Daily Papers

AI-assisted software generation has increased development speed, but it has also amplified a persistent engineering problem: systems that are functionally correct may still be structurally insecure. In practice, prompt-based security review with large language models often suffers from uneven coverage, weak reproducibility, unsupported findings, and the absence of an immutable audit trail. The ESAA architecture addresses a related governance problem in agentic software engineering by separating heuristic agent cognition from deterministic state mutation through append-only events, constrained outputs, and replay-based verification. This paper presents ESAA-Security, a domain-specific specialization of ESAA for agent-assisted security auditing of software repositories, with particular emphasis on AI-generated or AI-modified code. ESAA-Security structures auditing as a governed execution pipeline with four phases reconnaissance, domain audit execution, risk classification, and final reporting and operationalizes the workflow into 26 tasks, 16 security domains, and 95 executable checks. The framework produces structured check results, vulnerability inventories, severity classifications, risk matrices, remediation guidance, executive summaries, and a final markdown/JSON audit report. The central idea is that security review should not be modeled as a free-form conversation with an LLM, but as an evidence-oriented audit process governed by contracts and events. In ESAA-Security, agents emit structured intentions under constrained protocols; the orchestrator validates them, persists accepted outputs to an append-only log, reprojects derived views, and verifies consistency through replay and hashing. The result is a traceable, reproducible, and risk-oriented audit architecture whose final report is auditable by construction.

Autonomous agents such as indoor drones must learn new object classes in real-time while limiting catastrophic forgetting, motivating Class-Incremental Learning (CIL). However, most unmanned aerial vehicle (UAV) datasets focus on outdoor scenes and offer limited temporally coherent indoor videos. We introduce an indoor dataset of 14,400 frames capturing inter-drone and ground vehicle footage, annotated via a semi-automatic workflow with a 98.6% first-pass labeling agreement before final manual verification. Using this dataset, we benchmark 3 replay-based CIL strategies: Experience Replay (ER), Maximally Interfered Retrieval (MIR), and Forgetting-Aware Replay (FAR), using YOLOv11-nano as a resource-efficient detector for deployment-constrained UAV platforms. Under tight memory budgets (5-10% replay), FAR performs better than the rest, achieving an average accuracy (ACC, mAP_{50-95} across increments) of 82.96% with 5% replay. Gradient-weighted class activation mapping (Grad-CAM) analysis shows attention shifts across classes in mixed scenes, which is associated with reduced localization quality for drones. The experiments further demonstrate that replay-based continual learning can be effectively applied to edge aerial systems. Overall, this work contributes an indoor UAV video dataset with preserved temporal coherence and an evaluation of replay-based CIL under limited replay budgets. Project page: https://spacetime-vision-robotics-laboratory.github.io/learning-on-the-fly-cl

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

The deployment of autonomous AI agents capable of executing commercial transactions has motivated the adoption of mandate-based payment authorization protocols, including the Universal Commerce Protocol (UCP) and the Agent Payments Protocol (AP2). These protocols replace interactive, session-based authorization with cryptographically issued mandates, enabling asynchronous and autonomous execution. While AP2 provides specification-level guarantees through signature verification, explicit binding, and expiration semantics, real-world agentic execution introduces runtime behaviors such as retries, concurrency, and orchestration that challenge implicit assumptions about mandate usage. In this work, we present a security analysis of the AP2 mandate lifecycle and identify enforcement gaps that arise during runtime in agent-based payment systems. We propose a zero-trust runtime verification framework that enforces explicit context binding and consume-once mandate semantics using dynamically generated, time-bound nonces, ensuring that authorization decisions are evaluated at execution time rather than assumed from static issuance properties. Through simulation-based evaluation under high concurrency, we show that context-aware binding and consume-once enforcement address distinct and complementary attack classes, and that both are required to prevent replay and context-redirect attacks. The proposed framework mitigates all evaluated attacks while maintaining stable verification latency of approximately 3.8~ms at throughput levels up to 10{,}000 transactions per second. We further demonstrate that the required runtime state is bounded by peak concurrency rather than cumulative transaction history, indicating that robust runtime security for agentic payment execution can be achieved with minimal and predictable overhead.

Autonomous agents based on Large Language Models (LLMs) have evolved from reactive assistants to systems capable of planning, executing actions via tools, and iterating over environment observations. However, they remain vulnerable to structural limitations: lack of native state, context degradation over long horizons, and the gap between probabilistic generation and deterministic execution requirements. This paper presents the ESAA (Event Sourcing for Autonomous Agents) architecture, which separates the agent's cognitive intention from the project's state mutation, inspired by the Event Sourcing pattern. In ESAA, agents emit only structured intentions in validated JSON (agent.result or issue.report); a deterministic orchestrator validates, persists events in an append-only log (activity.jsonl), applies file-writing effects, and projects a verifiable materialized view (roadmap.json). The proposal incorporates boundary contracts (AGENT_CONTRACT.yaml), metaprompting profiles (PARCER), and replay verification with hashing (esaa verify), ensuring the immutability of completed tasks and forensic traceability. Two case studies validate the architecture: (i) a landing page project (9 tasks, 49 events, single-agent composition) and (ii) a clinical dashboard system (50 tasks, 86 events, 4 concurrent agents across 8 phases), both concluding with run.status=success and verify_status=ok. The multi-agent case study demonstrates real concurrent orchestration with heterogeneous LLMs (Claude Sonnet 4.6, Codex GPT-5, Antigravity/Gemini 3 Pro, and Claude Opus 4.6), providing empirical evidence of the architecture's scalability beyond single-agent scenarios.

Automated skill evolution enables Large Language Model (LLM) agents to continuously improve without expensive retraining. However, existing approaches typically treat skill evolution as a sequence of local updates, overlooking relationships among skills and often producing overfitted skill updates that fail to generalize across tasks. We propose GSE, a globalized skill evolution framework that jointly optimizes skill compatibility and skill generalization. To preserve consistency across the skill bank, GSE maintains a Skill Relation Graph (SRG) that explicitly models and co-evolves inter-skill relationships. To improve generalization, GSE performs cluster-based skill consolidation to abstract reusable capabilities from local updates and employs replay-driven verification to prevent overfitting and behavioral regressions. We evaluate GSE on two representative software engineering tasks: bug-revealing test generation and false-positive bug report filtering. Across two state-of-the-art coding agents, OpenHands and mini-SWE-agent, GSE consistently achieves the best precision, recall, and F1-score. Compared with existing evolution techniques, GSE improves precision and recall by 6.1%~34.1% and 31.8%~180.0% for test generation, and by 15.4%~96.4% and 13.1%~19.8% for false-positive filtering. Deployment on an internal industrial agent further yields a 61.4% improvement in F1-score, demonstrating the effectiveness and generalizability of GSE for evolving effective skills.

While Experience Replay - the practice of storing rollouts and reusing them multiple times during training - is a foundational technique in general RL, it remains largely unexplored in LLM post-training due to the prevailing belief that fresh, on-policy data is essential for high performance. In this work, we challenge this assumption. We present a systematic study of replay buffers for LLM post-training, formalizing the optimal design as a trade-off between staleness-induced variance, sample diversity and the high computational cost of generation. We show that strict on-policy sampling is suboptimal when generation is expensive. Empirically, we show that a well-designed replay buffer can drastically reduce inference compute without degrading - and in some cases even improving - final model performance, while preserving policy entropy.

Large Reasoning Models (LRMs) achieve strong performance by generating long reasoning traces with reflection. Through a large-scale empirical analysis, we find that a substantial fraction of reflective steps consist of self-verification (recheck) that repeatedly confirm intermediate results. These rechecks occur frequently across models and benchmarks, yet the vast majority are confirmatory rather than corrective, rarely identifying errors and altering reasoning outcomes. This reveals a mismatch between how often self-verification is activated and how often it is actually useful. Motivated by this, we propose a novel, experience-driven test-time framework that reduces the overused verification. Our method detects the activation of recheck behavior, consults an offline experience pool of past verification outcomes, and estimates whether a recheck is likely unnecessary via efficient retrieval. When historical experience suggests unnecessary, a suppression signal redirects the model to proceed. Across multiple model and benchmarks, our approach reduces token usage up to 20.3% while maintaining the accuracy, and in some datasets even yields accuracy improvements.

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.

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

Test-time scaling via solution sampling and aggregation has become a key paradigm for improving the reasoning performance of Large Language Models (LLMs). While reward model selection is commonly employed in this approach, it often fails to identify minority-yet-correct answers, which limits its effectiveness beyond that of simple majority voting. We argue that this limitation stems from a lack of informative critique signals during verifier training. To bridge this gap, we introduce Mirror-Critique, a framework that trains a verifier with informative critiques. Our key insight is to leverage the rich critique signal by contrasting model-generated solutions with ground-truth solutions. We deploy a small instruction-tuned model to synthesize high-quality critique data with rejection sampling that teaches the verifier not only what is wrong, but also why. The synthetic data is used to cold-start the LLMs in the RLVR process to further improve the verification ability. The resulting Mirror-Verifier is deployed to evaluate candidate solutions by generating multiple critiques per solution, aggregating them into a verify score used for weighted voting or selective abstention. The experimental results show that our Mirror-Verifier significantly outperforms majority voting in terms of solution accuracy and also improves the solver's honesty to recognize and abstain from answering beyond its capability boundaries.

Evaluation artifacts specify a forward computation: a task, scorer, and reported metric. They do not necessarily license the claim attached to that metric because the historical evidence and alternative semantics needed to replay it may be unbound. We formalize this missing claim-replay layer through a frozen substrate D, a grounded family F, a claim query q, and the resulting identified set. We then census all 124 mechanically eligible Inspect Evals units at a pinned commit. Every unit receives a terminal disposition; 110 stop before deterministic inference because required historical evidence or semantic grounding is unavailable. Where execution closes, exact values, winners, complete orders, and pairwise relations separate by claim resolution and by primary versus review family. The audit therefore returns typed stops, instability witnesses, and stable substructure rather than forcing one evaluator meaning or one robust/not-robust label.

Nowadays transformer-based Large Language Models (LLM) for code generation tasks usually apply sampling and filtering pipelines. Due to the sparse reward problem in code generation tasks caused by one-token incorrectness, transformer-based models will sample redundant programs till they find a correct one, leading to low efficiency. To overcome the challenge, we incorporate Experience Replay (ER) in the fine-tuning phase, where codes and programs produced are stored and will be replayed to give the LLM agent a chance to learn from past experiences. Based on the spirit of ER, we introduce a novel approach called BTP pipeline which consists of three phases: beam search sampling, testing phase, and prioritized experience replay phase. The approach makes use of failed programs collected by code models and replays programs with high Possibility and Pass-rate Prioritized value (P2Value) from the replay buffer to improve efficiency. P2Value comprehensively considers the possibility of transformers' output and pass rate and can make use of the redundant resources caused by the problem that most programs collected by LLMs fail to pass any tests. We empirically apply our approach in several LLMs, demonstrating that it enhances their performance in code generation tasks and surpasses existing baselines.

