Daily Papers

A service system may use the same categories to assign standard allocations and to check whether each service is fulfilled. Finer categories can match individual needs more closely, but they divide the observations available for monitoring. We study this conflict for a fixed menu from which participants select by declaring a category, with fulfilment assessed from each category's aggregate outcomes during a fixed period. We relate allocation loss to variation in preferred allocations within categories and identify conditions under which aggregate observations preserve the verification performance of individual records. For nested refinements under stated utility and observation assumptions, an allocation-loss tolerance and a per-category detection target define a feasibility band. Categories must be fine enough to provide suitable allocations but sufficiently populated to support verification. A source-dependent lower bound on declaration entropy and a minimum contributor requirement give necessary information and population constraints. For an explicit finite population with quadratic utility and binary service outcomes, we prove the exact feasible range across all categorical designs and exhibit designs attaining the information lower bound at specified tolerances. The results provide conditions for choosing categories jointly for allocation and verification.

Large language models (LLMs) combined with tool learning have gained impressive results in real-world applications. During tool learning, LLMs may call multiple tools in nested orders, where the latter tool call may take the former response as its input parameters. However, current research on the nested tool learning capabilities is still under-explored, since the existing benchmarks lack of relevant data instances. To address this problem, we introduce NesTools to bridge the current gap in comprehensive nested tool learning evaluations. NesTools comprises a novel automatic data generation method to construct large-scale nested tool calls with different nesting structures. With manual review and refinement, the dataset is in high quality and closely aligned with real-world scenarios. Therefore, NesTools can serve as a new benchmark to evaluate the nested tool learning abilities of LLMs. We conduct extensive experiments on 22 LLMs, and provide in-depth analyses with NesTools, which shows that current LLMs still suffer from the complex nested tool learning task.

Data refinement involves executing multi-step recipes over evolving text states, where both composition and execution order of processing operators determine the outcome. While existing benchmarks either isolate text editing or entangle it with code and tool execution, it remains unclear whether LLMs can directly and faithfully execute these compositional, order-sensitive data refinement recipes. To fill this gap, we introduce CDR-Bench, a comprehensive benchmark featuring 3,462 high-quality tasks spanning four real-world data refinement domains and 29 distinct operators. Our benchmark evaluates models across atomic, order-agnostic, and order-sensitive settings, leveraging deterministic reference outputs to enable exact evaluation. Experiments on 10+ state-of-the-art LLMs reveal consistent failure patterns: performance degrades sharply in compositional settings, and order-sensitive recipe success collapses. These findings underline that current LLMs lack the procedural faithfulness required for reliable compositional data refinement.

Derived datasets can be defined implicitly or explicitly. An implicit definition (of dataset O in terms of datasets I) is a logical specification involving the source data I and the interface data O. It is a valid definition of O in terms of I, if any two models of the specification agreeing on I agree on O. In contrast, an explicit definition is a query that produces O from I. Variants of Beth's theorem state that one can convert implicit definitions to explicit ones. Further, this conversion can be done effectively given a proof witnessing implicit definability in a suitable proof system. We prove the analogous effective implicit-to-explicit result for nested relations: implicit definitions, given in the natural logic for nested relations, can be effectively converted to explicit definitions in the nested relational calculus NRC. As a consequence, we can effectively extract rewritings of NRC queries in terms of NRC views, given a proof witnessing that the query is determined by the views.

Large Language Models' (LLM) reasoning can be improved using test-time aggregation strategies, i.e., generating multiple samples and voting among generated samples. While these improve performance, they often reach a saturation point. Refinement offers an alternative by using LLM-generated feedback to improve solution quality. However, refinement introduces 3 key challenges: (1) Excessive refinement: Uniformly refining all instances can over-correct and reduce the overall performance. (2) Inability to localize and address errors: LLMs have a limited ability to self-correct and struggle to identify and correct their own mistakes. (3) Insufficient refinement: Deciding how many iterations of refinement are needed is non-trivial, and stopping too soon could leave errors unaddressed. To tackle these issues, we propose MAgICoRe, which avoids excessive refinement by categorizing problem difficulty as easy or hard, solving easy problems with coarse-grained aggregation and hard ones with fine-grained and iterative multi-agent refinement. To improve error localization, we incorporate external step-wise reward model (RM) scores. Moreover, to ensure effective refinement, we employ a multi-agent loop with three agents: Solver, Reviewer (which generates targeted feedback based on step-wise RM scores), and the Refiner (which incorporates feedback). To ensure sufficient refinement, we re-evaluate updated solutions, iteratively initiating further rounds of refinement. We evaluate MAgICoRe on Llama-3-8B and GPT-3.5 and show its effectiveness across 5 math datasets. Even one iteration of MAgICoRe beats Self-Consistency by 3.4%, Best-of-k by 3.2%, and Self-Refine by 4.0% while using less than half the samples. Unlike iterative refinement with baselines, MAgICoRe continues to improve with more iterations. Finally, our ablations highlight the importance of MAgICoRe's RMs and multi-agent communication.

Deep Learning architectures, and in particular Transformers, are conventionally viewed as a composition of layers. These layers are actually often obtained as the sum of two contributions: a residual path that copies the input and the output of a Transformer block. As a consequence, the inner representations (i.e. the input of these blocks) can be interpreted as iterative refinement of a propagated latent representation. Under this lens, many works suggest that the inner space is shared across layers, meaning that tokens can be decoded at early stages. Mechanistic interpretability even goes further by conjecturing that some layers act as refinement layers. Following this path, we propose inference-time inner looping, which prolongs refinement in pretrained off-the-shelf language models by repeatedly re-applying a selected block range. Across multiple benchmarks, inner looping yields modest but consistent accuracy improvements. Analyses of the resulting latent trajectories suggest more stable state evolution and continued semantic refinement. Overall, our results suggest that additional refinement can be obtained through simple test-time looping, extending computation in frozen pretrained models.

Iterative refinement has been a promising paradigm to enable large language models (LLMs) to resolve difficult reasoning and problem-solving tasks. One of the key challenges, however, is how to effectively search through the enormous search space of possible refinements. Existing methods typically fall back on predefined heuristics, which are troubled by the exploration-exploitation dilemma and cannot adapt based on past refinement outcomes. We introduce Tree-Guided Policy Refinement (TGPR), a novel framework that combines GRPO with a Thompson-Sampling-based tree search. TGPR explores both failed and successful refinement paths actively, with denser training trajectories and more adaptive policies. On HumanEval, MBPP, and APPS benchmarks, our method achieves up to +4.2 percentage points absolute improvement in pass@1 (on MBPP) and up to +12.51 percentage points absolute improvement in pass@10 (on APPS) compared to a competitive GRPO baseline. Apart from debugging code, TGPR focuses on a principled approach to combining learned policies with structured search methods, offering a general framework for enhancing iterative refinement and stateful reasoning in LLMs.

Summarization refinement faces challenges when extending to multi-dimension. In this paper, we introduce ReFeed, a powerful summarization refinement pipeline that enhances multiple dimensions through reflective reasoning on feedback. To achieve this, we release SumFeed-CoT, a large-scale Long-CoT-based dataset optimized for training a lightweight model with reflective reasoning. Our experiments reveal how the number of dimensions, feedback exposure, and reasoning policy influence refinement performance, highlighting reflective reasoning and simultaneously addressing multiple feedback is crucial to mitigate trade-off between dimensions. Furthermore, ReFeed is robust to noisy feedback and feedback order. Lastly, our finding emphasizes that creating data with a proper goal and guideline constitutes a fundamental pillar of effective reasoning. The dataset and model will be released.

In evolutionary algorithms powered by language models, the LLM acts as a single operator that simultaneously updates structural components (like control flow) and continuous parameters. While LLMs can be good at the first, they are not efficient at the second, wasting tokens taking discrete jumps inside a trial and error loop. We resolve this by formalizing a hybrid nested search, in which an outer loop has the LLM propose a structural sketch, with numeric gaps, and an inner numerical optimizer tunes the sketch. Both the outer and inner solvers are pluggable: any text-based optimizer can be combined with a zero-order optimizer (CMA-ES), gradient-based routines, or MCMC samplers. We validate our framework across three scientific domains: (i) meta-optimizers on closed-form test functions, (ii) code-based policies for systems research and social dilemmas; and (iii) approximate Bayesian inference tasks. Across all three, the hybrid optimizer is superior to both vanilla LLM-driven search and pure numerical optimization baselines. Code at: https://github.com/vicgalle/hybrid-nested-search

State-of-the-art language models can exhibit impressive reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify when and where to refine without access to external feedback. Outcome-based Reward Models (ORMs), trained to predict correctness of the final answer indicating when to refine, offer one convenient solution for deciding when to refine. Process Based Reward Models (PRMs), trained to predict correctness of intermediate steps, can then be used to indicate where to refine. But they are expensive to train, requiring extensive human annotations. In this paper, we propose Stepwise ORMs (SORMs) which are trained, only on synthetic data, to approximate the expected future reward of the optimal policy or V^{star}. More specifically, SORMs are trained to predict the correctness of the final answer when sampling the current policy many times (rather than only once as in the case of ORMs). Our experiments show that SORMs can more accurately detect incorrect reasoning steps compared to ORMs, thus improving downstream accuracy when doing refinements. We then train global refinement models, which take only the question and a draft solution as input and predict a corrected solution, and local refinement models which also take as input a critique indicating the location of the first reasoning error. We generate training data for both models synthetically by reusing data used to train the SORM. We find combining global and local refinements, using the ORM as a reranker, significantly outperforms either one individually, as well as a best of three sample baseline. With this strategy we can improve the accuracy of a LLaMA-2 13B model (already fine-tuned with RL) on GSM8K from 53\% to 65\% when greedily sampled.

Generating natural language explanations for recommendations has become increasingly important in recommender systems. Traditional approaches typically treat user reviews as ground truth for explanations and focus on improving review prediction accuracy by designing various model architectures. However, due to limitations in data scale and model capability, these explanations often fail to meet key user-centric aspects such as factuality, personalization, and sentiment coherence, significantly reducing their overall helpfulness to users. In this paper, we propose a novel paradigm that refines initial explanations generated by existing explainable recommender models during the inference stage to enhance their quality in multiple aspects. Specifically, we introduce a multi-agent collaborative refinement framework based on large language models. To ensure alignment between the refinement process and user demands, we employ a plan-then-refine pattern to perform targeted modifications. To enable continuous improvements, we design a hierarchical reflection mechanism that provides feedback on the refinement process from both strategic and content perspectives. Extensive experiments on three datasets demonstrate the effectiveness of our framework.

Large language models (LLMs) have recently shown strong progress on scientific reasoning, yet two major bottlenecks remain. First, explicit retrieval fragments reasoning, imposing a hidden "tool tax" of extra tokens and steps. Second, multi-agent pipelines often dilute strong solutions by averaging across all candidates. We address these challenges with a unified framework that combines implicit retrieval and structured collaboration. At its foundation, a Monitor-based retrieval module operates at the token level, integrating external knowledge with minimal disruption to reasoning. On top of this substrate, Hierarchical Solution Refinement (HSR) iteratively designates each candidate as an anchor to be repaired by its peers, while Quality-Aware Iterative Reasoning (QAIR) adapts refinement to solution quality. On Humanity's Last Exam (HLE) Bio/Chem Gold, our framework achieves 48.3\% accuracy -- the highest reported to date, surpassing the strongest agent baseline by 13.4 points and leading frontier LLMs by up to 18.1 points, while simultaneously reducing token usage by 53.5\% and agent steps by 43.7\%. Results on SuperGPQA and TRQA confirm robustness across domains. Error analysis shows that reasoning failures and knowledge gaps co-occur in over 85\% of cases, while diversity analysis reveals a clear dichotomy: retrieval tasks benefit from solution variety, whereas reasoning tasks favor consensus. Together, these findings demonstrate how implicit augmentation and structured refinement overcome the inefficiencies of explicit tool use and uniform aggregation. Code is available at: https://github.com/tangxiangru/Eigen-1.

The ARC-AGI benchmark series serves as a critical measure of few-shot generalization on novel tasks, a core aspect of intelligence. The ARC Prize 2025 global competition targeted the newly released ARC-AGI-2 dataset, which features greater task complexity compared to its predecessor. The Kaggle competition attracted 1,455 teams and 15,154 entries, with the top score reaching 24% on the ARC-AGI-2 private evaluation set. Paper submissions nearly doubled year-over-year to 90 entries, reflecting the growing research interest in fluid intelligence and abstract reasoning. The defining theme of 2025 is the emergence of the refinement loop -- a per-task iterative program optimization loop guided by a feedback signal. Refinement loops come in a variety of forms, in particular evolutionary program synthesis approaches and application-layer refinements to commercial AI systems. Such refinement loops are also possible in weight space, as evidenced by zero-pretraining deep learning methods which are now achieving competitive performance with remarkably small networks (7M parameters). In parallel, four frontier AI labs (Anthropic, Google DeepMind, OpenAI, and xAI) reported ARC-AGI performance in public model cards in 2025, establishing ARC-AGI as an industry standard benchmark for AI reasoning. However, our analysis indicates that current frontier AI reasoning performance remains fundamentally constrained to knowledge coverage, giving rise to new forms of benchmark contamination. In this paper, we survey the top-performing methods, examine the role of refinement loops in AGI progress, discuss knowledge-dependent overfitting, and preview ARC-AGI-3, which introduces interactive reasoning challenges that require exploration, planning, memory, goal acquisition, and alignment capabilities.

Context: The software maintenance phase involves many activities such as code refactoring, bug fixing, code review or testing. Program comprehension is key to all these activities, as it demands developers to grasp the knowledge (e.g., implementation details) required to modify the codebase. Methods as main building blocks in a program can offer developers this knowledge source for code comprehension. However, reading entire method statements can be challenging, which necessitates precise and up-to-date comments. Objective: We propose a solution as an IntelliJ IDEA plugin, named SmartDoc, that assists developers in generating context-aware method comments. Method: This plugin acts as an Artificial Intelligence (AI) agent that has its own memory and is augmented by target methods' context. When a request is initiated by the end-user, the method content and all its nested method calls are used in the comment generation. At the beginning, these nested methods are visited and a call graph is generated. This graph is then traversed using depth-first search (DFS), enabling the provision of full-context to enrich Large Language Model (LLM) prompts. Result: The product is a software, as a plugin, developed for Java codebase and installable on IntelliJ IDEA. This plugin can serve concurrently for methods whose comments are being updated , and it shares memory across all flows to avoid redundant calls. o measure the accuracy of this solution, a dedicated test case is run to record SmartDoc generated comments and their corresponding ground truth. For each collected result-set, three metrics are computed, BERTScore, BLEU and ROUGE-1. These metrics will determine how accurate the generated comments are in comparison to the ground truth. Result: The obtained accuracy, in terms of the precision, recall and F1, is promising, and lies in the range of 0.80 to 0.90 for BERTScore.

