Daily Papers

Reinforcement learning (RL) promises to expand the capabilities of language models, but it is unclear if current RL techniques promote the discovery of novel behaviors, or simply sharpen those already present in the base model. In this paper, we investigate the value of deliberate exploration -- explicitly incentivizing the model to discover novel and diverse behaviors -- and aim to understand how the knowledge in pre-trained models can guide this search. Our main finding is that exploration with a simple, principled, representation-based bonus derived from the pre-trained language model's hidden states significantly improves diversity and pass@k rates -- both for post-training, and in a novel inference-time scaling setting we introduce. For inference-time, exploration with representation-based diversity improves efficiency, consistently improving pass@k rates across a variety of models and reasoning tasks. For example, for Qwen-2.5-14b-Instruct we obtain over 50% improvement in verifier efficiency on almost all tasks. For post-training, we show that integrating this exploration strategy into an RL pipeline improves reasoning performance over that of the initial model and over standard RL post-training. For example, on AIME 2024, our post-trained Qwen-2.5-7b-Instruct's pass@80 matches the pass@256 of GRPO on the same model, demonstrating a 3x improvement in test-time sample efficiency. Overall, our findings suggest that deliberate exploration -- with the right notion of diversity -- is a practical path toward discovery of new behaviors beyond sharpening.

There is intense interest in investigating how inference time compute (ITC) (e.g. repeated sampling, refinements, etc) can improve large language model (LLM) capabilities. At the same time, recent breakthroughs in reasoning models, such as Deepseek-R1, unlock the opportunity for reinforcement learning to improve LLM reasoning skills. An in-depth understanding of how ITC interacts with reasoning across different models could provide important guidance on how to further advance the LLM frontier. This work conducts a comprehensive analysis of inference-time scaling methods for both reasoning and non-reasoning models on challenging reasoning tasks. Specifically, we focus our research on verifier-free inference time-scaling methods due to its generalizability without needing a reward model. We construct the Pareto frontier of quality and efficiency. We find that non-reasoning models, even with an extremely high inference budget, still fall substantially behind reasoning models. For reasoning models, majority voting proves to be a robust inference strategy, generally competitive or outperforming other more sophisticated ITC methods like best-of-N and sequential revisions, while the additional inference compute offers minimal improvements. We further perform in-depth analyses of the association of key response features (length and linguistic markers) with response quality, with which we can improve the existing ITC methods. We find that correct responses from reasoning models are typically shorter and have fewer hedging and thinking markers (but more discourse markers) than the incorrect responses.

We show that verifier-free evolution is bottlenecked by both diversity and efficiency: without external correction, repeated evolution accelerates collapse toward narrow modes, while the uniform use of a high-cost model wastes compute and quickly becomes economically impractical. We introduce Squeeze Evolve, a unified multi-model orchestration framework for verifier-free evolutionary inference. Our approach is guided by a simple principle: allocate model capability where it has the highest marginal utility. Stronger models are reserved for high-impact stages, while cheaper models handle the other stages at much lower costs. This principle addresses diversity and cost-efficiency jointly while remaining lightweight. Squeeze Evolve naturally supports open-source, closed-source, and mixed-model deployments. Across AIME 2025, HMMT 2025, LiveCodeBench V6, GPQA-Diamond, ARC-AGI-V2, and multimodal vision benchmarks, such as MMMU-Pro and BabyVision, Squeeze Evolve consistently improves the cost-capability frontier over single-model evolution and achieves new state-of-the-art results on several tasks. Empirically, Squeeze Evolve reduces API cost by up to sim3times and increases fixed-budget serving throughput by up to sim10times. Moreover, on discovery tasks, Squeeze Evolve is the first verifier-free evolutionary method to match, and in some cases exceed, the performance of verifier-based evolutionary methods.

Code verifiers play a critical role in post-verification for LLM-based code generation, yet existing supervised fine-tuning methods suffer from data scarcity, high failure rates, and poor inference efficiency. While reinforcement learning (RL) offers a promising alternative by optimizing models through execution-driven rewards without labeled supervision, our preliminary results show that naive RL with only functionality rewards fails to generate effective unit tests for difficult branches and samples. We first theoretically analyze showing that branch coverage, sample difficulty, syntactic and functional correctness can be jointly modeled as RL rewards, where optimizing these signals can improve the reliability of unit-test-based verification. Guided by this analysis, we design syntax- and functionality-aware rewards and further propose branch- and sample-difficulty--aware RL using exponential reward shaping and static analysis metrics. With this formulation, CVeDRL achieves state-of-the-art performance with only 0.6B parameters, yielding up to 28.97% higher pass rate and 15.08% higher branch coverage than GPT-3.5, while delivering over 20times faster inference than competitive baselines. Code is available at https://github.com/LIGHTCHASER1/CVeDRL.git

Large Reasoning Models (LRMs) demonstrate exceptional capability in tackling complex mathematical, logical, and coding tasks by leveraging extended Chain-of-Thought (CoT) reasoning. Test-time scaling methods, such as prolonging CoT with explicit token-level exploration, can push LRMs' accuracy boundaries, but they incur significant decoding overhead. A key inefficiency source is LRMs often generate redundant thinking CoTs, which demonstrate clear structured overthinking and underthinking patterns. Inspired by human cognitive reasoning processes and numerical optimization theories, we propose TrimR, a verifier-based, training-free, efficient framework for dynamic CoT compression to trim reasoning and enhance test-time scaling, explicitly tailored for production-level deployment. Our method employs a lightweight, pretrained, instruction-tuned verifier to detect and truncate redundant intermediate thoughts of LRMs without any LRM or verifier fine-tuning. We present both the core algorithm and asynchronous online system engineered for high-throughput industrial applications. Empirical evaluations on Ascend NPUs and vLLM show that our framework delivers substantial gains in inference efficiency under large-batch workloads. In particular, on the four MATH500, AIME24, AIME25, and GPQA benchmarks, the reasoning runtime of Pangu Pro MoE, Pangu-R-38B, QwQ-32B, and DeepSeek-R1-Distill-Qwen-32B is improved by up to 70% with negligible impact on accuracy.

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.

Recent advances in large language models (LLMs) demonstrate their effectiveness in scaling test-time compute for software engineering tasks. However, these approaches often focus on high-level solutions, with limited attention to optimizing low-level CUDA kernel implementations. Additionally, existing kernel generation benchmarks suffer from exploitable loopholes and insufficient diversity in testing conditions, hindering true generalization assessment. To address these limitations, we introduce robust-kbench, a new benchmark for rigorous evaluation of kernel performance and correctness across varied scenarios. Furthermore, we present a comprehensive agentic framework that automates CUDA kernel discovery, verification, and optimization. This pipeline enables frontier LLMs to translate torch code to CUDA kernels and iteratively improve their runtime within our robust evaluation setting. Our sequential workflow first translates PyTorch code into equivalent CUDA kernels. It then optimizes their runtime using a novel evolutionary meta-generation procedure tailored to the CUDA ecosystem, guided by LLM-based verifiers for correctness and efficient filtering. Evaluated on robust-kbench, our approach produces CUDA kernels outperforming torch implementations for practical applications, including forward and backward passes. It can fuse operations and deploy various runtime optimization strategies. The verifier workflow accurately classifies incorrect kernels, enhancing hardware verification efficiency.

Recent work on enhancing the reasoning abilities of large language models (LLMs) has introduced explicit length control as a means of constraining computational cost while preserving accuracy. However, existing approaches rely on fixed-length training budgets, which do not take advantage of the natural progression from exploration to compression during learning. In this work, we propose a curriculum learning strategy for length-controlled reasoning using Group Relative Policy Optimization (GRPO). Our method starts with generous token budgets and gradually tightens them over training, encouraging models to first discover effective solution strategies and then distill them into more concise reasoning traces. We augment GRPO with a reward function that balances three signals: task correctness (via verifier feedback), length efficiency, and formatting adherence (via structural tags). Experiments on GSM8K, MATH500, SVAMP, College Math, and GSM+ demonstrate that curriculum-based training consistently outperforms fixed-budget baselines at the same final budget, achieving higher accuracy and significantly improved token efficiency. We further ablate the impact of reward weighting and decay schedule design, showing that progressive constraint serves as a powerful inductive bias for training efficient reasoning models. Our code and checkpoints are released at: https://github.com/hammoudhasan/curriculum_grpo.

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.

We introduce Gaia2, a benchmark for evaluating large language model agents in realistic, asynchronous environments. Unlike prior static or synchronous evaluations, Gaia2 introduces scenarios where environments evolve independently of agent actions, requiring agents to operate under temporal constraints, adapt to noisy and dynamic events, resolve ambiguity, and collaborate with other agents. Each scenario is paired with a write-action verifier, enabling fine-grained, action-level evaluation and making Gaia2 directly usable for reinforcement learning from verifiable rewards. Our evaluation of state-of-the-art proprietary and open-source models shows that no model dominates across capabilities: GPT-5 (high) reaches the strongest overall score of 42% pass@1 but fails on time-sensitive tasks, Claude-4 Sonnet trades accuracy and speed for cost, Kimi-K2 leads among open-source models with 21% pass@1. These results highlight fundamental trade-offs between reasoning, efficiency, robustness, and expose challenges in closing the "sim2real" gap. Gaia2 is built on a consumer environment with the open-source Agents Research Environments platform and designed to be easy to extend. By releasing Gaia2 alongside the foundational ARE framework, we aim to provide the community with a flexible infrastructure for developing, benchmarking, and training the next generation of practical agent systems.

Ensemble methods enhance Large Language Models (LLMs) by combining multiple models but suffer from high computational costs. In this paper, we introduce Speculative Ensemble, a novel framework that accelerates LLM ensembles without sacrificing performance, inspired by Speculative Decoding-where a small proposal model generates tokens sequentially, and a larger target model verifies them in parallel. Our approach builds on two key insights: (1) the verification distribution can be the ensemble distribution of both the proposal and target models, and (2) alternating each model as the proposer and verifier can further enhance efficiency. We generalize this method to ensembles with n models and theoretically prove that SE is never slower than a standard ensemble, typically achieving faster speed. Extensive experiments demonstrate speed improvements of 1.11x-2.23x over standard ensemble techniques without compromising generation quality. Our code is available at https://github.com/Kamichanw/Speculative-Ensemble/

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.

Verifiers are auxiliary models that assess the correctness of outputs generated by base large language models (LLMs). They play a crucial role in many strategies for solving reasoning-intensive problems with LLMs. Typically, verifiers are LLMs themselves, often as large (or larger) than the base model they support, making them computationally expensive. In this work, we introduce a novel lightweight verification approach, LiLaVe, which reliably extracts correctness signals from the hidden states of the base LLM. A key advantage of LiLaVe is its ability to operate with only a small fraction of the computational budget required by traditional LLM-based verifiers. To demonstrate its practicality, we couple LiLaVe with popular meta-generation strategies, like best-of-n or self-consistency. Moreover, we design novel LiLaVe-based approaches, like conditional self-correction or conditional majority voting, that significantly improve both accuracy and efficiency in generation tasks with smaller LLMs. Our work demonstrates the fruitfulness of extracting latent information from the hidden states of LLMs, and opens the door to scalable and resource-efficient solutions for reasoning-intensive applications.

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

Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited by selecting and prioritizing valid reasoning paths. However, we identify a critical limitation: scaling flaws, prevalent across different models (Mistral 7B and DeepSeekMath 7B), benchmarks (GSM8K and MATH), and verifiers (outcome value models and process reward models). As sample size increases, verifier-guided search exhibits diminishing advantages and eventually underperforms repeated sampling. Our analysis attributes this to verifier failures, where imperfect verifiers misrank candidates and erroneously prune all valid paths. These issues are further exacerbated in challenging and out-of-distribution problems, restricting search effectiveness. To mitigate verifier failures, we explore reducing reliance on verifiers and conduct preliminary investigations using two simple methods. Our findings reveal fundamental limitations in verifier-guided search and suggest future directions.