The continual learning capability of large language models (LLMs) is crucial for advancing artificial general intelligence. However, continual fine-tuning LLMs across various domains often suffers from catastrophic forgetting, characterized by: 1) significant forgetting of their general capabilities, and 2) sharp performance declines in previously learned tasks. To simultaneously address both issues in a simple yet stable manner, we propose General Sample Replay (GeRe), a framework that use usual pretraining texts for efficient anti-forgetting. Beyond revisiting the most prevalent replay-based practices under GeRe, we further leverage neural states to introduce a enhanced activation states constrained optimization method using threshold-based margin (TM) loss, which maintains activation state consistency during replay learning. We are the first to validate that a small, fixed set of pre-collected general replay samples is sufficient to resolve both concerns--retaining general capabilities while promoting overall performance across sequential tasks. Indeed, the former can inherently facilitate the latter. Through controlled experiments, we systematically compare TM with different replay strategies under the GeRe framework, including vanilla label fitting, logit imitation via KL divergence and feature imitation via L1/L2 losses. Results demonstrate that TM consistently improves performance and exhibits better robustness. Our work paves the way for efficient replay of LLMs for the future. Our code and data are available at https://github.com/Qznan/GeRe.

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

Retrieval-enhanced methods have become a primary approach in fact verification (FV); it requires reasoning over multiple retrieved pieces of evidence to verify the integrity of a claim. To retrieve evidence, existing work often employs off-the-shelf retrieval models whose design is based on the probability ranking principle. We argue that, rather than relevance, for FV we need to focus on the utility that a claim verifier derives from the retrieved evidence. We introduce the feedback-based evidence retriever(FER) that optimizes the evidence retrieval process by incorporating feedback from the claim verifier. As a feedback signal we use the divergence in utility between how effectively the verifier utilizes the retrieved evidence and the ground-truth evidence to produce the final claim label. Empirical studies demonstrate the superiority of FER over prevailing baselines.

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

Reinforcement learning (RL) for large language models is an energy-intensive endeavor: training can be unstable, and the policy may gradually drift away from its pretrained weights. We present RLEP\, -- \,Reinforcement Learning with Experience rePlay\, -- \,a two-phase framework that first collects verified trajectories and then replays them during subsequent training. At every update step, the policy is optimized on mini-batches that blend newly generated rollouts with these replayed successes. By replaying high-quality examples, RLEP steers the model away from fruitless exploration, focuses learning on promising reasoning paths, and delivers both faster convergence and stronger final performance. On the Qwen2.5-Math-7B base model, RLEP reaches baseline peak accuracy with substantially fewer updates and ultimately surpasses it, improving accuracy on AIME-2024 from 38.2% to 39.9%, on AIME-2025 from 19.8% to 22.3%, and on AMC-2023 from 77.0% to 82.2%. Our code, datasets, and checkpoints are publicly available at https://github.com/Kwai-Klear/RLEP to facilitate reproducibility and further research.

Training models through self-play alone (without any human data) has been a longstanding goal in AI, but its effectiveness for training large language models remains unclear, particularly in code generation where rewards based on unit tests are brittle and prone to error propagation. We study self-play in the verified code generation setting, where formal verification provides reliable correctness signals. We introduce Propose, Solve, Verify (PSV) a simple self-play framework where formal verification signals are used to create a proposer capable of generating challenging synthetic problems and a solver trained via expert iteration. We use PSV to train PSV-Verus, which across three benchmarks improves pass@1 by up to 9.6x over inference-only and expert-iteration baselines. We show that performance scales with the number of generated questions and training iterations, and through ablations identify formal verification and difficulty-aware proposal as essential ingredients for successful self-play.

To obtain a language model for a target domain (e.g. math), the current paradigm is to pre-train on a vast amount of generic web text and then fine-tune on the relatively limited amount of target data. Typically, generic data is only mixed in during fine-tuning to prevent catastrophic forgetting of the generic domain. We surprisingly find that replaying the generic data during fine-tuning can actually improve performance on the (less related) target task. Concretely, in a controlled pre-training environment with 4M target tokens, 4B total tokens, and 150M parameter models, generic replay increases target data efficiency by up to 1.87times for fine-tuning and 2.06times for mid-training. We further analyze data schedules that introduce target data during pre-training and find that replay helps more when there is less target data present in pre-training. We demonstrate the success of replay in practice for fine-tuning 8B parameter models, improving agentic web navigation success by 4.5% and Basque question-answering accuracy by 2%.

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.

Instruction tuning effectively optimizes Large Language Models (LLMs) for downstream tasks. Due to the changing environment in real-life applications, LLMs necessitate continual task-specific adaptation without catastrophic forgetting. Considering the heavy computational cost, replay-based Continual Learning (CL) methods are the simplest and most widely used for LLMs to address the forgetting issue. However, traditional replay-based methods do not fully utilize instructions to customize the replay strategy. In this work, we propose a novel paradigm called Instruction-based Continual Learning (InsCL). InsCL dynamically replays previous data based on task similarity, calculated by Wasserstein Distance with instructions. Moreover, we further introduce an Instruction Information Metric (InsInfo) to quantify the complexity and diversity of instructions. According to InsInfo, InsCL guides the replay process more inclined to high-quality data. We conduct extensive experiments over 16 tasks with different training orders, observing consistent performance improvements of InsCL. When all tasks have been trained, InsCL achieves performance gains of 3.0 Relative Gain compared with Random Replay, and 27.96 Relative Gain compared with No Replay.

Replaying data is a principal mechanism underlying the stability and data efficiency of off-policy reinforcement learning (RL). We present an effective yet simple framework to extend the use of replays across multiple experiments, minimally adapting the RL workflow for sizeable improvements in controller performance and research iteration times. At its core, Replay Across Experiments (RaE) involves reusing experience from previous experiments to improve exploration and bootstrap learning while reducing required changes to a minimum in comparison to prior work. We empirically show benefits across a number of RL algorithms and challenging control domains spanning both locomotion and manipulation, including hard exploration tasks from egocentric vision. Through comprehensive ablations, we demonstrate robustness to the quality and amount of data available and various hyperparameter choices. Finally, we discuss how our approach can be applied more broadly across research life cycles and can increase resilience by reloading data across random seeds or hyperparameter variations.

Continual Learning (CL) aims at incrementally learning new tasks without forgetting the knowledge acquired from old ones. Experience Replay (ER) is a simple and effective rehearsal-based strategy, which optimizes the model with current training data and a subset of old samples stored in a memory buffer. To further reduce forgetting, recent approaches extend ER with various techniques, such as model regularization and memory sampling. However, the prediction consistency between the new model and the old one on current training data has been seldom explored, resulting in less knowledge preserved when few previous samples are available. To address this issue, we propose a CL method with Strong Experience Replay (SER), which additionally utilizes future experiences mimicked on the current training data, besides distilling past experience from the memory buffer. In our method, the updated model will produce approximate outputs as its original ones, which can effectively preserve the acquired knowledge. Experimental results on multiple image classification datasets show that our SER method surpasses the state-of-the-art methods by a noticeable margin.

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.

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.

One-shot Program-of-Thought (PoT) emits a Python program that prints a primitive-action plan; a single invalid action silently invalidates the trajectory. We introduce RePoT (Recoverable PoT): a deterministic verified replay that walks the plan through the environment to its first invalid transition, then one LLM call that resumes from the verified prefix. RePoT costs at most one extra LLM call on the ~14% of problems where PoT fails. RePoT beats PoT by +3 to +11pp across four closed-model configurations on PuzzleZoo-775 and peaks at 96.9% vs 86.3% on gpt-5.4-mini-medium; against the matched-budget PoT-retry baseline, RePoT wins decisively on Gemini (+3.8pp, 95% CI [+2.2,+5.4]), is within sampling noise on GPT-medium and Claude, and loses on GPT-mini -- a capability-scaling pattern we begin to address with Adaptive RePoT, a rule-based dispatcher that routes between suffix repair and a fresh PoT retry based on verified-prefix length (preliminary). We replicate on PlanBench Blocksworld (+1.1 to +11.4pp) and on four open-weights models (+3.3 to +20.0pp on three of four). On Derail-550, our controlled recovery benchmark, every condition with access to checkpoint information clears >=30% on GPT-medium and >=70% on Gemini, vs <=3.1% for error-only feedback -- showing that checkpoint information, not the specific verified-prefix tail, is the load-bearing recovery signal.

Reinforcement learning with verifiable rewards (RLVR) has delivered impressive gains in mathematical and multimodal reasoning and has become a standard post-training paradigm for contemporary language and vision-language models. However, the RLVR recipe introduces a significant risk of capability regression, where models forget foundational skills after prolonged training without employing regularization strategies. We empirically confirm this concern, observing that open-source reasoning models suffer performance degradation on core capabilities such as perception and faithfulness. While imposing regularization terms like KL divergence can help prevent deviation from the base model, these terms are calculated on the current task, thus they do not guarantee broader knowledge. Meanwhile, commonly used experience replay across heterogeneous domains makes it nontrivial to decide how much training focus each objective should receive. To address this, we propose RECAP-a replay strategy with dynamic objective reweighting for general knowledge preservation. Our reweighting mechanism adapts in an online manner using short-horizon signals of convergence and instability, shifting the post-training focus away from saturated objectives and toward underperforming or volatile ones. Our method is end-to-end and readily applicable to existing RLVR pipelines without training additional models or heavy tuning. Extensive experiments on benchmarks based on Qwen2.5-VL-3B and Qwen2.5-VL-7B demonstrate the effectiveness of our method, which not only preserves general capabilities but also improves reasoning by enabling more flexible trade-offs among in-task rewards.

A key component of fact verification is thevevidence retrieval, often from multiple documents. Recent approaches use dense representations and condition the retrieval of each document on the previously retrieved ones. The latter step is performed over all the documents in the collection, requiring storing their dense representations in an index, thus incurring a high memory footprint. An alternative paradigm is retrieve-and-rerank, where documents are retrieved using methods such as BM25, their sentences are reranked, and further documents are retrieved conditioned on these sentences, reducing the memory requirements. However, such approaches can be brittle as they rely on heuristics and assume hyperlinks between documents. We propose a novel retrieve-and-rerank method for multi-hop retrieval, that consists of a retriever that jointly scores documents in the knowledge source and sentences from previously retrieved documents using an autoregressive formulation and is guided by a proof system based on natural logic that dynamically terminates the retrieval process if the evidence is deemed sufficient. This method is competitive with current state-of-the-art methods on FEVER, HoVer and FEVEROUS-S, while using 5 to 10 times less memory than competing systems. Evaluation on an adversarial dataset indicates improved stability of our approach compared to commonly deployed threshold-based methods. Finally, the proof system helps humans predict model decisions correctly more often than using the evidence alone.

Online class-incremental continual learning is a specific task of continual learning. It aims to continuously learn new classes from data stream and the samples of data stream are seen only once, which suffers from the catastrophic forgetting issue, i.e., forgetting historical knowledge of old classes. Existing replay-based methods effectively alleviate this issue by saving and replaying part of old data in a proxy-based or contrastive-based replay manner. Although these two replay manners are effective, the former would incline to new classes due to class imbalance issues, and the latter is unstable and hard to converge because of the limited number of samples. In this paper, we conduct a comprehensive analysis of these two replay manners and find that they can be complementary. Inspired by this finding, we propose a novel replay-based method called proxy-based contrastive replay (PCR). The key operation is to replace the contrastive samples of anchors with corresponding proxies in the contrastive-based way. It alleviates the phenomenon of catastrophic forgetting by effectively addressing the imbalance issue, as well as keeps a faster convergence of the model. We conduct extensive experiments on three real-world benchmark datasets, and empirical results consistently demonstrate the superiority of PCR over various state-of-the-art methods.

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.