We introduce region-specific image refinement as a dedicated problem setting: given an input image and a user-specified region (e.g., a scribble mask or a bounding box), the goal is to restore fine-grained details while keeping all non-edited pixels strictly unchanged. Despite rapid progress in image generation, modern models still frequently suffer from local detail collapse (e.g., distorted text, logos, and thin structures). Existing instruction-driven editing models emphasize coarse-grained semantic edits and often either overlook subtle local defects or inadvertently change the background, especially when the region of interest occupies only a small portion of a fixed-resolution input. We present RefineAnything, a multimodal diffusion-based refinement model that supports both reference-based and reference-free refinement. Building on a counter-intuitive observation that crop-and-resize can substantially improve local reconstruction under a fixed VAE input resolution, we propose Focus-and-Refine, a region-focused refinement-and-paste-back strategy that improves refinement effectiveness and efficiency by reallocating the resolution budget to the target region, while a blended-mask paste-back guarantees strict background preservation. We further introduce a boundary-aware Boundary Consistency Loss to reduce seam artifacts and improve paste-back naturalness. To support this new setting, we construct Refine-30K (20K reference-based and 10K reference-free samples) and introduce RefineEval, a benchmark that evaluates both edited-region fidelity and background consistency. On RefineEval, RefineAnything achieves strong improvements over competitive baselines and near-perfect background preservation, establishing a practical solution for high-precision local refinement. Project Page: https://limuloo.github.io/RefineAnything/.

Can language models (LMs) self-refine their own responses? This question is increasingly relevant as a wide range of real-world user interactions involve refinement requests. However, prior studies have largely tested LMs' refinement abilities on verifiable tasks such as competition math or symbolic reasoning with simplified scaffolds, whereas users often pose open-ended queries and provide varying degrees of feedback on what they desire. The recent advent of reasoning models that exhibit self-reflection patterns in their chains-of-thought further motivates this question. To analyze this, we introduce RefineBench, a benchmark of 1,000 challenging problems across 11 domains paired with a checklist-based evaluation framework. We evaluate two refinement modes: (1) guided refinement, where an LM is provided natural language feedback, and (2) self-refinement, where LMs attempt to improve without guidance. In the self-refinement setting, even frontier LMs such as Gemini 2.5 Pro and GPT-5 achieve modest baseline scores of 31.3% and 29.1%, respectively, and most models fail to consistently improve across iterations (e.g., Gemini-2.5-Pro gains only +1.8%, while DeepSeek-R1 declines by -0.1%). By contrast, in guided refinement, both proprietary LMs and large open-weight LMs (>70B) can leverage targeted feedback to refine responses to near-perfect levels within five turns. These findings suggest that frontier LMs require breakthroughs to self-refine their incorrect responses, and that RefineBench provides a valuable testbed for tracking progress.

NVIDIA's CUTLASS library provides a robust and expressive set of methods for describing and manipulating multi-dimensional tensor data on the GPU. These methods are conceptually grounded in the abstract notion of a CuTe layout and a rich algebra of such layouts, including operations such as composition, logical product, and logical division. In this paper, we present a categorical framework for understanding this layout algebra by focusing on a naturally occurring class of tractable layouts. To this end, we define two categories Tuple and Nest whose morphisms give rise to layouts. We define a suite of operations on morphisms in these categories and prove their compatibility with the corresponding layout operations. Moreover, we give a complete characterization of the layouts which arise from our construction. Finally, we provide a Python implementation of our categorical constructions, along with tests that demonstrate alignment with CUTLASS behavior. This implementation can be found at our git repository https://github.com/ColfaxResearch/layout-categories.

Hierarchical structures are popular in recent vision transformers, however, they require sophisticated designs and massive datasets to work well. In this paper, we explore the idea of nesting basic local transformers on non-overlapping image blocks and aggregating them in a hierarchical way. We find that the block aggregation function plays a critical role in enabling cross-block non-local information communication. This observation leads us to design a simplified architecture that requires minor code changes upon the original vision transformer. The benefits of the proposed judiciously-selected design are threefold: (1) NesT converges faster and requires much less training data to achieve good generalization on both ImageNet and small datasets like CIFAR; (2) when extending our key ideas to image generation, NesT leads to a strong decoder that is 8times faster than previous transformer-based generators; and (3) we show that decoupling the feature learning and abstraction processes via this nested hierarchy in our design enables constructing a novel method (named GradCAT) for visually interpreting the learned model. Source code is available https://github.com/google-research/nested-transformer.

Large language models (LLMs) have demonstrated the capacity to improve summary quality by mirroring a human-like iterative process of critique and refinement starting from the initial draft. Two strategies are designed to perform this iterative process: Prompt Chaining and Stepwise Prompt. Prompt chaining orchestrates the drafting, critiquing, and refining phases through a series of three discrete prompts, while Stepwise prompt integrates these phases within a single prompt. However, the relative effectiveness of the two methods has not been extensively studied. This paper is dedicated to examining and comparing these two methods in the context of text summarization to ascertain which method stands out as the most effective. Experimental results show that the prompt chaining method can produce a more favorable outcome. This might be because stepwise prompt might produce a simulated refinement process according to our various experiments. Since refinement is adaptable to diverse tasks, our conclusions have the potential to be extrapolated to other applications, thereby offering insights that may contribute to the broader development of LLMs.

This paper introduces a novel Deep Researcher architecture designed to generate detailed research reports on complex PhD level topics by addressing the inherent limitations of the Parallel Scaling paradigm. Our system utilizes two key innovations: Sequential Research Plan Refinement via Reflection and a Candidates Crossover algorithm. The sequential refinement process is demonstrated as an efficient method that allows the agent to maintain a centralized Global Research Context, enabling it to look back at current progress, reason about the research plan, and intelligently make changes at runtime. This dynamic adaptation contrasts with parallel approaches, which often suffer from siloed knowledge. The Candidates Crossover algorithm further enhances search efficiency by deploying multiple LLM candidates with varied parameters to explore a larger search space, with their findings synthesized to curate a comprehensive final research response. The process concludes with One Shot Report Generation, ensuring the final document is informed by a unified narrative and high fact density. Powered by the Gemini 2.5 Pro model, our Deep Researcher was evaluated on the DeepResearch Bench, a globally recognized benchmark of 100 doctoral level research tasks. Our architecture achieved an overall score of 46.21, demonstrating superior performance by surpassing leading deep research agents such as Claude Researcher, Nvidia AIQ Research Assistant, Perplexity Research, Kimi Researcher and Grok Deeper Search present on the DeepResearch Bench actively running leaderboard. This performance marginally exceeds our previous work, Static DRA, and reinforces the finding that sequential scaling consistently outperforms the parallel self consistency paradigm.

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.

In recent years, Large Language Models (LLMs) have demonstrated remarkable generative abilities, but can they judge the quality of their own generations? A popular concept, referred to as self-refinement, postulates that LLMs can detect and correct the errors in their generations when asked to do so. However, recent empirical evidence points in the opposite direction, suggesting that LLMs often struggle to accurately identify errors when reasoning is involved. To address this, we propose a reasoning with refinement objective called ART: Ask, Refine, and Trust, which asks necessary questions to decide when an LLM should refine its output, and either affirm or withhold trust in its refinement by ranking the refinement and the initial prediction. On two multistep reasoning tasks of mathematical word problems (GSM8K) and question answering (StrategyQA), ART achieves a performance gain of +5 points over self-refinement baselines, while using a much smaller model as the decision maker. We also demonstrate the benefit of using smaller models to make refinement decisions as a cost-effective alternative to fine-tuning a larger model.

Recent work has explored the capability of large language models (LLMs) to identify and correct errors in LLM-generated responses. These refinement approaches frequently evaluate what sizes of models are able to do refinement for what problems, but less attention is paid to what effective feedback for refinement looks like. In this work, we propose looking at refinement with feedback as a composition of three distinct LLM competencies: (1) identification of bad generations; (2) fine-grained natural language feedback generation; (3) refining with fine-grained feedback. The first step can be implemented with a high-performing discriminative model and steps 2 and 3 can be implemented either via prompted or fine-tuned LLMs. A key property of this approach is that the step 2 critique model can give fine-grained feedback about errors, made possible by offloading the discrimination to a separate model in step 1. We show that models of different capabilities benefit from refining with this approach on the task of improving factual consistency of document grounded summaries. Overall, our proposed method consistently outperforms existing end-to-end refinement approaches and current trained models not fine-tuned for factuality critiquing.

Code generation has attracted increasing attention with the rise of Large Language Models (LLMs). Many studies have developed powerful code LLMs by synthesizing code-related instruction data and applying supervised fine-tuning. However, these methods are limited by teacher model distillation and ignore the potential of iterative refinement by self-generated code. In this paper, we propose Adaptive Critique Refinement (ACR), which enables the model to refine itself by self-generated code and external critique, rather than directly imitating the code responses of the teacher model. Concretely, ACR includes a composite scoring system with LLM-as-a-Judge to evaluate the quality of code responses and a selective critique strategy with LLM-as-a-Critic to critique self-generated low-quality code responses. We develop the RefineCoder series by iteratively applying ACR, achieving continuous performance improvement on multiple code generation benchmarks. Compared to the baselines of the same size, our proposed RefineCoder series can achieve comparable or even superior performance using less data.

Recursive self-improvement (RSI) lets a system improve the model-building machinery from its own failures, so every later model inherits the gain. Yet RSI has been validated almost exclusively on coding and formal benchmarks such as science QA and mathematics. This format bound limits RSI to improvement within a machine-checkable slice, not general capability where questions are open and correctness is settled by argument, replication, or measurement. We argue RSI must next operate across real, diverse scientific, engineering, and meta-scientific domains, not where formal evaluation is merely tractable. To that end we present MetaRSI-v1, where improvement is the scheduled composition of three typed operators over one unified paradigm. Data-RSI amplifies existing competence and marks its boundary; Harness-RSI edits a five-slot scaffold without touching weights; Model-RSI internalizes capability into parameters through bounded training. Sharing one loop kernel and artifact vocabulary, they make data, scaffold, and model changes composable rather than exclusive. A two-axis optimizer jointly decides operator order and each operator's proposal policy, while a meta-level policy revises the schedule across terms. We validate MetaRSI-v1 under the field's standard evaluations, on code and closed-form science, with no external teacher: the target model plays every role in its own loop. MetaRSI-v1 reframes self-improvement from a single-surface edit to a composition across the full model-production pipeline, opening two paths: a model route internalizing capability through training, and a harness route leaving weights untouched and thus extending self-improvement to any model reachable through an interface, with Data-RSI redefined as the shared substrate feeding both. The framework further yields refutable laws on where loops exist, how operators compose, and what supervision buys.

Autonomous agent applications powered by large language models (LLMs) have recently risen to prominence as effective tools for addressing complex real-world tasks. At their core, agentic workflows rely on LLMs to plan and execute the use of tools and external Application Programming Interfaces (APIs) in sequence to arrive at the answer to a user's request. Various benchmarks and leaderboards have emerged to evaluate an LLM's capabilities for tool and API use; however, most of these evaluations only track single or multiple isolated API calling capabilities. In this paper, we present NESTFUL, a benchmark to evaluate LLMs on nested sequences of API calls, i.e., sequences where the output of one API call is passed as input to a subsequent call. NESTFUL has a total of 300 human annotated samples divided into two types - executable and non-executable. The executable samples are curated manually by crawling Rapid-APIs whereas the non-executable samples are hand picked by human annotators from data synthetically generated using an LLM. We evaluate state-of-the-art LLMs with function calling abilities on NESTFUL. Our results show that most models do not perform well on nested APIs in NESTFUL as compared to their performance on the simpler problem settings available in existing benchmarks.

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover error messages, remains an area that has yet to be thoroughly investigated. To enhance the effectiveness of LLMs in the field, we introduce the Lyra, a new framework that employs two distinct correction mechanisms: Tool Correction (TC) and Conjecture Correction (CC). To implement Tool Correction in the post-processing of formal proofs, we leverage prior knowledge to utilize predefined prover tools (e.g., Sledgehammer) for guiding the replacement of incorrect tools. Tool Correction significantly contributes to mitigating hallucinations, thereby improving the overall accuracy of the proof. In addition, we introduce Conjecture Correction, an error feedback mechanism designed to interact with prover to refine formal proof conjectures with prover error messages. Compared to the previous refinement framework, the proposed Conjecture Correction refines generation with instruction but does not collect paired (generation, error & refinement) prompts. Our method has achieved state-of-the-art (SOTA) performance on both miniF2F validation (48.0% -> 55.3%) and test (45.5% -> 51.2%). We also present 3 IMO problems solved by Lyra. We believe Tool Correction (post-process for hallucination mitigation) and Conjecture Correction (subgoal adjustment from interaction with environment) could provide a promising avenue for future research in this field.

Recent advances in long chain-of-thought (CoT) reasoning have largely prioritized answer accuracy and token efficiency, while overlooking aspects critical to trustworthiness. We argue that usable reasoning systems must be trustworthy, characterized by three properties: interpretability, faithfulness, and reliability. To this end, we propose ReFIne, a new training framework that integrates supervised fine-tuning with GRPO to encourage models to: (i) improve interpretability by producing structured, tag-based traces with high-level planning that are easier for humans to follow; (ii) enhance faithfulness by explicitly disclosing the decisive information guiding each solution, with consistent cross-section references; and (iii) promote reliability by providing self-assessments of both the derivation's soundness and the confidence of the final answer. We apply ReFIne to the Qwen3 models at multiple scales (1.7B/4B/8B) and evaluate across mathematical benchmarks of varying difficulty. Our experimental results show that ReFIne models generate clearer and better-structured reasoning traces (interpretability +44.0%), more faithfully expose their underlying decision process (faithfulness +18.8%), and offer informative confidence estimates (reliability +42.4%). These findings highlight an overlooked but important direction: reasoning models should be optimized not only for accuracy, but also for broader dimensions of trustworthiness. Our code is available at: https://github.com/Trustworthy-ML-Lab/Training_Trustworthy_LRM_with_Refine

Recent advances in self-refinement have demonstrated significant potential for improving the outputs of large language models (LLMs) through iterative refinement. However, most existing self-refinement methods rely on a reactive process with a fixed number of iterations, making it difficult to determine the optimal timing and content of refinement based on the evolving generation context. Inspired by the way humans dynamically refine their thoughts during execution, we propose ProActive Self-Refinement (PASR), a novel method that enables LLMs to refine their outputs during the generation process. Unlike methods that regenerate entire responses, PASR proactively decides whether, when, and how to refine based on the model's internal state and evolving context. We conduct extensive experiments on a diverse set of 10 tasks to evaluate the effectiveness of PASR. Experimental results show that PASR significantly enhances problem-solving performance. In particular, on Qwen3-8B, PASR reduces average token consumption by 41.6 percent compared to standard generation, while also achieving an 8.2 percent improvement in accuracy. Our code and all baselines used in the paper are available in the GitHub.