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

Large Language Models (LLMs), particularly Code LLMs, have demonstrated impressive performance in code generation. Current research primarily focuses on the correctness of generated code, while efficiency remains less explored. Recent works have focused on modifying the initial version of the code to improve its efficiency. However, such refinements are limited by the algorithmic design and overall logic of the initial code, resulting in only incremental improvements. In contrast, when human developers write high-quality code, they typically begin by designing several potential solutions at the logical level, evaluating various algorithms and their complexities, and then proceeding to implement and optimize the solution. In this study, we introduce \tool: Large Language Model for Code Efficiency, a novel framework that enables LLMs to generate code that balances both efficiency and correctness. Specifically, \tool divides the efficiency optimization process into two domains: algorithmic exploration in the logic domain and implementation optimization in the code domain. The correctness of the code is then guaranteed through a synthetic test case refinement process. This approach, which prioritizes efficiency before ensuring correctness, offers a new paradigm for efficient code generation. Experiments demonstrate that \tool consistently improves both efficiency and correctness, achieving new state-of-the-art performance in code efficiency benchmarks across various LLM backbones.

The widespread adoption of deep neural networks (DNNs) requires efficient techniques for verifying their safety. DNN verifiers are complex tools, which might contain bugs that could compromise their soundness and undermine the reliability of the verification process. This concern can be mitigated using proofs: artifacts that are checkable by an external and reliable proof checker, and which attest to the correctness of the verification process. However, such proofs tend to be extremely large, limiting their use in many scenarios. In this work, we address this problem by minimizing proofs of unsatisfiability produced by DNN verifiers. We present algorithms that remove facts which were learned during the verification process, but which are unnecessary for the proof itself. Conceptually, our method analyzes the dependencies among facts used to deduce UNSAT, and removes facts that did not contribute. We then further minimize the proof by eliminating remaining unnecessary dependencies, using two alternative procedures. We implemented our algorithms on top of a proof producing DNN verifier, and evaluated them across several benchmarks. Our results show that our best-performing algorithm reduces proof size by 37%-82% and proof checking time by 30%-88%, while introducing a runtime overhead of 7%-20% to the verification process itself.

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

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 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.

The evolution of machine learning has increasingly prioritized the development of powerful models and more scalable supervision signals. However, the emergence of foundation models presents significant challenges in providing effective supervision signals necessary for further enhancing their capabilities. Consequently, there is an urgent need to explore novel supervision signals and technical approaches. In this paper, we propose verifier engineering, a novel post-training paradigm specifically designed for the era of foundation models. The core of verifier engineering involves leveraging a suite of automated verifiers to perform verification tasks and deliver meaningful feedback to foundation models. We systematically categorize the verifier engineering process into three essential stages: search, verify, and feedback, and provide a comprehensive review of state-of-the-art research developments within each stage. We believe that verifier engineering constitutes a fundamental pathway toward achieving Artificial General Intelligence.

Common self-improvement approaches for large language models (LLMs), such as STaR (Zelikman et al., 2022), iteratively fine-tune LLMs on self-generated solutions to improve their problem-solving ability. However, these approaches discard the large amounts of incorrect solutions generated during this process, potentially neglecting valuable information in such solutions. To address this shortcoming, we propose V-STaR that utilizes both the correct and incorrect solutions generated during the self-improvement process to train a verifier using DPO that judges correctness of model-generated solutions. This verifier is used at inference time to select one solution among many candidate solutions. Running V-STaR for multiple iterations results in progressively better reasoners and verifiers, delivering a 4% to 17% test accuracy improvement over existing self-improvement and verification approaches on common code generation and math reasoning benchmarks with LLaMA2 models.

The emergence of large language models (LLMs) has significantly pushed the frontiers of program synthesis. Advancement of LLM-based program synthesis calls for a thorough evaluation of LLM-generated code. Most evaluation frameworks focus on the (functional) correctness of generated code; efficiency, as an important measure of code quality, has been overlooked in existing evaluations. In this work, we develop ENAMEL (EfficeNcy AutoMatic EvaLuator), a rigorous and high-standard benchmark for evaluating the capability of LLMs in generating efficient code. Firstly, we propose a new efficiency metric called eff@k, which generalizes the pass@k metric from correctness to efficiency and appropriately handles right-censored execution time. Furthermore, we derive an unbiased and variance-reduced estimator of eff@k via Rao--Blackwellization; we also provide a numerically stable implementation for the new estimator. Secondly, to set a high-standard for efficiency evaluation, we employ a human expert to design best algorithms and implementations as our reference solutions of efficiency, many of which are much more efficient than existing canonical solutions in HumanEval and HumanEval+. Moreover, to ensure a rigorous evaluation, we employ a human expert to curate strong test case generators to filter out wrong code and differentiate suboptimal algorithms. An extensive study across 30 popular LLMs using our benchmark ENAMEL shows that LLMs still fall short of generating expert-level efficient code. Using two subsets of our problem set, we demonstrate that such deficiency is because current LLMs struggle in designing advanced algorithms and are barely aware of implementation optimization. Our benchmark is publicly available at https://github.com/q-rz/enamel .

One way to increase confidence in the outputs of Large Language Models (LLMs) is to support them with reasoning that is clear and easy to check -- a property we call legibility. We study legibility in the context of solving grade-school math problems and show that optimizing chain-of-thought solutions only for answer correctness can make them less legible. To mitigate the loss in legibility, we propose a training algorithm inspired by Prover-Verifier Game from Anil et al. (2021). Our algorithm iteratively trains small verifiers to predict solution correctness, "helpful" provers to produce correct solutions that the verifier accepts, and "sneaky" provers to produce incorrect solutions that fool the verifier. We find that the helpful prover's accuracy and the verifier's robustness to adversarial attacks increase over the course of training. Furthermore, we show that legibility training transfers to time-constrained humans tasked with verifying solution correctness. Over course of LLM training human accuracy increases when checking the helpful prover's solutions, and decreases when checking the sneaky prover's solutions. Hence, training for checkability by small verifiers is a plausible technique for increasing output legibility. Our results suggest legibility training against small verifiers as a practical avenue for increasing legibility of large LLMs to humans, and thus could help with alignment of superhuman models.

In real-world Tool-Integrated Reasoning (TIR) scenarios, where LLMs interleave reasoning with external tool calls, a major source of inefficiency is that the toolcalls create pauses between LLM requests and cause KV-Cache eviction, forcing recomputation. Also, the long, unfiltered response returned by external tools inflates the KV-Cache, so each decode step spends more time loading the growing cache and thus becomes steadily slower as context length increases. However, existing efficiency metrics like token counts and toolcall counts fail to capture the real model inference latency. To address this, we introduce PTE (Prefill Token Equivalents), a hardware-aware TIR-efficiency metric that unifies internal reasoning and external tool-use costs while explicitly accounting for non-reusable KV-Cache and long-tool-response scenarios. Validation in a high-concurrency industrial setting indicates that PTE aligns significantly better with wall-clock latency than standard token counts, while maintaining consistent efficiency rankings across diverse hardware profiles. We conduct extensive experiments across five TIR benchmarks, quantify their PTE costs, and identify four inefficiency patterns that appear in TIR. We also discover that trajectories with higher PTE costs tend to have lower reasoning correctness, indicating that simply using more tools does not improve the quality of the answer.

We introduce Differential Performance Evaluation (DPE), a framework designed to reliably evaluate Large Language Models (LLMs) for efficient code generation. Traditional coding benchmarks often fail to provide reliable insights into code efficiency, due to their reliance on simplistic test inputs and the absence of effective compound metrics. DPE addresses these issues by focusing on efficiency-demanding programming tasks and establishing an insightful compound metric for performance evaluation. DPE operates in two phases: To curate efficiency datasets, it selects efficiency-demanding tasks from existing coding benchmarks and generates computationally expensive inputs to stress the efficiency of LLM solutions. To assess the code efficiency, DPE profiles the new solution and compares it globally against a set of reference solutions that exhibit distinct efficiency levels, where the matched level defines its efficiency score. As a proof of concept, we use DPE to create EvalPerf, a benchmark with 121 performance-challenging coding tasks. Our comprehensive evaluation draws interesting findings on the efficiency impact of model sizes, instruction tuning, and prompting. For example, while the scaling law fails to account for code efficiency, general instruction tuning benefits both code correctness and efficiency. We also evaluate the evaluation by examining the effectiveness of DPE, showing that EvalPerf is reliable and convenient to use even across platforms.

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

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

Test-time scaling (TTS) has emerged as a new frontier for scaling the performance of Large Language Models. In test-time scaling, by using more computational resources during inference, LLMs can improve their reasoning process and task performance. Several approaches have emerged for TTS such as distilling reasoning traces from another model or exploring the vast decoding search space by employing a verifier. The verifiers serve as reward models that help score the candidate outputs from the decoding process to diligently explore the vast solution space and select the best outcome. This paradigm commonly termed has emerged as a superior approach owing to parameter free scaling at inference time and high performance gains. The verifiers could be prompt-based, fine-tuned as a discriminative or generative model to verify process paths, outcomes or both. Despite their widespread adoption, there is no detailed collection, clear categorization and discussion of diverse verification approaches and their training mechanisms. In this survey, we cover the diverse approaches in the literature and present a unified view of verifier training, types and their utility in test-time scaling. Our repository can be found at https://github.com/elixir-research-group/Verifierstesttimescaling.github.io.

Efficiency is a key property to foster inclusiveness and reduce environmental costs, especially in an era of LLMs. In this work, we provide a comprehensive evaluation of efficiency for MT evaluation metrics. Our approach involves replacing computation-intensive transformers with lighter alternatives and employing linear and quadratic approximations for alignment algorithms on top of LLM representations. We evaluate six (reference-free and reference-based) metrics across three MT datasets and examine 16 lightweight transformers. In addition, we look into the training efficiency of metrics like COMET by utilizing adapters. Our results indicate that (a) TinyBERT provides the optimal balance between quality and efficiency, (b) CPU speed-ups are more substantial than those on GPU; (c) WMD approximations yield no efficiency gains while reducing quality and (d) adapters enhance training efficiency (regarding backward pass speed and memory requirements) as well as, in some cases, metric quality. These findings can help to strike a balance between evaluation speed and quality, which is essential for effective NLG systems. Furthermore, our research contributes to the ongoing efforts to optimize NLG evaluation metrics with minimal impact on performance. To our knowledge, ours is the most comprehensive analysis of different aspects of efficiency for MT metrics conducted so far.

As deep learning models scale, their training cost has surged significantly. Due to both hardware advancements and limitations in current software stacks, the need for data efficiency has risen. Data efficiency refers to the effective hiding of data access latency and the avoidance of unnecessary data movements. Major challenges arise from the growing disparity between GPU memory bandwidth and computational throughput, imminent GPU memory capacity limitations, and inefficiencies in the PyTorch software stack, including a lack of device-specific PCIe transfer optimizations and high-level domain-specific abstractions. To effectively mitigate these data inefficiencies for deep learning training, this dissertation analyzes data inefficiency in representative deep training tasks, specifically in graph neural networks (GNNs) and large language models (LLMs). It then proposes novel runtime and code generation techniques to mitigate these challenges and implements these optimizations seamlessly within the PyTorch stack while maintaining strong programmability and interoperability. First, PyTorch-Direct is devised to incorporate the GPU-centric PCIe data transfer paradigm in PyTorch for GNN training. Next, Hector intermediate representation (IR) and its code generator are proposed to introduce domain-specific high-level abstraction and systematically address memory-intensive performance challenges for relational GNNs. Finally, in LLM training, the throughput has been increasingly constrained by GPU memory capacity. To mitigate this, the SSDTrain offloading framework is designed and implemented. Together, these contributions show that code generation and runtime techniques can systematically mitigate the data management bottlenecks in deep learning training, which stem from the data-intensive nature of workloads and the oversimplification inherent in the deep learning training software stack.

One common strategy for improving the performance of Large Language Models (LLMs) on downstream tasks involves using a verifier model to either select the best answer from a pool of candidates or to steer the auto-regressive generation process towards better outputs. This class of methods typically results in improved accuracy at the cost of increased computation at test-time, a paradigm known as test-time scaling. However, most existing approaches increase computation uniformly across all samples and generation steps, without considering the complexity of individual instances, leading to inefficient resource use. We address this limitation by proposing an approach, called Locally Adaptive Test-Time Scaling (LATTS), that allocates variable compute across generation steps. Specifically, at each generation step, LATTS employs a verifier-based acceptance criterion to decide whether to resample, backtrack, restart, or stop the generation process. This criterion effectively adjusts the per-step computational effort based on a precise notion of local difficulty derived from the verifier model. Empirical results show that LATTS achieves significantly superior accuracy--compute tradeoffs compared to standard verifier-based methods.