Mining specifications from execution traces presents an automated way of capturing characteristic system behaviors. However, existing approaches are largely restricted to Boolean abstractions of events, limiting their ability to express data-aware properties. In this paper, we extend mining procedures to operate over richer datatypes. We first establish candidate functions in our domain that cover the set of traces by leveraging Syntax Guided Synthesis (SyGuS) techniques. To capture these function applications temporally, we formalize the semantics of TSL_f, a finite-prefix interpretation of Temporal Stream Logic (TSL) that extends LTL_f with support for first-order predicates and functional updates. This allows us to unify a corresponding procedure for learning the data transformations and temporal specifications of a system. We demonstrate our approach synthesizing reactive programs from mined specifications on the OpenAI-Gymnasium ToyText environments, finding that our method is more robust and orders of magnitude more sample-efficient than passive learning baselines on generalized problem instances.

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

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) suffer from high inference latency due to the auto-regressive decoding process. Speculative decoding accelerates inference by generating multiple draft tokens using a lightweight model and verifying them in parallel. However, existing verification methods rely heavily on distributional consistency while overlooking semantic correctness, thereby limiting the potential speedup of speculative decoding. While some methods employ additional models for relaxed verification of draft tokens, they often fail to generalize effectively to more diverse or open-domain settings. In this work, we propose Reflective Verification, a training-free and semantics-aware approach that achieves a better trade-off between correctness and efficiency. Specifically, we leverage the inherent reflective capacity of LLMs to semantically assess the correctness of draft tokens in parallel during verification. Using prompt-based probing, we obtain both the original and reflective distributions of draft tokens in a single forward pass. The fusion of these distributions enables semantic-level verification of draft tokens that incorporates both consistency and correctness. Experiments across multiple domain benchmarks and model scales demonstrate that our method significantly increases the acceptance length of draft tokens without compromising model performance. Furthermore, we find that the proposed Reflective Verification is orthogonal to existing statistical verification methods, and their combination yields additional 5sim15\% improvements in decoding speed.

Evaluating Computer Use Agents (CUAs) on interactive environments is fraught with methodological pitfalls that the field has yet to systematically address. We show that a 1MB replay script that blindly executes a recorded action sequence without ever observing the screen outperforms frontier models on prominent static benchmarks, and prove that its expected success rate is exactly equal to the source agent's pass@k in deterministic environments. We trace this and other failures to two root causes: non-principled environment design (static, unsandboxed, or unreliably verified environments) and non-principled evaluation methodology (naive aggregation and misuse of pass@k for stateful UI interactions). To address the first, we propose PRISM, five design principles for CUA environments (privileged verification, realistic environments, integrity-checked configurations, sandboxed execution, and multifactorial variability) and instantiate them in DigiWorld, a benchmark of 15 realistic sandboxed mobile applications able to evaluate agents in over 3.2 million verified unique configurations. To address the second, we develop an aggregation framework pairing Wilson score intervals with hierarchical bootstrap, producing confidence intervals that correctly account for the nested structure of CUA benchmarks, as we empirically demonstrate. All together, we show that principled environment design and rigorous evaluation methodology are not optional refinements but prerequisites for meaningful CUA research.

Reinforcement learning with verifiable rewards (RLVR) plays a crucial role in expanding the capacities of LLM reasoning, but GRPO-style training is dominated by expensive rollouts and wastes compute on unusable prompts. We propose Prompt Replay, an overhead-free online data selection method for GRPO that reuses prompts only (not trajectories), to preserve on-policy optimization. After each step, we insert prompts with medium difficulty into a buffer, and prioritize prompts closer to a pass rate of 0.5 (half answers correct, half wrong) to maximize the advantage, thus learning signal. Training batches are formed by mixing reused prompts with fresh samples, with cooldown steps and max reuse times controlling aggressiveness vs risk of overfitting. Across multiple model families (Llama-3.2- 3B, Qwen3-8B) and training datasets (Dolci, Polaris), evaluated using average accuracy on six standard math benchmarks, Prompt Replay reduces zero-variance prompts, increases mean absolute advantage and shows faster initial accuracy gains. Yet, it plateaus and converges with the baseline, as too aggressive configuration was used. The method is most efficient when the rollouts are the primary bottleneck and the dataset is difficult for the model. We additionally observe that Qwen2.5-Math can exhibit spurious-reward effects that invalidates ablations, raising a warning signal for using it as a sole testbed for GRPO method research.

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.

Reinforcement learning (RL) is vital for optimizing large language models (LLMs). Recent Group Relative Policy Optimization (GRPO) estimates advantages using multiple on-policy outputs per prompt, leading to high computational costs and low data efficiency. To address this, we introduce Replay-Enhanced Policy Optimization (RePO), which leverages diverse replay strategies to retrieve off-policy samples from a replay buffer, allowing policy optimization based on a broader and more diverse set of samples for each prompt. Experiments on five LLMs across seven mathematical reasoning benchmarks demonstrate that RePO achieves absolute average performance gains of 18.4 and 4.1 points for Qwen2.5-Math-1.5B and Qwen3-1.7B, respectively, compared to GRPO. Further analysis indicates that RePO increases computational cost by 15% while raising the number of effective optimization steps by 48% for Qwen3-1.7B, with both on-policy and off-policy sample numbers set to 8. The repository can be accessed at https://github.com/SihengLi99/RePO.

People learn throughout life. However, incrementally updating conventional neural networks leads to catastrophic forgetting. A common remedy is replay, which is inspired by how the brain consolidates memory. Replay involves fine-tuning a network on a mixture of new and old instances. While there is neuroscientific evidence that the brain replays compressed memories, existing methods for convolutional networks replay raw images. Here, we propose REMIND, a brain-inspired approach that enables efficient replay with compressed representations. REMIND is trained in an online manner, meaning it learns one example at a time, which is closer to how humans learn. Under the same constraints, REMIND outperforms other methods for incremental class learning on the ImageNet ILSVRC-2012 dataset. We probe REMIND's robustness to data ordering schemes known to induce catastrophic forgetting. We demonstrate REMIND's generality by pioneering online learning for Visual Question Answering (VQA).

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

Large language models have achieved strong performance on medical reasoning benchmarks, yet their deployment in clinical settings demands rigorous verification to ensure factual accuracy. While reward models offer a scalable approach for reasoning trace verification, existing methods face two limitations: they produce only scalar reward values without explicit justification, and they rely on single-pass retrieval that precludes adaptive knowledge access as verification unfolds. We introduce method, an agentic framework that addresses these limitations by training medical reasoning verifiers to iteratively query external medical corpora during evaluation. Our approach combines tool-augmented verification with an iterative reinforcement learning paradigm that requires only trace-level supervision, alongside an adaptive curriculum mechanism that dynamically adjusts training data distribution. Across four medical reasoning benchmarks, method achieves substantial gains over existing methods, improving MedQA accuracy by 23.5% and MedXpertQA by 32.0% relative to the base generator in particular. Crucially, method demonstrates an 8times reduction in sampling budget requirement compared to prior reward model baselines. These findings establish that grounding verification in dynamically retrieved evidence offers a principled path toward more reliable medical reasoning systems.

Replay methods have shown to be successful in mitigating catastrophic forgetting in continual learning scenarios despite having limited access to historical data. However, storing historical data is cheap in many real-world applications, yet replaying all historical data would be prohibited due to processing time constraints. In such settings, we propose learning the time to learn for a continual learning system, in which we learn replay schedules over which tasks to replay at different time steps. To demonstrate the importance of learning the time to learn, we first use Monte Carlo tree search to find the proper replay schedule and show that it can outperform fixed scheduling policies in terms of continual learning performance. Moreover, to improve the scheduling efficiency itself, we propose to use reinforcement learning to learn the replay scheduling policies that can generalize to new continual learning scenarios without added computational cost. In our experiments, we show the advantages of learning the time to learn, which brings current continual learning research closer to real-world needs.

A major problem with Active Learning (AL) is high training costs since models are typically retrained from scratch after every query round. We start by demonstrating that standard AL on neural networks with warm starting fails, both to accelerate training and to avoid catastrophic forgetting when using fine-tuning over AL query rounds. We then develop a new class of techniques, circumventing this problem, by biasing further training towards previously labeled sets. We accomplish this by employing existing, and developing novel, replay-based Continual Learning (CL) algorithms that are effective at quickly learning the new without forgetting the old, especially when data comes from an evolving distribution. We call this paradigm Continual Active Learning (CAL). We show CAL achieves significant speedups using a plethora of replay schemes that use model distillation and that select diverse, uncertain points from the history. We conduct experiments across many data domains, including natural language, vision, medical imaging, and computational biology, each with different neural architectures and dataset sizes. CAL consistently provides a 3x reduction in training time, while retaining performance.

Continual instruction tuning updates a language model through a sequence of new domains, yet each update can progressively erode previously learned capabilities and alignment behavior. Replay is the standard mitigation, but fixed replay ratios are inherently limited because the optimal mixture varies with the current domain, the training stage, and the evolving vulnerability of prior behaviors. We propose PROX-YMIX, a framework that learns a dynamic replay controller on a small proxy model and transfers the frozen controller to a larger target. The controller never observes future tasks and constructs its state from normalized validation losses and their temporal dynamics, producing a masked mixture over the current task and accessible replay buffers. Our core empirical hypothesis is forgetting mirroring: task vulnerability rankings remain largely consistent across model scales even when absolute loss magnitudes differ. We validate this assumption empirically before transferring controllers across scales. On LLaMA-3-8B across five continual instruction tuning sequences, PROXYMIX improves average accuracy by 3.4 points, reduces final forgetting by 3.5 points, and raises safety score by 5.8 points over the strongest non-oracle baseline, at roughly 50x lower policy learning cost than Oracle Target RL. The framework is leakage free and architecture independent at the interface level, and we also identify settings where the proxy assumption breaks down, highlighting limitations for robust deployment.

Large language models (LLMs) can generate plausible code but offer limited guarantees of correctness. Formally verifying that implementations satisfy specifications requires constructing machine-checkable proofs, a task that remains beyond current automation. We propose a hierarchical proof search framework for automated code verification in Lean~4 that decomposes complex verification goals into structurally simpler subgoals before attempting tactic-level proving. Central to our approach is a principled decomposition score that combines constructive justification with structural effectiveness. Crucially, this score serves as both the training reward and the inference-time ranking criterion, ensuring strict alignment between optimization and deployment. We train Goedel-Code-Prover-8B, a single unified policy for both decomposition and completion, via supervised initialization followed by hybrid reinforcement learning, where a continuous decomposition reward drives planning exploration while supervised replay stabilizes proof generation. On three Lean-based code verification benchmarks comprising 427 tasks, our 8B-parameter model achieves a 62.0\% prove success rate, a 2.6times improvement over the strongest baseline, surpassing neural provers up to 84times larger. We further observe consistent inference-time scaling: success rates improve monotonically with search iterations and sampling budget, with our trained model achieving greater efficiency than frontier off-the-shelf models of comparable scale.

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

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.