Much of the recent progress made in image classification research can be credited to training procedure refinements, such as changes in data augmentations and optimization methods. In the literature, however, most refinements are either briefly mentioned as implementation details or only visible in source code. In this paper, we will examine a collection of such refinements and empirically evaluate their impact on the final model accuracy through ablation study. We will show that, by combining these refinements together, we are able to improve various CNN models significantly. For example, we raise ResNet-50's top-1 validation accuracy from 75.3% to 79.29% on ImageNet. We will also demonstrate that improvement on image classification accuracy leads to better transfer learning performance in other application domains such as object detection and semantic segmentation.

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a recursively defined function: one is for its recursive calls and the other is for its calls outside its definition. Bimorphic recursion in this paper can be nested. This paper shows bimorphic recursion has principal types and decidable type inference. Hence bimorphic recursion gives us flexible typing for recursion with decidable type inference. This paper also shows that its typability becomes undecidable because of nesting of recursions when one removes the instantiation property from the bimorphic recursion.

The OpenAI o1-series models have demonstrated that leveraging long-form Chain of Thought (CoT) can substantially enhance performance. However, the recursive thinking capabilities of Large Language Models (LLMs) remain limited, particularly in the absence of expert-curated data for distillation. In this paper, we propose AvR: Alignment via Refinement, a novel method aimed at unlocking the potential of LLMs for recursive reasoning through long-form CoT. AvR introduces a refinement process that integrates criticism and improvement actions, guided by differentiable learning techniques to optimize refinement-aware rewards. As a result, the synthesized multi-round data can be organized as a long refinement thought, further enabling test-time scaling. Experimental results show that AvR significantly outperforms conventional preference optimization methods. Notably, with only 3k synthetic samples, our method boosts the performance of the LLaMA-3-8B-Instruct model by over 20\% in win rate on AlpacaEval 2.0. Our code is available at Github (https://github.com/Banner-Z/AvR.git).

Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training neural networks to mimic this ability in formal mathematical theorem proving. We show on a set of unseen proofs, REFACTOR is able to extract 19.6% of the theorems that humans would use to write the proofs. When applying the model to the existing Metamath library, REFACTOR extracted 16 new theorems. With newly extracted theorems, we show that the existing proofs in the MetaMath database can be refactored. The new theorems are used very frequently after refactoring, with an average usage of 733.5 times, and help shorten the proof lengths. Lastly, we demonstrate that the prover trained on the new-theorem refactored dataset proves more test theorems and outperforms state-of-the-art baselines by frequently leveraging a diverse set of newly extracted theorems. Code can be found at https://github.com/jinpz/refactor.

The Abstraction and Reasoning Corpus (ARC) tests whether a model can infer an unseen transformation from a few input-output examples and apply it to a new grid. Looped visual reasoners refine predictions over multiple iterations, but conventional training constrains only the final output, leaving intermediate refinements unconstrained. We propose that these refinements should instead follow the transformation step by step. We introduce TraceViT, a looped visual reasoner trained with semantically monotonic transformation chains. We obtain these chains by rewriting and verifying programmatic task implementations, decomposing each solution into intermediate grid states. Each iteration is grounded by a task reference derived from the few-shot demonstrations and an object workspace representing the current grid state. Because these chains may differ in length from the loop, soft trace alignment enforces only their ordering, letting the model allocate iterations freely. TraceViT achieves 67.8% pass@2 on ARC-AGI-1 and 24.3% on ARC-AGI-2. Controlled ablations on ARC-AGI-1 show that trace supervision becomes beneficial only when paired with grounding. Code and data will be available at https://github.com/LiuBinnan/TraceViT.

Designers craft and edit graphic designs in a layer representation, but layer-based editing becomes impossible once composited into a raster image. In this work, we propose LayerD, a method to decompose raster graphic designs into layers for re-editable creative workflow. LayerD addresses the decomposition task by iteratively extracting unoccluded foreground layers. We propose a simple yet effective refinement approach taking advantage of the assumption that layers often exhibit uniform appearance in graphic designs. As decomposition is ill-posed and the ground-truth layer structure may not be reliable, we develop a quality metric that addresses the difficulty. In experiments, we show that LayerD successfully achieves high-quality decomposition and outperforms baselines. We also demonstrate the use of LayerD with state-of-the-art image generators and layer-based editing.

Context. Behaviour-Driven Development (BDD) software test suites accumulate duplicated step subsequences. Three published refactoring patterns are available (within-file Background, within-repo reusable-scenario invocation, cross-organisational shared higher-level step), but no prior work automates which recurring subsequences are worth extracting or which mechanism applies. Objective. Rank recurring step subsequences ("slices") by refactoring suitability (extraction-worthy), pre-map each to one of the three patterns, and quantify prevalence across the public BDD ecosystem. Method. Every contiguous L-step window (L in [2, 18]) in a 339-repository / 276-upstream-owner Gherkin corpus is keyed by paraphrase-robust cluster identifiers and counted under three scopes. Sentence-BERT (SBERT) / Uniform Manifold Approximation and Projection (UMAP) / Hierarchical Density-Based Clustering (HDBSCAN) recovers paraphrase-equivalent slices. Three authors label a stratified 200-slice pool against a written rubric. An eXtreme Gradient Boosting (XGBoost) extraction-worthy classifier trained under 5-fold cross-validation is compared with a tuned rule baseline and two open-weight Large Language Model (LLM) judges. Results. The miner produces 5,382,249 slices collapsing to 692,020 recurring patterns. Three-author Fleiss' kappa = 0.56 (extraction-worthy) and 0.79 (mechanism). The classifier reaches out-of-fold F1 = 0.891 (95% CI [0.852, 0.927]), outperforming both the rule baseline (F1 = 0.836, p = 0.017) and the better LLM judge (F1 = 0.728, p < 1e-4). 75.0%, 59.5%, and 11.7% of scenarios carry a within-file Background, within-repo reusable-scenario, or cross-organisational shared-step candidate. Conclusion. Paraphrase-robust subscenario discovery yields a corpus-wide census of BDD refactoring opportunities; pipeline, classifier predictions, labelled pool, and rubric are released under Apache-2.0.

Recent improvements in text generation have leveraged human feedback to improve the quality of the generated output. However, human feedback is not always available, especially during inference. In this work, we propose an inference time optimization method FITO to use fine-grained actionable feedback in the form of error type, error location and severity level that are predicted by a learned error pinpoint model for iterative refinement. FITO starts with an initial output, then iteratively incorporates the feedback via a refinement model that generates an improved output conditioned on the feedback. Given the uncertainty of consistent refined samples at iterative steps, we formulate iterative refinement into a local search problem and develop a simulated annealing based algorithm that balances exploration of the search space and optimization for output quality. We conduct experiments on three text generation tasks, including machine translation, long-form question answering (QA) and topical summarization. We observe 0.8 and 0.7 MetricX gain on Chinese-English and English-German translation, 4.5 and 1.8 ROUGE-L gain at long form QA and topic summarization respectively, with a single iteration of refinement. With our simulated annealing algorithm, we see further quality improvements, including up to 1.7 MetricX improvements over the baseline approach.

Recent advancements in large language models (LLMs) have demonstrated that progressive refinement, rather than providing a single answer, results in more accurate and thoughtful outputs. However, existing methods often rely heavily on supervision signals to evaluate previous responses, making it difficult to assess output quality in more open-ended scenarios effectively. Additionally, these methods are typically designed for specific tasks, which limits their generalization to new domains. To address these limitations, we propose Progressive Thought Refinement (PTR), a framework that enables LLMs to refine their responses progressively. PTR operates in two phases: (1) Thought data construction stage: We propose a weak and strong model collaborative selection strategy to build a high-quality progressive refinement dataset to ensure logical consistency from thought to answers, and the answers are gradually refined in each round. (2) Thought-Mask Fine-Tuning Phase: We design a training structure to mask the "thought" and adjust loss weights to encourage LLMs to refine prior thought, teaching them to implicitly understand "how to improve" rather than "what is correct." Experimental results show that PTR significantly enhances LLM performance across ten diverse tasks (avg. from 49.6% to 53.5%) without task-specific fine-tuning. Notably, in more open-ended tasks, LLMs also demonstrate substantial improvements in the quality of responses beyond mere accuracy, suggesting that PTR truly teaches LLMs to self-improve over time.

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.

With the development of large language models, their ability to follow simple instructions has significantly improved. However, adhering to complex instructions remains a major challenge. Current approaches to generating complex instructions are often irrelevant to the current instruction requirements or suffer from limited scalability and diversity. Moreover, methods such as back-translation, while effective for simple instruction generation, fail to leverage the rich contents and structures in large web corpora. In this paper, we propose a novel automatic iterative refinement framework to generate complex instructions with constraints, which not only better reflects the requirements of real scenarios but also significantly enhances LLMs' ability to follow complex instructions. The AIR framework consists of two stages: (1)Generate an initial instruction from a document; (2)Iteratively refine instructions with LLM-as-judge guidance by comparing the model's output with the document to incorporate valuable constraints. Finally, we construct the AIR-10K dataset with 10K complex instructions and demonstrate that instructions generated with our approach significantly improve the model's ability to follow complex instructions, outperforming existing methods for instruction generation.

3D fragment reassembly aims to recover the rigid poses of unordered fragment point clouds or meshes in a common object coordinate system to reconstruct the complete shape. The problem becomes particularly challenging as the number of fragments grows, since the target shape is unknown and fragments provide weak semantic cues. Existing end-to-end approaches are prone to cascading failures due to unreliable contact reasoning, most notably inaccurate fragment adjacencies. To address this, we propose Structure-Aware Reassembly (SARe), a generative framework with SARe-Gen for Euclidean-space assembly generation and SARe-Refine for inference-time refinement, with explicit contact modeling. SARe-Gen jointly predicts fracture-surface token probabilities and an inter-fragment contact graph to localize contact regions and infer candidate adjacencies. It adopts a query-point-based conditioning scheme and extracts aligned local geometric tokens at query locations from a frozen geometry encoder, yielding queryable structural representations without additional structural pretraining. We further introduce an inference-time refinement stage, SARe-Refine. By verifying candidate contact edges with geometric-consistency checks, it selects reliable substructures and resamples the remaining uncertain regions while keeping verified parts fixed, leading to more stable and consistent assemblies in the many-fragment regime. We evaluate SARe across three settings, including synthetic fractures, simulated fractures from scanned real objects, and real physically fractured scans. The results demonstrate state-of-the-art performance, with more graceful degradation and higher success rates as the fragment count increases in challenging large-scale reassembly.

Refactoring is a common software engineering practice that improves code quality without altering program behavior. Although tools like ReExtractor+, RefactoringMiner, and RefDiff have been developed to detect refactorings automatically, they rely on complex rule definitions and static analysis, making them difficult to extend and generalize to other programming languages. In this paper, we investigate the viability of using foundation models for refactoring detection, implemented in a tool named RefModel. We evaluate Phi4-14B, and Claude 3.5 Sonnet on a dataset of 858 single-operation transformations applied to artificially generated Java programs, covering widely-used refactoring types. We also extend our evaluation by including Gemini 2.5 Pro and o4-mini-high, assessing their performance on 44 real-world refactorings extracted from four open-source projects. These models are compared against RefactoringMiner, RefDiff, and ReExtractor+. RefModel is competitive with, and in some cases outperform, traditional tools. In real-world settings, Claude 3.5 Sonnet and Gemini 2.5 Pro jointly identified 97% of all refactorings, surpassing the best-performing static-analysis-based tools. The models showed encouraging generalization to Python and Golang. They provide natural language explanations and require only a single sentence to define each refactoring type.

Agent-compiled knowledge bases provide persistent external knowledge for large language model (LLM) agents in open-ended, knowledge-intensive downstream tasks. Yet their quality is systematically limited by incompleteness, incorrectness, and redundancy, manifested as missing evidence or cross-document links, low-confidence or imprecise claims, and ambiguous or coreference resolution issues. Such defects compound under iterative use, degrading retrieval fidelity and downstream task performance. We present DeepRefine, a general LLM-based reasoning model for agent-compiled knowledge refinement that improves the quality of any pre-constructed knowledge bases with user queries to make it more suitable for the downstream tasks. DeepRefine performs multi-turn interactions with the knowledge base and conducts abductive diagnosis over interaction history, localizes likely defects, and executes targeted refinement actions for incremental knowledge base updates. To optimize refinement policies of DeepRefine without gold references, we introduce a Gain-Beyond-Draft (GBD) reward and train the reasoning process end-to-end via reinforcement learning. Extensive experiments demonstrate consistent downstream gains over strong baselines.

Graphic design generation demands a delicate balance between high visual fidelity and fine-grained structural editability. However, existing approaches typically bifurcate into either non-editable raster image synthesis or abstract layout generation devoid of visual content. Recent combinations of these two approaches attempt to bridge this gap but often suffer from rigid composition schemas and unresolvable visual dissonances (e.g., text-background conflicts) due to their inexpressive representation and open-loop nature. To address these challenges, we propose DesignAsCode, a novel framework that reimagines graphic design as a programmatic synthesis task using HTML/CSS. Specifically, we introduce a Plan-Implement-Reflect pipeline, incorporating a Semantic Planner to construct dynamic, variable-depth element hierarchies and a Visual-Aware Reflection mechanism that iteratively optimizes the code to rectify rendering artifacts. Extensive experiments demonstrate that DesignAsCode significantly outperforms state-of-the-art baselines in both structural validity and aesthetic quality. Furthermore, our code-native representation unlocks advanced capabilities, including automatic layout retargeting, complex document generation (e.g., resumes), and CSS-based animation.

We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language theorem statement, and a natural language proof. The problems are primarily drawn from popular undergraduate pure mathematics textbooks and cover topics such as real and complex analysis, linear algebra, abstract algebra, and topology. We intend for ProofNet to be a challenging benchmark that will drive progress in autoformalization and automatic theorem proving. We report baseline results on statement autoformalization via in-context learning. Moreover, we introduce two novel statement autoformalization methods: prompt retrieval and distilled backtranslation.