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

Artificial Intelligence (AI) is starting to transform the research process as we know it by automating the discovery of new solutions. Given a task, the typical AI-driven approach is (i) to generate a set of diverse solutions, and then (ii) to verify these solutions and select one that solves the problem. Crucially, this approach assumes the existence of a reliable verifier, i.e., one that can accurately determine whether a solution solves the given problem. We argue that systems research, long focused on designing and evaluating new performance-oriented algorithms, is particularly well-suited for AI-driven solution discovery. This is because system performance problems naturally admit reliable verifiers: solutions are typically implemented in real systems or simulators, and verification reduces to running these software artifacts against predefined workloads and measuring performance. We term this approach as AI-Driven Research for Systems (ADRS), which iteratively generates, evaluates, and refines solutions. Using penEvolve, an existing open-source ADRS instance, we present case studies across diverse domains, including load balancing for multi-region cloud scheduling, Mixture-of-Experts inference, LLM-based SQL queries, and transaction scheduling. In multiple instances, ADRS discovers algorithms that outperform state-of-the-art human designs (e.g., achieving up to 5.0x runtime improvements or 50% cost reductions). We distill best practices for guiding algorithm evolution, from prompt design to evaluator construction, for existing frameworks. We then discuss the broader implications for the systems community: as AI assumes a central role in algorithm design, we argue that human researchers will increasingly focus on problem formulation and strategic guidance. Our results highlight both the disruptive potential and the urgent need to adapt systems research practices in the age of AI.

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.

Reinforcement learning with verifiable rewards has enabled strong post-training gains in domains such as math and coding, though many open-ended settings rely on rubric-based rewards. We study reward hacking in rubric-based RL, where a policy is optimized against a training verifier but evaluated against a cross-family panel of three frontier judges, reducing dependence on any single evaluator. Our framework separates two sources of divergence: verifier failure, where the training verifier credits rubric criteria that reference verifiers reject, and rubric-design limitations, where even strong rubric-based verifiers favor responses that rubric-free judges rate worse overall. Across medical and science domains, weak verifiers produce large proxy-reward gains that do not transfer to the reference verifiers; exploitation grows over training and concentrates in recurring failures such as partial satisfaction of compound criteria, treating implicit content as explicit, and imprecise topical matching. Stronger verifiers substantially reduce, but do not eliminate, verifier exploitation. We also introduce a self-internalization gap, a verifier-free diagnostic based on policy log-probabilities, which tracks reference-verifier quality, detecting when the policy trained using the weak verifier stops improving. Finally, in our setting, stronger verification does not prevent reward hacking when the rubric leaves important failure modes unspecified: rubric-based verifiers prefer the RL checkpoint, while rubric-free judges prefer the base model. These disagreements coincide with gains concentrated in completeness and presence-based criteria, alongside declines in factual correctness, conciseness, relevance, and overall quality. Together, these results suggest that stronger verification reduces reward hacking, but does not by itself ensure that rubric gains correspond to broader quality gains.

Large language models (LLMs) have exhibited impressive capabilities across a myriad of tasks, yet they occasionally yield undesirable outputs. We posit that these limitations are rooted in the foundational autoregressive architecture of LLMs, which inherently lacks mechanisms for differentiating between desirable and undesirable results. Drawing inspiration from the dual-process theory of human cognition, we introduce LLM2, a novel framework that combines an LLM (System 1) with a process-based verifier (System 2). Within LLM2, the LLM is responsible for generating plausible candidates, while the verifier provides timely process-based feedback to distinguish desirable and undesirable outputs. The verifier is trained with a pairwise comparison loss on synthetic process-supervision data generated through our token quality exploration strategy. Empirical results on mathematical reasoning benchmarks substantiate the efficacy of LLM2, exemplified by an accuracy enhancement from 50.3 to 57.8 (+7.5) for Llama3-1B on GSM8K. Furthermore, when combined with self-consistency, LLM2 achieves additional improvements, boosting major@20 accuracy from 56.2 to 70.2 (+14.0).

We present EfficientViT-SAM, a new family of accelerated segment anything models. We retain SAM's lightweight prompt encoder and mask decoder while replacing the heavy image encoder with EfficientViT. For the training, we begin with the knowledge distillation from the SAM-ViT-H image encoder to EfficientViT. Subsequently, we conduct end-to-end training on the SA-1B dataset. Benefiting from EfficientViT's efficiency and capacity, EfficientViT-SAM delivers 48.9x measured TensorRT speedup on A100 GPU over SAM-ViT-H without sacrificing performance. Our code and pre-trained models are released at https://github.com/mit-han-lab/efficientvit.

Code generation models have increasingly become integral to aiding software development, offering assistance in tasks such as code completion, debugging, and code translation. Although current research has thoroughly examined the correctness of code produced by code generation models, a vital aspect, i.e., the efficiency of the generated code, has often been neglected. This paper presents EffiBench, a benchmark with 1,000 efficiency-critical coding problems for assessing the efficiency of code generated by code generation models. EffiBench contains a diverse set of LeetCode coding problems. Each problem is paired with an executable human-written canonical solution. With EffiBench, we empirically examine the capability of 21 Large Language Models (13 open-sourced and 8 closed-sourced) in generating efficient code. The results demonstrate that GPT-4-turbo generates the most efficient code, significantly outperforming Palm-2-chat-bison, Claude-instant-1, Gemini-pro, GPT-4, and GPT-3.5. Nevertheless, its code efficiency is still worse than the efficiency of human-written canonical solutions. In particular, the average and worst execution time of GPT-4-turbo generated code is 1.69 and 45.49 times that of the canonical solutions.

Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling. To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary {0,1} during training. This choice carries a cost: it introduces false negatives (rejecting correct answers, FNs) and false positives (accepting incorrect ones, FPs). For instance, a rule-based checker may mark the correct fraction 12{36} as wrong when compared against the canonical 1{3} due to brittle parsing/equivalence rules (FN), while a large language model (LLM) judges can be gamed by superficial cues or even a single adversarial token, yielding inflated correctness for wrong solutions (FP). We formalize verifier unreliability by modeling the verifier as a stochastic reward channel with asymmetric noise rates. From this abstraction, we derive two correction algorithms for verifier errors. The first is a backward correction that de-biases the observed binary reward to recover an unbiased estimator of the clean policy gradient. The second is a forward correction that reweights score-function terms so that the expected update direction aligns with the clean gradient; notably, it requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimization (GRPO)-based RLVR pipeline and evaluate them on math-reasoning models and benchmarks. Across models and datasets, both corrections improve over uncorrected training; the forward variant converges faster and remains stable under heavier noise. Finally, we show a practical appeal mechanism in which a lightweight LLM verifier estimates the FN rate online by rechecking rule-based negatives, obtaining outperformance compared with other state-of-the-art contenders.

The recent paradigm shift towards training large language models (LLMs) using DeepSeek-R1-Zero-style reinforcement learning (RL) on verifiable rewards has led to impressive advancements in code and mathematical reasoning. However, this methodology is limited to tasks where rule-based answer verification is possible and does not naturally extend to real-world domains such as chemistry, healthcare, engineering, law, biology, business, and economics. Current practical workarounds use an additional LLM as a model-based verifier; however, this introduces issues such as reliance on a strong verifier LLM, susceptibility to reward hacking, and the practical burden of maintaining the verifier model in memory during training. To address this and extend DeepSeek-R1-Zero-style training to general reasoning domains, we propose a verifier-free method (VeriFree) that bypasses answer verification and instead uses RL to directly maximize the probability of generating the reference answer. We compare VeriFree with verifier-based methods and demonstrate that, in addition to its significant practical benefits and reduced compute requirements, VeriFree matches and even surpasses verifier-based methods on extensive evaluations across MMLU-Pro, GPQA, SuperGPQA, and math-related benchmarks. Moreover, we provide insights into this method from multiple perspectives: as an elegant integration of training both the policy and implicit verifier in a unified model, and as a variational optimization approach. Code is available at https://github.com/sail-sg/VeriFree.

Verifiers or reward models are often used to enhance the reasoning performance of large language models (LLMs). A common approach is the Best-of-N method, where N candidate solutions generated by the LLM are ranked by a verifier, and the best one is selected. While LLM-based verifiers are typically trained as discriminative classifiers to score solutions, they do not utilize the text generation capabilities of pretrained LLMs. To overcome this limitation, we instead propose training verifiers using the ubiquitous next-token prediction objective, jointly on verification and solution generation. Compared to standard verifiers, such generative verifiers (GenRM) can benefit from several advantages of LLMs: they integrate seamlessly with instruction tuning, enable chain-of-thought reasoning, and can utilize additional inference-time compute via majority voting for better verification. We demonstrate that when using Gemma-based verifiers on algorithmic and grade-school math reasoning tasks, GenRM outperforms discriminative verifiers and LLM-as-a-Judge, showing a 16-64% improvement in the percentage of problems solved with Best-of-N. Furthermore, we show that GenRM scales favorably across dataset size, model capacity, and inference-time compute.

Security of model parameters and user data is critical for Transformer-based services, such as ChatGPT. While recent strides in secure two-party protocols have successfully addressed security concerns in serving Transformer models, their adoption is practically infeasible due to the prohibitive cryptographic overheads involved. Drawing insights from our hands-on experience in developing two real-world Transformer-based services, we identify the inherent efficiency bottleneck in the two-party assumption. To overcome this limitation, we propose a novel three-party threat model. Within this framework, we design a semi-symmetric permutation-based protection scheme and present STIP, the first secure Transformer inference protocol without any inference accuracy loss. Experiments on representative Transformer models in real systems show that STIP has practical security and outperforms state-of-the-art secure two-party protocols in efficiency by millions of times.

Agent systems often decompose a task across multiple roles, but these roles are typically specified by prompts rather than enforced by access controls. Without enforcement, a team pass rate can mask whether agents actually coordinated or whether one role effectively did another role's work. We present TeamBench, a benchmark with 851 task templates and 931 seeded instances for evaluating agent coordination under operating system-enforced role separation. TeamBench separates specification access, workspace editing, and final certification across Planner, Executor, and Verifier roles, so that no role can read the full requirements, modify the workspace, and certify the final answer. Prompt-only and sandbox-enforced teams reach statistically indistinguishable pass rates, but prompt-only runs produce 3.6 times more cases where the verifier attempts to edit the executor's code. Verifiers approve 49% of submissions that fail the deterministic grader, and removing the verifier improves mean partial score in the ablation. Team value is also conditional. Teams benefit when single agents struggle, but hurt when single agents already perform well. A 40-session human study under the same role separation shows that our benchmark exposes interaction patterns that pass rate misses. Solo participants work through the task directly, human participants paired with agents often collapse into quick approval, and human teams spend more effort coordinating missing information across roles.

Recent advances in large language models (LLMs) have greatly improved their reasoning and decision-making abilities when deployed as agents. Richer reasoning, however, often comes at the cost of longer chain of thought (CoT), hampering interaction efficiency in real-world scenarios. Nevertheless, there still lacks systematic definition of LLM agent efficiency, hindering targeted improvements. To this end, we introduce dual-efficiency, comprising (i) step-level efficiency, which minimizes tokens per step, and (ii) trajectory-level efficiency, which minimizes the number of steps to complete a task. Building on this definition, we propose DEPO, a dual-efficiency preference optimization method that jointly rewards succinct responses and fewer action steps. Experiments on WebShop and BabyAI show that DEPO cuts token usage by up to 60.9% and steps by up to 26.9%, while achieving up to a 29.3% improvement in performance. DEPO also generalizes to three out-of-domain math benchmarks and retains its efficiency gains when trained on only 25% of the data. Our project page is at https://opencausalab.github.io/DEPO.

