchmark produced with over 500 hours of human labor. Hard2Verify is designed to rigorously assess step-level verifiers at the frontier: Verifiers must provide step-level annotations or identify the first error in responses generated by frontier LLMs for very recent, challenging, and open-ended math questions. We evaluate 29 generative critics and process reward models, demonstrating that, beyond a few standouts, open-source verifiers lag closed source models. We subsequently analyze what drives poor performance in step-level verification, the impacts of scaling verifier compute, as well as fundamental questions such as self-verification and verification-generation dynamics.

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

Large language models can generate fluent answers that are unfaithful to the provided context, while many safeguards rely on external verification or a separate judge after generation. We introduce internal flow signatures that audit decision formation from depthwise dynamics at a fixed inter-block monitoring boundary. The method stabilizes token-wise motion via bias-centered monitoring, then summarizes trajectories in compact moving readout-aligned subspaces constructed from the top token and its close competitors within each depth window. Neighboring window frames are aligned by an orthogonal transport, yielding depth-comparable transported step lengths, turning angles, and subspace drift summaries that are invariant to within-window basis choices. A lightweight GRU validator trained on these signatures performs self-checking without modifying the base model. Beyond detection, the validator localizes a culprit depth event and enables a targeted refinement: the model rolls back to the culprit token and clamps an abnormal transported step at the identified block while preserving the orthogonal residual. The resulting pipeline provides actionable localization and low-overhead self-checking from internal decision dynamics. Code is available at github.com/EavnJeong/Internal-Flow-Signatures-for-Self-Checking-and-Refinement-in-LLMs.

We study the right to be forgotten (GDPR Art. 17) for large language models and frame unlearning as a reproducible systems problem. Our approach treats training as a deterministic program and logs a minimal per-microbatch record (ordered ID hash, RNG seed, learning-rate value, optimizer-step counter, and accumulation boundary). Under a pinned stack and deterministic kernels, replaying the training tail while filtering only the forget closure yields the same parameters as training on the retain set (bit-identical in the training dtype) when preconditions hold. To meet latency and availability constraints, we add complementary paths: (i) exact reverts of recent steps via micro-checkpoints or dense per-step deltas, (ii) cohort-scoped adapter deletion when the base is frozen, and (iii) a curvature-guided anti-update followed by a short retain-tune, audit-gated with escalation to exact replay. We report storage/latency budgets and a toy artifact validating mechanics; in a controlled run that satisfies the preconditions we demonstrate byte-identical equality of model and optimizer states.

Large Language Models (LLMs) have become increasingly popular for generating RTL code. However, producing error-free RTL code in a zero-shot setting remains highly challenging for even state-of-the-art LLMs, often leading to issues that require manual, iterative refinement. This additional debugging process can dramatically increase the verification workload, underscoring the need for robust, automated correction mechanisms to ensure code correctness from the start. In this work, we introduce AIvril2, a self-verifying, LLM-agnostic agentic framework aimed at enhancing RTL code generation through iterative corrections of both syntax and functional errors. Our approach leverages a collaborative multi-agent system that incorporates feedback from error logs generated by EDA tools to automatically identify and resolve design flaws. Experimental results, conducted on the VerilogEval-Human benchmark suite, demonstrate that our framework significantly improves code quality, achieving nearly a 3.4times enhancement over prior methods. In the best-case scenario, functional pass rates of 77% for Verilog and 66% for VHDL were obtained, thus substantially improving the reliability of LLM-driven RTL code generation.

Large language models (LLMs) have advanced code generation, where executable feedback provides a more reliable learning signal than textual imitation alone. Hardware verification is an important application of code generation and accounts for a substantial fraction of modern chip design effort, with high-coverage testbench stimulus generation as a key task. We present CHORUS, a post-training framework that pushes performance beyond what a conventional supervised fine-tuning (SFT)-to-reinforcement learning (RL) pipeline achieves. CHORUS builds on two observations. First, staged SFT produces behaviorally diverse checkpoints, and dense-reward RL turns them into strong experts with comparable aggregate performance but distinct task-level strengths. Second, these complementary strengths can be exploited through either training-free model merging or further post-training to outperform the best individual expert. By consolidating the resulting specialists into a single 4B model, CHORUS achieves 88.0% Pass@1 on CVDP-ECov, outperforming DeepSeek-R1 (671B) by 13.5 percentage points.