Abstract reasoning ability reflects the intelligence and generalization capacity of LLMs to extract and apply abstract rules. However, accurately measuring this ability remains challenging: existing benchmarks either rely on expensive manual annotation, limiting their scale, or risk measuring memorization rather than genuine reasoning. To address this, we introduce an automated pipeline named A2RBench, encompassing generation, expansion, evaluation, and analysis. Specifically, in the generation stage, LLMs create diverse tasks demanding genuine reasoning; in the expansion stage, LLMs reuse validated rules and expand new input spaces to generate task variations, achieving scaling. However, such a process may cause hallucinations. To eliminate it, we further establish a theoretical framework and prove that programmatic verification--testing whether the inverse operation perfectly reverses the forward operation (cycle consistency)--guarantees a unique solution. Through extensive evaluations on mainstream LLMs, we find: (1) Current LLMs exhibit fundamental deficiencies in abstract reasoning, with top models significantly underperforming humans on a representative subset (39.8% vs. 68.5%). (2) Current LLMs fall far short of 2D and 1D in the complexity of generated 3D tasks, revealing their lack of understanding of high-dimensional tasks. (3) Counterintuitively, inputs with higher information complexity can simplify the reasoning process.

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

Continual RL requires an agent to learn new tasks without forgetting previous ones, while improving on both past and future tasks. The most common approaches use model-free algorithms and replay buffers can help to mitigate catastrophic forgetting, but often struggle with scalability due to large memory requirements. Biologically inspired replay suggests replay to a world model, aligning with model-based RL; as opposed to the common setting of replay in model-free algorithms. Model-based RL offers benefits for continual RL by leveraging knowledge of the environment, independent of policy. We introduce WMAR (World Models with Augmented Replay), a model-based RL algorithm with a memory-efficient distribution-matching replay buffer. WMAR extends the well known DreamerV3 algorithm, which employs a simple FIFO buffer and was not tested in continual RL. We evaluated WMAR and DreamerV3, with the same-size replay buffers. They were tested on two scenarios: tasks with shared structure using OpenAI Procgen and tasks without shared structure using the Atari benchmark. WMAR demonstrated favourable properties for continual RL considering metrics for forgetting as well as skill transfer on past and future tasks. Compared to DreamerV3, WMAR showed slight benefits in tasks with shared structure and substantially better forgetting characteristics on tasks without shared structure. Our results suggest that model-based RL with a memory-efficient replay buffer can be an effective approach to continual RL, justifying further research.

Large language models (LLMs) increasingly rely on reinforcement learning (RL) to enhance their reasoning capabilities through feedback. A critical challenge is verifying the consistency of model-generated responses and reference answers, since these responses are often lengthy, diverse, and nuanced. Rule-based verifiers struggle with complexity, prompting the use of model-based verifiers. However, specialized verifiers lack flexibility, while general LLM judges can be inconsistent. Existing research primarily focuses on building better verifiers, yet a systematic evaluation of different types of verifiers' performance across domains remains lacking, severely constraining the reliable development of Reinforcement Learning with Verifiable Reward (RLVR). To address this, we propose VerifyBench--a cross-domain comprehensive benchmark for systematically evaluating verifiers. We construct 4,000 expert-level questions covering mathematics, physics, chemistry, and biology. Each question is equipped with reference answers and diverse responses. The reliability of the evaluation is ensured through a rigorous annotation process conducted by a multidisciplinary expert team. We design a four-dimensional experimental framework to comprehensively compare the performance boundaries of specialized verifiers and general LLMs under combined conditions of extracted answers vs. complete responses, and short vs. long outputs. Our evaluation uncovers fundamental trade-offs in verifiers: while specialized verifiers achieve leading accuracy, they exhibit deficiencies in recall; general models show stronger inclusivity but unstable precision. More importantly, we discover verifiers' high sensitivity to input structure and inherent limitations in cross-domain generalization, providing critical insights into the bottlenecks of current verifier technology.

Recent work pairs LLMs with evolutionary search to iteratively generate, modify, and select code using task-specific feedback. These systems have produced strong results in mathematical discovery and algorithm design, yet a fundamental question remains: what do they actually evolve? Progress is typically summarized by the best score a run reaches under a task-specific evaluator, but that score can reflect several different mechanisms: new algorithmic structure, re-tuning an existing strategy, recombining ideas already in the model's internal knowledge, or overfitting to the evaluator. Distinguishing these mechanisms requires inspecting the search process itself, not only its final outcome. We introduce EvoTrace, a dataset of evolutionary coding traces spanning four evolutionary frameworks, reasoning and non-reasoning models, and 16 tasks across mathematics and algorithm design. To analyze these traces, we develop EvoReplay, a replay-based methodology that reconstructs the local search states behind high-scoring solutions and tests controlled interventions, including adjusting constants, removing program components and substituting models or prompting contexts. We annotate every code edit in EvoTrace with one of nine recurring edit types using an LLM-as-judge pipeline validated against blind human re-annotation. Across EvoTrace, most score gains come from a small subset of these edit types. We further find a deterministic cycling pattern: about 30% of code lines added during search are byte-identical re-introductions of previously-deleted lines, present throughout nearly every run. These results show that benchmark gains in evolutionary coding agents can arise from qualitatively different mechanisms, only some of which correspond to new algorithmic structure. EvoTrace enables more diagnostic evaluation of evolutionary coding agents beyond final benchmark scores.

Ray tracing has become a standard for accurate radio propagation modeling, but suffers from exponential computational complexity, as the number of candidate paths scales with the number of objects raised to the power of the interaction order. This bottleneck limits its use in large-scale or real-time applications, forcing traditional tools to rely on heuristics to reduce the number of path candidates at the cost of potentially reduced accuracy. To overcome this limitation, we propose a comprehensive machine-learning-assisted framework that replaces exhaustive path searching with intelligent sampling via Generative Flow Networks. Applying such generative models to this domain presents significant challenges, particularly sparse rewards due to the rarity of valid paths, which can lead to convergence failures and trivial solutions when evaluating high-order interactions in complex environments. To ensure robust learning and efficient exploration, our framework incorporates three key architectural components. First, we implement an experience replay buffer to capture and retain rare valid paths. Second, we adopt a uniform exploratory policy to improve generalization and prevent the model from overfitting to simple geometries. Third, we apply a physics-based action masking strategy that filters out physically impossible paths before the model even considers them. As demonstrated in our experimental validation, the proposed model achieves substantial speedups over exhaustive search -- up to 10times faster on GPU and 1000times faster on CPU -- while maintaining high coverage accuracy and successfully uncovering complex propagation paths. The complete source code, tests, and tutorial are available at https://github.com/jeertmans/sampling-paths.

A promising research direction in enabling LLMs to generate consistently correct code involves addressing their inability to properly estimate program execution, particularly for code they generate. In this work, we demonstrate that Code LLMs can be trained to simulate program execution in a step-by-step manner and that this capability can be leveraged to improve competitive programming performance. Our approach combines supervised fine-tuning on natural language execution traces, textual explanations grounded in true execution, with reinforcement learning using verifiable rewards. We introduce two complementary objectives: output prediction given code and inputs, and solving competitive programming tasks with either ground-truth or self-predicted execution feedback. These objectives enable models to perform self-verification over multiple candidate solutions, and iterative self-fixing by simulating test execution. Across multiple competitive programming benchmarks, our method yields consistent improvements over standard reasoning approaches. We further present ablations and analysis to elucidate the role of execution simulation and its limitations.

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.

Self-awareness, i.e., the ability to assess and correct one's own generation, is a fundamental aspect of human intelligence, making its replication in large language models (LLMs) an important yet challenging task. Previous works tackle this by employing extensive reinforcement learning or rather relying on large external verifiers. In this work, we propose Refine via Intrinsic Self-Verification (ReVISE), an efficient and effective framework that enables LLMs to self-correct their outputs through self-verification. The core idea of ReVISE is to enable LLMs to verify their reasoning processes and continually rethink reasoning trajectories based on its verification. We introduce a structured curriculum based upon online preference learning to implement this efficiently. Specifically, as ReVISE involves two challenging tasks (i.e., self-verification and reasoning correction), we tackle each task sequentially using curriculum learning, collecting both failed and successful reasoning paths to construct preference pairs for efficient training. During inference, our approach enjoys natural test-time scaling by integrating self-verification and correction capabilities, further enhanced by our proposed confidence-aware decoding mechanism. Our experiments on various reasoning tasks demonstrate that ReVISE achieves efficient self-correction and significantly improves reasoning performance.

We show how replay attacks undermine audio deepfake detection: By playing and re-recording deepfake audio through various speakers and microphones, we make spoofed samples appear authentic to the detection model. To study this phenomenon in more detail, we introduce ReplayDF, a dataset of recordings derived from M-AILABS and MLAAD, featuring 109 speaker-microphone combinations across six languages and four TTS models. It includes diverse acoustic conditions, some highly challenging for detection. Our analysis of six open-source detection models across five datasets reveals significant vulnerability, with the top-performing W2V2-AASIST model's Equal Error Rate (EER) surging from 4.7% to 18.2%. Even with adaptive Room Impulse Response (RIR) retraining, performance remains compromised with an 11.0% EER. We release ReplayDF for non-commercial research use.

Answer verification methods are widely employed in language model training pipelines spanning data curation, evaluation, and reinforcement learning with verifiable rewards (RLVR). While prior work focus on developing unified verifiers applicable across multiple reasoning scenarios, significant challenges remain in computation-oriented scientific domains, such as algebraic equivalence checking and physical constant substitution. In this paper, we introduce \model, a tool-augmented verifier that leverages external executors to perform precise computations and symbolic simplifications. \model enables robust verification that goes beyond simple semantic matching. We propose a novel two-stage pipeline, which begin with cold-start fine-tuning and followed by multi-turn reinforcement learning with tool integration. Extensive experiments conducted on STEM subjects, general QA, and long-form reasoning tasks demonstrates strong generalization of \model. The results shows that the \model achieves state-of-the-art performance on VerifyBench-Hard and SCI-Bench. And we also employ our \model in RLVR as a reward model, the results show that it consistently outperforms both rubric-based and model-based verifiers on AIME'24 and AIME'25, demonstrating strong potential to enhance reasoning capabilities of LLM. Our model is released at https://huggingface.co/Nanbeige/CoSineVerifier-Tool-4B{https://huggingface.co/Nanbeige/CoSineVerifier-Tool-4B}.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for improving code generation in large language models, but its effectiveness is limited by weak and static verification signals in existing coding RL datasets. In this paper, we propose a solution-conditioned and adversarial verification framework that iteratively refines test cases based on the execution behaviors of candidate solutions, with the goal of increasing difficulty, improving discriminative power, and reducing redundancy. Based on this framework, we introduce EvolveCoder-22k, a large-scale coding reinforcement learning dataset constructed through multiple rounds of adversarial test case evolution. Empirical analysis shows that iterative refinement substantially strengthens verification, with pass@1 decreasing from 43.80 to 31.22. Reinforcement learning on EvolveCoder-22k yields stable optimization and consistent performance gains, improving Qwen3-4B by an average of 4.2 points across four downstream benchmarks and outperforming strong 4B-scale baselines. Our results highlight the importance of adversarial, solution-conditioned verification for effective and scalable reinforcement learning in code generation.

RTL implementations frequently lack up-to-date or consistent specifications, making comprehension, maintenance, and verification costly and error-prone. While prior work has explored generating specifications from RTL using large language models (LLMs), ensuring that the generated documents faithfully capture design intent remains a major challenge. We present SpecLoop, an agentic framework for RTL-to-specification generation with a formal-verification-driven iterative feedback loop. SpecLoop first generates candidate specifications and then reconstructs RTL from these specifications; it uses formal equivalence checking tools between the reconstructed RTL and the original design to validate functional consistency. When mismatches are detected, counterexamples are fed back to iteratively refine the specifications until equivalence is proven or no further progress can be made. Experiments across multiple LLMs and RTL benchmarks show that incorporating formal verification feedback substantially improves specification correctness and robustness over LLM-only baselines, demonstrating the effectiveness of verification-guided specification generation.