We present OpenComputer, a verifier-grounded framework for constructing verifiable software worlds for computer-use agents. OpenComputer integrates four components: (1) app-specific state verifiers that expose structured inspection endpoints over real applications, (2) a self-evolving verification layer that improves verifier reliability using execution-grounded feedback, (3) a task-generation pipeline that synthesizes realistic and machine-checkable desktop tasks, and (4) an evaluation harness that records full trajectories and computes auditable partial-credit rewards. In its current form, OpenComputer covers 33 desktop applications and 1,000 finalized tasks spanning browsers, office tools, creative software, development environments, file managers, and communication applications. Experiments show that OpenComputer's hard-coded verifiers align more closely with human adjudication than LLM-as-judge evaluation, especially when success depends on fine-grained application state. Frontier agents struggle with end-to-end completion despite partial progress, and open-source models exhibit sharp drops from their OSWorld-Verified scores, exposing a persistent gap in robust computer automation.

Existing code generation benchmarks primarily evaluate functional correctness, with limited focus on code efficiency and often restricted to a single language like Python. To address this gap, we introduce EffiBench-X, the first multi-language benchmark designed to measure the efficiency of LLM-generated code. EffiBench-X supports Python, C++, Java, JavaScript, Ruby, and Golang. It comprises competitive programming tasks with human-expert solutions as efficiency baselines. Evaluating state-of-the-art LLMs on EffiBench-X reveals that while models generate functionally correct code, they consistently underperform human experts in efficiency. Even the most efficient LLM-generated solutions (Qwen3-32B) achieve only around 62\% of human efficiency on average, with significant language-specific variations. LLMs show better efficiency in Python, Ruby, and JavaScript than in Java, C++, and Golang. For instance, DeepSeek-R1's Python code is significantly more efficient than its Java code. These results highlight the critical need for research into LLM optimization techniques to improve code efficiency across diverse languages. The dataset and evaluation infrastructure are submitted and available at https://github.com/EffiBench/EffiBench-X.git and https://huggingface.co/datasets/EffiBench/effibench-x.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

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.

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

Large reasoning models (LRMs) are often evaluated using metrics such as final-answer accuracy or token count. However, identical scores on these metrics can hide fundamentally different reasoning structures. To address this limitation, we introduce a scalable LRM benchmark of logic puzzles and a pipeline that converts unstructured traces into verifiable reasoning graphs of claims and dependencies. This turns reasoning into a structured, measurable object whose topology can be quantitatively analyzed. Building on this, we define a reasoning efficiency metric that quantifies how concentrated the model's logical flow is. Our analysis on open-source reasoning models shows that structural measurements separate behaviors that token count and accuracy conflate, providing a practical tool for diagnosing failure modes and comparing how reasoning scales with puzzle difficulty.

Algorithmic efficiency techniques such as distillation (hinton2015distillation) are useful in improving model quality without increasing serving costs, provided a larger teacher model is available for a smaller student model to learn from during training. Standard distillation methods are limited to only forcing the student to match the teacher's outputs. Given the costs associated with training a large model, we believe we should be extracting more useful information from a teacher model than by just making the student match the teacher's outputs. In this paper, we introduce \guide (Guided Initialization and Distillation of Embeddings). \guide can be considered a distillation technique that forces the student to match the teacher in the parameter space. Using \guide we show 25-26\% reduction in the teacher-student quality gap when using large student models (400M - 1B parameters) trained on approx 20B tokens. We also present a thorough analysis demonstrating that \guide can be combined with knowledge distillation with near additive improvements. Furthermore, we show that applying \guide alone leads to substantially better model quality than applying knowledge distillation by itself. Most importantly, \guide introduces no training or inference overhead and hence any model quality gains from our method are virtually free.

Verifiers have been demonstrated to enhance LLM reasoning via test-time scaling (TTS). Yet, they face significant challenges in complex domains. Error propagation from incorrect intermediate reasoning can lead to false positives for seemingly plausible solutions, while lacking external grounding makes verifiers unreliable on computation or knowledge-intensive tasks. To address these challenges, we propose Agentic Verifier, a framework that transforms reward modeling into a multi-turn, tool-augmented deliberative process. We introduce complementary forward and backward agents: one traces solutions from premises to conclusions, while the other re-checks conclusions against their underlying premises. This bidirectional process enables a comprehensive, reliable, and interpretable assessment of solutions. To facilitate practical deployment, we propose AgentV-RL. Through proactive exploration and reinforcement learning, the verifier autonomously interleaves tool-use with internal reasoning. Extensive experiments show that Agentic Verifier yields consistent performance gains under both parallel and sequential TTS. Notably, our 4B variant surpasses state-of-the-art ORMs by 25.2%, positioning it as a promising paradigm for agentic reward modeling.

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

Verifiable delay functions have found a lot of applications in blockchain technology in recent times. Continuous verifiable delay functions are an improvement over the basic notion of VDFs with recursive capabilities. We are proposing the application of VDF for constructing more space time-efficient provers and simulators required for the iterative non-interactive zero-knowledge systems.

Large language models (LLMs) are increasingly integrated in software development, but ensuring correctness in LLM-generated code remains challenging and often requires costly manual review. Verifiable code generation -- jointly generating code, specifications, and proofs of code-specification alignment -- offers a promising path to address this limitation and further unleash LLMs' benefits in coding. Yet, there exists a significant gap in evaluation: current benchmarks often lack support for end-to-end verifiable code generation. In this paper, we introduce Verina (Verifiable Code Generation Arena), a high-quality benchmark enabling a comprehensive and modular evaluation of code, specification, and proof generation as well as their compositions. Verina consists of 189 manually curated coding tasks in Lean, with detailed problem descriptions, reference implementations, formal specifications, and extensive test suites. Our extensive evaluation of state-of-the-art LLMs reveals significant challenges in verifiable code generation, especially in proof generation, underscoring the need for improving LLM-based theorem provers in verification domains. The best model, OpenAI o4-mini, generates only 61.4% correct code, 51.0% sound and complete specifications, and 3.6% successful proofs, with one trial per task. We hope Verina will catalyze progress in verifiable code generation by providing a rigorous and comprehensive benchmark. We release our dataset on https://huggingface.co/datasets/sunblaze-ucb/verina and our evaluation code on https://github.com/sunblaze-ucb/verina.

Efficiency and trustworthiness are two eternal pursuits when applying deep learning in real-world applications. With regard to efficiency, dataset distillation (DD) endeavors to reduce training costs by distilling the large dataset into a tiny synthetic dataset. However, existing methods merely concentrate on in-distribution (InD) classification in a closed-world setting, disregarding out-of-distribution (OOD) samples. On the other hand, OOD detection aims to enhance models' trustworthiness, which is always inefficiently achieved in full-data settings. For the first time, we simultaneously consider both issues and propose a novel paradigm called Trustworthy Dataset Distillation (TrustDD). By distilling both InD samples and outliers, the condensed datasets are capable of training models competent in both InD classification and OOD detection. To alleviate the requirement of real outlier data, we further propose to corrupt InD samples to generate pseudo-outliers, namely Pseudo-Outlier Exposure (POE). Comprehensive experiments on various settings demonstrate the effectiveness of TrustDD, and POE surpasses the state-of-the-art method Outlier Exposure (OE). Compared with the preceding DD, TrustDD is more trustworthy and applicable to open-world scenarios. Our code is available at https://github.com/mashijie1028/TrustDD

Mathematical verfier achieves success in mathematical reasoning tasks by validating the correctness of solutions. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedbacks as rationale labels (i.e., the correctness of the current step and the explanations). In this paper, we propose Math-Minos, a natural language feedback enhanced verifier by constructing automatically-generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set (30k) of natural language feedbacks can significantly boost the performance of the verifier by the accuracy of 1.6\% (86.6\% rightarrow 88.2\%) on GSM8K and 0.8\% (37.8\% rightarrow 38.6\%) on MATH. We have released our code and data for further exploration.

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

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}.

Large Language Models (LLMs) are increasingly used to automate hardware design tasks, including the generation of Verilog code. While early benchmarks focus primarily on functional correctness, efficient hardware design demands additional optimization for synthesis metrics such as area, delay, and power. Existing benchmarks fall short in evaluating these aspects comprehensively: they often lack optimized baselines or testbenches for verification. To address these gaps, we present Pluto, a benchmark and evaluation framework designed to assess the efficiency of LLM-generated Verilog designs. Pluto presents a comprehensive evaluation set of 114 problems with self-checking testbenches and multiple Pareto-optimal reference implementations. Experimental results show that state-of-the-art LLMs can achieve high functional correctness, reaching 78.3\% at pass@1, but their synthesis efficiency still lags behind expert-crafted implementations, with area efficiency of 63.8\%, delay efficiency of 65.9\%, and power efficiency of 64.0\% at eff@1. This highlights the need for efficiency-aware evaluation frameworks such as Pluto to drive progress in hardware-focused LLM research.

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.

Deep Learning has revolutionized the fields of computer vision, natural language understanding, speech recognition, information retrieval and more. However, with the progressive improvements in deep learning models, their number of parameters, latency, resources required to train, etc. have all have increased significantly. Consequently, it has become important to pay attention to these footprint metrics of a model as well, not just its quality. We present and motivate the problem of efficiency in deep learning, followed by a thorough survey of the five core areas of model efficiency (spanning modeling techniques, infrastructure, and hardware) and the seminal work there. We also present an experiment-based guide along with code, for practitioners to optimize their model training and deployment. We believe this is the first comprehensive survey in the efficient deep learning space that covers the landscape of model efficiency from modeling techniques to hardware support. Our hope is that this survey would provide the reader with the mental model and the necessary understanding of the field to apply generic efficiency techniques to immediately get significant improvements, and also equip them with ideas for further research and experimentation to achieve additional gains.

By utilizing more computational resources at test-time, large language models (LLMs) can improve without additional training. One common strategy uses verifiers to evaluate candidate outputs. In this work, we propose a novel scaling dimension for test-time compute: scaling the number of verifiers. We introduce Multi-Agent Verification (MAV) as a test-time compute paradigm that combines multiple verifiers to improve performance. We propose using Aspect Verifiers (AVs), off-the-shelf LLMs prompted to verify different aspects of outputs, as one possible choice for the verifiers in a MAV system. AVs are a convenient building block for MAV since they can be easily combined without additional training. Moreover, we introduce BoN-MAV, a simple multi-agent verification algorithm that combines best-of-n sampling with multiple verifiers. BoN-MAV demonstrates stronger scaling patterns than self-consistency and reward model verification, and we demonstrate both weak-to-strong generalization, where combining weak verifiers improves even stronger LLMs, and self-improvement, where the same base model is used to both generate and verify outputs. Our results establish scaling the number of verifiers as a promising new dimension for improving language model performance at test-time.

Metrics like FactScore and VeriScore that evaluate long-form factuality operate by decomposing an input response into atomic claims and then individually verifying each claim. While effective and interpretable, these methods incur numerous LLM calls and can take upwards of 100 seconds to evaluate a single response, limiting their practicality in large-scale evaluation and training scenarios. To address this, we propose VeriFastScore, which leverages synthetic data to fine-tune Llama3.1 8B for simultaneously extracting and verifying all verifiable claims within a given text based on evidence from Google Search. We show that this task cannot be solved via few-shot prompting with closed LLMs due to its complexity: the model receives ~4K tokens of evidence on average and needs to concurrently decompose claims, judge their verifiability, and verify them against noisy evidence. However, our fine-tuned VeriFastScore model demonstrates strong correlation with the original VeriScore pipeline at both the example level (r=0.80) and system level (r=0.94) while achieving an overall speedup of 6.6x (9.9x excluding evidence retrieval) over VeriScore. To facilitate future factuality research, we publicly release our VeriFastScore model and synthetic datasets.

Step-by-step verifiers -- also known as process reward models (PRMs) -- are a key ingredient for test-time scaling. PRMs require step-level supervision, making them expensive to train. This work aims to build data-efficient PRMs as verbalized step-wise reward models that verify every step in the solution by generating a verification chain-of-thought (CoT). We propose ThinkPRM, a long CoT verifier fine-tuned on orders of magnitude fewer process labels than those required by discriminative PRMs. Our approach capitalizes on the inherent reasoning abilities of long CoT models, and outperforms LLM-as-a-Judge and discriminative verifiers -- using only 1% of the process labels in PRM800K -- across several challenging benchmarks. Specifically, ThinkPRM beats the baselines on ProcessBench, MATH-500, and AIME '24 under best-of-N selection and reward-guided search. In an out-of-domain evaluation on a subset of GPQA-Diamond and LiveCodeBench, our PRM surpasses discriminative verifiers trained on the full PRM800K by 8% and 4.5%, respectively. Lastly, under the same token budget, ThinkPRM scales up verification compute more effectively compared to LLM-as-a-Judge, outperforming it by 7.2% on a subset of ProcessBench. Our work highlights the value of generative, long CoT PRMs that can scale test-time compute for verification while requiring minimal supervision for training. Our code, data, and models will be released at https://github.com/mukhal/thinkprm.