Resolving a real software issue with a large language model (LLM) agent is a long repair episode, often tens to hundreds of steps spanning exploration, hypothesis, implementation, and verification. Success depends on both the base model's local reasoning and the agent's ability to maintain an evolving plan and remember observations across phases. Existing repository-level agents typically strengthen planning or memory in isolation, leaving long trajectories vulnerable to stale evidence, repeated failed edits, and verification inferred from the agent's own claims instead of execution evidence. We present PMCoder, an issue-resolution agent that couples a hierarchical phase planner with episodic memory. The coupling is bidirectional: the current plan phase conditions memory retrieval, while memory-derived trajectory statistics inform stuck detection and replanning. When available, issue-reproduction verdicts ground verification progress in execution evidence rather than self-reported completion. On SWE-bench Verified, PMCoder resolves an average of 25 more cases (+5.0pp) than a harness-matched baseline, with gains persisting even where the reproduction gate never fires. Further Verified-500 evaluations show the same positive direction across Claude Haiku 4.5, DeepSeek-V4-Flash, and an OpenHands port, with at least 14 additional resolved cases (+2.8pp). Separately, evaluation on TerminalWorld's official sample suggests that the plan-memory substrate transfers beyond issue reports. Ablation and trajectory analyses show where the gains come from: coupling planning and memory outperforms either component alone and reduces repeated failed actions, empty-patch exits, and context-window exhaustion.

Process attestation systems verify that a continuous physical process, such as human authorship, actually occurred, rather than merely checking system state. These systems face a fundamental dependability challenge: the evidence collection infrastructure must remain available and tamper-resistant even when the attesting party controls the platform. Trusted Execution Environments (TEEs) provide hardware-enforced isolation that can address this challenge, but their integration with continuous process attestation introduces novel resilience requirements not addressed by existing frameworks. We present the first architecture for continuous process attestation evidence collection inside TEEs, providing hardware-backed tamper resistance against trust-inverted adversaries with graduated input assurance from software-channel integrity (Tier 1) through hardware-bound input (Tier 3). We develop a Markov-chain dependability model quantifying Evidence Chain Availability (ECA), Mean Time Between Evidence Gaps (MTBEG), and Recovery Time Objectives (RTO). We introduce a resilient evidence chain protocol maintaining chain integrity across TEE crashes, network partitions, and enclave migration. Our security analysis derives formal bounds under combined threat models including trust inversion and TEE side channels, parameterized by a conjectural side-channel leakage bound esc that requires empirical validation. Evaluation on Intel SGX demonstrates under 25% per-checkpoint CPU overhead (<0.3% of the 30 s checkpoint interval), >99.5% Evidence Chain Availability (ECA) (the fraction of session time with active evidence collection) in Monte Carlo simulation under Poisson failure models, and sealed-state recovery under 200 ms.

While Large Language Models (LLMs) have substantially advanced text-to-code synthesis, many real programming tasks specify intent through visual artifacts such as screenshots, charts, vector drawings, videos, and interactive states. These tasks require models to connect visual perception to executable programs, because correctness depends not only on syntax but also on layout, data semantics, interaction behavior, and domain-specific constraints that apply after execution. This survey examines Multimodal Code Intelligence, covering systems that generate, edit, refine, or reason with code under visually grounded inputs and outputs. We first formulate the field by the role that code plays in each task, distinguishing code as a rendered artifact, an editable symbolic structure, a scientific representation, an intermediate reasoning trace, or an executable policy or tool interface. We then organize benchmarks and methods into four domains: Graphical User Interface, Scientific Visualization, Structured Graphics, and Frontier Tasks and Frameworks. This taxonomy connects mature artifact-generation problems to emerging agentic and unified settings and allows us to compare how different tasks treat evidence of correctness. Looking ahead, we argue that future research may benefit from four verification-centered directions. Multi-signal validation can combine complementary evidence of correctness, multi-state verification can test behavior across execution trajectories, cross-task transfer testing can probe reusable visual-code skills, and verifiable agent traces can reveal whether agent actions are grounded in visual evidence. Together, these directions may move this field from single-output imitation toward evidence-grounded executable systems. An ongoing project and resources are available on https://github.com/xjywhu/Awesome-Multimodal-LLM-for-Code{GitHub}.

Large language models (LLMs) have recently emerged as a promising approach for automating Verilog code generation; however, existing methods primarily emphasize syntactic correctness and often rely on commercial models or external verification tools, which introduces concerns regarding cost, data privacy, and limited guarantees of functional correctness. This work proposes a unified multi-agent framework for reasoning-oriented training data generation with integrated testbench-driven verification, enabling locally fine-tuned LLMs, SiliconMind-V1, to iteratively generate, test, and debug Register-Transfer Level (RTL) designs through test-time scaling. Experimental results on representative benchmarks (VerilogEval-v2, RTLLM-v2, and CVDP) demonstrate that the proposed approach outperforms the state-of-the-art QiMeng-CodeV-R1 in functional correctness while using fewer training resources.

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.