Code LLMs still struggle with code execution reasoning, especially in smaller models. Existing methods rely on supervised fine-tuning (SFT) with teacher-generated explanations, primarily in two forms: (1) input-output (I/O) prediction chains and (2) natural-language descriptions of execution traces. However, intermediate execution steps cannot be explicitly verified during SFT, so the training objective can reduce to merely matching teacher explanations. Moreover, training data is typically collected without explicit control over task difficulty. We introduce ExecVerify, which goes beyond text imitation by incorporating verifiable white-box rewards derived from execution traces, including next-statement prediction and variable value/type prediction. Our work first builds a dataset with multiple difficulty levels via constraint-based program synthesis. Then, we apply reinforcement learning (RL) to reward correct answers about both intermediate execution steps and final outputs, aligning the training objective with semantic correctness at each execution step. Finally, we adopt a two-stage training pipeline that first enhances execution reasoning and then transfers to code generation. Experiments demonstrate that a 7B model trained with ExecVerify achieves performance comparable to 32B models on code reasoning benchmarks and improves pass@1 by up to 5.9\% on code generation tasks over strong post-training baselines.

Most agent frameworks are built around the language model: a conversation loop comes first, then tools, then rules, and finally a logging layer bolted on for observability, with state persisted as retrievable "memory." We describe ActiveGraph, a runtime that inverts this arrangement. The append-only event log is the source of truth; the working graph is a deterministic projection of that log; and behaviors--ordinary functions, classes, LLM-backed routines, or logic attached to typed edges--react to changes in the graph and emit new events. No component instructs another; coordination happens entirely through the shared graph. This single design decision yields three properties that retrieval-and-summarization memory systems do not provide: deterministic replay of any run from its log, cheap forking that branches a run at any event without re-executing the shared prefix, and end-to-end lineage from a high-level goal down to the individual model call that produced each artifact. We present the architecture, a determinism contract that makes replay sound, and a worked diligence example whose full causal structure is reconstructable from the log alone. We discuss--without claiming to demonstrate--why this substrate is unusually well suited to self-improving agents, and how it extends the BabyAGI lineage and prior graph-memory research.

Extending CoT through RL has been widely used to enhance the reasoning capabilities of LLMs. However, due to the sparsity of reward signals, it can also induce undesirable thinking patterns such as overthinking, i.e., generating redundant intermediate reasoning content. In this work, we argue that a major source of such redundancy is inefficient reflection, which often manifests in two problematic patterns: Indiscriminate Reflection, where the model performs broad, low-impact checks throughout reasoning, and Repetitive Reflection, where it repeatedly re-verifies an already established conclusion. To address this, we introduce a graph-based CoT optimization framework. Specifically, we convert each linear CoT into a directed acyclic graph (DAG) with explicit dependency edges, and design a dual pruning strategy: branch-level pruning removes weakly contributing reflection branches, while depth-level pruning eliminates late-stage re-verification. We distill this behavior via a three-stage pipeline: (1) SFT to initialize the policy on pruned concise traces, (2) DPO to prefer correct but less redundant trajectories, and (3) GRPO with length penalty to jointly optimize answer correctness and efficiency. Experiments show that our approach reduces the average reasoning tokens by 42\% while maintaining or improving accuracy.

Deep research requires agents to find answers that jointly satisfy multiple constraints. Discovering such answers is costly, whereas verifying a candidate can often be decomposed into tractable constraint-wise checks. This discovery--verification asymmetry suggests that a research agent should do more than simply search longer: it should recursively improve its current answer by verifying intermediate results and using the partially verified state to guide subsequent refinement. We introduce AREX, a family of Recursively Self-Improving (RSI) deep research agents. AREX alternates between an inner research loop that gathers evidence and constructs a provisional answer, and an outer self-improvement loop that audits the answer constraint-wise, identifies unresolved claims, and launches targeted follow-up research. To sustain RSI over long horizons, AREX learns an autonomous context-update tool that compresses growing interaction history into a compact improvement state preserving verified evidence and unresolved constraints, without relying on an external model. We train AREX on verified synthetic tasks and high-quality trajectories through agentic mid-training and long-horizon reinforcement learning. To mitigate sparse final rewards during long horizon learning, we emphasize key steps where decisive evidence is acquired or erroneous research directions are corrected. We instantiate a dense 4B model and a 122B-A10B Mixture-of-Experts model. Across BrowseComp, WideSearch, DeepSearchQA, Humanity's Last Exam (HLE), and other reasoning and tool-use benchmarks, AREX substantially outperforms comparable-scale baselines and remains competitive with models using substantially more activated parameters.

Recent advances in large reasoning models have leveraged reinforcement learning with verifiable rewards (RLVR) to improve reasoning capabilities. However, scaling these methods typically requires extensive rollout computation and large datasets, leading to high training costs and low data efficiency. To mitigate this issue, we propose DEPO, a Data-Efficient Policy Optimization pipeline that combines optimized strategies for both offline and online data selection. In the offline phase, we curate a high-quality subset of training samples based on diversity, influence, and appropriate difficulty. During online RLVR training, we introduce a sample-level explorability metric to dynamically filter samples with low exploration potential, thereby reducing substantial rollout computational costs. Furthermore, we incorporate a replay mechanism for under-explored samples to ensure adequate training, which enhances the model's final convergence performance. Experiments across five reasoning benchmarks show that DEPO consistently outperforms existing methods in both offline and online data selection scenarios. Notably, using only 20% of the training data, our approach achieves a 1.85 times speed-up on AIME24 and a 1.66 times speed-up on AIME25 compared to GRPO trained on the full dataset.

Online continual learning (OCL) aims to continuously learn new data from a single pass over the online data stream. It generally suffers from the catastrophic forgetting issue. Existing replay-based methods effectively alleviate this issue by replaying part of old data in a proxy-based or contrastive-based replay manner. In this paper, we conduct a comprehensive analysis of these two replay manners and find they can be complementary. Inspired by this finding, we propose a novel replay-based method called proxy-based contrastive replay (PCR), which replaces anchor-to-sample pairs with anchor-to-proxy pairs in the contrastive-based loss to alleviate the phenomenon of forgetting. Based on PCR, we further develop a more advanced method named holistic proxy-based contrastive replay (HPCR), which consists of three components. The contrastive component conditionally incorporates anchor-to-sample pairs to PCR, learning more fine-grained semantic information with a large training batch. The second is a temperature component that decouples the temperature coefficient into two parts based on their impacts on the gradient and sets different values for them to learn more novel knowledge. The third is a distillation component that constrains the learning process to keep more historical knowledge. Experiments on four datasets consistently demonstrate the superiority of HPCR over various state-of-the-art methods.

Large language models have achieved remarkable success on final-answer mathematical problems, largely due to the ease of applying reinforcement learning with verifiable rewards. However, the reasoning underlying these solutions is often flawed. Advancing to rigorous proof-based mathematics requires reliable proof verification capabilities. We begin by analyzing multiple evaluation setups and show that focusing on a single benchmark can lead to brittle or misleading conclusions. To address this, we evaluate both proof-based and final-answer reasoning to obtain a more reliable measure of model performance. We then scale two major generative verification methods (GenSelect and LLM-as-a-Judge) to millions of tokens and identify their combination as the most effective framework for solution verification and selection. We further show that the choice of prompt for LLM-as-a-Judge significantly affects the model's performance, but reinforcement learning can reduce this sensitivity. However, despite improving proof-level metrics, reinforcement learning does not enhance final-answer precision, indicating that current models often reward stylistic or procedural correctness rather than mathematical validity. Our results establish practical guidelines for designing and evaluating scalable proof-verification and selection systems.

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.

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models fail to robustly verify their own outputs. We introduce RISE (Reinforcing Reasoning with Self-Verification), a novel online RL framework designed to tackle this. RISE explicitly and simultaneously trains an LLM to improve both its problem-solving and self-verification abilities within a single, integrated RL process. The core mechanism involves leveraging verifiable rewards from an outcome verifier to provide on-the-fly feedback for both solution generation and self-verification tasks. In each iteration, the model generates solutions, then critiques its own on-policy generated solutions, with both trajectories contributing to the policy update. Extensive experiments on diverse mathematical reasoning benchmarks show that RISE consistently improves model's problem-solving accuracy while concurrently fostering strong self-verification skills. Our analyses highlight the advantages of online verification and the benefits of increased verification compute. Additionally, RISE models exhibit more frequent and accurate self-verification behaviors during reasoning. These advantages reinforce RISE as a flexible and effective path towards developing more robust and self-aware reasoners.

Reinforcement learning for code generation relies on verifiable rewards from unit test pass rates. Yet high-quality test suites are scarce, existing datasets offer limited coverage, and static rewards fail to adapt as models improve. Recent self-play methods unify code and test generation in a single model, but face a inherent dilemma: white-box access leads to self-collusion where the model produces trivial tests for easy rewards, yet black-box restriction yields generic tests that miss implementation-specific bugs. We introduce Code-A1, an adversarial co-evolution framework that jointly optimizes a Code LLM and a Test LLM with opposing objectives. The Code LLM is rewarded for passing more tests, while the Test LLM is rewarded for exposing more defects. This architectural separation eliminates self-collusion risks and safely enables white-box test generation, where the Test LLM can inspect candidate code to craft targeted adversarial tests. We further introduce a Mistake Book mechanism for experience replay and a composite reward balancing test validity with adversarial difficulty. Experiments on Qwen2.5-Coder models demonstrate that Code-A1 achieves code generation performance matching or exceeding models trained on human-annotated tests, while significantly improving test generation capability.

Automated formal verification remains challenging for large language models because data for proof assistants and verification-aware languages is scarce, and correctness depends on satisfying precise machine-checkable specifications rather than producing plausible code. This thesis studies how verifier environments can improve LLM generation of verified programs and proofs through reinforcement learning from verifiable rewards (RLVR) and verifier-guided inference-time search. First, we train open-source models in Dafny with RLVR using Group Relative Policy Optimization (GRPO) and related variants, assembling generated candidates into complete programs and scoring them with compiler and verifier outcomes. Initial experiments on an APPS-derived Dafny dataset increased verified reward from 2.2% to 58.1%, but revealed specification hacking, where models exploit weak formal specifications instead of implementing the intended solutions. After filtering underspecified and vulnerable tasks, multi-turn RLVR on the refined benchmark improves the verified pass rate from 9.7% to 31.1%. Second, we develop a verifier-guided inference scaffold in Lean that treats proof generation as structured search over decomposed subgoals, verifier feedback, diagnostics, and repair. With a fixed base model, the full scaffold with proof reviser improves pass rate on an initial VeriCoding pilot set from 46.2% under direct repair to 69.2%. On the larger VERINA dataset, whole-task decomposition plus proof reviser solves 7 of 42 previously unsolved tasks. We also introduce Dalek-Bench, a repository-scale Lean benchmark derived from the Rust curve25519-dalek verification project; preliminary results remain weak, indicating that stronger progress evaluation and task-specific tool-use policies are still needed.