Proof autoformalization aims to translate a mathematical informal proof written in natural language into a formal proof in a formal language such as Lean~4. Several works have developed LLM-based models for proof autoformalization. However, existing evaluations have typically focused on translating well-formed informal proofs from curated datasets. We argue that a robust proof autoformalizer must remain faithful even for informal proofs that diverge from these idealized ones, and we present the first study on the robustness of proof autoformalization models. We formulate two categories of perturbations and evaluate robustness under each: a global perturbation paraphrases the informal proof in a different style, under which the formalization should remain consistent; a local perturbation alters a value, symbol, or proof step, possibly in a counterfactual way, and a robust formalization should faithfully reflect the perturbation rather than reverting to the original one or inferring a different one on its own. We build a benchmark with both perturbations on miniF2F and MATH-500, and automatically measure how stable a proof autoformalization's correctness is under global perturbations and how faithfully its output reflects local perturbations. We evaluate seven recent models, all of which are sensitive to global perturbations and mostly fail to remain faithful under local perturbations. Code and data are available via https://github.com/ucr-rai/robust-proof-autoformalization.

Large language model (LLM)-based search agents have proven promising for addressing knowledge-intensive problems by incorporating information retrieval capabilities. Existing works largely focus on optimizing the reasoning paradigms of search agents, yet the quality of intermediate search queries during reasoning remains overlooked. As a result, the generated queries often remain inaccurate, leading to unexpected retrieval results and ultimately limiting search agents' overall effectiveness. To mitigate this issue, we introduce SmartSearch, a framework built upon two key mechanisms: (1) Process rewards, which provide fine-grained supervision for the quality of each intermediate search query through Dual-Level Credit Assessment. (2) Query refinement, which promotes the optimization of query generation by selectively refining low-quality search queries and regenerating subsequent search rounds based on these refinements. To enable the search agent to progressively internalize the ability to improve query quality under the guidance of process rewards, we design a three-stage curriculum learning framework. This framework guides the agent through a progression from imitation, to alignment, and ultimately to generalization. Experimental results show that SmartSearch consistently surpasses existing baselines, and additional quantitative analyses further confirm its significant gains in both search efficiency and query quality. The code is available at https://github.com/MYVAE/SmartSearch.

Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on producing executable code, but they frequently fail to preserve the semantic meaning and logical structure of the original human-written argument. To address this, we introduce ProofFlow, a novel pipeline that treats structural fidelity as a primary objective. ProofFlow first constructs a directed acyclic graph (DAG) to map the logical dependencies between proof steps. Then, it employs a novel lemma-based approach to systematically formalize each step as an intermediate lemma, preserving the logical structure of the original argument. To facilitate evaluation, we present a new benchmark of 184 undergraduate-level problems, manually annotated with step-by-step solutions and logical dependency graphs, and introduce ProofScore, a new composite metric to evaluate syntactic correctness, semantic faithfulness, and structural fidelity. Experimental results show our pipeline sets a new state-of-the-art for autoformalization, achieving a ProofScore of 0.545, substantially exceeding baselines like full-proof formalization (0.123), which processes the entire proof at once, and step-proof formalization (0.072), which handles each step independently. Our pipeline, benchmark, and score metric are open-sourced to encourage further progress at https://github.com/Huawei-AI4Math/ProofFlow.

With the rapid advancement of Large Language Models (LLMs), developing effective critic modules for precise guidance has become crucial yet challenging. In this paper, we initially demonstrate that supervised fine-tuning for building critic modules (which is widely adopted in current solutions) fails to genuinely enhance models' critique abilities, producing superficial critiques with insufficient reflections and verifications. To unlock the unprecedented critique capabilities, we propose RefCritic, a long-chain-of-thought critic module based on reinforcement learning with dual rule-based rewards: (1) instance-level correctness of solution judgments and (2) refinement accuracies of the policy model based on critiques, aiming to generate high-quality evaluations with actionable feedback that effectively guides model refinement. We evaluate RefCritic on Qwen2.5-14B-Instruct and DeepSeek-R1-Distill-Qwen-14B across five benchmarks. On critique and refinement settings, RefCritic demonstrates consistent advantages across all benchmarks, e.g., 6.8\% and 7.2\% gains on AIME25 for the respective base models. Notably, under majority voting, policy models filtered by RefCritic show superior scaling with increased voting numbers. Moreover, despite training on solution-level supervision, RefCritic outperforms step-level supervised approaches on ProcessBench, a benchmark to identify erroneous steps in mathematical reasoning.

Pre-trained code language models have achieved promising performance in code generation and improved the programming efficiency of human developers. However, their self-refinement capability is typically overlooked by the existing evaluations of code LMs, which focus only on the accuracy of the one-time prediction. For the cases when code LMs fail to implement the correct program, developers actually find it hard to debug and fix the faulty prediction since it is not written by the developers themselves. Unfortunately, our study reveals that code LMs cannot efficiently self-refine their faulty generations as well. In this paper, we propose CYCLE framework, learning to self-refine the faulty generation according to the available feedback, such as the execution results reported by the test suites. We evaluate CYCLE on three popular code generation benchmarks, HumanEval, MBPP, and APPS. The results reveal that CYCLE successfully maintains, sometimes improves, the quality of one-time code generation, while significantly improving the self-refinement capability of code LMs. We implement four variants of CYCLE with varied numbers of parameters across 350M, 1B, 2B, and 3B, and the experiments show that CYCLE consistently boosts the code generation performance, by up to 63.5%, across benchmarks and varied model sizes. We also notice that CYCLE outperforms code LMs that have 3times more parameters in self-refinement.

Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models can generate syntactically correct formal statements, they often fail to preserve the original problem's semantic intent. This limitation arises from the LLM approaches' treating autoformalization as a simplistic translation task which lacks mechanisms for self-reflection and iterative refinement that human experts naturally employ. To address these issues, we propose ReForm, a Reflective Autoformalization method that tightly integrates semantic consistency evaluation into the autoformalization process. This enables the model to iteratively generate formal statements, assess its semantic fidelity, and self-correct identified errors through progressive refinement. To effectively train this reflective model, we introduce Prospective Bounded Sequence Optimization (PBSO), which employs different rewards at different sequence positions to ensure that the model develops both accurate autoformalization and correct semantic validations, preventing superficial critiques that would undermine the purpose of reflection. Extensive experiments across four autoformalization benchmarks demonstrate that ReForm achieves an average improvement of 17.2 percentage points over the strongest baselines. To further ensure evaluation reliability, we introduce ConsistencyCheck, a benchmark of 859 expert-annotated items that not only validates LLMs as judges but also reveals that autoformalization is inherently difficult: even human experts produce semantic errors in up to 38.5% of cases.

Encoding input coordinates with sinusoidal functions into multi-layer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of surfaces defined as zero-level sets. However, existing methods often struggle to balance training efficiency, rendering speed, and noise robustness: single-MLP approaches are expensive at inference, grid-based representations are fast but can limit surface smoothness and overfit input noise, and previous multiscale approaches frequently capture noise and produce artifacts due to hard spectral truncation. To address these limitations, we propose M-plicits, a multiscale framework that models surfaces as a residual sum of MLPs trained via a sequence of nested neighborhoods. Unlike existing residual approaches that rely on standard domain-wide sampling and require costly mesh extraction for visualization, our method strictly localizes supervision to narrow bands around the previous zero-level sets. This nested design naturally provides robustness against noisy input data: the coarse network acts as a low-pass filter that establishes a clean geometric prior, while subsequent residuals progressively refine the geometry without fitting to high-frequency artifacts. We further introduce a multiscale sphere-tracing algorithm and a GEMM-based analytical normal computation that bypasses auto-differentiation entirely, yielding high-fidelity real-time rendering. On Stanford and Thingi32, M-plicits achieves the best mean Chamfer distance in the coarse configuration and the best median Chamfer distance and IoU in the fine configuration, with substantially better noise robustness than iNGP, BACON, and IDF, while using an order of magnitude fewer parameters than grid-based baselines. Code, models, and data are available at https://github.com/dsilvavinicius/m-plicits.

The foundational capabilities of large language models (LLMs) are deeply influenced by the quality of their pre-training corpora. However, enhancing data quality at scale remains a significant challenge, primarily due to the trade-off between refinement effectiveness and processing efficiency. While rule-based filtering remains the dominant paradigm, it typically operates at the document level and lacks the granularity needed to refine specific content within documents. Inspired by emerging work such as ProX, we propose RefineX, a novel framework for large-scale, surgical refinement of pre-training data through programmatic editing tasks. RefineX enables efficient and fine-grained data refinement while reliably preserving the diversity and naturalness of raw text. The core strength of RefineX lies in distilling high-quality, expert-guided end-to-end refinement results into minimal edit-based deletion programs. This high-precision distillation pipeline is used to train an efficient and reliable refine model that can systematically improve every instance in the corpus at scale. We evaluate RefineX across from-scratch pre-training at multiple model scales and find that it consistently outperforms models trained on raw, filtered, or alternatively refined data across diverse downstream tasks. On the 750M model, RefineX yields 2.6%-7.2% average gains on lighteval tasks, and achieves comparable performance using significantly fewer training tokens. Further analysis shows that RefineX reliably enhances text quality with both high efficiency and precision, outperforming prior approaches such as end-to-end generation and Prox-C. These results position RefineX as a scalable, effective, and reliable solution for optimizing pre-training data in modern LLM pipelines.

We seek a hierarchical resolution of residual error under a composite learning objective as a principled mechanism for identifying and exploiting additional information, particularly under distribution shift and perturbation. Inspired by the System 1/System 2 paradigm, we formulate this principle as a two-loop mechanism serving a common inference goal. A fast, System 1-like loop resolves the residual addressable by the available evidence; the remaining epistemic residual triggers a medium speed, System 2-like loop that actively acquires additional evidence and measures its informational value through residual reduction. Over nested solution spaces, the medium-loop optimum is provably no worse than the fast-loop optimum. Experiments show that the resulting two-loop model consistently improves upon the fast loop at approximately half the computation of the medium loop, including under unseen corruptions, and, when provided a cleaner observation, outperforms staged classifiers and learning-to-defer methods at equal computational cost.

As the demand for high-quality data in model training grows, researchers and developers are increasingly generating synthetic data to tune and train LLMs. A common assumption about synthetic data is that sampling from instruct-tuned models is sufficient; however, these models struggle to produce diverse outputs-a key requirement for generalization. Despite various prompting methods, in this work we show that achieving meaningful diversity from instruct-tuned models remains challenging. In contrast, we find base models without post-training exhibit greater diversity, but are less capable at instruction following and hence of lower quality. Leveraging this insight, we propose Base-Refine (BARE), a synthetic data generation method that combines the diversity of base models with the quality of instruct-tuned models through a two-stage process. With minimal few-shot examples and curation, BARE generates diverse and high-quality datasets, improving downstream task performance. We show that fine-tuning with as few as 1,000 BARE-generated samples can reach performance comparable to the best similarly sized models on LiveCodeBench tasks. Furthermore, fine-tuning with BARE-generated data achieves a 101% improvement over instruct-only data on GSM8K and a 18.4% improvement over SOTA methods on RAFT.

Text-to-SQL systems have unlocked easier access to critical data insights by enabling natural language queries over structured databases. However, deploying such systems in enterprise environments remains challenging due to factors such as large, complex schemas (> 3000 columns), diverse SQL dialects (e.g., BigQuery, Snowflake) and sophisticated query requirements (e.g., transformation, analytics). Current state-of-the-art performance on the Spider 2.0 dataset -- a benchmark built to mimic such complex environments -- remains limited at 20%. Key limitations include inadequate instruction-following, poor long-context comprehension, weak self-refinement, and insufficient dialect-specific knowledge. To address these gaps, we propose ReFoRCE (Self-Refinement Agent with Format Restriction and Column Exploration) which introduces (1) table compression to mitigate long-context limitations (2) format restriction to ensure accurate answer format, and (3) iterative column exploration for enhanced schema understanding. Additionally, it employs self-refinement pipeline consisting of (1) parallelized workflows with voting mechanisms and (2) a Common Table Expression (CTE) based refinement approach to handle unresolved cases. ReFoRCE achieves state-of-the-art results scoring 31.26 on the Spider 2.0-Snow and scoring 30.35 on the Spider 2.0-Lite tasks.

In this paper, we address the problem of degradation in inpainting quality of neural networks operating at high resolutions. Inpainting networks are often unable to generate globally coherent structures at resolutions higher than their training set. This is partially attributed to the receptive field remaining static, despite an increase in image resolution. Although downscaling the image prior to inpainting produces coherent structure, it inherently lacks detail present at higher resolutions. To get the best of both worlds, we optimize the intermediate featuremaps of a network by minimizing a multiscale consistency loss at inference. This runtime optimization improves the inpainting results and establishes a new state-of-the-art for high resolution inpainting. Code is available at: https://github.com/geomagical/lama-with-refiner/tree/refinement.

Multi-cellular robot design aims to create robots comprised of numerous cells that can be efficiently controlled to perform diverse tasks. Previous research has demonstrated the ability to generate robots for various tasks, but these approaches often optimize robots directly in the vast design space, resulting in robots with complicated morphologies that are hard to control. In response, this paper presents a novel coarse-to-fine method for designing multi-cellular robots. Initially, this strategy seeks optimal coarse-grained robots and progressively refines them. To mitigate the challenge of determining the precise refinement juncture during the coarse-to-fine transition, we introduce the Hyperbolic Embeddings for Robot Design (HERD) framework. HERD unifies robots of various granularity within a shared hyperbolic space and leverages a refined Cross-Entropy Method for optimization. This framework enables our method to autonomously identify areas of exploration in hyperbolic space and concentrate on regions demonstrating promise. Finally, the extensive empirical studies on various challenging tasks sourced from EvoGym show our approach's superior efficiency and generalization capability.

In SPARQL, the query forms SELECT and CONSTRUCT have been the subject of several studies, both theoretical and practical. However, the composition of such queries and their interweaving when forming involved nested queries has not yet received much interest in the literature. We mainly tackle the problem of composing such queries. For this purpose, we introduce a language close to SPARQL where queries can be nested at will, involving either CONSTRUCT or SELECT query forms and provide a formal semantics for it. This semantics is based on a uniform interpretation of queries. This uniformity is due to an extension of the notion of RDF graphs to include isolated items such as variables. As a key feature of this work, we show how classical SELECT queries can be easily encoded as a particular case of CONSTRUCT queries.