State-of-the-art language models can match human performance on many tasks, but they still struggle to robustly perform multi-step mathematical reasoning. To diagnose the failures of current models and support research, we introduce GSM8K, a dataset of 8.5K high quality linguistically diverse grade school math word problems. We find that even the largest transformer models fail to achieve high test performance, despite the conceptual simplicity of this problem distribution. To increase performance, we propose training verifiers to judge the correctness of model completions. At test time, we generate many candidate solutions and select the one ranked highest by the verifier. We demonstrate that verification significantly improves performance on GSM8K, and we provide strong empirical evidence that verification scales more effectively with increased data than a finetuning baseline.

A rule-based logic solver resolves every instance in our benchmark in under 50 microseconds with 100% accuracy; the best frontier language model reaches 65% at best and drops to 23.5% under rendering-robust evaluation (worst case over four surface renderings). We introduce DeFAb (Defeasible Abduction Benchmark), a dataset and generation pipeline that converts four decades of publicly funded knowledge bases into formally grounded instances for defeasible abduction: constructing hypotheses that explain anomalies by overriding defaults while preserving unrelated expectations. Because every hypothesis must pass polynomial-time checks for valid derivation, conservativity, and minimality, DeFAb makes logical rigor the instrument for measuring creativity and theoretical reasoning, scoring the disciplined construction of theory revisions rather than fluent but theory-destroying prose. The pipeline pairs taxonomic hierarchies (OpenCyc, YAGO, Wikidata) with behavioral property graphs (ConceptNet, UMLS) to produce 372,648+ instances across 33.75M materialized rules from 18 sources, in three levels with polynomial-time verifiable gold standards. Four frontier models do not reliably internalize defeasible reasoning: rendering-robust Level 2 accuracy is 7.8-23.5%; chain-of-thought variance (~36 pp) exceeds any inter-model gap; and a matched contamination control isolates a +19.4 pp Level 3 gap. We further release DeFAb-Hard (a 235-instance Level 3 difficulty variant; best model 53.3% vs 100% symbolic) and CONJURE (a kernel-verified transformative-creativity variant of 560 Lean 4/Mathlib instances whose gold answers are definitions the proof kernel did not previously contain, judge-free verifier; a pilot finds zero novel concepts). The same verifier doubles as an exact reward for preference optimization (DPO, RLVR/GRPO). Released under MIT at https://huggingface.co/datasets/PatrickAllenCooper/DeFAb.

The key limitation of the verification performance lies in the ability of error detection. With this intuition we designed several variants of pessimistic verification, which are simple workflows that could significantly improve the verification of open-ended math questions. In pessimistic verification we construct multiple parallel verifications for the same proof, and the proof is deemed incorrect if any one of them reports an error. This simple technique significantly improves the performance across many math verification benchmarks without incurring substantial computational resources. Its token efficiency even surpassed extended long-CoT in test-time scaling. Our case studies further indicate that the majority of false negatives in stronger models are actually caused by annotation errors in the original dataset, so our method's performance is in fact underestimated. Self-verification for mathematical problems can effectively improve the reliability and performance of language model outputs, and it also plays a critical role in enabling long-horizon mathematical tasks. We believe that research on pessimistic verification will help enhance the mathematical capabilities of language models across a wide range of tasks.

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

Verifiers play a crucial role in large language model (LLM) reasoning, needed by post-training techniques such as reinforcement learning. However, reliable verifiers are hard to get for difficult coding problems, because a well-disguised wrong solution may only be detected by carefully human-written edge cases that are difficult to synthesize. To address this issue, we propose HARDTESTGEN, a pipeline for high-quality test synthesis using LLMs. With this pipeline, we curate a comprehensive competitive programming dataset HARDTESTS with 47k problems and synthetic high-quality tests. Compared with existing tests, HARDTESTGEN tests demonstrate precision that is 11.3 percentage points higher and recall that is 17.5 percentage points higher when evaluating LLM-generated code. For harder problems, the improvement in precision can be as large as 40 points. HARDTESTS also proves to be more effective for model training, measured by downstream code generation performance. We will open-source our dataset and synthesis pipeline at https://leililab.github.io/HardTests/.

Since the breakthrough performance of AlexNet in 2012, convolutional neural networks (convnets) have grown into extremely powerful vision models. Deep learning researchers have used convnets to perform vision tasks with accuracy that was unachievable a decade ago. Confronted with the immense computation that convnets use, deep learning researchers also became interested in efficiency. However, the engineers who deployed efficient convnets soon realized that they were slower than the previous generation, despite using fewer operations. Many reverted to older models that ran faster. Hence researchers switched the objective of their search from arithmetic complexity to latency and produced a new wave of models that performed better. Paradoxically, these models also used more operations. Skepticism grew among researchers and engineers alike about the relevance of arithmetic complexity. Contrary to the prevailing view that latency and arithmetic complexity are irreconcilable, a simple formula relates both through computational efficiency. This insight enabled us to co-optimize the separate factors that determine latency. We observed that the degenerate conv2d layers that produce the best accuracy--complexity trade-off also use significant memory resources and have low computational efficiency. We devised block fusion algorithms to implement all the layers of a residual block in a single kernel, thereby creating temporal locality, avoiding communication, and reducing workspace size. Our ConvFirst model with block-fusion kernels has less arithmetic complexity and greater computational efficiency than baseline models and kernels, and ran approximately four times as fast as ConvNeXt. We also created novel tools, including efficiency gap plots and waterline analysis. Our unified approach to convnet efficiency envisions a new era of models and kernels that achieve greater accuracy at lower cost.

The success of deep neural networks (DNNs) is attributable to three factors: increased compute capacity, more complex models, and more data. These factors, however, are not always present, especially for edge applications such as autonomous driving, augmented reality, and internet-of-things. Training DNNs requires a large amount of data, which is difficult to obtain. Edge devices such as mobile phones have limited compute capacity, and therefore, require specialized and efficient DNNs. However, due to the enormous design space and prohibitive training costs, designing efficient DNNs for different target devices is challenging. So the question is, with limited data, compute capacity, and model complexity, can we still successfully apply deep neural networks? This dissertation focuses on the above problems and improving the efficiency of deep neural networks at four levels. Model efficiency: we designed neural networks for various computer vision tasks and achieved more than 10x faster speed and lower energy. Data efficiency: we developed an advanced tool that enables 6.2x faster annotation of a LiDAR point cloud. We also leveraged domain adaptation to utilize simulated data, bypassing the need for real data. Hardware efficiency: we co-designed neural networks and hardware accelerators and achieved 11.6x faster inference. Design efficiency: the process of finding the optimal neural networks is time-consuming. Our automated neural architecture search algorithms discovered, using 421x lower computational cost than previous search methods, models with state-of-the-art accuracy and efficiency.

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.

Recent years have seen the remarkable capabilities of large language models (LLMs) for code generation. Different from existing work that evaluate the correctness of the code generated by LLMs, we propose to further evaluate its efficiency. More efficient code can lead to higher performance and execution efficiency of programs and software completed by LLM-assisted programming. First, we evaluate the efficiency of the code generated by LLMs on two benchmarks, HumanEval and MBPP. Then, we choose a set of programming problems from the online judge platform LeetCode to conduct a more difficult evaluation. Finally, we explore several prompts that would enable LLMs to generate more efficient code.

Deep research agents have demonstrated remarkable capabilities in complex information-seeking tasks, yet this power comes at a steep computational cost. Driven by accuracy-focused training paradigms, current models adopt brute-force strategies characterized by blind tool dependency and performative reasoning-generating long, redundant trajectories that are far from necessary for resolving these tasks, leading to wasteful tool calls and excessive token consumption. To overcome this efficiency trap, we propose SlimSearcher, a principled framework that pushes the Pareto frontier between accuracy and computational cost across both Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL). In the SFT stage, SlimSearcher employs Pareto-efficient filtration to distill trajectories that are both successful and economical, guiding the model toward inherently efficiency-aware search behaviors. During RL, we introduce Adaptive Reward Gating, a dynamic reward-shaping mechanism that evaluates relative tool and token efficiency within a sampled cohort. By cascading these adaptive efficiency metrics with a strict correctness gate, our approach effectively avoids the brevity bias associated with absolute penalties and mitigates reward hacking. Extensive experiments on long-horizon benchmarks, including GAIA, BrowseComp, and XBenchDeepSearch, demonstrate that SlimSearcher reduces average tool-call rounds by 17%-58% while maintaining or improving accuracy.

Code generation has largely improved development efficiency in the era of large language models (LLMs). With the ability to follow instructions, current LLMs can be prompted to generate code solutions given detailed descriptions in natural language. Many research efforts are being devoted to improving the correctness of LLM-generated code, and many benchmarks are proposed to evaluate the correctness comprehensively. Despite the focus on correctness, the time efficiency of LLM-generated code solutions is under-explored. Current correctness benchmarks are not suitable for time efficiency evaluation since their test cases cannot well distinguish the time efficiency of different code solutions. Besides, the current execution time measurement is not stable and comprehensive, threatening the validity of the time efficiency evaluation. To address the challenges in the time efficiency evaluation of code generation, we propose COFFE, a code generation benchmark for evaluating the time efficiency of LLM-generated code solutions. COFFE contains 398 and 358 problems for function-level and file-level code generation, respectively. To improve the distinguishability, we design a novel stressful test case generation approach with contracts and two new formats of test cases to improve the accuracy of generation. For the time evaluation metric, we propose efficienct@k based on CPU instruction count to ensure a stable and solid comparison between different solutions. We evaluate 14 popular LLMs on COFFE and identify four findings. Based on the findings, we draw some implications for LLM researchers and software practitioners to facilitate future research and usage of LLMs in code generation.

Efficiency, as a critical practical challenge for LLM-driven agentic and reasoning systems, is increasingly constrained by the inherent latency of autoregressive (AR) decoding. Speculative decoding mitigates this cost through a draft-verify scheme, yet existing approaches rely on AR draft models (a.k.a., drafters), which introduce two fundamental issues: (1) step-wise uncertainty accumulation leads to a progressive collapse of trust between the target model and the drafter, and (2) inherently sequential decoding of AR drafters. Together, these factors cause limited speedups. In this paper, we show that a diffusion large language model (dLLM) drafters can naturally overcome these issues through its fundamentally different probabilistic modeling and efficient parallel decoding strategy. Building on this insight, we introduce DEER, an efficient speculative decoding framework that drafts with diffusion and verifies with AR models. To enable high-quality drafting, DEER employs a two-stage training pipeline to align the dLLM-based drafters with the target AR model, and further adopts single-step decoding to generate long draft segments. Experiments show DEER reaches draft acceptance lengths of up to 32 tokens, far surpassing the 10 tokens achieved by EAGLE-3. Moreover, on HumanEval with Qwen3-30B-A3B, DEER attains a 5.54x speedup, while EAGLE-3 achieves only 2.41x. Code, model, demo, etc, will be available at https://czc726.github.io/DEER/

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

Large reasoning models (LRMs) have recently achieved significant progress in complex reasoning tasks, aided by reinforcement learning with verifiable rewards. However, LRMs often suffer from overthinking, expending excessive computation on simple problems and reducing efficiency. Existing efficient reasoning methods typically require accurate task assessment to preset token budgets or select reasoning modes, which limits their flexibility and reliability. In this work, we revisit the essence of overthinking and identify that encouraging effective steps while penalizing ineffective ones is key to its solution. To this end, we propose a novel rule-based verifiable stepwise reward mechanism (VSRM), which assigns rewards based on the performance of intermediate states in the reasoning trajectory. This approach is intuitive and naturally fits the step-by-step nature of reasoning tasks. We conduct extensive experiments on standard mathematical reasoning benchmarks, including AIME24 and AIME25, by integrating VSRM with PPO and Reinforce++. Results show that our method achieves substantial output length reduction while maintaining original reasoning performance, striking an optimal balance between efficiency and accuracy. Further analysis of overthinking frequency and pass@k score before and after training demonstrates that our approach in deed effectively suppresses ineffective steps and encourages effective reasoning, fundamentally alleviating the overthinking problem. All code will be released upon acceptance.