Users often omit essential details in their requests to LLM-based agents, resulting in under-specified inputs for tool use. This poses a fundamental challenge for tool-augmented agents, as API execution typically requires complete arguments, highlighting the need for personalized tool calling. To study this problem, we introduce MPT, a benchmark comprising 265 multi-session dialogues that cover three challenges: Preference Recall, Preference Induction, and Preference Transfer. We also propose PRefine, a test-time memory-augmented method that represents user preferences as evolving hypotheses. Through a generate--verify--refine loop, it extracts reusable constraints from history and improves tool-calling accuracy while using only 1.24% of the tokens required by full-history prompting. These results indicate that robust personalization in agentic systems depends on memory that captures the reasons behind user choices, not just the choices themselves.

Continual learning aims to enable a single model to learn a sequence of tasks without catastrophic forgetting. Top-performing methods usually require a rehearsal buffer to store past pristine examples for experience replay, which, however, limits their practical value due to privacy and memory constraints. In this work, we present a simple yet effective framework, DualPrompt, which learns a tiny set of parameters, called prompts, to properly instruct a pre-trained model to learn tasks arriving sequentially without buffering past examples. DualPrompt presents a novel approach to attach complementary prompts to the pre-trained backbone, and then formulates the objective as learning task-invariant and task-specific "instructions". With extensive experimental validation, DualPrompt consistently sets state-of-the-art performance under the challenging class-incremental setting. In particular, DualPrompt outperforms recent advanced continual learning methods with relatively large buffer sizes. We also introduce a more challenging benchmark, Split ImageNet-R, to help generalize rehearsal-free continual learning research. Source code is available at https://github.com/google-research/l2p.

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

As scaling laws push the training of frontier large language models (LLMs) toward ever-growing data requirements, training pipelines are approaching a regime where much of the publicly available online text may be consumed. At the same time, widespread LLM usage increases the volume of machine-generated content on the web; together, these trends raise the likelihood of generated text re-entering future training corpora, increasing the associated risk of performance degradation often called model collapse. In practice, model developers address this concern through data cleaning, watermarking, synthetic-data policies, or, in some cases, blissful ignorance. However, the problem of model collapse in generative models has not been examined from a learning-theoretic perspective: we study it through the theoretical lens of the language generation in the limit framework, introducing a replay adversary that augments the example stream with the generator's own past outputs. Our main contribution is a fine-grained learning-theoretic characterization of when replay fundamentally limits generation: while replay is benign for the strongest notion of uniform generation, it provably creates separations for the weaker notions of non-uniform generation and generation in the limit. Interestingly, our positive results mirror heuristics widely used in practice, such as data cleaning, watermarking, and output filtering, while our separations show when these ideas can fail.

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.

Test-time scaling for complex reasoning tasks shows that leveraging inference-time compute, by methods such as independently sampling and aggregating multiple solutions, results in significantly better task outcomes. However, a critical bottleneck is verification: sampling is only effective if correct solutions can be reliably identified among candidates. While existing approaches typically evaluate candidates independently via scalar scoring, we demonstrate that models are substantially stronger at pairwise self-verification. Leveraging this insight, we introduce V_1, a framework that unifies generation and verification through efficient pairwise ranking. V_1 comprises two components: V_1-Infer, an uncertainty-guided algorithm using a tournament-based ranking that dynamically allocates self-verification compute to candidate pairs whose relative correctness is most uncertain; and V_1-PairRL, an RL framework that jointly trains a single model as both generator and pairwise self-verifier, ensuring the verifier adapts to the generator's evolving distribution. On code generation (LiveCodeBench, CodeContests, SWE-Bench) and math reasoning (AIME, HMMT) benchmarks, V_1-Infer improves Pass@1 by up to 10% over pointwise verification and outperforms recent test-time scaling methods while being significantly more efficient. Furthermore, V_1-PairRL achieves 7--9% test-time scaling gains over standard RL and pointwise joint training, and improves base Pass@1 by up to 8.7% over standard RL in a code-generation setting.

Due to the expanding capabilities and pre-training data, Large Language Models (LLMs) are facing increasingly serious evaluation challenges. On one hand, the data leakage issue cause over-estimation on existing benchmarks. On the other hand, periodically curating datasets manually is costly. In this paper, we propose to automate dataset updates for reliable and timely evaluation. The basic idea is to generate unseen and high-quality testing samples based on existing ones to mitigate leakage issues. In specific, we propose two strategies with systematically verification. First, the mimicking strategy employs LLMs to create new samples resembling existing ones, to the maximum extent preserving the stylistic of the original dataset. Our experiments demonstrate its evaluation stability across multiple instantiations and its effectiveness in dealing with data leakage issues in most cases. Second, for the cases that mimicking dataset works poorly, we design an extending strategy that adjusts the difficulty of the generated samples according to varying cognitive levels. This not only makes our evaluation more systematic, but also, with a balanced difficulty, even discern model capabilities better at fine-grained levels.

We introduce Replay, a collection of multi-view, multi-modal videos of humans interacting socially. Each scene is filmed in high production quality, from different viewpoints with several static cameras, as well as wearable action cameras, and recorded with a large array of microphones at different positions in the room. Overall, the dataset contains over 4000 minutes of footage and over 7 million timestamped high-resolution frames annotated with camera poses and partially with foreground masks. The Replay dataset has many potential applications, such as novel-view synthesis, 3D reconstruction, novel-view acoustic synthesis, human body and face analysis, and training generative models. We provide a benchmark for training and evaluating novel-view synthesis, with two scenarios of different difficulty. Finally, we evaluate several baseline state-of-the-art methods on the new benchmark.

Comprehensively retrieving diverse documents is crucial to address queries that admit a wide range of valid answers. We introduce retrieve-verify-retrieve (RVR), a multi-round retrieval framework designed to maximize answer coverage. Initially, a retriever takes the original query and returns a candidate document set, followed by a verifier that identifies a high-quality subset. For subsequent rounds, the query is augmented with previously verified documents to uncover answers that are not yet covered in previous rounds. RVR is effective even with off-the-shelf retrievers, and fine-tuning retrievers for our inference procedure brings further gains. Our method outperforms baselines, including agentic search approaches, achieving at least 10% relative and 3% absolute gain in complete recall percentage on a multi-answer retrieval dataset (QAMPARI). We also see consistent gains on two out-of-domain datasets (QUEST and WebQuestionsSP) across different base retrievers. Our work presents a promising iterative approach for comprehensive answer recall leveraging a verifier and adapting retrievers to a new inference scenario.

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

Coding agents can fix a failing example without preserving the domain rule that made it fail, so later generations can repeat the same plausible mistake. We present agentic synthesis against counterexample-supplemented sketches, a repository-native method for systems whose governing policy is discovered during implementation. A human starts with a partial, code-shaped sketch, and a coding agent generates the first implementation. When a concrete failure exposes missing or mistaken policy, an operator explicitly approves the corrected behavior and rule. The agent then revises the sketch and repairs or regenerates code and prompt surfaces for that one counterexample. The full archive preserves provenance; a selected regression set gates each revision before the next candidate is revealed; and periodic clean regeneration tests whether the evolved sketch, rather than prompt history or accumulated examples, carries the learned policy. We demonstrate the method with CatSynth, a synthetic browser application and captured coding-agent experiment. In one open-world run with GPT-5.4-mini, 8 of 14 frozen candidate cases became counterexamples. The rebuild controls inherited that promotion schedule, and all three paths passed the 8 accepted cases. Rebuilding from the evolved sketch passed 19 of 21 withheld cases, compared with 15 of 21 when rebuilding from the initial sketch and replaying all accepted examples. Retaining code across counterexamples required 9 Developer calls and 719 lines of cumulative artifact churn, versus 15 calls and 2,394 lines for replay-all, and passed 18 of 21 withheld cases. These results provide inspectable evidence that the evolved sketch carried reviewed policy and that retaining code reduced rework in this run; with one model and one reveal order, they do not establish general superiority or correctness beyond the encoded checks.

There is growing excitement about the potential of Language Models (LMs) to accelerate scientific discovery. Falsifying hypotheses is key to scientific progress, as it allows claims to be iteratively refined over time. This process requires significant researcher effort, reasoning, and ingenuity. Yet current benchmarks for LMs predominantly assess their ability to generate solutions rather than challenge them. We advocate for developing benchmarks that evaluate this inverse capability - creating counterexamples for subtly incorrect solutions. To demonstrate this approach, we start with the domain of algorithmic problem solving, where counterexamples can be evaluated automatically using code execution. Specifically, we introduce REFUTE, a dynamically updating benchmark that includes recent problems and incorrect submissions from programming competitions, where human experts successfully identified counterexamples. Our analysis finds that the best reasoning agents, even OpenAI o3-mini (high) with code execution feedback, can create counterexamples for only <9% of incorrect solutions in REFUTE, even though ratings indicate its ability to solve up to 48% of these problems from scratch. We hope our work spurs progress in evaluating and enhancing LMs' ability to falsify incorrect solutions - a capability that is crucial for both accelerating research and making models self-improve through reliable reflective reasoning.

Tool-using large language model agents frequently replan, retry failed operations, delegate tasks, and resume after crashes. These behaviors can cause one user authorization to be requested and executed multiple times under freshly issued token identifiers, even when each individual token is single-use. We call this failure semantic replay: exceeding the execution budget of a token-independent authorization instance rather than merely reusing an old token identifier. We show that identifier-local token consumption cannot prevent fresh reissuance unless the issuer retains monotonic durable state over the authorized action, confirmation event, and remaining execution budget. We introduce CapLease, an authorization-consumption layer that follows proposal- and authority-level defenses, binds an authenticated user confirmation to a canonical action, and enforces transactional Issue-Prepare-Commit transitions. Across LLM-agent replanning, retry, delegation, concurrency, confirmation-replay, and crash-recovery scenarios, identifier-local tokens permit fresh semantic reissuance, whereas CapLease and an equally stateful Server Ledger prevent duplicate admission and, with an idempotent sink, duplicate external effects. Our results identify durable authorization state, rather than token representation alone, as the systems requirement for replay-resistant agent execution.

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.

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.

Since the emergence of the Large Language Model (LLM), LLM has been widely used in fields such as writing, translating, and searching. However, there is still great potential for LLM-based methods in handling complex tasks such as decision-making in the StarCraft II environment. To address problems such as lack of relevant knowledge and poor control over subtasks of varying importance, we propose a Hierarchical Expert Prompt (HEP) for LLM. Our method improves the understanding of game situations through expert-level tactical knowledge, improving the processing quality of tasks of varying importance through a hierarchical framework. Our approach defeated the highest level (Elite) standard built-in agent in TextStarCraft II for the first time and consistently outperformed the baseline method in other difficulties. Our experiments suggest that the proposed method is a practical solution for tackling complex decision-making challenges. The replay video can be viewed on https://www.bilibili.com/video/BV1uz42187EF and https://youtu.be/dO3PshWLV5M, and our codes have been open-sourced on https://github.com/luchang1113/HEP-LLM-play-StarCraftII.

A crucial factor for successful human and AI interaction is the ability of language models or chatbots to follow human instructions precisely. A common feature of instructions are output constraints like ``only answer with yes or no" or ``mention the word `abrakadabra' at least 3 times" that the user adds to craft a more useful answer. Even today's strongest models struggle with fulfilling such constraints. We find that most models strongly overfit on a small set of verifiable constraints from the benchmarks that test these abilities, a skill called precise instruction following, and are not able to generalize well to unseen output constraints. We introduce a new benchmark, IFBench, to evaluate precise instruction following generalization on 58 new, diverse, and challenging verifiable out-of-domain constraints. In addition, we perform an extensive analysis of how and on what data models can be trained to improve precise instruction following generalization. Specifically, we carefully design constraint verification modules and show that reinforcement learning with verifiable rewards (RLVR) significantly improves instruction following. In addition to IFBench, we release 29 additional new hand-annotated training constraints and verification functions, RLVR training prompts, and code.