If autoresearch is itself a form of research, then autoresearch can be applied to research itself. We present Bilevel Autoresearch, a bilevel framework in which an outer autoresearch loop improves an inner autoresearch loop by reading its code and traces, identifying bottlenecks, and generating injectable Python search mechanisms at runtime. The inner loop optimizes task performance; the outer loop optimizes how the inner loop searches. Both loops use the same LLM, so improvements come from the bilevel architecture rather than a stronger meta-level model, although the outer loop consumes additional inference and wall-clock budget. On Karpathy's GPT pretraining benchmark, the meta-autoresearch outer loop achieves a 5x improvement over the standard inner loop alone (-0.045 vs. -0.009 val_bpb), while parameter-level adjustment without mechanism change yields no reliable gain. The outer loop instantiates mechanisms from adjacent search domains, including combinatorial optimization, multi-armed bandits, and design of experiments, without human specification of the final mechanism design. Trace analysis suggests that these mechanisms break deterministic search patterns and force exploration of directions the LLM's priors avoid. The experiments demonstrate, on this benchmark, a first bilevel step: an outer loop improves the search behavior of an inner loop. Code is the mechanism carrier in this implementation, but skills, prompts, workflows, evaluators, domain principles, world-model assumptions, and memory schemas can also encode mechanisms that shape future agent behavior. This suggests a path toward recursive bootstrapping, where mechanisms discovered for the inner loop can be fed back to improve the meta-level loop itself.

Finetuning large language models on instruction data is crucial for enhancing pre-trained knowledge and improving instruction-following capabilities. As instruction datasets proliferate, selecting optimal data for effective training becomes increasingly important. This work addresses the question: How can we determine the optimal subset of data for effective training? While existing research often emphasizes local criteria like instance quality for subset selection, we argue that a global approach focused on data diversity is more critical. Our method employs k-means clustering to ensure the selected subset effectively represents the full dataset. We propose an iterative refinement method inspired by active learning techniques to resample instances from clusters, reassessing each cluster's importance and sampling weight in every training iteration. This approach reduces the effect of outliers and automatically filters out clusters containing low-quality data. Through extensive evaluation across natural language reasoning, general world knowledge, code and math reasoning tasks, and by fine-tuning models from various families, we observe consistent improvements, achieving a 7% increase over random selection and a 3.8% improvement over state-of-the-art sampling methods. Our work highlights the significance of diversity-first sampling when finetuning LLMs to enhance performance across a broad array of evaluation tasks. Our code is available at https://github.com/for-ai/iterative-data-selection.

This paper demonstrates that language models are strong structure-based protein designers. We present LM-Design, a generic approach to reprogramming sequence-based protein language models (pLMs), that have learned massive sequential evolutionary knowledge from the universe of natural protein sequences, to acquire an immediate capability to design preferable protein sequences for given folds. We conduct a structural surgery on pLMs, where a lightweight structural adapter is implanted into pLMs and endows it with structural awareness. During inference, iterative refinement is performed to effectively optimize the generated protein sequences. Experiments show that LM-Design improves the state-of-the-art results by a large margin, leading to up to 4% to 12% accuracy gains in sequence recovery (e.g., 55.65%/56.63% on CATH 4.2/4.3 single-chain benchmarks, and >60% when designing protein complexes). We provide extensive and in-depth analyses, which verify that LM-Design can (1) indeed leverage both structural and sequential knowledge to accurately handle structurally non-deterministic regions, (2) benefit from scaling data and model size, and (3) generalize to other proteins (e.g., antibodies and de novo proteins)

Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4. However, faithful formalization requires more than translation. Models must map mathematical concepts to the complex hierarchy of types and definitions in formal libraries such as Mathlib, while ensuring that generated statements preserve the meaning of the source propositions. Existing approaches struggle because they rely heavily on the model's parametric memory for library-specific knowledge, while common data construction pipelines often resort to filtering single-pass outputs and lack mechanisms for feedback-driven revision. To address these challenges, we introduce MathForm, an autoformalization framework for constructing verified training data through Mathlib knowledge retrieval and verification-guided iterative refinement. Before generation, a retrieval planner gathers relevant definitions and existing formalizations from Mathlib to guide the formalization generator. Generated statements are then revised using compiler diagnostics and semantic-consistency feedback. Using this framework, we construct FormalVerse, a Lean 4 dataset containing approximately 367K verified examples across diverse mathematical domains and sources. We then train MathForm-8B through supervised fine-tuning followed by reinforcement learning. Across six benchmarks, MathForm-8B achieves average Pass@8 rates of 88.06% under Syntax Check (SC) and 72.37% under Consistency Check (CC), outperforming multiple specialized 32B autoformalizers. On the challenging FATE-H and FATE-X subsets, it attains CC pass rates of 63% and 37%, exceeding the strongest specialized baselines in both cases.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

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

Text-guided image editing must introduce the requested changes while preserving unrelated source content. Diffusion-based editors rely on spatial controls whose inaccuracies can leave edits incomplete or alter unrelated regions. Causal autoregressive editors face a further constraint: their fixed decoding order limits revision of earlier decisions. We introduce RefineEdit, a training-free prompt-to-prompt image editing framework built on a Generative Refinement Network. Our key idea is to couple edit localization with content generation through the global refinement of binary image codes, allowing editing evidence to be reassessed as the image evolves. RefineEdit initializes an editing branch from an intermediate source state, reusing the emerging layout. We compare the probabilities assigned by the two branches to the same source-sampled bits, using their signed differences to select editable positions and bits. Selected bits follow editing refinement, while the remaining bits copy the evolving source state. To stabilize editing across refinement steps, adaptive spatial freezing limits unnecessary mask expansion, while finite bit locking keeps recently selected bits editable. The framework requires no additional training, external masks, or attention control. Across nine editing categories of PIE-Bench, RefineEdit achieves the best background-preservation scores in PSNR, LPIPS, MSE and SSIM, together with the highest whole-image and edited-region CLIP scores among the evaluated methods.

Text-to-Image (T2I) models and Unified Multimodal Models (UMMs) have achieved remarkable progress in visual generation. However, their reliance on a single-pass generation paradigm limits their ability to handle complex prompts requiring iterative refinement. To enable multi-round Reflective Visual Generation (RVG), we formalize the Reason-Reflect-Rectify (R^3) loop as a core framework and introduce R^3-Bench, a benchmark of over 600 expert-annotated instances that quantifies iterative reasoning and rectification capabilities. Evaluation on R^3-Bench reveals a critical gap: while state-of-the-art models can identify generation errors, they fail to generate actionable rectification instructions. To bridge this gap, we propose R^3-Refiner, a dual-stage framework leveraging Group Relative Policy Optimization (GRPO) and a Hierarchical Reward Mechanism (HRM) to better align rectification with reflective reasoning. Experiments show that R^3-Refiner achieves significant improvements on R^3-Bench (+12.0% in Reflective Verdict Score, +9.0% in Rectification Score), and can be seamlessly integrated with various MLLMs to enhance the generation quality of different T2I models on GenEval++ and T2I-CompBench. Code is available at https://github.com/xiaomoguhz/R3-Bench.

We present a complete formalization in Isabelle/HOL of the object part of an equivalence between L-mosaics and bounded join-semilattices, employing an AI-assisted methodology that integrates large language models as reasoning assistants throughout the proof development process. The equivalence was originally established by Cangiotti, Linzi, and Talotti in their study of hypercompositional structures related to orthomodular lattices and quantum logic. Our formalization rigorously verifies the main theoretical result and demonstrates the mutual inverse property of the transformations establishing this equivalence. The development showcases both the mathematical depth of multivalued algebraic operations and the potential for AI-enhanced interactive theorem proving in tackling complex formalization projects.

Visual agents for symbolic graphics reasoning depend on executable world representations, yet continued improvement remains bottlenecked by ambiguous supervision from final renders. Recent agentic systems refine scenes through repeated interaction, but they lack mechanisms to recursively extract actionable evidence from execution traces, overlooking which proposed symbolic edits survived, disappeared, or interfered during program execution. To address this, we propose VETR (Verified Execution Trajectories for Refinement), a framework that enables agentic recursive self-improvement over executable world representations for symbolic graphics reasoning. Within each task, VETR retains aligned program/render records with bounded runtime observations and introduces an execution refiner that compiles observed writes and state changes into constrained alternative programs. The refiner validates their endpoints and preservation conditions against captured runtime state; the ordinary visual verifier then assesses goal relevance. Repair construction makes no additional language-model calls, but can require additional executions. Evaluations on BlenderGym (280 tasks) and BlenderBench (27 released tasks) with GPT-5.6-luna and Qwen3.8-27B show that VETR consistently outperforms existing refinement strategies, including BlenderAlchemy and VIGA. Controlled ablations evaluate the contributions of execution refinement and role-asymmetric evidence organization under fixed generator-interaction caps.

Tiny Recursive Models (TRMs) have recently demonstrated remarkable performance on ARC-AGI, showing that very small models can compete against large foundation models through a two-step refinement mechanism that updates an internal reasoning state z and the predicted output y. Naturally, such refinement is of interest for any predictor; it is therefore natural to wonder whether the TRM mechanism could be effectively re-adopted in autoregressive models. However, TRMs cannot be simply compared to standard models because they lack causal predictive structures and contain persistent latent states that make it difficult to isolate specific performance gains. In this paper, we propose the Autoregressive TRM and evaluate it on small autoregressive tasks. To understand its efficacy, we propose a suite of models that gradually transform a standard Transformer to a Tiny Autoregressive Recursive Model in a controlled setting that fixes the block design, token stream, and next-token objective. Across compute-matched experiments on character-level algorithmic tasks, we surprisingly find that there are some two-level refinement baselines that show strong performance. Contrary to expectations, we find no reliable performance gains from the full Autoregressive TRM architecture. These results offer potential promise for two-step refinement mechanisms more broadly but caution against investing in the autoregressive TRM-specific model as a fruitful research direction.

Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes subgoal-based proofs with expert learning to enhance LLMs' capabilities in formal theorem proving within the Isabelle environment. SubgoalXL addresses two critical challenges: the scarcity of specialized mathematics and theorem-proving data, and the need for improved multi-step reasoning abilities in LLMs. By optimizing data efficiency and employing subgoal-level supervision, SubgoalXL extracts richer information from limited human-generated proofs. The framework integrates subgoal-oriented proof strategies with an expert learning system, iteratively refining formal statement, proof, and subgoal generators. Leveraging the Isabelle environment's advantages in subgoal-based proofs, SubgoalXL achieves a new state-of-the-art performance of 56.1\% in Isabelle on the standard miniF2F dataset, marking an absolute improvement of 4.9\%. Notably, SubgoalXL successfully solves 41 AMC12, 9 AIME, and 3 IMO problems from miniF2F. These results underscore the effectiveness of maximizing limited data utility and employing targeted guidance for complex reasoning in formal theorem proving, contributing to the ongoing advancement of AI reasoning capabilities. The implementation is available at https://github.com/zhaoxlpku/SubgoalXL.

While large language models (LLMs) have demonstrated strong performance on complex reasoning tasks such as competitive programming (CP), existing methods predominantly focus on single-attempt settings, overlooking their capacity for iterative refinement. In this paper, we present RefineRL, a novel approach designed to unleash the self-refinement capabilities of LLMs for CP problem solving. RefineRL introduces two key innovations: (1) Skeptical-Agent, an iterative self-refinement agent equipped with local execution tools to validate generated solutions against public test cases of CP problems. This agent always maintains a skeptical attitude towards its own outputs and thereby enforces rigorous self-refinement even when validation suggests correctness. (2) A reinforcement learning (RL) solution to incentivize LLMs to self-refine with only standard RLVR data (i.e., problems paired with their verifiable answers). Extensive experiments on Qwen3-4B and Qwen3-4B-2507 demonstrate that our method yields substantial gains: after our RL training, these compact 4B models integrated with the Skeptical-Agent not only outperform much larger 32B models but also approach the single-attempt performance of 235B models. These findings suggest that self-refinement holds considerable promise for scaling LLM reasoning, with significant potential for further advancement.

The drive for predictable LLM reasoning in their integration with compound systems has popularized structured outputs, yet concerns remain about performance trade-offs compared to unconstrained natural language. At the same time, training on unconstrained Chain of Thought (CoT) traces has brought about a new class of strong reasoning models that nevertheless present novel compute budget and faithfulness challenges. This paper introduces iSelf-Discover, an instance-level adaptation of the Self-Discover framework, and using it compares dynamically generated structured JSON reasoning with its unstructured counterpart. Our empirical evaluation across diverse benchmarks using state-of-the-art open-source models supports a consistent advantage for unstructured reasoning. Notably, on the complex MATH benchmark, unstructured plans achieved relative performance improvements of up to 18.90\% over structured approaches. Zero-shot unstructured iSelf-Discover variants are also shown to outperform their five-shot structured counterparts, underscoring the significance of this gap, even when structured plans are dynamically generated to ensure reasoning precedes the final answer. We further demonstrate that the optimal granularity of plan generation (instance-level vs. task-level) is context-dependent. These findings invite re-evaluation of the reliance on structured formats for complex problem-solving and how compound systems should be organized.

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

Large language models hold promise as scientific assistants, yet existing agents either rely solely on algorithm evolution or on deep research in isolation, both of which face critical limitations. Pure algorithm evolution, as in AlphaEvolve, depends only on the internal knowledge of LLMs and quickly plateaus in complex domains, while pure deep research proposes ideas without validation, resulting in unrealistic or unimplementable solutions. We present DeepEvolve, an agent that integrates deep research with algorithm evolution, uniting external knowledge retrieval, cross-file code editing, and systematic debugging under a feedback-driven iterative loop. Each iteration not only proposes new hypotheses but also refines, implements, and tests them, avoiding both shallow improvements and unproductive over-refinements. Across nine benchmarks in chemistry, mathematics, biology, materials, and patents, DeepEvolve consistently improves the initial algorithm, producing executable new algorithms with sustained gains. By bridging the gap between unguided evolution and research without grounding, DeepEvolve provides a reliable framework for advancing scientific algorithm discovery. Our code is available at https://github.com/liugangcode/deepevolve.