Vision Transformers (ViT) have shown rapid progress in computer vision tasks, achieving promising results on various benchmarks. However, due to the massive number of parameters and model design, e.g., attention mechanism, ViT-based models are generally times slower than lightweight convolutional networks. Therefore, the deployment of ViT for real-time applications is particularly challenging, especially on resource-constrained hardware such as mobile devices. Recent efforts try to reduce the computation complexity of ViT through network architecture search or hybrid design with MobileNet block, yet the inference speed is still unsatisfactory. This leads to an important question: can transformers run as fast as MobileNet while obtaining high performance? To answer this, we first revisit the network architecture and operators used in ViT-based models and identify inefficient designs. Then we introduce a dimension-consistent pure transformer (without MobileNet blocks) as a design paradigm. Finally, we perform latency-driven slimming to get a series of final models dubbed EfficientFormer. Extensive experiments show the superiority of EfficientFormer in performance and speed on mobile devices. Our fastest model, EfficientFormer-L1, achieves 79.2% top-1 accuracy on ImageNet-1K with only 1.6 ms inference latency on iPhone 12 (compiled with CoreML), which runs as fast as MobileNetV2times 1.4 (1.6 ms, 74.7% top-1), and our largest model, EfficientFormer-L7, obtains 83.3% accuracy with only 7.0 ms latency. Our work proves that properly designed transformers can reach extremely low latency on mobile devices while maintaining high performance.

Recent years have witnessed the rapid advancements of large language models (LLMs) and their expanding applications, leading to soaring demands for computational resources. The widespread adoption of test-time scaling further aggravates the tension between model capability and resource consumption, highlighting the importance of inference efficiency. However, a unified metric that accurately reflects an LLM's efficiency across different model sizes and architectures remains absent. Motivated by the correlation between compression and intelligence, we introduce information capacity, a measure of model efficiency based on text compression performance relative to computational complexity. Larger models can predict the next token more accurately, achieving greater compression gains but at higher computational costs. Empirical evaluations on mainstream open-source models show that models of varying sizes within a series exhibit consistent information capacity. This metric enables a fair efficiency comparison across model series and accurate performance prediction within a model series. A distinctive feature of information capacity is that it incorporates tokenizer efficiency, which affects both input and output token counts but is often neglected in LLM evaluations. We assess the information capacity of 49 models on 5 heterogeneous datasets and observe consistent results on the influences of tokenizer efficiency, pretraining data, and the mixture-of-experts architecture.

Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct limitations, while training specialized large models still requires significant computational resources. This paper introduces ProofCompass, a novel hybrid methodology that achieves remarkable computational efficiency by strategically guiding existing specialized prover methods, such as DeepSeek-Prover-v1.5-RL (DSP-v1.5) with a Large Language Model (LLM) without requiring additional model training. The LLM provides natural language proof strategies and analyzes failed attempts to select intermediate lemmas, enabling effective problem decomposition. On the miniF2F benchmark, ProofCompass demonstrates substantial resource efficiency: it outperforms DSP-v1.5 (54.9% rightarrow 55.3%) while using 25x fewer attempts (3200 rightarrow 128). Our synergistic approach paves the way for simultaneously improving computational efficiency and accuracy in formal theorem proving.

Large Language Models (LLMs) demonstrate strong capabilities for solving scientific and mathematical problems, yet they struggle to produce valid, challenging, and novel problems - an essential component for advancing LLM training and enabling autonomous scientific research. Existing problem generation approaches either depend on expensive human expert involvement or adopt naive self-play paradigms, which frequently yield invalid problems due to reward hacking. This work introduces VHG, a verifier-enhanced hard problem generation framework built upon three-party self-play. By integrating an independent verifier into the conventional setter-solver duality, our design constrains the setter's reward to be jointly determined by problem validity (evaluated by the verifier) and difficulty (assessed by the solver). We instantiate two verifier variants: a Hard symbolic verifier and a Soft LLM-based verifier, with evaluations conducted on indefinite integral tasks and general mathematical reasoning tasks. Experimental results show that VHG substantially outperforms all baseline methods by a clear margin.

Compressing high-capability Large Language Models (LLMs) has emerged as a favored strategy for resource-efficient inferences. While state-of-the-art (SoTA) compression methods boast impressive advancements in preserving benign task performance, the potential risks of compression in terms of safety and trustworthiness have been largely neglected. This study conducts the first, thorough evaluation of three (3) leading LLMs using five (5) SoTA compression techniques across eight (8) trustworthiness dimensions. Our experiments highlight the intricate interplay between compression and trustworthiness, revealing some interesting patterns. We find that quantization is currently a more effective approach than pruning in achieving efficiency and trustworthiness simultaneously. For instance, a 4-bit quantized model retains the trustworthiness of its original counterpart, but model pruning significantly degrades trustworthiness, even at 50% sparsity. Moreover, employing quantization within a moderate bit range could unexpectedly improve certain trustworthiness dimensions such as ethics and fairness. Conversely, extreme quantization to very low bit levels (3 bits) tends to significantly reduce trustworthiness. This increased risk cannot be uncovered by looking at benign performance alone, in turn, mandating comprehensive trustworthiness evaluation in practice. These findings culminate in practical recommendations for simultaneously achieving high utility, efficiency, and trustworthiness in LLMs. Models and code are available at https://decoding-comp-trust.github.io/.

Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification, making theorem proving reliable. However, even with formal verification, LLMs still struggle with long proofs and complex mathematical formalizations. While Lean with LLMs offers valuable assistance with retrieving lemmas, generating tactics, or even complete proofs, it lacks a crucial capability: providing a sense of proof progress. This limitation particularly impacts the overall development efficiency in large formalization projects. We introduce LeanProgress, a method that predicts the progress in the proof. Training and evaluating our models made on a large corpus of Lean proofs from Lean Workbook Plus and Mathlib4 and how many steps remain to complete it, we employ data preprocessing and balancing techniques to handle the skewed distribution of proof lengths. Our experiments show that LeanProgress achieves an overall prediction accuracy of 75.1\% in predicting the amount of progress and, hence, the remaining number of steps. When integrated into a best-first search framework using Reprover, our method shows a 3.8\% improvement on Mathlib4 compared to baseline performances of 41.2\%, particularly for longer proofs. These results demonstrate how proof progress prediction can enhance both automated and interactive theorem proving, enabling users to make more informed decisions about proof strategies.

Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-based proof automation are drawn from mathematics in the Mathlib ecosystem, whereas proofs in software verification are developed inside definition-rich codebases with substantial project-specific libraries. We introduce VeriSoftBench, a benchmark of 500 Lean 4 proof obligations drawn from open-source formal-methods developments and packaged to preserve realistic repository context and cross-file dependencies. Our evaluation of frontier LLMs and specialized provers yields three observations. First, provers tuned for Mathlib-style mathematics transfer poorly to this repository-centric setting. Second, success is strongly correlated with transitive repository dependence: tasks whose proofs draw on large, multi-hop dependency closures are less likely to be solved. Third, providing curated context restricted to a proof's dependency closure improves performance relative to exposing the full repository, but nevertheless leaves substantial room for improvement. Our benchmark and evaluation suite are released at https://github.com/utopia-group/VeriSoftBench.

We present a low-cost ultraviolet to infrared absolute quantum efficiency detector characterization system developed using commercial off-the-shelf components. The key components of the experiment include a light source,a regulated power supply, a monochromator, an integrating sphere, and a calibrated photodiode. We provide a step-by-step procedure to construct the photon and quantum efficiency transfer curves of imaging sensors. We present results for the GSENSE 2020 BSI CMOS sensor and the Sony IMX 455 BSI CMOS sensor. As a reference for similar characterizations, we provide a list of parts and associated costs along with images of our setup.

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

We revisit the longstanding open problem of implementing Nakamoto's proof-of-work (PoW) consensus based on a real-world computational task T(x) (as opposed to artificial random hashing), in a truly permissionless setting where the miner itself chooses the input x. The challenge in designing such a Proof-of-Useful-Work (PoUW) protocol, is using the native computation of T(x) to produce a PoW certificate with prescribed hardness and with negligible computational overhead over the worst-case complexity of T(cdot) -- This ensures malicious miners cannot ``game the system" by fooling the verifier to accept with higher probability compared to honest miners (while using similar computational resources). Indeed, obtaining a PoUW with O(1)-factor overhead is trivial for any task T, but also useless. Our main result is a PoUW for the task of Matrix Multiplication MatMul(A,B) of arbitrary matrices with 1+o(1) multiplicative overhead compared to naive MatMul (even in the presence of Fast Matrix Multiplication-style algorithms, which are currently impractical). We conjecture that our protocol has optimal security in the sense that a malicious prover cannot obtain any significant advantage over an honest prover. This conjecture is based on reducing hardness of our protocol to the task of solving a batch of low-rank random linear equations which is of independent interest. Since MatMuls are the bottleneck of AI compute as well as countless industry-scale applications, this primitive suggests a concrete design of a new L1 base-layer protocol, which nearly eliminates the energy-waste of Bitcoin mining -- allowing GPU consumers to reduce their AI training and inference costs by ``re-using" it for blockchain consensus, in exchange for block rewards (2-for-1). This blockchain is currently under construction.

We present MaxProof, a population-level test-time scaling framework for competition-level mathematical proof in the MiniMax-M3 series. M3 first trains three proof-oriented capabilities -- proof generation, proof verification, and critique-conditioned proof repair -- using a defense-in-depth generative verifier engineered for low false-positive rate. These capabilities are merged into a single released M3 model. At test time, MaxProof treats the model as a generator, verifier, refiner, and ranker, searches over a population of candidate proofs, and returns one final proof through tournament selection. With MaxProof test-time scaling, the M3 model reaches 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both.

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

Large language models (LLMs) 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.

A paraphrase-quality audit of MathCheck (ICLR 2025) detected 4 semantically incorrect paraphrases in 129 groups (3.1%); removing them drops GPT-4o from rank 2 to rank 4 and elevates Claude Haiku and DeepSeek V3 above it; these ranking changes are invisible to any single-model evaluation. Cross-model unanimity found these errors automatically (>= 3/4 models for MathCheck; >= 6/9 for our primary evaluation) for under $10; in our own dataset the same protocol found that 47% of auto-generated connective-variation paraphrases were semantically incorrect. That flaw compounds a deeper measurement gap: Claude Haiku 4.5 achieves 86% accuracy yet SCR=50%, meaning half its theorems are answered differently under semantically equivalent restatements, while aggregate accuracy across 9 models spans only 86-96% yet Semantic Consistency Rates (SCR) span 50-82% -- a 32-point gap invisible to standard benchmarks. Formally, for any target ranking over 9 frontier models there exists a weighting over paraphrase families that realizes it (No-Free-Benchmark corollary), because no model Pareto-dominates all families -- so benchmark designers who select families are implicitly choosing which model wins. FormInv supplies the audit protocol (replicated on external benchmarks at 100% recall), SCR and per-theorem Cochran's Q as primary invariance measures evaluated on 9 models across 366-811 items (on Lean4-verified theorems), and FormInvSelector for regime-aware model selection.

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.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Agent benchmarks score submissions with outcome verifiers that are typically hand-written and brittle, leaving them open to reward hacking. We audit 1,968 tasks across five terminal-agent benchmarks and find 323 (16%) hackable by frontier models given only the task description. This corrupts both leaderboard rankings and RL training signal, yet the standard response is manual and reactive. We introduce the hacker-fixer loop, a method for building exploit-resistant verifiers without per-task manual patching. The loop alternates three LLM agents: a hacker tries to pass the verifier without solving the task, a fixer patches the verifier to reject each discovered exploit, and a solver confirms the patched verifier still admits legitimate solutions. The loop iterates: each patch reshapes what the verifier rewards, surfacing the next exploit. We further add verifier access, and let patches transfer across tasks, to broaden the exploits the loop discovers. On KernelBench, the loop drives the attack success rate from 62% to 0% on a held-out corpus of publicly reported exploits. We also find that weaker agents in the loop can defend against much stronger hackers: Gemini 3 Flash's loop drives the stronger Gemini 3.1 Pro and Claude Opus 4.7's attack success rate from 76% and 61% to 0% on KernelBench, and Gemini 3.1 Pro's from 39% to 17% on Terminal Bench across 77 tasks. We release Terminal Wrench (323 hackable environments, 3,632 hack trajectories) as a snapshot of the current attack surface, our patched verifiers, the exploits the loop discovered, and our implementation as a basis for future work.