Reliable verifiable data has become a key driver of capability gains in modern language models, enabling stable reinforcement learning with verifiable rewards and effective distillation that transfers competence across math, coding, and agentic tasks. Yet constructing generalizable synthetic verifiable data remains difficult due to hallucination-prone generation, and weak or trivial verification artifacts that fail to separate strong from weak solutions. Existing approaches often rely on task-specific heuristics or post-hoc filters that do not transfer across domains and lack a principled, universal evaluator of verifiability. In this work, we introduce an evolutionary, task-agnostic, strategy-guided, executably-checkable data synthesis framework that, from minimal seed supervision, jointly synthesizes problems, diverse candidate solutions, and verification artifacts, and iteratively discovers strategies via a consistency-based evaluator that enforces agreement between human-annotated and strategy-induced checks. This pipeline upgrades filtering into principled synthesis: it reliably assembles coherent, verifiable training instances and generalizes without domain-specific rules. Our experiments demonstrate the effectiveness of the proposed approach under both RLVR and model distillation training paradigms. The results show that training with our synthesized data yields significant improvements on both the LiveCodeBench and AgentBench-OS tasks, highlighting the robust generalization of our framework.

We present Verified Multi-Agent Orchestration (VMAO), a framework that coordinates specialized LLM-based agents through a verification-driven iterative loop. Given a complex query, our system decomposes it into a directed acyclic graph (DAG) of sub-questions, executes them through domain-specific agents in parallel, verifies result completeness via LLM-based evaluation, and adaptively replans to address gaps. The key contributions are: (1) dependency-aware parallel execution over a DAG of sub-questions with automatic context propagation, (2) verification-driven adaptive replanning that uses an LLM-based verifier as an orchestration-level coordination signal, and (3) configurable stop conditions that balance answer quality against resource usage. On 25 expert-curated market research queries, VMAO improves answer completeness from 3.1 to 4.2 and source quality from 2.6 to 4.1 (1-5 scale) compared to a single-agent baseline, demonstrating that orchestration-level verification is an effective mechanism for multi-agent quality assurance.

Reasoning language models (RLMs) have demonstrated impressive performance in domains such as mathematics and coding. These domains permit reliable verification of model outputs, which is important for enabling the reinforcement learning that drives RLM performance gains. However, training RLMs on domains that lack reliable verifiers remains challenging. Meanwhile, for both verifiable and unverifiable domains, large amounts of unused supervised fine-tuning data with human-written solutions exist. In this work, we show that these data can be used efficiently to further improve RLM performance. For this, we first use classic instruction tuning, supervised fine-tuning without reasoning traces, on the RLM. Next, we merge our instruction-tuned model with the original reasoning model, recovering its reasoning behavior on the target domain. Our extensive evaluation demonstrates that our technique improves RLM performance in both verifiable and hard-to-verify domains, including coding and text summarization, while preserving RLM capabilities across other domains. Importantly, our method is highly cost-effective, enabling such improvements for less than USD $3.

Test-time scaling has been widely adopted to enhance the capabilities of Large Language Model (LLM) agents in software engineering (SWE) tasks. However, the standard approach of repeatedly sampling trajectories from scratch is computationally expensive. While recent methods have attempted to mitigate costs using specialized value agents, they can suffer from model miscalibration and fail to generalize to modern agents that synthesize custom bash scripts as tools. In this paper, we introduce SWE-Replay, the first efficient and generalizable test-time scaling technique for modern agents without reliance on potentially noisy value estimates. SWE-Replay optimizes the scaling process by recycling trajectories from prior trials, dynamically choosing to either explore from scratch or exploit archived experience by branching at critical intermediate steps. This selection of intermediate steps is driven by the potential and reasoning significance of repository exploration, rather than external LLM-based quality estimates. Our evaluation shows that, on SWE-Bench Verified, SWE-Replay consistently outperforms naive scaling, reducing costs by up to 17.4% while maintaining or even improving performance by up to 3.8%. Further evaluation on SWE-Bench Pro and Multilingual validates the generalizability of SWE-Replay, establishing it as a robust foundation for efficient test-time scaling of software engineering agents.

A classical intuition holds that verifying a solution is easier than producing one. For today's coding agents, this intuition is being inverted: as foundation models develop stronger reasoning capabilities and engineering harnesses grow more sophisticated, generating complex candidate solutions is no longer difficult -- reliably verifying them has become the harder problem. Every verifier we can build is only a proxy for human intent, never the intent itself. This makes verification subject to a twofold difficulty: first, intent is underspecified by nature, making it inherently hard to faithfully check whether it has been fulfilled; second, during model training, optimization widens the gap between proxy and intent -- manifesting as reward hacking or signal saturation. To address this, we characterize the quality of verification signals along three dimensions -- scalability, faithfulness, and robustness -- and argue that achieving all three simultaneously is the central challenge. We further study four reward constructions: a test verifier for general coding tasks, a rubric verifier for frontend tasks, the user as verifier for real-world agent tasks, and an automated agent verifier for long-horizon tasks. Across different task types and policy capability levels, we conduct in-depth analysis and experiments on the core challenges of reward design and how to more effectively leverage reward signals. Experiments show that targeted verification design can effectively suppress reward hacking, improve task completion quality, and achieve significant gains across multiple internal and public benchmarks. These experiences collectively point to a core observation: no fixed reward function can remain effective as policy capability continues to grow; and verification must co-evolve with the generator.

Self-Correction aims to enable large language models (LLMs) to self-verify and self-refine their initial responses without external feedback. However, LLMs often fail to effectively self-verify and generate correct feedback, further misleading refinement and leading to the failure of self-correction, especially in complex reasoning tasks. In this paper, we propose Program-driven Self-Correction (ProgCo). First, program-driven verification (ProgVe) achieves complex verification logic and extensive validation through self-generated, self-executing verification pseudo-programs. Then, program-driven refinement (ProgRe) receives feedback from ProgVe, conducts dual reflection and refinement on both responses and verification programs to mitigate misleading of incorrect feedback in complex reasoning tasks. Experiments on three instruction-following and mathematical benchmarks indicate that ProgCo achieves effective self-correction, and can be further enhance performance when combined with real program tools.

Dealing with sparse rewards is one of the biggest challenges in Reinforcement Learning (RL). We present a novel technique called Hindsight Experience Replay which allows sample-efficient learning from rewards which are sparse and binary and therefore avoid the need for complicated reward engineering. It can be combined with an arbitrary off-policy RL algorithm and may be seen as a form of implicit curriculum. We demonstrate our approach on the task of manipulating objects with a robotic arm. In particular, we run experiments on three different tasks: pushing, sliding, and pick-and-place, in each case using only binary rewards indicating whether or not the task is completed. Our ablation studies show that Hindsight Experience Replay is a crucial ingredient which makes training possible in these challenging environments. We show that our policies trained on a physics simulation can be deployed on a physical robot and successfully complete the task.

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.

Continual learning (CL) has traditionally focused on minimizing exemplar memory, a constraint often misaligned with modern systems where GPU time, not storage, is the primary bottleneck. This paper challenges this paradigm by investigating a more realistic regime: one where memory is abundant enough to mitigate forgetting, but full retraining from scratch remains prohibitively expensive. In this practical "middle ground", we find that the core challenge shifts from stability to plasticity, as models become biased toward prior tasks and struggle to learn new ones. Conversely, improved stability allows simple replay baselines to outperform the state-of-the-art methods at a fraction of the GPU cost. To address this newly surfaced trade-off, we propose Weight Space Consolidation, a lightweight method that combines (1) rank-based parameter resets to restore plasticity with (2) weight averaging to enhance stability. Validated on both class-incremental learning with image classifiers and continual instruction tuning with large language models, our approach outperforms strong baselines while matching the low computational cost of replay, offering a scalable alternative to expensive full-retraining. These findings challenge long-standing CL assumptions and establish a new, cost-efficient baseline for real-world CL systems where exemplar memory is no longer the limiting factor.

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.

Large language models are increasingly solving tasks that are commonly believed to require human-level reasoning ability. However, these models still perform very poorly on benchmarks of general intelligence such as the Abstraction and Reasoning Corpus (ARC). In this paper, we approach ARC as a programming-by-examples problem, and introduce a novel and scalable method for language model self-improvement called Code Iteration (CodeIt). Our method iterates between 1) program sampling and hindsight relabeling, and 2) learning from prioritized experience replay. By relabeling the goal of an episode (i.e., the target program output given input) to the realized output produced by the sampled program, our method effectively deals with the extreme sparsity of rewards in program synthesis. Applying CodeIt to the ARC dataset, we demonstrate that prioritized hindsight replay, along with pre-training and data-augmentation, leads to successful inter-task generalization. CodeIt is the first neuro-symbolic approach that scales to the full ARC evaluation dataset. Our method solves 15% of ARC evaluation tasks, achieving state-of-the-art performance and outperforming existing neural and symbolic baselines.

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.

Going beyond predicting robot actions, World Action Models (WAMs) can also generate future visual observations. We build on this generative capability to propose Recurrent Generative Replay (REGEN), a continual imitation learning framework that synthesizes pseudo-replay trajectories, enabling a robot policy to rehearse previously learned tasks without storing their original human demonstrations. During continual adaptation, REGEN recursively queries the WAM to synthesize pseudo-replay trajectories conditioned only on prior task instructions and current-task observations. Experiments in both simulation and real-world manipulation settings show that REGEN reduces catastrophic forgetting by up to 50% relative to sequential fine-tuning, while approaching the performance of privileged experience replay methods that require access to real replay data. Finally, we analyze the factors limiting generated replay, identifying long-horizon visual degradation and action-observation inconsistency as the primary bottlenecks. Our results establish WAMs as a promising foundation for continual robot learning without stored demonstrations.

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.

Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based theorem provers like Lean, applying these approaches directly to TLA+ faces significant challenges due to the hierarchical proof structure of the TLA+ proof system. We present a prompt-based approach that leverages LLMs to guide hierarchical decomposition of complex proof obligations into simpler sub-claims, while relying on symbolic provers for verification. Our key insight is to constrain LLMs to generate normalized claim decompositions rather than complete proofs, significantly reducing syntax errors. We also introduce a benchmark suite of 119 theorems adapted from (1) established mathematical collections and (2) inductive proofs of distributed protocols. Our approach consistently outperforms baseline methods across the benchmark suite.