While Large Language Models (LLMs) have revolutionized code generation, standard "System 1" approaches, generating solutions in a single forward pass, often hit a performance ceiling when faced with complex algorithmic tasks. Existing iterative refinement strategies attempt to bridge this gap at inference time, yet they predominantly rely on external oracles, execution feedback, or computationally expensive prompt-response cycles. In this work, we propose ReflexiCoder, a novel reinforcement learning (RL) framework that internalizes the structured reasoning trajectory, encompassing initial generation, bug and optimization aware reflection, and self-correction, directly into the model's weights. Unlike prior methods, ReflexiCoder shifts the paradigm from external-dependent refinement to an intrinsic, fully autonomous self-reflection and self-correction capabilities at inference time. We utilize an RL-zero training paradigm with granular reward functions to optimize the entire reflection-correction trajectory, teaching the model how to debug without reliance on ground-truth feedback or execution engines at inference time. Extensive experiments across seven benchmarks demonstrate that our ReflexiCoder-8B establishes a new state-of-the-art (SOTA) among leading open-source models in the 1.5B-14B range, achieving 94.51% (87.20%) on HumanEval (Plus), 81.80% (78.57%) on MBPP (Plus), 35.00% on BigCodeBench, 52.21% on LiveCodeBench, and 37.34% on CodeForces in a single-attempt setting, rivaling or surpassing proprietary models like GPT-5.1. Notably, our framework is significantly more token-efficient than base models, reducing inference-time compute overhead by approximately 40% through disciplined, high-speed reasoning and reflection patterns. Source code is available at https://github.com/juyongjiang/ReflexiCoder.

Interactive theorem provers (ITPs) require manual formalization, which is labor-intensive and demands expert knowledge. While automated formalization offers a potential solution, it faces two major challenges: model hallucination (e.g., undefined predicates, symbol misuse, and version incompatibility) and the semantic gap caused by ambiguous or missing premises in natural language descriptions. To address these issues, we propose CRAMF, a Concept-driven Retrieval-Augmented Mathematical Formalization framework. CRAMF enhances LLM-based autoformalization by retrieving formal definitions of core mathematical concepts, providing contextual grounding during code generation. However, applying retrieval-augmented generation (RAG) in this setting is non-trivial due to the lack of structured knowledge bases, the polymorphic nature of mathematical concepts, and the high precision required in formal retrieval. We introduce a framework for automatically constructing a concept-definition knowledge base from Mathlib4, the standard mathematical library for the Lean 4 theorem prover, indexing over 26,000 formal definitions and 1,000+ core mathematical concepts. To address conceptual polymorphism, we propose contextual query augmentation with domain- and application-level signals. In addition, we design a dual-channel hybrid retrieval strategy with reranking to ensure accurate and relevant definition retrieval. Experiments on miniF2F, ProofNet, and our newly proposed AdvancedMath benchmark show that CRAMF can be seamlessly integrated into LLM-based autoformalizers, yielding consistent improvements in translation accuracy, achieving up to 62.1% and an average of 29.9% relative improvement.

Reasoning training incentivizes LLMs to produce long chains of thought (long CoT), which among other things, allows them to explore solution strategies with self-checking. This results in higher accuracy, but inflates context length, token/compute cost, and answer latency. We ask: Can current models leverage their metacognition to provide other combinations on this Pareto frontier, e.g., better accuracy with lower context length and/or latency? Abstractly, we view the model as an improvement operator on its own "thoughts" with a continuum of possible strategies. We identify an interesting inference family Parallel-Distill-Refine (PDR), which performs the following: (i) generate diverse drafts in parallel; (ii) distill them into a bounded, textual workspace; and (iii) refine conditioned on this workspace, producing an output that seeds the next round. Importantly, context length (hence compute cost) is controllable via degree of parallelism, and is no longer conflated with the total number of generated tokens. We report PDR instantiations of current models that give better accuracy than long CoT while incurring lower latency. Setting degree of parallelism to 1 yields an interesting subcase, Sequential Refinement (SR) (iteratively improve a single candidate answer) which provides performance superior to long CoT. Success of such model orchestrations raises the question whether further training could shift the Pareto frontier. To this end, we train an 8B thinking model with Reinforcement Learning (RL) to make it consistent with PDR as the inference method. On math tasks with verifiable answers, iterative pipelines surpass single-pass baselines at matched sequential budgets, with PDR delivering the largest gains (e.g., +11% on AIME 2024 and +9% on AIME 2025).

Tools enhance the reasoning capabilities of large language models (LLMs) in complex problem-solving tasks, but not all tasks have available tools. In the absence of predefined tools, prior works have explored instructing LLMs to generate tools on their own. However, such approaches rely heavily on the models' internal knowledge and would fail in domains beyond the LLMs' knowledge scope. To address this limitation, we propose RefTool, a reference-guided framework for automatic tool creation that leverages structured external materials such as textbooks. RefTool consists of two modules: (1) tool creation, where LLMs generate executable tools from reference content, validate them using illustrative examples, and organize them hierarchically into a toolbox; and (2) tool utilization, where LLMs navigate the toolbox structure to select and apply the appropriate tools to solve problems. Experiments on causality, physics, and chemistry benchmarks demonstrate that RefTool outperforms existing tool-creation and domain-specific reasoning methods by 11.3% on average accuracy, while being cost-efficient and broadly generalizable. Analyses reveal that grounding tool creation in references produces accurate and faithful tools, and that the hierarchical structure facilitates effective tool selection. RefTool enables LLMs to overcome knowledge limitations, demonstrating the value of grounding tool creation in external references for enhanced and generalizable reasoning.

In this paper, we introduce Nested Low-Rank Adaptation (NoRA), a novel approach to parameter-efficient fine-tuning that extends the capabilities of Low-Rank Adaptation (LoRA) techniques. Vanilla LoRA overlooks pre-trained weight inheritance and still requires fine-tuning numerous parameters. To addresses these issues, our NoRA adopts a dual-layer nested structure with Singular Value Decomposition (SVD), effectively leveraging original matrix knowledge while reducing tunable parameters. Specifically, NoRA freezes the outer LoRA weights and utilizes an inner LoRA design, providing enhanced control over model optimization. This approach allows the model to more precisely adapt to specific tasks while maintaining a compact parameter space. By freezing outer LoRA weights and using an inner LoRA design, NoRA enables precise task adaptation with a compact parameter space. Evaluations on tasks including commonsense reasoning with large language models, fine-tuning vision-language models, and subject-driven generation demonstrate NoRA's superiority over LoRA and its variants. Code will be released upon acceptance.

A story premise succinctly defines a story's main idea, foundation, and trajectory. It serves as the initial trigger in automatic story generation. Existing sources of story premises are limited by a lack of diversity, uneven quality, and high costs that make them difficult to scale. In response, we introduce Modular Story Premise Synthesis (MoPS) which breaks down story premises into modules like background and persona for automated design and generation. MoPS consists of three phases: (1) Precollect a consistent set of candidates for each module to form a nested dictionary. (2) Extract a key path from the nested dictionary as the premise design. (3) Instruct an LLM to integrate the design into a coherent premise sentence. Thorough evaluations demonstrate that our synthesized premises excel in diversity, fascination, completeness, and originality compared to those induced from large language models and captured from public story datasets. Similarly, the extended novels and scripts generated from our premises also exhibit higher quality. In supplementary materials, we provide the MoPS code suite, along with 7.6k generated premises and 1k extended stories. Code: https://github.com/GAIR-NLP/MoPS.

Optimizing deployed AI systems increasingly amounts to editing prompts, skills, harnesses, and code rather than model weights. Existing approaches commonly optimize these artifacts through propose-evaluate-select procedures, where candidate configurations are evaluated and only those meeting an acceptance criterion are selected. Yet our analysis shows that discarded candidates often contain information critical for subsequent optimization. Discarding them causes later proposals to revisit the same failure modes. We introduce Mara Chain, a refinement procedure that turns rejected candidates into stepping stones. Rather than discarding a rejected candidate, Mara Chain retains and iteratively refines it using evidence accumulated across preceding attempts. The procedure limits each refinement chain to a fixed depth and applies Pareto-filtered Top-N selection to bound the candidate pool. Across AppWorld skill optimization, TerminalBench 2.1 harness optimization, and MuSiQue retrieval-pipeline optimization, Mara Chain delivers greater task-performance gains with fewer rollouts. It outperforms GEPA, ACE, and SkillOpt-Lite by up to 20.5% in relative performance on AppWorld, reaching the target score with 65.5% fewer rollouts than GEPA. It improves the pass rate by 20.2 and 22.5 percentage points over AHE and Meta-Harness on TerminalBench 2.1, respectively, and improves MuSiQue test nDCG@10 and Recall@10 by 0.104 and 0.131 over a hand-written retrieval pipeline.

Software engineers mainly write code by editing existing programs. In contrast, large language models (LLMs) autoregressively synthesize programs in a single pass. One explanation for this is the scarcity of open-sourced edit data. While high-quality instruction data for code synthesis is already scarce, high-quality edit data is even scarcer. To fill this gap, we develop a synthetic data generation algorithm called LintSeq. This algorithm refactors existing code into a sequence of code edits by using a linter to procedurally sample across the error-free insertions that can be used to sequentially write programs. It outputs edit sequences as text strings consisting of consecutive program diffs. To test LintSeq, we use it to refactor a dataset of instruction + program pairs into instruction + program-diff-sequence tuples. Then, we instruction finetune a series of smaller LLMs ranging from 2.6B to 14B parameters on both the re-factored and original versions of this dataset, comparing zero-shot performance on code synthesis benchmarks. We show that during repeated sampling, edit sequence finetuned models produce more diverse programs than baselines. This results in better inference-time scaling for benchmark coverage as a function of samples, i.e. the fraction of problems "pass@k" solved by any attempt given "k" tries. For example, on HumanEval pass@50, small LLMs finetuned on synthetic edit sequences are competitive with GPT-4 and outperform models finetuned on the baseline dataset by +20% (+/-3%) in absolute score. Finally, we also pretrain our own tiny LMs for code understanding. We show that finetuning tiny models on synthetic code edits results in state-of-the-art code synthesis for the on-device model class. Our 150M parameter edit sequence LM matches or outperforms code models with twice as many parameters, both with and without repeated sampling, including Codex and AlphaCode.

A supervised learning algorithm searches over a set of functions A to B parametrised by a space P to find the best approximation to some ideal function fcolon A to B. It does this by taking examples (a,f(a)) in Atimes B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.

Flow-matching models generate samples through iterative velocity predictions, but typically do not revisit these predictions using the intermediate representations that produced them. We introduce CorrFlow, a self-correcting flow-matching framework that reuses this information through a lightweight refiner. Under rectified-flow interpolation, the error of the one-step clean prediction equals the realized velocity residual scaled by the noise level. Motivated by this identity, the refiner learns to predict residual corrections from the base model's clean prediction, conditioning, noise level and hidden states from the same forward pass. The correction is added to the base velocity before each sampling update, so subsequent predictions are made from the corrected state. This requires no additional base-model evaluations and only one lightweight refiner evaluation per step. Our theoretical analyses establish conditions under which feature reuse outperforms raw-input affine predictors and refiner training achieves greater residual-risk reduction than continued base-model training under a matched training compute budget. Experiments on class-conditional image generation, text-to-video generation and image-to-video generation show consistent improvements over the corresponding base models, including gains in visual quality and physical consistency. Project Page: https://fogradio.github.io/corrflow-project

Large language models (LLMs) can refine their responses based on feedback, enabling self-improvement through iterative training or test-time refinement. However, existing methods predominantly focus on refinement within the same reasoning format, which may lead to non-correcting behaviors. We propose CaP, a novel approach that uses external tools to refine chain-of-thought (CoT) responses generated by the same or other LLMs. CaP employs a two-stage training process: supervised fine-tuning followed by preference optimization with DPO variants. Our observations highlight the critical role of preference optimization in enabling effective refinement. Additionally, we compare several sampling strategies to leverage CoT and tools at inference time. Experimental results demonstrate CaP's potential for effective cross-reasoning refinement and efficient inference.

Tool learning, which allows Large Language Models (LLMs) to leverage external tools for solving complex user tasks, has emerged as a promising avenue for extending model capabilities. However, current approaches primarily focus on data synthesis for fine-tuning LLMs to invoke tools effectively, largely ignoring how to fully stimulate the potential of the model. In this paper, we propose ToolACE-R, a novel method that introduces adaptive self-refinement for tool invocations. Our approach features a model-aware iterative training procedure that progressively incorporates more training samples based on the model's evolving capabilities. Additionally, it allows LLMs to iteratively refine their tool calls, optimizing performance without requiring external feedback. To further enhance computational efficiency, we integrate an adaptive mechanism when scaling the inference time, enabling the model to autonomously determine when to stop the refinement process. We conduct extensive experiments across several benchmark datasets, showing that ToolACE-R achieves competitive performance compared to advanced API-based models, even without any refinement. Furthermore, its performance can be further improved efficiently through adaptive self-refinement. Our results demonstrate the effectiveness of the proposed method, which is compatible with base models of various sizes, offering a promising direction for more efficient tool learning.

We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of contest or textbook-style problems as proxies for mathematical research. Instead, we establish an updatable benchmark evaluating models directly on the latest research results in mathematics. This consists of an automatic pipeline that extracts lemmas from arXiv and rewrites them into self-contained statements by making all assumptions and required definitions explicit. It results in a benchmark that can be updated regularly with new problems taken directly from human mathematical research, while previous instances can be used for training without compromising future evaluations. We benchmark current state-of-the-art LLMs, which obtain around 10-15% accuracy in theorem proving (pass@1) depending on the model, showing that there is currently a large margin of progression for LLMs to reach human-level proving capabilities in a research context.

In the domain of code generation, self-debugging is crucial. It allows LLMs to refine their generated code based on execution feedback. This is particularly important because generating correct solutions in one attempt proves challenging for complex tasks. Prior works on self-debugging mostly focus on prompting methods by providing LLMs with few-shot examples, which work poorly on small open-sourced LLMs. In this work, we propose a training framework that significantly improves self-debugging capability of LLMs. Intuitively, we observe that a chain of explanations on the wrong code followed by code refinement helps LLMs better analyze the wrong code and do refinement. We thus propose an automated pipeline to collect a high-quality dataset for code explanation and refinement by generating a number of explanations and refinement trajectories and filtering via execution verification. We perform supervised fine-tuning (SFT) and further reinforcement learning (RL) on both success and failure trajectories with a novel reward design considering code explanation and refinement quality. SFT improves the pass@1 by up to 15.92% and pass@10 by 9.30% over four benchmarks. RL training brings additional up to 3.54% improvement on pass@1 and 2.55% improvement on pass@10. The trained LLMs show iterative refinement ability, and can keep refining code continuously. Lastly, our human evaluation shows that the LLMs trained with our framework generate more useful code explanations and help developers better understand bugs in source code.