Model efficiency is a critical aspect of developing and deploying machine learning models. Inference time and latency directly affect the user experience, and some applications have hard requirements. In addition to inference costs, model training also have direct financial and environmental impacts. Although there are numerous well-established metrics (cost indicators) for measuring model efficiency, researchers and practitioners often assume that these metrics are correlated with each other and report only few of them. In this paper, we thoroughly discuss common cost indicators, their advantages and disadvantages, and how they can contradict each other. We demonstrate how incomplete reporting of cost indicators can lead to partial conclusions and a blurred or incomplete picture of the practical considerations of different models. We further present suggestions to improve reporting of efficiency metrics.

Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require, wasting compute, latency, and context budgets. While introducing length-based efficiency rewards during reinforcement learning offers a natural remedy, existing methods struggle with two fundamental challenges: the optimal balance between correctness and efficiency is non-stationary throughout training, and intrinsic reasoning budgets vary drastically across problems. Relying on static reward weights and global length constraints inevitably forces a compromise between degraded accuracy and unrealized compression. To overcome these limitations, we propose LEAD (Length-Efficient Adaptive and Dynamic reasoning), a method that replaces static heuristics with online, self-adaptive mechanisms. LEAD dynamically calibrates the correctness-efficiency trade-off at each step using a Potential-Scaled Instability, directing optimization capacity to the most informative learning signal. Furthermore, it estimates an adaptive per-problem target length online based on the model's own correct rollouts, applying a symmetric efficiency reward that penalizes both overthinking and over-compression. Evaluated on five mathematical reasoning benchmarks, LEAD achieves the highest accuracy and Accuracy-Efficiency Score among RL-trained efficient-reasoning methods while producing substantially shorter outputs than the base model.

Recent years have witnessed increasing interest in extending large language models into agentic systems. While the effectiveness of agents has continued to improve, efficiency, which is crucial for real-world deployment, has often been overlooked. This paper therefore investigates efficiency from three core components of agents: memory, tool learning, and planning, considering costs such as latency, tokens, steps, etc. Aimed at conducting comprehensive research addressing the efficiency of the agentic system itself, we review a broad range of recent approaches that differ in implementation yet frequently converge on shared high-level principles including but not limited to bounding context via compression and management, designing reinforcement learning rewards to minimize tool invocation, and employing controlled search mechanisms to enhance efficiency, which we discuss in detail. Accordingly, we characterize efficiency in two complementary ways: comparing effectiveness under a fixed cost budget, and comparing cost at a comparable level of effectiveness. This trade-off can also be viewed through the Pareto frontier between effectiveness and cost. From this perspective, we also examine efficiency oriented benchmarks by summarizing evaluation protocols for these components and consolidating commonly reported efficiency metrics from both benchmark and methodological studies. Moreover, we discuss the key challenges and future directions, with the goal of providing promising insights.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g. human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on the dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, the combination of the ease of learning the relatively simple RM (verifier) from the preference data, coupled with the ability of the downstream RL procedure to then filter its search space to the subset of policies (generators) that are optimal for relatively simple verifiers is what leads to the superior performance of online FT.

We often interact with untrusted parties. Prioritization of privacy can limit the effectiveness of these interactions, as achieving certain goals necessitates sharing private data. Traditionally, addressing this challenge has involved either seeking trusted intermediaries or constructing cryptographic protocols that restrict how much data is revealed, such as multi-party computations or zero-knowledge proofs. While significant advances have been made in scaling cryptographic approaches, they remain limited in terms of the size and complexity of applications they can be used for. In this paper, we argue that capable machine learning models can fulfill the role of a trusted third party, thus enabling secure computations for applications that were previously infeasible. In particular, we describe Trusted Capable Model Environments (TCMEs) as an alternative approach for scaling secure computation, where capable machine learning model(s) interact under input/output constraints, with explicit information flow control and explicit statelessness. This approach aims to achieve a balance between privacy and computational efficiency, enabling private inference where classical cryptographic solutions are currently infeasible. We describe a number of use cases that are enabled by TCME, and show that even some simple classic cryptographic problems can already be solved with TCME. Finally, we outline current limitations and discuss the path forward in implementing them.

Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess these paths. However, existing verifiers, typically trained on binary-labeled reasoning paths, fail to fully utilize the relative merits of intermediate steps, thereby limiting the effectiveness of the feedback provided. To overcome this limitation, we propose Tree-based Preference Learning Verifier (Tree-PLV), a novel approach that constructs reasoning trees via a best-first search algorithm and collects step-level paired data for preference training. Compared to traditional binary classification, step-level preferences more finely capture the nuances between reasoning steps, allowing for a more precise evaluation of the complete reasoning path. We empirically evaluate Tree-PLV across a range of arithmetic and commonsense reasoning tasks, where it significantly outperforms existing benchmarks. For instance, Tree-PLV achieved substantial performance gains over the Mistral-7B self-consistency baseline on GSM8K (67.55% to 82.79%), MATH (17.00% to 26.80%), CSQA (68.14% to 72.97%), and StrategyQA (82.86% to 83.25%).Additionally, our study explores the appropriate granularity for applying preference learning, revealing that step-level guidance provides feedback that better aligns with the evaluation of the reasoning process.

Recent advancements in tree search algorithms guided by verifiers have significantly enhanced the reasoning capabilities of large language models (LLMs), but at the cost of increased computational resources. In this work, we identify two key challenges contributing to this inefficiency: over-exploration due to redundant states with semantically equivalent content, and under-exploration caused by high variance in verifier scoring leading to frequent trajectory switching. To address these issues, we propose FETCH, an efficient tree search framework, which is a flexible, plug-and-play system compatible with various tree search algorithms. Our framework mitigates over-exploration by merging semantically similar states using agglomerative clustering of text embeddings obtained from a fine-tuned SimCSE model. To tackle under-exploration, we enhance verifiers by incorporating temporal difference learning with adjusted lambda-returns during training to reduce variance, and employing a verifier ensemble to aggregate scores during inference. Experiments on GSM8K, GSM-Plus, and MATH datasets demonstrate that our methods significantly improve reasoning accuracy and computational efficiency across four different tree search algorithms, paving the way for more practical applications of LLM-based reasoning. The code is available at https://github.com/Soistesimmer/Fetch.

Large language models (LLMs) power many state-of-the-art systems in natural language processing. However, these models are extremely computationally expensive, even at inference time, raising the natural question: when is the extra cost of deploying a larger model worth the anticipated boost in capabilities? Better understanding this tradeoff fundamentally could benefit from an inference efficiency metric that is both (i) easily comparable across models from different providers, and (ii) representative of the true cost of running queries in an isolated performance environment. Unfortunately, access to LLMs today is largely restricted to black-box text generation APIs and raw runtimes measured through this interface do not satisfy these desiderata: model providers can apply various software and hardware optimizations orthogonal to the model, and models served on shared infrastructure are susceptible to performance contention. To circumvent these problems, we propose a new metric for comparing inference efficiency across models. This metric puts models on equal footing as though they were served (i) on uniform hardware and software, and (ii) without performance contention. We call this metric the idealized runtime, and we propose a methodology to efficiently estimate this metric for autoregressive Transformer models. We also propose cost-aware variants that incorporate the number of accelerators needed to serve the model. Using these metrics, we compare ten state-of-the-art LLMs to provide the first analysis of inference efficiency-capability tradeoffs; we make several observations from this analysis, including the fact that the superior inference runtime performance of certain APIs is often a byproduct of optimizations within the API rather than the underlying model. Our methodology also facilitates the efficient comparison of different software and hardware stacks.

Multimodal foundation models are transformative in sequential recommender systems, leveraging powerful representation learning capabilities. While Parameter-efficient Fine-tuning (PEFT) is commonly used to adapt foundation models for recommendation tasks, most research prioritizes parameter efficiency, often overlooking critical factors like GPU memory efficiency and training speed. Addressing this gap, our paper introduces IISAN (Intra- and Inter-modal Side Adapted Network for Multimodal Representation), a simple plug-and-play architecture using a Decoupled PEFT structure and exploiting both intra- and inter-modal adaptation. IISAN matches the performance of full fine-tuning (FFT) and state-of-the-art PEFT. More importantly, it significantly reduces GPU memory usage - from 47GB to just 3GB for multimodal sequential recommendation tasks. Additionally, it accelerates training time per epoch from 443s to 22s compared to FFT. This is also a notable improvement over the Adapter and LoRA, which require 37-39 GB GPU memory and 350-380 seconds per epoch for training. Furthermore, we propose a new composite efficiency metric, TPME (Training-time, Parameter, and GPU Memory Efficiency) to alleviate the prevalent misconception that "parameter efficiency represents overall efficiency". TPME provides more comprehensive insights into practical efficiency comparisons between different methods. Besides, we give an accessible efficiency analysis of all PEFT and FFT approaches, which demonstrate the superiority of IISAN. We release our codes and other materials at https://github.com/GAIR-Lab/IISAN.

Large language models (LLMs) have recently achieved notable success in code-generation benchmarks such as HumanEval and LiveCodeBench. However, a detailed examination reveals that these evaluation suites often comprise only a limited number of homogeneous test cases, resulting in subtle faults going undetected. This not only artificially inflates measured performance but also compromises accurate reward estimation in reinforcement learning frameworks utilizing verifiable rewards (RLVR). To address these critical shortcomings, we systematically investigate the test-case generation (TCG) task by proposing multi-dimensional metrics designed to rigorously quantify test-suite thoroughness. Furthermore, we introduce a human-LLM collaborative method (SAGA), leveraging human programming expertise with LLM reasoning capability, aimed at significantly enhancing both the coverage and the quality of generated test cases. In addition, we develop a TCGBench to facilitate the study of the TCG task. Experiments show that SAGA achieves a detection rate of 90.62% and a verifier accuracy of 32.58% on TCGBench. The Verifier Accuracy (Verifier Acc) of the code generation evaluation benchmark synthesized by SAGA is 10.78% higher than that of LiveCodeBench-v6. These results demonstrate the effectiveness of our proposed method. We hope this work contributes to building a scalable foundation for reliable LLM code evaluation, further advancing RLVR in code generation, and paving the way for automated adversarial test synthesis and adaptive benchmark integration.

While AI agents have shown remarkable performance at various tasks, they still struggle with complex multi-modal applications, structured generation and strategic planning. Improvements via standard fine-tuning is often impractical, as solving agentic tasks usually relies on black box API access without control over model parameters. Inference-time methods such as Best-of-N (BON) sampling offer a simple yet effective alternative to improve performance. However, BON lacks iterative feedback integration mechanism. Hence, we propose Iterative Agent Decoding (IAD) which combines iterative refinement with dynamic candidate evaluation and selection guided by a verifier. IAD differs in how feedback is designed and integrated, specifically optimized to extract maximal signal from reward scores. We conduct a detailed comparison of baselines across key metrics on Sketch2Code, Text2SQL, and Webshop where IAD consistently outperforms baselines, achieving 3--6% absolute gains on Sketch2Code and Text2SQL (with and without LLM judges) and 8--10% gains on Webshop across multiple metrics. To better understand the source of IAD's gains, we perform controlled experiments to disentangle the effect of adaptive feedback from stochastic sampling, and find that IAD's improvements are primarily driven by verifier-guided refinement, not merely sampling diversity. We also show that both IAD and BON exhibit inference-time scaling with increased compute when guided by an optimal verifier. Our analysis highlights the critical role of verifier quality in effective inference-time optimization and examines the impact of noisy and sparse rewards on scaling behavior. Together, these findings offer key insights into the trade-offs and principles of effective inference-time optimization.