The reasoning capabilities of large language models (LLMs) have been significantly improved through reinforcement learning (RL). Nevertheless, LLMs still struggle to consistently verify their own reasoning traces. This raises the research question of how to enhance the self-verification ability of LLMs and whether such an ability can further improve reasoning performance. In this work, we propose GRPO-Verif, an algorithm that jointly optimizes solution generation and self-verification within a unified loss function, with an adjustable hyperparameter controlling the weight of the verification signal. Experimental results demonstrate that our method enhances self-verification capability while maintaining comparable performance in reasoning.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective approach for enhancing the reasoning capabilities of Large Language Models (LLMs). Despite its efficacy, RLVR faces a meta-learning bottleneck: it lacks mechanisms for error attribution and experience internalization intrinsic to the human learning cycle beyond practice and verification, thereby limiting fine-grained credit assignment and reusable knowledge formation. We term such reusable knowledge representations derived from past errors as meta-experience. Based on this insight, we propose Meta-Experience Learning (MEL), a novel framework that incorporates self-distilled meta-experience into the model's parametric memory. Building upon standard RLVR, we introduce an additional design that leverages the LLM's self-verification capability to conduct contrastive analysis on paired correct and incorrect trajectories, identify the precise bifurcation points where reasoning errors arise, and summarize them into generalizable meta-experience. The meta-experience is further internalized into the LLM's parametric memory by minimizing the negative log-likelihood, which induces a language-modeled reward signal that bridges correct and incorrect reasoning trajectories and facilitates effective knowledge reuse. Experimental results demonstrate that MEL achieves consistent improvements on benchmarks, yielding 3.92%--4.73% Pass@1 gains across varying model sizes.

Execution-aware LLM agents offer a promising paradigm for learning from tool feedback, but such feedback is often expensive and slow to obtain, making online reinforcement learning (RL) impractical. High-coverage hardware verification exemplifies this challenge due to its reliance on industrial simulators and non-differentiable execution signals. We propose LLM4Cov, an offline agent-learning framework that models verification as memoryless state transitions guided by deterministic evaluators. Building on this formulation, we introduce execution-validated data curation, policy-aware agentic data synthesis, and worst-state-prioritized sampling to enable scalable learning under execution constraints. We further curate a reality-aligned benchmark adapted from an existing verification suite through a revised evaluation protocol. Using the proposed pipeline, a compact 4B-parameter model achieves 69.2% coverage pass rate under agentic evaluation, outperforming its teacher by 5.3% and demonstrating competitive performance against models an order of magnitude larger.

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

Reasoning methods such as chain-of-thought prompting and self-consistency have shown immense potential to improve the accuracy of large language models across various reasoning tasks. However such methods involve generation of lengthy reasoning chains, which substantially increases token consumption, computational cost, and latency. To address this inefficiency, we propose ProofSketch, a verification-guided reasoning framework that integrates symbolic closure computation, lexicographic verification and adaptive sketch generation. Our experiments show that ProofSketch consistently reduces token usage while improving accuracy, demonstrating that this approach offers a promising path for efficient and trustworthy reasoning.

The capability of continuously learning new skills via a sequence of pre-collected offline datasets is desired for an agent. However, consecutively learning a sequence of offline tasks likely leads to the catastrophic forgetting issue under resource-limited scenarios. In this paper, we formulate a new setting, continual offline reinforcement learning (CORL), where an agent learns a sequence of offline reinforcement learning tasks and pursues good performance on all learned tasks with a small replay buffer without exploring any of the environments of all the sequential tasks. For consistently learning on all sequential tasks, an agent requires acquiring new knowledge and meanwhile preserving old knowledge in an offline manner. To this end, we introduced continual learning algorithms and experimentally found experience replay (ER) to be the most suitable algorithm for the CORL problem. However, we observe that introducing ER into CORL encounters a new distribution shift problem: the mismatch between the experiences in the replay buffer and trajectories from the learned policy. To address such an issue, we propose a new model-based experience selection (MBES) scheme to build the replay buffer, where a transition model is learned to approximate the state distribution. This model is used to bridge the distribution bias between the replay buffer and the learned model by filtering the data from offline data that most closely resembles the learned model for storage. Moreover, in order to enhance the ability on learning new tasks, we retrofit the experience replay method with a new dual behavior cloning (DBC) architecture to avoid the disturbance of behavior-cloning loss on the Q-learning process. In general, we call our algorithm offline experience replay (OER). Extensive experiments demonstrate that our OER method outperforms SOTA baselines in widely-used Mujoco environments.

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

As a typical open-ended generation task, creative writing lacks verifiable reference answers, which has long constrained reward modeling and automatic evaluation due to high human annotation costs, evaluative bias, and coarse feedback signals. To address these challenges, this paper first designs a multi-agent collaborative workflow based on Grounded Theory, performing dimensional decomposition and hierarchical induction of the problem to dynamically produce interpretable and reusable fine-grained criteria. Furthermore, we propose the Memory-augmented Replay Policy Optimization (MRPO) algorithm: on the one hand, without additional training, MRPO guides models to engage in self-reflection based on dynamic criteria, enabling controlled iterative improvement; on the other hand, we adopt the training paradigm that combines supervised fine-tuning with reinforcement learning to convert evaluation criteria into reward signals, achieving end-to-end optimization. Experimental results demonstrate that the automatically constructed criteria achieve performance gains comparable to human annotations. Writer-R1-4B models trained with this approach outperform baselines across multiple creative writing tasks and surpass some 100B+ parameter open-source models.

Multi-agent reasoning systems often use agreement, confidence, or automated scores to decide which messages should shape a final answer. Such filtering assumes that a message likely to be correct is also worth keeping. Yet a wrong answer can contain a useful decomposition, constraint, or scientific principle. We test this distinction with Diverse Hypothesis Deliberation (DHD), a controlled measurement protocol that caches five independently generated messages and replays the same downstream solver, called the integrator, with each message available or hidden. The replay comparison measures a message's trajectory value: whether making the message available helps or harms subsequent reasoning. Across five mathematics and science benchmarks and two openly available model families, gpt-oss-120b and gemma-4-31B-it, wrong-helpful messages appear in every benchmark-model combination. Among wrong-answer messages that change final correctness, more than four in ten changes are helpful in each model. Controlled repeats show that the number of repeatable message effects is unlikely to arise from replay variation alone (p=0.0002). A focused intervention on repeatable wrong-helpful messages finds that the complete message works best, while retaining its reasoning preserves more success than retaining only its answer; the source of the complete-message advantage remains open. Within the same problem, repeated trajectory-value evidence also identifies a better keep-or-remove choice than answer correctness alone. Answer correctness is therefore informative but does not determine trajectory value. DHD measures this missing property and produces reusable labels for learning when agents should listen.

Legal reasoning requires not only correct outcomes but also procedurally compliant reasoning processes. However, existing methods lack mechanisms to verify intermediate reasoning steps, allowing errors such as inapplicable statute citations to propagate undetected through the reasoning chain. To address this, we propose LawThinker, an autonomous legal research agent that adopts an Explore-Verify-Memorize strategy for dynamic judicial environments. The core idea is to enforce verification as an atomic operation after every knowledge exploration step. A DeepVerifier module examines each retrieval result along three dimensions of knowledge accuracy, fact-law relevance, and procedural compliance, with a memory module for cross-round knowledge reuse in long-horizon tasks. Experiments on the dynamic benchmark J1-EVAL show that LawThinker achieves a 24% improvement over direct reasoning and an 11% gain over workflow-based methods, with particularly strong improvements on process-oriented metrics. Evaluations on three static benchmarks further confirm its generalization capability. The code is available at https://github.com/yxy-919/LawThinker-agent .

Retrieval-augmented generation (RAG) is increasingly deployed in enterprise search and document-centric assistants, where responses must be grounded in long and complex source materials. In practice, verifying that generated answers faithfully reflect retrieved documents is difficult: large language models can check long contexts but are too slow and costly for interactive services, while lightweight classifiers operate within strict context limits and frequently miss evidence outside truncated passages. We present the design of a real-time verification component integrated into a production RAG pipeline that enables full-document grounding under latency constraints. The system processes documents up to 32K tokens and employs adaptive inference strategies to balance response time and verification coverage across workloads. We describe the architectural decisions, operational trade-offs, and evaluation methodology used to deploy the verifier, and show that full-context verification substantially improves detection of unsupported responses compared with truncated validation. Our experience highlights when long-context verification is necessary, why chunk-based checking often fails in real documents, and how latency budgets shape model design. These findings provide practical guidance for practitioners building reliable large-scale retrieval-augmented applications. (Model, benchmark, and code: https://huggingface.co/llm-semantic-router)

Recent advances in reinforcement learning (RL) with verifiable outcome rewards have significantly improved the reasoning capabilities of large language models (LLMs), especially when combined with multi-turn tool interactions. However, existing methods lack both meaningful verification signals from realistic environments and explicit optimization for verification, leading to unreliable self-verification. To address these limitations, we propose ReVeal, a multi-turn reinforcement learning framework that interleaves code generation with explicit self-verification and tool-based evaluation. ReVeal enables LLMs to autonomously generate test cases, invoke external tools for precise feedback, and improves performance via a customized RL algorithm with dense, per-turn rewards. As a result, ReVeal fosters the co-evolution of a model's generation and verification capabilities through RL training, expanding the reasoning boundaries of the base model, demonstrated by significant gains in Pass@k on LiveCodeBench. It also enables test-time scaling into deeper inference regimes, with code consistently evolving as the number of turns increases during inference, ultimately surpassing DeepSeek-R1-Zero-Qwen-32B. These findings highlight the promise of ReVeal as a scalable and effective paradigm for building more robust and autonomous AI agents.

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

A commonly used heuristic in RL is experience replay (e.g.~lin1993reinforcement, mnih2015human), in which a learner stores and re-uses past trajectories as if they were sampled online. In this work, we initiate a rigorous study of this heuristic in the setting of tabular Q-learning. We provide a convergence rate guarantee, and discuss how it compares to the convergence of Q-learning depending on important parameters such as the frequency and number of replay iterations. We also provide theoretical evidence showing when we might expect this heuristic to strictly improve performance, by introducing and analyzing a simple class of MDPs. Finally, we provide some experiments to support our theoretical findings.

The real world is non-stationary and infinitely complex, requiring intelligent agents to learn continually without the prohibitive cost of retraining from scratch. While online continual learning offers a framework for this setting, learning new information often interferes with previously acquired knowledge, causes forgetting and degraded generalization. To address this, we propose Abstraction-Augmented Training (AAT), a loss-level modification encouraging models to capture the latent relational structure shared across examples. By jointly optimizing over concrete instances and their abstract representations, AAT introduces a memory-efficient inductive bias that stabilizes learning in strictly online data streams, eliminating the need for a replay buffer. To capture the multi-faceted nature of abstraction, we introduce and evaluate AAT on two benchmarks: a controlled relational dataset where abstraction is realized through entity masking, and a narrative dataset where abstraction is expressed through shared proverbs. Our results show that AAT achieves performance comparable to or exceeding strong experience replay (ER) baselines, despite requiring zero additional memory and only minimal changes to the training objective. This work highlights structural abstraction as a powerful, memory-free alternative to ER.

Large Language Models have demonstrated remarkable capabilities in code generation, yet they often struggle with complex programming tasks that require deep algorithmic reasoning. While process supervision through learned reward models shows promise in guiding reasoning steps, it requires expensive training data and suffers from unreliable evaluation. We propose Outcome-Refining Process Supervision, a novel paradigm that treats outcome refinement itself as the process to be supervised. Our framework leverages concrete execution signals to ground the supervision of reasoning steps, while using tree-structured exploration to maintain multiple solution trajectories simultaneously. Experiments demonstrate that our approach enables even smaller models to achieve high success accuracy and performance metrics on competitive programming tasks, creates more reliable verification than traditional reward models without requiring training PRMs. Our approach achieves significant improvements across 5 models and 3 datasets: an average of 26.9% increase in correctness and 42.2% in efficiency. The results suggest that providing structured reasoning space with concrete verification signals is crucial for solving complex programming tasks. We open-source all our code and data at: https://github.com/zhuohaoyu/ORPS