We propose a framework that amortizes the cost of inference-time reasoning by converting transient critiques into retrievable guidelines, through a file-based memory system and agent-controlled tool calls. We evaluate this method on the Rubric Feedback Bench, a novel dataset for rubric-based learning. Experiments demonstrate that our augmented LLMs rapidly match the performance of test-time refinement pipelines while drastically reducing inference cost.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often fall short on inductive reasoning, despite achieving impressive success on research benchmarks. In this work, we conduct a systematic study of the inductive reasoning capabilities of LMs through iterative hypothesis refinement, a technique that more closely mirrors the human inductive process than standard input-output prompting. Iterative hypothesis refinement employs a three-step process: proposing, selecting, and refining hypotheses in the form of textual rules. By examining the intermediate rules, we observe that LMs are phenomenal hypothesis proposers (i.e., generating candidate rules), and when coupled with a (task-specific) symbolic interpreter that is able to systematically filter the proposed set of rules, this hybrid approach achieves strong results across inductive reasoning benchmarks that require inducing causal relations, language-like instructions, and symbolic concepts. However, they also behave as puzzling inductive reasoners, showing notable performance gaps between rule induction (i.e., identifying plausible rules) and rule application (i.e., applying proposed rules to instances), suggesting that LMs are proposing hypotheses without being able to actually apply the rules. Through empirical and human analyses, we further reveal several discrepancies between the inductive reasoning processes of LMs and humans, shedding light on both the potentials and limitations of using LMs in inductive reasoning tasks.

In this work, we present two results: The first result is the formalization of Tutte's theorem in Lean, a key theorem concerning matchings in graph theory. As this formalization is ready to be integrated in Lean's mathlib, it provides a valuable step in the path towards formalizing research-level mathematics in this area. The second result is a framework for doing educational formalization projects. This framework provides a structure to learn to formalize mathematics with minimal teacher input. This framework applies to both traditional academic settings and independent community-driven environments. We demonstrate the framework's use by connecting it to the process of formalizing Tutte's theorem.

Design-to-code translates high-fidelity UI designs into executable front-end implementations, but progress remains hard to compare due to inconsistent datasets, toolchains, and evaluation protocols. We introduce 1D-Bench, a benchmark grounded in real e-commerce workflows, where each instance provides a reference rendering and an exported intermediate representation that may contain extraction errors. 1D is short for one day, representing the efficient completion of design-to-code tasks in less than one day. Models take both as input, using the intermediate representation as structural cues while being evaluated against the reference rendering, which tests robustness to intermediate representation defects rather than literal adherence. 1D-Bench requires generating an executable React codebase under a fixed toolchain with an explicit component hierarchy, and defines a multi-round setting in which models iteratively apply component-level edits using execution feedback. Experiments on commercial and open-weight multimodal models show that iterative editing generally improves final performance by increasing rendering success and often improving visual similarity. We further conduct a pilot study on post-training with synthetic repair trajectories and reinforcement learning based editing, and observe limited and unstable gains that may stem from sparse terminal rewards and high-variance file-level updates. The data and scripts used in this study are available in an anonymized repository at https://anonymous.4open.science/r/d2c-benchmark-A9C4/.

Practical video editing is not only pixel generation: an editor must turn a brief, a clip pool, music metadata, and hard constraints into an executable timeline. We study this decision layer as executable video-editing planning and introduce RefineCut, which, unlike workflow systems that wrap a prompted frontier model, trains a compact open-weight planner for it. The planner edits a typed timeline through structured patches covering clip selection, trimming, ordering, transitions, and duration and music alignment; a deterministic verifier applies each patch and checks it against an explicit constraint ledger. Because editing has no single ground-truth repair, we do not imitate teachers directly: RefineCut replays every multi-teacher branch through the verifier and keeps verifier-best repairs as supervision. A second stage, RefineCut-Evo, lets the student score its own repairs with the verifier and a task rubric and trains on high-margin preference pairs, so the final 8B planner runs in a closed verifier loop with no teacher calls at inference. On RefineCut-Bench (3{,}578 tasks, 7{,}971 captioned clips, 499 music tracks, explicit ledgers), verifier-replayed distillation lifts the planner from 0.620 to 0.858 on the protocol-specific Video-Editing Score and RefineCut-Evo reaches 0.924; the gain transfers to Llama-3.1-8B and GLM-4-9B, and in the same closed loop the 8B planner matches or exceeds its frontier teachers. Code and RefineCut-Bench are publicly released; see the Data Availability statement.

Large Language Models (LLMs) have significantly automated the process of scientific discovery over the past few years. However, existing systems share one core limitation: they generate and optimize ideas independently for either Quality or Diversity. This often leads to the generation of ideas in close proximity to one another or to a large set of trivial, unsound, or unclear concepts. In this work, we instead argue that research ideation should be treated as a conjunction of both objectives and framed as a Quality-Diversity (QD) search. In line with this perspective, we introduce IDEAgent, a multi-agent framework that manages the evolution of ideas through lineages. We jointly drive Quality using multi-objective feedback for dedicated repair and refinement, while Diversity is achieved through lightweight sequential memory and explicit comparison against completed ideas, their historical ancestors, and rejected proposals. To systematically evaluate this QD conjunction, we develop Yield, a joint metric that computes the largest set of mutually diverse ideas that satisfy a predetermined quality threshold. Finally, through evaluations across 32 topics spanning 8 domains of Computer Science, we show that IDEAgent outperforms the best baseline by 3.89x on Yield, while achieving non-zero Yield on 8x more topics. We further corroborate these findings through an analysis of quality improvements, showing that repair and refinement are crucial for building logical rigor and clarity while preserving non-obviousness. To encourage future research on QD-search-based ideation, we open-source IDEAgent at https://github.com/declare-lab/IDEAgent.

Large language models (LLMs) have advanced automatic program repair (APR) to the point where agentic systems routinely resolve real-world, repository-level issues. Yet the generated patch has received little scrutiny beyond whether it passes tests. In this paper, we identify patch verbosity as a major yet overlooked concern in LLM-based APR. Characterizing 28 state-of-the-art approaches on SWE-bench Verified, we find that even successful patches are consistently larger and more complex than developer patches, with the median approach producing 121.78% more total changes, 80.91% more net changes, and 43.99% higher cyclomatic complexity. We further show that this verbosity is rooted in capability-oriented design choices such as iterative refinement and broad context, and can hardly be reduced by surface-level controls such as output format or minimality prompts. Motivated by these findings, we formulate post-generation patch refinement and propose RECAP, a lightweight, plug-and-play adapter that attaches to existing repair frameworks after generation. RECAP's refiner is trained via supervised fine-tuning and direct preference optimization with distilled reasoning traces, on a dataset of patch pairs we construct from multiple sources. Across four host systems, prompting, commit-untangling, and minimality-aware baselines reduce patch size only by sacrificing 49 to 217 resolved instances. In contrast, RECAP achieves a substantially better size-correctness tradeoff, cutting average total changes from +242.14% to +4.24% and net changes from +348.24% to -39.75% relative to developer patches while preserving or improving resolution by up to 42 instances. Our results indicate that minimality cannot be simply reduced to syntactic compression, and that decoupling minimization from generation offers a practical path to more reviewable repairs.

Self-improving LLM agents refine answers, not the process that produces those answers. Systems that add a meta-level hold that level fixed, and those that edit themselves must leave part of their own editing machinery untouched to stay stable, capping the meta-depth they realize at roughly two. We present Meta^n, which keeps the meta-operation fixed and recurses on its input instead. That operation, Ω, is applied repeatedly to its own products, reading the traces of the solver stack below together with the code that produced them, then writing the next layer as a strategic pre-process and a library of callable helpers. Because Ω never changes, it cannot destabilize the system, and because its input strictly grows, each layer reasons from a higher vantage than the last. Depth is set by convergence rather than fixed in advance, and an evolutionary archive searches over layer chains. Across two backbones, Meta^n outperforms prior self-improving agents on all eight benchmark families. The sharpest case is ARC-AGI-2, built to resist skill memorization, where it alone scores above zero. Ablations indicate that most of the gain from recursion comes from the conditioning each layer passes to the next, and distinct layer roles emerge with depth although no prompt prescribes them. Code available at https://github.com/minnesotanlp/meta-n

Atomic-scale simulations have been transformed by machine-learning models that predict the properties of atomistic structures with the accuracy of quantum calculations, but at a small fraction of the cost. These models have increased dramatically in generality, thanks to the availability of synthetic datasets of ever-increasing size and scope. The proliferation of datasets, with properties often computed using different levels of electronic-structure approximation, is problematic, as there is often overlap between different datasets, and strong correlations between structures obtained with short molecular dynamics trajectories or geometry optimization. To address these problems, we introduce a protocol to stratify a dataset into a hierarchy of nested subsets, subsampling from the coarsest to the finest resolution based on an "ecumetric" built to reflect the latent space representation of several popular universal machine-learning interatomic potentials. We then use this approach to combine most of the open structural datasets currently available, consolidating them into MAD-COSMO, a well-organized collection of almost 1.7 billion structures, whose 2^{24} most diverse members form the MAD-CORE stratified coreset, which can be easily used for all sorts of tasks, from exploratory experiments to the training of foundation models at scale. We envision that this collection will guide and help coordinate future efforts, focusing them on the most relevant and/or undersampled regions of chemical and structural space, and that it will be further extended to incorporate the outcomes of the collective work of this community.

Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check whether a formal proof is correct or not almost instantaneously, but generating a completely correct formal proof with large language models (LLMs) remains a formidable task. The usual approach in the literature is to prompt the LLM many times (up to several thousands) until one of the generated proofs passes the verification system. In this work, we present APOLLO (Automated PrOof repair via LLM and Lean cOllaboration), a modular, model-agnostic pipeline that combines the strengths of the Lean compiler with an LLM's reasoning abilities to achieve better proof-generation results at a low sampling budget. Apollo directs a fully automated process in which the LLM generates proofs for theorems, a set of agents analyze the proofs, fix the syntax errors, identify the mistakes in the proofs using Lean, isolate failing sub-lemmas, utilize automated solvers, and invoke an LLM on each remaining goal with a low top-K budget. The repaired sub-proofs are recombined and reverified, iterating up to a user-controlled maximum number of attempts. On the miniF2F benchmark, we establish a new state-of-the-art accuracy of 75.0% among 7B-parameter models while keeping the sampling budget below one thousand. Moreover, Apollo raises the state-of-the-art accuracy for Goedel-Prover-SFT to 65.6% while cutting sample complexity from 25,600 to a few hundred. General-purpose models (o3-mini, o4-mini) jump from 3-7% to over 40% accuracy. Our results demonstrate that targeted, compiler-guided repair of LLM outputs yields dramatic gains in both efficiency and correctness, suggesting a general paradigm for scalable automated theorem proving.

Autoformalization translates informal natural language into formal, machine-verifiable languages. While most work focuses on individual statements, real formalization efforts are inherently theory-level: they require an entire web of axioms, definitions, and lemmas before target theorems can even be stated. In this position paper, we argue for theory-level autoformalization: formalizing complete theories, including all their inter-dependencies, as structured libraries. We examine the significance of this shift, address alternative views, identify open challenges, and propose three promising paths forward. Our survey of autoformalization is available at https://github.com/marcusm117/Awesome-Autoformalization.

Reinforcement Learning from Human Feedback (RLHF) has been commonly used to align the behaviors of Large Language Models (LLMs) with human preferences. Recently, a popular alternative is Direct Policy Optimization (DPO), which replaces an LLM-based reward model with the policy itself, thus obviating the need for extra memory and training time to learn the reward model. However, DPO does not consider the relative qualities of the positive and negative responses, and can lead to sub-optimal training outcomes. To alleviate this problem, we investigate the use of intrinsic knowledge within the on-the-fly fine-tuning LLM to obtain relative qualities and help to refine the loss function. Specifically, we leverage the knowledge of the LLM to design a refinement function to estimate the quality of both the positive and negative responses. We show that the constructed refinement function can help self-refine the loss function under mild assumptions. The refinement function is integrated into DPO and its variant Identity Policy Optimization (IPO). Experiments across various evaluators indicate that they can improve the performance of the fine-tuned models over DPO and IPO.

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis, and artificial intelligence. While the long-term goal of autoformalization seemed elusive for a long time, we show large language models provide new prospects towards this goal. We make the surprising observation that LLMs can correctly translate a significant portion (25.3%) of mathematical competition problems perfectly to formal specifications in Isabelle/HOL. We demonstrate the usefulness of this process by improving a previously introduced neural theorem prover via training on these autoformalized theorems. Our methodology results in a new state-of-the-art result on the MiniF2F theorem proving benchmark, improving the proof rate from 29.6% to 35.2%.

Existing Programming-By-Example (PBE) systems often rely on simplified benchmarks that fail to capture the high structural complexity of real-world regexes, such as deeper nesting and frequent use of union operations. To overcome the resulting performance drop, we propose ReSyn, a synthesizer-agnostic divide-and-conquer framework that decomposes complex synthesis problem into manageable sub-problems. We also introduce Set2Regex, a parameter-efficient synthesizer capturing the permutation invariance of examples. Experimental results demonstrate that ReSyn significantly boosts accuracy across various synthesizers, and its combination with Set2Regex establishes a new state-of-the-art on challenging real-world benchmark. The complete source code, datasets, and pre-trained model checkpoints are publicly available at https://github.com/mrseongminkim/ReSyn.

Evolutionary search with large language models (LLMs) can stall when progress requires external knowledge the model lacks. Supplying relevant documents helps, but simply adding web search tool can keep returning the same pages as solutions change. We introduce EvoDuet, a bi-level optimization method that co-evolves solutions and search queries with fixed model parameters. At each iteration, a retrieval gate lets the LLM assess its knowledge gap and choose to retrieve new documents, reuse stored ones, or proceed without them. An inner loop refines queries and ranks documents by the solution scores they are predicted to yield; an outer loop generates candidates in parallel from these documents and records the evaluated outcomes for later searches. Across 21 optimization tasks with one candidate per iteration, EvoDuet raises OpenEvolve's normalized discovery gain from 74.1% to 78.0% with GPT-5.6-Luna and from 61.3% to 82.3% with Gemini-3.8-Flash, whereas Qwen3.5-9B does not benefit. Our best runs surpass the previously reported best scores on eight tasks, including Swap Reduction on Q20 and Rosetta, and match them on three more. EvoDuet also improves with other scaffolds (e.g., Top-K, EvoX) on Sums/Diffs and Denoising, demonstrating its applicability across evolutionary search scaffolds.