Test-time scaling is a powerful strategy for boosting the performance of large language models on complex reasoning tasks. While state-of-the-art approaches often employ generative verifiers to select the best solution from a pool of candidates, this method incurs prohibitive computational costs, limiting its practicality. In this work, we shift the focus to a more budget-aware paradigm: discriminative verification. We conduct a thorough empirical analysis and demonstrate that while discriminative verifiers may underperform in isolation, combining them with self-consistency in a hybrid approach creates a powerful and efficient test-time scaling mechanism. Notably, under a fixed compute budget, this hybrid approach surpasses state-of-the-art generative verification by a significant margin: achieving up to 15.3\% higher accuracy on AIME2025. Our findings establish that for practical, real-world applications, budget-aware scaling with discriminative verifiers is not only a "free" upgrade over self-consistency, but also a more effective and efficient alternative to costly generative techniques. Code is available at https://github.com/wang-research-lab/verification.

Tool-augmented LLM agents call APIs whose intermediate outputs, such as presigned URLs, session tokens, and OAuth state parameters, are observation contracts: artifacts whose later use is constrained by the external system that produced them. We show that observation contract compliance (preserving the temporal validity and byte-level integrity) is an emergent, regression-prone capability: it is neither guaranteed by general tool-use ability nor consistently improved by larger or newer models. To measure this, we introduce ContractBench, a benchmark of 33 dual-axis tasks that probe two orthogonal failure modes no existing benchmark evaluates: validity failures (using an artifact after expiry) and integrity failures (corrupting an artifact's bytes through the observation-to-action pipeline). Our evaluation is deterministic and programmatic, with a virtual clock controlling time and SHA-256 hashes verifying byte integrity. We assign each outcome a failure label drawn from real-world API specifications. We evaluate 38 models and report four findings: (i) no evaluated model clears 80%, with Claude-Opus-4.6 leading at 77.8%, revealing that current frontier models still fail to comply with observation contracts; (ii) a sharp within-family capability cliff in Qwen 3.5 between 4B (0%) and 9B (56.6%), smoothing to 70.7% at 397B-A17B: what emerges across the cliff is mid-trajectory restraint, not tool-call competence; (iii) non-monotonic scaling across the GPT-5 family: agentic post-training can erode compliance through sycophancy-driven regression; (iv) our failure taxonomy works as an actionable in-context reward signal, yielding +7.1 pp on 42 paired GPT-5.1 failures.

This paper presents a simple, effective, and cost-efficient strategy to improve LLM performance by scaling test-time compute. Our strategy builds upon the repeated-sampling-then-voting framework, with a novel twist: incorporating multiple models, even weaker ones, to leverage their complementary strengths that potentially arise from diverse training data and paradigms. By using consistency as a signal, our strategy dynamically switches between models. Theoretical analysis highlights the efficiency and performance advantages of our strategy. Extensive experiments on six datasets demonstrate that our strategy not only outperforms self-consistency and state-of-the-art multi-agent debate approaches, but also significantly reduces inference costs. Additionally, ModelSwitch requires only a few comparable LLMs to achieve optimal performance and can be extended with verification methods, demonstrating the potential of leveraging multiple LLMs in the generation-verification paradigm.

We present DafnyPro, an inference-time framework that enhances LLMs for generating verification annotations in Dafny. DafnyPro comprises three key components: a diff-checker that prevents modifications to base program logic, a pruner that removes unnecessary invariants, and a hint-augmentation system that retrieves and applies predefined, problem-independent proof strategies. We evaluate DafnyPro using Claude Sonnet 3.5 and 3.7 on four benchmarks: Clover, MBPP-Dafny, HumanEval-Dafny, and DafnyBench, achieving consistent performance gains in all cases. Notably, on DafnyBench, the most challenging benchmark, Claude Sonnet 3.5 enhanced with DafnyPro achieves 86% correct proofs, a 16 pp improvement over the base model. We also fine-tune two Qwen models on training data derived from verification attempts by larger models enhanced with DafnyPro. Our 7B and 14B models achieve 68% and 70% correct proofs on DafnyBench, respectively, demonstrating that smaller models can maintain high verification accuracy.

This paper presents the Neural Network Verification (NNV) software tool, a set-based verification framework for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS). The crux of NNV is a collection of reachability algorithms that make use of a variety of set representations, such as polyhedra, star sets, zonotopes, and abstract-domain representations. NNV supports both exact (sound and complete) and over-approximate (sound) reachability algorithms for verifying safety and robustness properties of feed-forward neural networks (FFNNs) with various activation functions. For learning-enabled CPS, such as closed-loop control systems incorporating neural networks, NNV provides exact and over-approximate reachability analysis schemes for linear plant models and FFNN controllers with piecewise-linear activation functions, such as ReLUs. For similar neural network control systems (NNCS) that instead have nonlinear plant models, NNV supports over-approximate analysis by combining the star set analysis used for FFNN controllers with zonotope-based analysis for nonlinear plant dynamics building on CORA. We evaluate NNV using two real-world case studies: the first is safety verification of ACAS Xu networks and the second deals with the safety verification of a deep learning-based adaptive cruise control system.

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

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.