Large Reasoning Models (LRMs) have demonstrated remarkable performance on tasks such as mathematics and code generation. Motivated by these strengths, recent work has empirically demonstrated the effectiveness of LRMs as guard models in improving harmful query detection. However, LRMs typically generate long reasoning traces during inference, causing substantial computational overhead. In this paper, we introduce PSRT, a method that replaces the model's reasoning process with a Prefilled Safe Reasoning Trace, thereby significantly reducing the inference cost of LRMs. Concretely, PSRT prefills "safe reasoning virtual tokens" from a constructed dataset and learns over their continuous embeddings. With the aid of indicator tokens, PSRT enables harmful-query detection in a single forward pass while preserving the classification effectiveness of LRMs. We evaluate PSRT on 7 models, 13 datasets, and 8 jailbreak methods. In terms of efficiency, PSRT completely removes the overhead of generating reasoning tokens during inference. In terms of classification performance, PSRT achieves nearly identical accuracy, with only a minor average F1 drop of 0.015 across 7 models and 5 datasets.

AI coding agents are increasingly used to write real-world software, but ensuring that their outputs are correct remains a fundamental challenge. Formal verification offers a promising path: an agent generates code together with a machine-checked proof, guaranteeing that the code satisfies a formal specification. However, there is no guarantee that the formal spec itself matches the user's intent. In this work, we study specification autoformalization: whether LLM agents can translate informal programming problems into faithful formal specifications. We introduce Verus-SpecBench, a benchmark of 581 spec-writing tasks derived from Codeforces problems targeting Verus, a verifier for Rust, and Verus-SpecGym, an agentic environment in which models interact with Verus, bash, & the filesystem to develop these specs. The central challenge is evaluation: expert-written reference specs are expensive to write, & LLM judges can miss subtle mistakes. We address this by (a) extending Verus's exec_spec mechanism so that generated specs can be executed as Rust code, & (b) testing them against official Codeforces tests & adversarial cases extracted from Codeforces "hacks", which are edge cases written by competitors to break incorrect solutions. On Verus-SpecBench, the strongest model, Gemini 3.1 Pro, solves 77.8% of tasks, other frontier models solve 51.1--57.8% & OSS models reach only 21.5--25.5%. Our analysis of failure modes shows that model-generated specs can omit important input assumptions, accept incorrect outputs, & reject valid ones. We also find that LLM-as-a-judge evaluation misses 26% of the failures our evaluator catches. Overall, our results suggest that spec autoformalization is within reach for frontier agents but remains brittle even on problems where they can already generate correct code. The code, data, & logs can be found at https://github.com/formal-verif-is-cool/verus-spec-gym

Despite advancements in evaluating Large Language Models (LLMs) for code synthesis, benchmarks have predominantly focused on functional correctness, overlooking the importance of code efficiency. We present Mercury, the first benchmark designated for assessing the code efficiency of LLM code synthesis tasks. Mercury consists of 1,889 programming tasks covering diverse difficulty levels alongside test case generators generating unlimited cases for comprehensive evaluation. Unlike existing benchmarks, Mercury integrates a novel metric Beyond@K to measure normalized code efficiency based on historical submissions, leading to a new evaluation indicator for code synthesis, which encourages generating functionally correct and computationally efficient code, mirroring the real-world software development standard. Our findings reveal that while LLMs demonstrate the remarkable capability to generate functionally correct code, there still exists a substantial gap in their efficiency output, underscoring a new frontier for LLM research and development.

Large language models (LLMs) have achieved significant progress in solving complex reasoning tasks by Reinforcement Learning with Verifiable Rewards (RLVR). This advancement is also inseparable from the oversight automated by reliable verifiers. However, current outcome-based verifiers (OVs) are unable to inspect the unreliable intermediate steps in the long reasoning chains of thought (CoTs). Meanwhile, current process-based verifiers (PVs) have difficulties in reliably detecting errors in the complex long CoTs, limited by the scarcity of high-quality annotations due to the prohibitive costs of human annotations. Therefore, we propose the Outcome-based Process Verifier (OPV), which verifies the rationale process of summarized outcomes from long CoTs to achieve both accurate and efficient verification and enable large-scale annotation. To empower the proposed verifier, we adopt an iterative active learning framework with expert annotations to progressively improve the verification capability of OPV with fewer annotation costs. Specifically, in each iteration, the most uncertain cases of the current best OPV are annotated and then subsequently used to train a new OPV through Rejection Fine-Tuning (RFT) and RLVR for the next round. Extensive experiments demonstrate OPV's superior performance and broad applicability. It achieves new state-of-the-art results on our held-out OPV-Bench, outperforming much larger open-source models such as Qwen3-Max-Preview with an F1 score of 83.1 compared to 76.3. Furthermore, OPV effectively detects false positives within synthetic dataset, closely align with expert assessment. When collaborating with policy models, OPV consistently yields performance gains, e.g., raising the accuracy of DeepSeek-R1-Distill-Qwen-32B from 55.2% to 73.3% on AIME2025 as the compute budget scales.

System logs are crucial for monitoring and diagnosing modern computing infrastructure, but their scale and complexity require reliable and efficient automated interpretation. Since severity levels are predefined metadata in system log messages, having a model merely classify them offers limited standalone practical value, revealing little about its underlying ability to interpret system logs. We argue that severity classification is more informative when treated as a benchmark for probing runtime log comprehension rather than as an end task. Using real-world journalctl data from Linux production servers, we evaluate nine small language models (SLMs) and small reasoning language models (SRLMs) under zero-shot, few-shot, and retrieval-augmented generation (RAG) prompting. The results reveal strong stratification. Qwen3-4B achieves the highest accuracy at 95.64% with RAG, while Gemma3-1B improves from 20.25% under few-shot prompting to 85.28% with RAG. Notably, the tiny Qwen3-0.6B reaches 88.12% accuracy despite weak performance without retrieval. In contrast, several SRLMs, including Qwen3-1.7B and DeepSeek-R1-Distill-Qwen-1.5B, degrade substantially when paired with RAG. Efficiency measurements further separate models: most Gemma and Llama variants complete inference in under 1.2 seconds per log, whereas Phi-4-Mini-Reasoning exceeds 228 seconds per log while achieving <10% accuracy. These findings suggest that (1) architectural design, (2) training objectives, and (3) the ability to integrate retrieved context under strict output constraints jointly determine performance. By emphasizing small, deployable models, this benchmark aligns with real-time requirements of digital twin (DT) systems and shows that severity classification serves as a lens for evaluating model competence and real-time deployability, with implications for root cause analysis (RCA) and broader DT integration.

Although randomized smoothing has demonstrated high certified robustness and superior scalability to other certified defenses, the high computational overhead of the robustness certification bottlenecks the practical applicability, as it depends heavily on the large sample approximation for estimating the confidence interval. In existing works, the sample size for the confidence interval is universally set and agnostic to the input for prediction. This Input-Agnostic Sampling (IAS) scheme may yield a poor Average Certified Radius (ACR)-runtime trade-off which calls for improvement. In this paper, we propose Input-Specific Sampling (ISS) acceleration to achieve the cost-effectiveness for robustness certification, in an adaptive way of reducing the sampling size based on the input characteristic. Furthermore, our method universally controls the certified radius decline from the ISS sample size reduction. The empirical results on CIFAR-10 and ImageNet show that ISS can speed up the certification by more than three times at a limited cost of 0.05 certified radius. Meanwhile, ISS surpasses IAS on the average certified radius across the extensive hyperparameter settings. Specifically, ISS achieves ACR=0.958 on ImageNet (sigma=1.0) in 250 minutes, compared to ACR=0.917 by IAS under the same condition. We release our code in https://github.com/roy-ch/Input-Specific-Certification.

While text-to-image models offer numerous benefits, they also pose significant societal risks. Detecting AI-generated images is crucial for mitigating these risks. Detection methods can be broadly categorized into passive and watermark-based approaches: passive detectors rely on artifacts present in AI-generated images, whereas watermark-based detectors proactively embed watermarks into such images. A key question is which type of detector performs better in terms of effectiveness, robustness, and efficiency. However, the current literature lacks a comprehensive understanding of this issue. In this work, we aim to bridge that gap by developing ImageDetectBench, the first comprehensive benchmark to compare the effectiveness, robustness, and efficiency of passive and watermark-based detectors. Our benchmark includes four datasets, each containing a mix of AI-generated and non-AI-generated images. We evaluate five passive detectors and four watermark-based detectors against eight types of common perturbations and three types of adversarial perturbations. Our benchmark results reveal several interesting findings. For instance, watermark-based detectors consistently outperform passive detectors, both in the presence and absence of perturbations. Based on these insights, we provide recommendations for detecting AI-generated images, e.g., when both types of detectors are applicable, watermark-based detectors should be the preferred choice. Our code and data are publicly available at https://github.com/moyangkuo/ImageDetectBench.git.

While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem simplicity or the viability of guessing or memorization. Crucially, they capture only a narrow subset of relevant math problems. To address this research gap, we introduce \mc, a new benchmark of 126 challenging problems sourced from various math competitions, which targets constructive proofs, a widely encountered problem type requiring the construction of mathematical objects with specific properties. These proofs are particularly suitable for LLM evaluation, as solution correctness can be easily verified. Our automated verifiers also enable MathConstruct to generate problem variations, used to evaluate robustness. State-of-the-art LLMs solve only 54% of MathConstruct problems, highlighting its complexity and importance for LLM evaluation.

Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of Transformers. For one, we replace dot-product attention by one that uses locality-sensitive hashing, changing its complexity from O(L^2) to O(Llog L), where L is the length of the sequence. Furthermore, we use reversible residual layers instead of the standard residuals, which allows storing activations only once in the training process instead of N times, where N is the number of layers. The resulting model, the Reformer, performs on par with Transformer models while being much more memory-efficient and much faster on long sequences.

Improving open-source models on real-world SWE tasks (solving GITHUB issues) faces two key challenges: 1) scalable curation of execution environments to train these models, and, 2) optimal scaling of test-time compute. We introduce AgentGym, the largest procedurally-curated executable gym environment for training real-world SWE-agents, consisting of more than 8.7K tasks. AgentGym is powered by two main contributions: 1) SYNGEN: a synthetic data curation recipe that enables scalable curation of executable environments using test-generation and back-translation directly from commits, thereby reducing reliance on human-written issues or unit tests. We show that this enables more scalable training leading to pass@1 performance of 34.4% on SWE-Bench Verified benchmark with our 32B model. 2) Hybrid Test-time Scaling: we provide an in-depth analysis of two test-time scaling axes; execution-based and execution-free verifiers, demonstrating that they exhibit complementary strengths and limitations. Test-based verifiers suffer from low distinguishability, while execution-free verifiers are biased and often rely on stylistic features. Surprisingly, we find that while each approach individually saturates around 42-43%, significantly higher gains can be obtained by leveraging their complementary strengths. Overall, our approach achieves 51% on the SWE-Bench Verified benchmark, reflecting a new state-of-the-art for open-weight SWE-agents and for the first time showing competitive performance with proprietary models such as o1, o1-preview and sonnet-3.5-v2 (with tools). We will open-source our environments, models, and agent trajectories.

Machine reading comprehension (MRC) is an AI challenge that requires machine to determine the correct answers to questions based on a given passage. MRC systems must not only answer question when necessary but also distinguish when no answer is available according to the given passage and then tactfully abstain from answering. When unanswerable questions are involved in the MRC task, an essential verification module called verifier is especially required in addition to the encoder, though the latest practice on MRC modeling still most benefits from adopting well pre-trained language models as the encoder block by only focusing on the "reading". This paper devotes itself to exploring better verifier design for the MRC task with unanswerable questions. Inspired by how humans solve reading comprehension questions, we proposed a retrospective reader (Retro-Reader) that integrates two stages of reading and verification strategies: 1) sketchy reading that briefly investigates the overall interactions of passage and question, and yield an initial judgment; 2) intensive reading that verifies the answer and gives the final prediction. The proposed reader is evaluated on two benchmark MRC challenge datasets SQuAD2.0 and NewsQA, achieving new state-of-the-art results. Significance tests show that our model is significantly better than the strong ELECTRA and ALBERT baselines. A series of analysis is also conducted to interpret the effectiveness of the proposed reader.