Language models (LMs) have recently shown remarkable performance on reasoning tasks by explicitly generating intermediate inferences, e.g., chain-of-thought prompting. However, these intermediate inference steps may be inappropriate deductions from the initial context and lead to incorrect final predictions. Here we introduce REFINER, a framework for finetuning LMs to explicitly generate intermediate reasoning steps while interacting with a critic model that provides automated feedback on the reasoning. Specifically, the critic provides structured feedback that the reasoning LM uses to iteratively improve its intermediate arguments. Empirical evaluations of REFINER on three diverse reasoning tasks show significant improvements over baseline LMs of comparable scale. Furthermore, when using GPT-3.5 or ChatGPT as the reasoner, the trained critic significantly improves reasoning without finetuning the reasoner. Finally, our critic model is trained without expensive human-in-the-loop data but can be substituted with humans at inference time.

Procedures are inherently hierarchical. To "make videos", one may need to "purchase a camera", which in turn may require one to "set a budget". While such hierarchical knowledge is critical for reasoning about complex procedures, most existing work has treated procedures as shallow structures without modeling the parent-child relation. In this work, we attempt to construct an open-domain hierarchical knowledge-base (KB) of procedures based on wikiHow, a website containing more than 110k instructional articles, each documenting the steps to carry out a complex procedure. To this end, we develop a simple and efficient method that links steps (e.g., "purchase a camera") in an article to other articles with similar goals (e.g., "how to choose a camera"), recursively constructing the KB. Our method significantly outperforms several strong baselines according to automatic evaluation, human judgment, and application to downstream tasks such as instructional video retrieval. A demo with partial data can be found at https://wikihow-hierarchy.github.io. The code and the data are at https://github.com/shuyanzhou/wikihow_hierarchy.

To further enhance the ability of Large Language Models (LLMs) to solve complex, multi-step reasoning problems, test-time scaling (TTS) methods have gained widespread attention. Existing approaches such as Best-of-N and majority voting are limited as their performance depends on the quality of candidate responses, making them unable to produce a correct solution when all candidates are incorrect. Introducing an additional model to select the best response also incurs significant deployment costs. To this end, we introduce Generative Self-Refinement (GSR), a novel parallel test-time scaling framework where a unified model first generates a set of candidate responses in parallel and then performs self-refinement to synthesize a new superior solution based on a prompt consisting of the problem and these candidates. However, LLMs struggle to perform refinement effectively when prompted directly. Therefore, we design a hybrid training pipeline by jointly optimizing for two complementary objectives, solving problems directly and refining candidate responses. Experimental results demonstrate that our method achieves state-of-the-art performance across five mathematical benchmarks. We further show that this learned self-refinement skill is a model-agnostic enhancement, robust across different model scales and generalizing to out-of-distribution reasoning tasks.

We perform a thorough analysis of the formal and informal statements in the miniF2F benchmark from the perspective of an AI system that is tasked to participate in a math Olympiad consisting of the problems in miniF2F. In such setting, the model has to read and comprehend the problems in natural language, formalize them in Lean language, then proceed with proving the problems, and it will get credit for each problem if the formal proof corresponds to the original informal statement presented to the model. Our evaluation results reveal that the best accuracy of such pipeline can be about 36% using the SoTA models in the literature, considerably lower than the individual SoTA accuracies, 97% and 69% reported in the autoformalization and theorem proving literature. Analyzing the failure modes, we trace back a considerable portion of this drop to discrepancies between the formal and informal statements for more than half of the problems in miniF2F. We proceed with correcting all the errors, discrepancies and simplifications in formal and informal statements, and present the miniF2F-v2 with fully verified formal and informal statements and proofs. Evaluating the full theorem proving pipeline on miniF2F-v2 leads to the best accuracy of 70%, a significant improvement from the 40% on the original miniF2F, yet indicating considerable misalignment between the autoformalization models and theorem provers. Our deep analysis suggests that a higher quality benchmark can help the community better evaluate progress in the field of formal reasoning and also better diagnose the failure and success modes of autoformalization and theorem proving models. Our dataset is available at https://github.com/roozbeh-yz/miniF2F_v2.

Recent advances in LLM agents have largely built on reasoning backbones like ReAct, which interleave thought and action in complex environments. However, ReAct often produces ungrounded or incoherent reasoning steps, leading to misalignment between the agent's actual state and goal. Our analysis finds that this stems from ReAct's inability to maintain consistent internal beliefs and goal alignment, causing compounding errors and hallucinations. To address this, we introduce ReflAct, a novel backbone that shifts reasoning from merely planning next actions to continuously reflecting on the agent's state relative to its goal. By explicitly grounding decisions in states and enforcing ongoing goal alignment, ReflAct dramatically improves strategic reliability. This design delivers substantial empirical gains: ReflAct surpasses ReAct by 27.7% on average, achieving a 93.3% success rate in ALFWorld. Notably, ReflAct even outperforms ReAct with added enhancement modules (e.g., Reflexion, WKM), showing that strengthening the core reasoning backbone is key to reliable agent performance.

We introduce and release ScienceBuddy, an interactive scientific research workspace that brings continually improving scientific agents into researchers' everyday workflows. ScienceBuddy supports researchers in carrying out scientific tasks while transforming their requests, feedback, and execution evidence into tasks and evaluation rubrics for continual learning. At its core is recursive-in-recursive self-improvement, a paradigm that couples harness evolution with model reinforcement learning: the inner recursion improves the harness with the model fixed, while the outer recursion trains the model under the improved harness. Harness evolution shapes training experience, and model learning creates new opportunities for harness adaptation. We present case studies of researcher interaction, harness refinement, and model learning, with the benchmark cases spanning four scientific task families. By releasing ScienceBuddy as a research product, we make this paradigm available to the scientific community and take a step toward discovery intelligence: scientific AI that advances through sustained collaboration with researchers and evolves alongside the research it supports. Website: http://science-buddy.io

Mathematical reasoning has proven to be a critical yet challenging task for large language models (LLMs), as they often struggle with complex multi-step problems. To address these limitations, we introduce the Monte Carlo Nash Equilibrium Self-Refine Tree (MC-NEST) algorithm, an enhancement of the Monte Carlo Tree Self-Refine (MCTSr) approach. By integrating Nash Equilibrium strategies with LLM-based self-refinement and self-evaluation processes, MC-NEST aims to improve decision-making for complex mathematical reasoning tasks. This method ensures balanced exploration and exploitation of potential solutions, leveraging Upper Confidence Bound (UCT) scores and various selection policies. Through iterative critique and refinement, MC-NEST enhances the reasoning capabilities of LLMs, particularly for problems requiring strategic decision-making. Comparative analysis reveals that GPT-4o, equipped with MC-NEST using an Importance Sampling Policy, achieved superior accuracy in domains such as Number Theory and Geometry. These results suggest that both LLMs GPT-4o and Phi-3-mini can benefit from MC-NEST, with iterative self-refinement proving especially effective in expanding the reasoning capacity and problem-solving performance of LLMs. We evaluate the effectiveness of MC-NEST on challenging Olympiad-level benchmarks, demonstrating its potential to significantly boost complex mathematical reasoning performance in LLMs.

A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons. We first show that a representative example, the "hat" polykite, can form clusters called "metatiles", for which substitution rules can be defined. Because the metatiles admit tilings of the plane, so too does the hat. We then prove that generic members of our continuum of polygons are aperiodic, through a new kind of geometric incommensurability argument. Separately, we give a combinatorial, computer-assisted proof that the hat must form hierarchical -- and hence aperiodic -- tilings.

Expert-written natural language skills can improve tool-using agents, yet agent-authored skills perform 8-11 points worse than using no skill. This gap suggests that following procedural guidance and improving it from execution evidence are distinct capabilities. Inference time loops can repair skills but do not improve the model that writes the next one. We study how to organize execution experience from intermediate skills into training states for an optimizer. We introduce WER (Write, Execute, and Refine), a multi-phase framework that trains a Skill Optimizer outside a frozen executor. The optimizer proposes skills, a frozen agent executes each repeatedly, and a programmatic verifier scores the outcomes. The scores provide relative credit and select mixed-outcome records. Matched successful and failed trajectories from these records form the next phase's refinement states, so the optimizer learns from the consequences of its earlier outputs. On BFCL v4 multi-turn and tau2-bench, WER improves average Pass@1 over the no-skill baseline by 7.80 and 3.85 points, respectively. Under an identical refinement workflow, it outperforms the same backbone without optimizer training by 9.35 and 10.29 points. The trained 4B optimizer reaches 76.63 percent on BFCL v4, outperforming all evaluated off-the-shelf general-purpose models used as skill optimizers on average.

The strong performance of large language models (LLMs) on natural language processing tasks raises extensive discussion on their application to code generation. Recent work suggests multiple sampling approaches to improve initial code generation accuracy or program repair approaches to refine the code. However, these methods suffer from LLMs' inefficiencies and limited reasoning capacity. In this work, we propose an LLM programming workflow (LPW) designed to improve both initial code generation and subsequent refinements within a structured two-phase workflow. Specifically, in the solution generation phase, the LLM first outlines a solution plan that decomposes the problem into manageable sub-problems and then verifies the generated solution plan through visible test cases. Subsequently, in the code implementation phase, the LLM initially drafts a code according to the solution plan and its verification. If the generated code fails the visible tests, the plan verification serves as the intended natural language solution to inform the refinement process for correcting bugs. We further introduce SLPW, a sampling variant of LPW, which initially generates multiple solution plans and plan verifications, produces a program for each plan and its verification, and refines each program as necessary until one successfully passes the visible tests. Compared to the state-of-the-art methods across various existing LLMs, our experimental results show that LPW significantly improves the Pass@1 accuracy by up to 16.4% on well-established text-to-code generation benchmarks, especially with a notable improvement of around 10% on challenging benchmarks. Additionally, SLPW demonstrates up to a 5.6% improvement over LPW and sets new state-of-the-art Pass@1 accuracy on various benchmarks, e.g., 98.2% on HumanEval, 84.8% on MBPP, 64.0% on APPS, and 35.3% on CodeContest, using GPT-4o as the backbone.

Recent advances in large language models have made automatic game generation increasingly feasible, yet reliably improving generated games beyond a playable version remains challenging. Naive iterative refinement can easily overfit a small set of test cases, producing fragile games with unresolved bugs, missing behaviors, and poor generalization to broader player interactions. We introduce RSIGame, an autonomous agentic game development framework with recursive self-improvement. RSIGame organizes development into complementary local and global loops. Concretely, a local explore-diagnose-improve loop broadly explores the executable game, diagnoses and prioritizes discovered issues, and performs evidence-grounded revision, where an evolving checklist continually accumulates new testing and improvement guidance. A global loop tracks overall quality, preserves the best checkpoint, and detects saturation or regression over long-horizon development. Beyond test-time improvement, RSIGame further internalizes successful development experience into the generator through training. Across 140 GameCraft-Bench tasks, two game engines, and five generators, RSIGame consistently improves game quality under matched development budgets. Notably, experience internalization enables Qwen3.8-27B to reach 61.38 on Godot and 58.53 on Phaser, exceeding GPT-5.5 one-shot scores while reducing Qwen's generation tokens by 11 times.

This paper provides a novel approach to reconciling complex low-level memory model features, such as pointer--integer casts, with desired refinements that are needed to justify the correctness of program transformations. The idea is to use a "two-phased" memory model, one with and unbounded memory and corresponding unbounded integer type, and one with a finite memory; the connection between the two levels is made explicit by our notion of refinement that handles out-of-memory behaviors. This approach allows for more optimizations to be performed and establishes a clear boundary between the idealized semantics of a program and the implementation of that program on finite hardware. To demonstrate the utility of this idea in practice, we instantiate the two-phase memory model in the context of Zakowski et al.'s VIR semantics, yielding infinite and finite memory models of LLVM IR, including low-level features like undef and bitcast. Both the infinite and finite models, which act as specifications, can provably be refined to executable reference interpreters. The semantics justify optimizations, such as dead-alloca-elimination, that were previously impossible or difficult to prove correct.

We show how to "compile" human-readable programs into standard decoder-only transformer models. Our compiler, Tracr, generates models with known structure. This structure can be used to design experiments. For example, we use it to study "superposition" in transformers that execute multi-step algorithms. Additionally, the known structure of Tracr-compiled models can serve as ground-truth for evaluating interpretability methods. Commonly, because the "programs" learned by transformers are unknown it is unclear whether an interpretation succeeded. We demonstrate our approach by implementing and examining programs including computing token frequencies, sorting, and parenthesis checking. We provide an open-source implementation of Tracr at https://github.com/google-deepmind/tracr.

Large language models (LLMs) with Chain-of-Thought (CoT) reasoning have achieved strong performance across diverse tasks, including mathematics, coding, and general reasoning. A distinctive ability of these reasoning models is self-reflection: the ability to review and revise previous reasoning steps. While self-reflection enhances reasoning performance, it also increases inference cost. In this work, we study self-reflection through the lens of representation engineering. We segment the model's reasoning into steps, identify the steps corresponding to reflection, and extract a reflection direction in the latent space that governs this behavior. Using this direction, we propose a stepwise steering method that can control reflection frequency. We call our framework ReflCtrl. Our experiments show that (1) in many cases reflections are redundant, especially in stronger models (in our experiments, we can save up to 33.6 percent of reasoning tokens while preserving performance), and (2) the model's reflection behavior is highly correlated with an internal uncertainty signal, implying self-reflection may be controlled by the model's uncertainty.

Deformable image registration is crucial for aligning medical images in a non-linear fashion across different modalities, allowing for precise spatial correspondence between varying anatomical structures. This paper presents NestedMorph, a novel network utilizing a Nested Attention Fusion approach to improve intra-subject deformable registration between T1-weighted (T1w) MRI and diffusion MRI (dMRI) data. NestedMorph integrates high-resolution spatial details from an encoder with semantic information from a decoder using a multi-scale framework, enhancing both local and global feature extraction. Our model notably outperforms existing methods, including CNN-based approaches like VoxelMorph, MIDIR, and CycleMorph, as well as Transformer-based models such as TransMorph and ViT-V-Net, and traditional techniques like NiftyReg and SyN. Evaluations on the HCP dataset demonstrate that NestedMorph achieves superior performance across key metrics, including SSIM, HD95, and SDlogJ, with the highest SSIM of 0.89, and the lowest HD95 of 2.5 and SDlogJ of 0.22. These results highlight NestedMorph's ability to capture both local and global image features effectively, leading to superior registration performance. The promising outcomes of this study underscore NestedMorph's potential to significantly advance deformable medical image registration, providing a robust framework for future research and clinical applications. The source code and our implementation are available at: https://bit.ly/3zdVqcg